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MULTIQUARK HADRONS
This work summarizes the salient features of current and planned experiments into
multiquark hadrons, describing various inroads to accommodate them within a theoretical
framework. At a pedagogical level, authors review the salient aspects of Quantum
Chromodynamics (QCD), the theory of strong interactions, which has been brought to
the fore by high-energy physics experiments over recent decades. Compact diquarks as
building blocks of a new spectroscopy are presented and confronted with alternative
explanations of the XYZ resonances. Ways to distinguish among theoretical alternatives are
illustrated, to be tested with the help of high-luminosity LHC, electron-positron colliders,
and the proposed Tera-Z colliders. Non-perturbative treatments of multiquark hadrons,
such as large N expansion, lattice QCD simulations, and predictions about doubly heavy
multiquarks are reviewed in considerable detail. With a broad appeal across high-energy
physics, this work is pertinent to researchers focused on experiments, phenomenology or
lattice QCD.
ahmed ali is an emeritus staff member in theoretical physics at the high-energy physics
laboratory, DESY, in Hamburg, and was a professor of physics at the University of Ham-
burg. Working on the phenomenology of high-energy physics, his main research interests
are flavor physics, QCD, and multiquark hadrons. He has worked as a scientific associate
at CERN for several years and is also a fellow of the American Physical Society.
luciano maiani is an emeritus professor of theoretical physics at Sapienza University
of Rome. He has been president of the Italian Institute for Nuclear Physics (INFN), director-
general of CERN in Geneva, and president of the Italian National Council for Research
(CNR). He is a member of the Italian Lincean Academy and a fellow of the American
Physical Society.
antonio d. polosa is a professor at the Department of Physics in Sapienza University
of Rome. His research focuses primarily on heavy meson decays, high energy hadron
collider physics, and exotic hadron spectroscopy. He has held positions at the University of
Helsinki, CERN, LAPP-TH, and INFN-Rome.

MULTIQUARK HADRONS
AHMED ALI
German Electron Synchrotron (DESY) Hamburg
LUCIANO MAIANI
Sapienza University of Rome
ANTONIO D. POLOSA
Sapienza University of Rome

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www.cambridge.org
Information on this title: www.cambridge.org/9781107171589
DOI: 10.1017/9781316761465
© Ahmed Ali, Luciano Maiani, and Antonio D. Polosa 2019
This publication is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without the written
permission of Cambridge University Press.
First published 2019
Printed in the United Kingdom by TJ International Ltd, Padstow Cornwall
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Library of Congress Cataloging-in-Publication Data
Names: Ali, A. (Ahmed), author. | Maiani, L. (Luciano), author. | Polosa, Antonio D., author.
Title: Multiquark hadrons / Ahmed Ali (German Electron Synchrotron (DESY) Hamburg),
Luciano Maiani (Sapienza University of Rome), Antonio D. Polosa (Sapienza University of Rome).
Description: Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2019. |
Includes bibliographical references and index.
Identifiers: LCCN 2018048314| ISBN 9781107171589 (hardback ; alk. paper) |
ISBN 110717158X (hardback ; alk. paper)
Subjects: LCSH: Hadrons. | Quark models.
Classification: LCC QC793.5.H32 A45 2019 | DDC 539.7/216–dc23
LC record available at https://lccn.loc.gov/2018048314
ISBN 978-1-107-17158-9 Hardback
Cambridge University Press has no responsibility for the persistence or accuracy
of URLs for external or third-party internet websites referred to in this publication
and does not guarantee that any content on such websites is, or will remain,
accurate or appropriate.

Contents
Preface page ix
1 Introduction 1
2 XYZ and Pc Phenomenology 14
2.1 Charmonium Taxonomy 14
2.2 Hidden cc̄ Exotics 15
2.3 Hidden bb̄ Exotics 23
2.4 The Charged Pentaquarks P ±
c (4350) and P ±
c (4450) 28
3 Color Forces and Constituent Quark Model 30
3.1 Color Forces in the One-Gluon Approximation 30
3.2 New Hadrons 33
3.3 Classical Hadrons with Charm and Beauty 38
3.4 Attempts at Improving CQM 45
4 Hadron Molecules 47
4.1 The Molecular Paradigm 47
4.2 The Size of a Loosely Bound Molecule 49
4.3 Prompt Production in High Energy Colliders 51
4.4 Production through cc̄ 56
4.5 Molecular Decays 58
4.6 One Pion Exchange: The Haves and the Have Not 59
4.7 Composite versus Confined? 59
5 Light Scalar Mesons 64
5.1 Lightest Scalar Mesons as Tetraquarks 65
5.2 The Heavier Scalar Mesons 69
5.3 Instanton Effects 70
5.4 S → P P Decays 72
v

vi Contents
5.5 The Overall View 76
5.6 Constituent Quark Picture of Light Tetraquarks 76
6 Mass Formulae for P -Wave, qq̄ Mesons 78
6.1 Hamiltonian for L = 1 Mesons 78
6.2 Matrix Elements of the Tensor Operator 79
6.3 Mass Formulae for cc̄ and bb̄ Mesons 80
6.4 Light Flavor Mesons 81
7 Compact Tetraquarks 83
7.1 Compact Tetraquarks in S-Wave 83
7.2 Fierz Transformations 86
7.3 Hyperfine Structure 88
7.4 Mass Spectrum of Tetraquarks: A Novel Ansatz 90
7.5 Structures in J/ψ φ Spectrum as Tetraquarks 92
7.6 Two Lengths Inside Tetraquarks? 94
8 The Xu − Xd Puzzle 96
8.1 Isospin Breaking in Tetraquarks 96
8.2 Properties of X from B-Meson Decays 98
8.3 X-Decay Amplitudes 99
8.4 Discussion 104
9 Y States as P -Wave Tetraquarks 105
9.1 Two Scenarios 105
9.2 Effective Hamiltonian for X and Y 107
9.3 Tensor Couplings in P -Wave Diquarkonium 108
9.4 Mass Formulae 109
9.5 Best Fit and Parameters in the Two Scenarios 110
10 Pentaquark Models 113
10.1 Rescattering-Induced Kinematic Effects 115
10.2 Pentaquarks as Meson-Baryon Molecules 117
10.3 Pentaquarks in the Compact Diquark Models 118
11 Tetraquarks in Large N QCD 132
11.1 QCD at Large N: A Reminder 132
11.2 Current Correlators 136
11.3 Meson Interactions in the 1/N Expansion 137
11.4 Diquarks and Tetraquarks for Any N 137
11.5 Tetraquark Correlation Functions at Large N 139
11.6 Need of Nonplanar Diagrams 140
11.7 A Consistent Solution 143

Contents vii
12 QCD Sum Rules and Lattice QCD 147
12.1 QCD Sum Rules 147
12.2 Lattice QCD 150
13 Phenomenology of Beauty Quark Exotics 158
13.1 Heavy-Quark-Spin Flip in ϒ(10890) → hb(1P,2P)ππ 158
13.2 The Process e+e− → ϒ(1S)(π+π−,K+K−,ηπ0) Near ϒ(5S) 162
13.3 Drell–Yan Production at LHC and Tevatron 166
14 Hidden Heavy Flavor Tetraquarks: Overview 171
15 Tetraquarks with Double Heavy Quarks 173
15.1 Heavy Quark-Heavy Diquark Symmetry 174
15.2 Quark Model Mass Estimates 178
15.3 Masses from Heavy-Quark Symmetry 180
15.4 Lattice Estimates: Born–Oppenheimer Approximation 183
15.5 Lattice Estimates: Nonrelativistic QCD 189
15.6 Stable bb Tetraquarks at a Tera-Z Factory 194
15.7 Production of Double-Heavy Tetraquarks in Z Decays 198
15.8 Stable Doubly Heavy Tetraquarks at the LHC 198
15.9 Lifetimes 200
15.10 Weak Decays of T
{bb}
[ūd̄]
201
16 Outlook 205
Appendix A Low Energy p − n Scattering Amplitude 208
Appendix B Wigner’s 6-j Symbols 212
References 216
Index 231

Preface
Multiquark physics started essentially with the discovery of X(3872) in 2003 by
the Belle collaboration at the KEK-B factory. It profited greatly from the high-
luminosity particle accelerators: the e+
e−
B factories and BEPC, and the hadron
colliders Tevatron and LHC.
Well over a dozen exotic mesons, and two charged baryons, which do not fit
in the quark model, have been observed. They are called XYZ mesons and Pc
baryons. Some of these exotic mesons, such as Z(3900) and Zb(10650), decaying
into J/ψπ±
and ϒ(1S)π±
, respectively, have a minimum of four quarks in the
valence approximation. They are generically called tetraquarks. Likewise, the two
exotic charged baryons, Pc(4380) and Pc(4450), whose discovery mode is J/ψp,
require a minimum of five valence quarks, and are called pentaquarks. They have
received, and continue to receive, a lot of experimental and theoretical attention.
It is fair to say that multiquark physics has moved from its exploratory, and at times
contentious, stage to the mainstream of hadronic physics.
This book summarizes the main results in this field. We intended to focus on the
experimental discoveries, which serve as milestones, and hence are highlighted in
a number of chapters. The bulk, however, is an attempt to describe the main theo-
retical ideas and the methods, which have been used to understand the underlying
dynamics. This is still very much a work in progress, as quantitative results from lat-
tice QCD (Quantum Chromodynamics), the reliable workhorse of particle physics ,
are still lacking due to the complex nature of multiquark hadrons. Consequently, at
present there is no theoretical consensus on the templates used in constructing these
hadrons. In the absence of first principle calculations, various approximate schemes
and phenomenological approaches have been adopted. Some of these methods are
borrowed from nuclear physics, and treat the exotic hadrons as hadronic molecules,
in which the pion- and other light-meson-exchanges play a fundamental role. Some
others are inspired by the phenomenologically successful constituent quark model,
in which diquarks, having well-defined color and spin-parity quantum numbers,
ix

x Preface
are introduced, in addition to quarks, with the dynamics governed by the spin-
spin interactions embedded in QCD. These models have been subjected to respect
the well-established heavy-quark and chiral symmetries of QCD. An important aid
in establishing firmly the multiquark states, tetraquarks and pentaquarks, and in
studying their decays is played by the QCD methods in the large-N limit (N being
the number of colors). A chapter is devoted in the book to illustrate this.
Light scalar mesons, such as σ, κ, f0, and a0, have been put forward as candi-
dates for tetraquark states. Their case rests on the inverted mass hierarchy in the
isospin-mass plots, compared to the well-known pseudoscalar and vector mesons,
which all fit in as quark-antiquark bound states. Being low in mass, they are also
sensitive to the infrared sector of QCD, in which instantons play an important role.
We discuss this in a chapter in this book.
Apart from the light scalars, the other candidate tetraquark and pentaquark states
observed so far have a common thread which runs through all of them, namely
they have a hidden heavy quark-antiquark pair, charm-anticharm, cc̄, or beauty-
antibeauty, bb̄, in their Fock space. It seems that heavy quarks (and antiquarks) are
essential in discovering deeper structures in QCD. This is a recurrent theme of this
book and illustrated in a number of cases of interest, culminating in the predictions
of doubly heavy tetraquarks, such as bbūd̄ and bbūs̄, which are widely anticipated
to be stable under strong interactions.
In our opinion, a new chapter of QCD has opened up in the form of a second layer
of hadrons, beneath the well-established quark-antiquark mesons and the three-
quark baryons. If this view is tenable, then we anticipate a very rich spectroscopy of
multiquark hadrons, which we outline using the diquark model as a guide. Clearly,
a lot of this remains to be tested experimentally. Depending on the outcome of
these experiments, some of the theoretical schemes may have to be modified, or
even abandoned. The book aims at pointing out these crucial measurements and
in stimulating a theoretical discourse, enabling in turn to achieve a consensus.
However, it is not intended to be either a comprehensive review or a text book.
For that, we would have been forced to enlarge its size far beyond the 200-page
length that we intended to write. We do provide a bibliography which is detailed
enough to follow up on some of the topics in which the readers may be interested
for further details. We hope that as a research monograph on an emerging field,
this book will stimulate the new entrants to this field, triggering new ideas and in
developing quantitative techniques, such as lattice QCD.
We acknowledge the experimental collaborations ALICE, BaBar, Belle, BES,
CMS, and LHCb for reprinting some of their published results (figures and tables)
in this book. We thank their members, and the publishers of the scientific journals
for their permission, granted explicitly or implicitly under the Open Access agree-
ments. We have benefited from intense and helpful discussions with a number of

Preface xi
colleagues. In particular, we thank Abdur Rahman, Alessandro Pilloni, Alexander
Parkhomenko, Alexis Pompili, Anatoly Borisov, Angelo Esposito, Ben Grinstein,
Chang-Zheng Yuan, Christoph Hanhart, Eric Braaten, Estia Eichten, Fulvio Pic-
cinini, Gerrit Schierholz, Gunnar Bali, Ishtiaq Ahmed, Jamil Aslam, Jens Sören
Lange, Marco Pappagallo, Marek Karliner, Misha Voloshin, Qiang Zhao, Qin Qin,
Riccardo Faccini, Richard Lebed, Rinaldo Baldini, Roberto Mussa, Sheldon Stone,
Simon Eydelman, Simone Pacetti, Tomasz Skwarniki, Umberto Tamponi, Wei-
Wang, Xiao-Yan Shen. We thank Nicholas (Nick) Gibbons, Sarah Lambert, and
Roisin Munnely of the Cambridge University Press for their constant help and
advice in preparing this manuscript. The efforts of the copy editor, Kevin Eagan, in
correcting the text are likewise thankfully acknowledged.
Part of this work was done at CERN, the Frascati Laboratories of INFN, IHEP-
Beijing, and T. D. Lee Institute, Shanghai. We thank Fabiola Gianotti, Pierluigi
Campana, Yifang Wang, and Xiangdong Ji for their hospitality.

1
Introduction
For long, we lived with the simplest paradigm1
:
Mesons = qq̄; Baryons = qqq, (1.1)
which rested on the absence of I = 2, ππ resonances, and of S > 0 baryons. Here
I and S stand for isospin and strangeness, respectively. The case had to be revisited,
however, because the lowest lying octet of scalar mesons, σ(500), κ(800), f0(980),
and a0(980), does not fit in this picture, as seen in terms of their inverted mass
hierarchies compared to the nonets of the pseudoscalar, vector, and axial-vector
mesons.
It has been argued that the spectroscopy of the scalar nonet is better understood
if one interprets them as consisting of tetraquarks. For example, f0(980) is assigned
the quark structure
f0(980) =
[su][s̄ū] + [sd][s̄d̄]
√
2
. (1.2)
Here [sq] ([s̄q̄]), q = u,d, are diquarks (antidiquarks) having definite spin and
color quantum numbers. The tetraquark interpretation of the lowest-lying scalar
nonet was pointed out long time ago (Jaffe, 1977; Alford and Jaffe, 2000). In
addition, it was later stressed (Fariborz et al., 2008; ’t Hooft et al., 2008) that
tetraquark assignment may help explain a couple of other puzzles in this sector
through the intervention of nonperturbative instanton effects, such as the decay
f0(980) → ππ. Their interpretation as KK̄ hadron molecule states has also been
put forward in a number of earlier papers (Weinstein and Isgur, 1990; Janssen et al.,
1995; Locher et al., 1998). There is a good phenomenological case that the lowest-
lying scalar nonet are non-qq̄ mesons (Amsler and Tornqvist, 2004; Patrignani
1 Baryons can now be constructed from quarks using the combinations (qqq), (qqqqq̄), etc., while mesons are
made out of (qq̄), (qqq̄q̄), etc., Murray Gell-Mann, 1964 (Gell-Mann, 1964; Zweig, 1964).
1

2 Introduction
et al., 2016; Pelaez, 2016). We review the tetraquark interpretation in a chapter
in this book, illustrating the role of instantons, and discuss the qq̄ scalar mesons,
which are higher in mass.
Experimental evidence for multiquark hadrons in the so-called heavy-light
meson sector is not overwhelming. Two narrow states D∗
s0(2317)±
and D∗
s1(2463)±
have so far been seen in data at the B factories. A narrow state was found by
BaBar (Aubert et al., 2003) at around 2.32 GeV in D±
s π0
, in the data both on and
off the ϒ(4S) resonance, having a width compatible with the detector resolution.
This is identified as D∗
s0(2317)±
. Following this, CLEO II (Besson et al., 2003)
found a narrow resonance decaying into D∗±
s π0
, having a mass around 2.46 GeV.
This is identified with D∗
s1(2463)±
. Their quark flavor content is either cs̄ (if they
are excited quark-antiquark states) or cs̄qq̄ (if they are multiquark states), and they
have the orbital angular momentum L = 1, and spin-parity JP
= 0+
(scalar) and
1+
(axial-vector), respectively. However, their masses are much below the predicted
ones for the cs̄ P states and they are uncharacteristically narrow. Due to these
features, D∗
s0(2317)±
and D∗
s1(2463)±
have been interpreted as [cq][q̄s̄], q = u,d;
tetraquarks (Cheng and Hou, 2003; Terasaki, 2003; Maiani et al., 2005). They have
also been interpreted as DK(DK∗
) molecules (Barnes et al., 2003; Kolomeitsev
and Lutz, 2004; Faessler et al., 2007; Lutz and Soyeur, 2008; Liu et al., 2013), using
methods which range from phenomenological approaches to lattice QCD in which
scattering of light pseudoscalar mesons (π,K) on charmed mesons (D,Ds) is
studied. In particular, a decay width (D∗
s0(2317)±
→ D±
s π0
) = (133±22) keV is
predicted in the molecular interpretation (Liu et al., 2013). The corresponding width
in the compact tetraquark interpretation is estimated to be typically O(10) keV
(Colangelo and De Fazio, 2003; Godfrey, 2003). These estimates are far below the
current upper limit of 3.8 MeV (Patrignani et al., 2016).
It is likely that D∗
s0(2317)±
and D∗
s1(2463)±
can be accommodated as excited cs̄
P -wave states. A calculation in the heavy quark limit (Bardeen et al., 2003), which
treats the 0+
and 0−
cs̄ mesons as chiral partners, reproduces the experimental mass
difference D∗
s0(2317)±
− D±
s = 348 MeV, though the power O( QCD/mc) correc-
tions are not expected to be small. In a quenched lattice QCD calculation (Bali,
2003), significantly larger 0+
− 0−
meson mass splittings are predicted than what
has been measured experimentally. This would suggest a non-cs̄ interpretation.
However, the non-cs̄ approaches, mentioned above, predict lot more states, none
of which has been seen so far. The heavy-light excited charm meson sector is
remarkably quiet experimentally, and has not come up with any new candidates
since the discovery of D∗
s0(2317)±
and D∗
s1(2463)±
, and hence we shall not discuss
this sector any more.
The situation with the heavy-light multiquark states in the beauty quark sector is
not too dissimilar from the charm sector just discussed, i.e., there are no confirmed

Introduction 3
multiquark hadron states having the quark content [bq][ ¯
qs̄], q,q
= u,d (or its
conjugate).2
A couple of years ago, there was a lot of excitement in the multihadron
community as the D0 experiment at Fermilab reported the observation of a new
narrow structure in the B0
s π+
invariant mass (Abazov et al., 2016). Based on 10.4
fb−1
of pp̄ collision data at
√
s = 1.96 TeV, this candidate resonance, dubbed
X±
(5568), had a mass M = 5568 MeV and decay width = 22 MeV. A state
such as X±
(5568) would be distinct in that a charged light quark pair cannot be
created from the vacuum, leading to the unambiguous composition in terms of four
valence quarks with different flavors – b̄d̄su. This promptly attracted considerable
attention (see Ali et al. (2016a and references quoted therein), but skepticism was
also raised (Burns and Swanson, 2016). Exciting a discovery as it would have been,
X±
(5568) has not been confirmed by the LHC experiments. Based on 3 fb−1
of
pp collision data at
√
s = 7 and 8 TeV, yielding a data sample of B0
s mesons 20
times higher than that of the D0 collaboration, and adding then a charged pion, the
B0
s π+
invariant mass measured by LHCb has shown no structure from the B0
s π+
threshold up to MB0
s π+ ≤ 5700 MeV. Consequently, an upper limit on the ratio
ρ(X(5568)/B0
s ) 0.024 for pT (B0
s ) 10 GeV at 95 % C.L. has been set by
LHCb (Aaij et al., 2016b), where the ratio ρ(X(5568)/B0
s ) is defined as
ρ(X(5568)/B0
s ) ≡
σ(pp → X±
(5568) + anything) × B(X±
(5568) → B0
s π±
)
σ(pp → B0
s + anything)
.
(1.3)
A similar negative search for the X±
(5568) is reported by the CMS collaboration,
with an upper limit ρ(X(5568)/B0
s ) 0.011 for pT (B0
s ) 10 GeV at 95 %
C.L. (Sirunyan et al., 2017). This is to be compared with ρ(X(5568)/B0
s ) = (8.6±
2.4)% measured by D0 (Abazov et al., 2016).
The current experimental evidence for the multiquark states is based on hadrons
with hidden charm (cc̄) or hidden beauty (bb̄) and a light quark-antiquark pair
(qq̄) in the valence approximation. The remarkable accuracy with which the
spectra of QQ̄ states (Q = c,b) are predicted and measured has made it possible
to discover by difference new states, where the valence quarks, indirectly or
directly, do not agree with the standard paradigm (1.1). In 2003, Belle discovered
the X(3872) (Choi et al., 2003), a narrow width resonance, which decays into
J/ψ + (2π,3π) and does not fit into the charmonium sequence of states. Since
then, BaBar (Aubert et al., 2005b), CDF (Acosta et al., 2004), D0 (Abazov et al.,
2004), CMS (Chatrchyan et al., 2013), and LHCb (Aaij et al., 2013a) have
confirmed the X(3872) and reported many other states, called X(JPC
= 1++
)
and Y(JPC
= 1−−
) mesons, which do not fit in the charmonium picture either.
2 We use the term beauty for the fifth quark, the weak isospin partner of the top quark, but denote the bound
bb̄ state as bottomonium, following the standard usage.

4 Introduction
A new chapter was opened by Belle in 2007, with the observation of a charged
charmonium (Choi et al., 2008), called Z+
(4430), in the decays of the B0
meson3
:
B0
→ K−
+ J/ψ + π+
. (1.4)
The hadron Z+
(4430) appeared as a peak in the distribution of the J/ψ π+
invari-
ant mass and it obviously had to have a valence quark composition made by two
different pairs: cc̄ and ud̄. However, Babar later suggested (Aubert et al., 2009) that,
rather than a genuine resonance, the Z+
(4430) peak could simply be a reflection
of the many K resonances present in the Kπ channel. Finally, in 2014, with
much larger statistics, LHCb gave convincing evidence (Aaij et al., 2014c) for the
Z+
(4430) to be a genuine Breit-Wigner resonance.
In the meanwhile, other similar states, Z+
(3900) and Z+
(4020), have been dis-
covered by BES III (Ablikim et al., 2013a,b) and confirmed by BELLE (Liu et al.,
2013) and by CLEO (Xiao et al., 2013). Last but not least, in 2015, two baryon
resonances decaying in J/ψ+p were discovered by LHCb (Aaij et al., 2015b), with
valence quark composition cuudc̄, promptly called pentaquarks. The existence of
hadrons with a valence quark composition not fitting the paradigm (1.1) is by now
established. It is an easy prediction that the unorthodox part of the hadron spectrum
is bound to expand substantially in the next run of experiments at e+
e−
and proton
colliders. We show in Fig. 1.1 the mass spectrum of the “anticipated” charmonia
and the “unanticipated” charmonia-like states. The latter are called charged and
neutral XYZ mesons, and the four exotic states, discovered by LHCb (Aaij et al.,
2017b) in the J/ψφ channel from the amplitude analysis of the B+
→ J/ψφK+
decay, are also shown.
The exotic spectroscopy consisting of the X, Y, and Z hadrons is not confined
to the charmonium sector alone, similar hadrons have been discovered in the
bottomonium sector as well. The evidence for the first of these, dubbed as
Yb(10890), is circumstantial, and it was triggered by the “anomalies” seen in
2008 by Belle (Chen et al., 2008) in the dipionic transitions ϒ(nS)π+
π−
(nS =
1S,2S,3S), and ϒ(1S)K+
K−
, near the peak of the ϒ(5S) resonance at
√
s ∼
10.874 GeV. Interpreting these events as coming from the process
e+
e−
→ ϒ(5S) → π+
π−
+ (ϒ(1S),ϒ(2S),ϒ(3S));K+
K−
+ ϒ(1S), (1.5)
yielded partial decay widths in the range (0.52 − 0.85) MeV for the ϒ(nS)π+
π−
channels, and 0.067 MeV for the ϒ(1S)K+
K−
channel. These decay widths are
to be compared with the Zweig-forbidden dipionic transitions from the decays of
the lower-mass ϒ(mS) states (mS = 2S,3S,4S) in the final state ϒ(1S)π+
π−
,
which have partial decay widths ranging from 0.9 to 6 keV. Thus, the partial decay
3 Throughout this book, charge conjugate states and processes are implied.

Introduction 5
X(4700)
X(4500)
X(4274)
Xc2(23
P2)
Xc2(13
P2)
Xc1(13
P1)
Xc0(13
P0)
Xc2(33
P2)
Xc0(33
P0)
Xc0(23
P0)
Zc(4200)+
Zc(4020)+
Zc(3900)+
Z1(4050)+
Z(4430)+
ψ(43
S1)
ψ(23
D1)
ψ(33
S1)
ψ˝(13
D1)
ψ´(23
S1)
Y(4360)
Y(4260)
X(4160)
X(3940) X(3915)
X(4140)
X(3872)
established cc states
predicted, undiscovered
neutral XYZ mesons
charged XYZ mesons
J/ψφ mesons
ηc(41
S0)
ηc´(21
S0)
ηc(31
S0)
hc(31
P1)
hc(11
P1)
J/ψ(13
S1)
JPC
ηc(11
S0)
Z2(4250)+
4.6
4.4
4.2
4.0
3.8
2MD
MD+MD
3.6
3.4
3.2
3.0
0–+ 1–– 1+– 0++ 1++ 2++
MASS
[GeV/c
2
]
Xc1(33
P1)
Figure 1.1 Anticipated charmonia and exotic charmonia-like states, called the
charged and neutral XYZ mesons, as of 2015. Figure from Olsen (2015) updated
by Sheldon Stone (2017) by including the four exotic J/ψφ states discovered
subsequently by LHCb (Aaij et al., 2017b).
widths in (1.5) are typically more than two orders of magnitude larger. Moreover,
the dipion invariant mass spectra from (1.5) are very different than in the Zweig-
forbidden ϒ(4S) → π+
π−
+ ϒ(nS) decays.
Since an exotic state, Y(4260), having JPC
= 1−−
, was seen in the charmo-
nium sector in the decay channel J/ψπ+
π−
, it was argued that the anomalous
events in (1.5) could possibly be coming from the production and decays of

6 Introduction
the bottomonium-counterpart (Hou, 2006). The production cross sections for the
states (ϒ(1S),ϒ(2S),ϒ(3S))π+
π−
was subsequently measured as a function
of
√
s between 10.83 GeV and 11.02 GeV, and it was found that the data did
not agree with the line shape of the ϒ(5S). The mass and decay width of the
resonance, Yb(10890), was measured as [10888.4+2.7
−2.6 (stat) ± 1.2 (syst)] MeV
and [30.7+8.3
−7.0 (stat) ± 3.1 (syst)] MeV, respectively (Adachi et al., 2008). The
phenomenology of Yb(10890) was subsequently worked out in a number of
papers (Ali et al., 2010a, 2011; Ali and Wang, 2011; Chen et al., 2011b).
The status of Yb at this stage is not clear, as it lies very close in mass to the
canonical and well-established bottomonium state ϒ(5S), and both of them have
the same quantum numbers JPC
= 1−−
. A search for Yb(10890) through the
so-called Rb energy-scan at the KEK B-factory, with
Rb ≡
σ(e+
e−
→ bb̄)
σ(e+e− → μ+μ−)
(1.6)
did not confirm its existence and Belle has put an upper bound on the electronic
width (Yb → e+
e−
) ≤ 9 eV at 90% confidence level (Santel et al., 2016). On
the other hand, very clear peaks are seen in the Rϒ(nS)π+π− energy-scan at the KEK
B-factory, where
Rϒ(nS)π+π− ≡
σ(e+
e−
→ ϒ(nS)π+
π−
)
σ(e+e− → μ+μ−)
, (1.7)
in the ϒ(5S) and ϒ(6S) regions (Santel et al., 2016). These peaks, with rather
large branching ratios in the decays of ϒ(5S) and ϒ(6S), remain enigmatic. Apart
from the processes shown in Eq. (1.5), other dipionic transitions from ϒ(5S) are
also found to have very high decay rates, such as π + π + hb(1P,2P ), with
hb(1P,2P ) the bottomonium spin-singlet P-wave states. The dipion recoil mass
spectrum from the ϒ(5S) is shown in Fig. 1.2. Understanding this spectrum without
the intervention of multiquark states is not possible. Apart from the dichotomy
Yb(10890)/ϒ(5S), the four-quark states Z±
b (10610) and Z±
b (10650), discovered
later by Belle, play a fundamental role, as discussed below and in detail in this
book.
Unfortunately, the dipionic transitions from the regions near the ϒ(5S) and
ϒ(6S), which have led to the discovery of a number of anticipated bottomonium
states hb(nP ), and exotic states, Z±
b (10610) and Z±
b (10650), have not been checked
by independent experiments, as no e+
e−
annihilation experiment in this energy
range is available at present, and the next e+
e−
experiment under construction,
Belle II, will start taking data only in 2019. In our opinion, high-luminosity data
from Belle II is direly needed to settle several open issues, of which the existence
of Yb(10890) is one.

Introduction 7
9.4
0
1
2
3 Υ(1S)
Υ(3S)→Υ(1S)
Υ(2S)
Υ(2S)→Υ(1S)
Υ(3S)
Υ(1D)
hb(2P)
hb(1P)
4
×104
9.6
Mmiss(GeV/c2)
Events
/
5MeV/c
2
9.8 10 10.2 10.4
2541011-001
Figure 1.2 The mass spectrum of the hadrons (called Mmiss), recoiling against the
π+π− pair in the e+e− annihilation data taken near the peak of the ϒ(5S). The
data, with the combinatoric background and K0
S contribution subtracted (points
with error bars) and signal component of the fit functions (overlaid) (Adachi et al.,
2012). Reprinted with permission from [I. Adachi et al. (Belle Collaboration),
Phys. Rev. Lett., 108, 032001, 2012; http:/dx.doi.org/10.1103/PhysRevLett.108
.032001]. Copyright (2012) by the American Physical Society.
The spectrum shown in Fig. 1.2 strongly suggests that experiments at the LHC
could measure the production of ϒ(5S) and ϒ(6S) through the Drell-Yan mecha-
nism or in strong interaction production processes. For this, one has to concentrate
on the decays ϒ(5S) → ϒ(nS)π+
π−
, and likewise for ϒ(6S) → ϒ(nS)π+
π−
,
though with reduced rates. Searching for the resonances in a Drell-Yan process
and hadronic collisions in four charged-particle final states, such as μ+
μ−
π+
π−
,
has the potential of discovering J/ψ-like and ϒ-like multiquark states. The tradi-
tional method of measuring the bottomonium states through the dileptonic (e+
e−
or μ+
μ−
) final states will not work, however, as the corresponding branching ratios
are tiny. Apart from this, Yb-like hadrons, with JPC
= 1−−
, can also be searched
for in e+
e−
annihilation, in the so-called radiative return process
e+
e−
→ γ + Y(JPC
= 1−−
) (1.8)
but, again, their production cross sections are expected to be rather small due to
the small anticipated electronic decay widths (Y) → e+
e−
. No Xb(JPC
= 1++
)
exotic hadron has been discovered so far in the bottomonium sector, though they
are being searched for by the ATLAS and CMS collaborations at the LHC, but the
current experimental sensitivity falls way short of the discovery threshold.

8 Introduction
The charged bottomonium-like hadrons, Z±
b (10610) and Z±
b (10650), have been
discovered in the decays
Yb(10890)/ϒ(5S) → Z±
b (10610) + π∓
,
Yb(10890)/ϒ(5S) → Z±
b (10650) + π∓
, (1.9)
with the subsequent decays into hb(1P,2P )π±
, and ϒ(1S,2S,3S)π±
, going at
almost the same rate. Since hb(1P,2P ) are spin-singlet states, and ϒ(1S,2S,3S)
are spin-triplets, similar rates of the dipionic transitions in these final states from
Yb(10890)/ϒ(5S) pose a challenge. This is yet another anomalous feature of the
ϒ(5S) decays. Here also, multiquark states come to the rescue. Tetraquark inter-
pretation of the Z±
b (10610) and Z±
b (10650), which have in their Fock space both
spin-0 and spin-1 components, offer a natural explanation, though they can also
be accommodated in the hadron molecule interpretation. More data are needed for
the classification of the exotic hadrons in the bottomonium sector. Apart from the
dipionic transitions, other decay channels, such as
Yb(10890)/ϒ(5S) → ϒ(1S) + (K+
K−
,η π0
) (1.10)
are expected to be quite revealing, and the dipion-, dikaon-, and the (η π0
)- invari-
ant mass distributions as well. We anticipate that the exotic spectroscopy in the
bottomonium sector will take a central place in Belle II measurements, and, in all
likelihood, also in the high-luminosity LHC run at
√
s = 13 TeV, which is well
under way.
What about the exotic baryons? Pentaquarks, consisting of four quarks and an
antiquark, are the much sought after exotic mesons whose discovery had to wait
for the commissioning of the LHC. Since most of the tetraquarks are observed in
the decays of the B and Bs mesons, it was a natural expectation that the decays of
the b-baryons may reveal similar exotic baryonic structures. LHC is, among other
things, a b factory, as they are profusely produced in high-energy pp collisions. In
particular, in the acceptance of the LHCb experiment, about 20% of all b-flavored
hadrons are 0
bs (Aaij et al., 2012a). The baryonic analog of the well-studied
B-meson decay B0
→ J/ψK+
K−
is the b decay 0
b → J/ψK−
p, yielding
four charged particles (J/ψ → μ+
μ−
)K−
p, which could be used effectively
to pin down the 0
b decay vertex, thus offering an excellent method to precisely
measure the 0
b lifetime. With this motivation, a dedicated study of the process
pp → bb̄ → bX; b → K−
J/ψp, (1.11)
was undertaken by the LHCb collaboration, using some 26,000 signal candidates
with about 1400 background events (Aaij et al., 2014d). A closer examination of
the decay products, in particular the Dalitz-distribution m2
J/ψp versus m2
Kp, showed

Introduction 9
an anomalous feature (Aaij et al., 2015b). There were vertical bands (in m2
Kp)
in the data, corresponding to the anticipated ∗
→ K−
p resonant structures,
and an unexpected horizontal band (in m2
J/ψp) near 19.5 GeV2
. The Dalitz plot
projections showed significant structures in the K−
p spectrum, coming essentially
from the Feynman diagram (a) in Fig. 2.13, but there was also a peak in the J/ψp
mass spectrum. A statistically good fit of the mJ/ψp distribution was shown to be
consistent with the presence of two resonant states, henceforth called Pc(4450)+
and Pc(4380)+
, with the following characteristics
M = 4449.8 ± 1.7 ± 2.5 MeV; = 39 ± 5 ± 19 MeV, (1.12)
and
M = 4380 ± 8 ± 29 MeV; = 205 ± 18 ± 86 MeV. (1.13)
Both of these states carry a unit of baryonic number and have the valence quarks
P +
c = c̄cuud. The preferred JP
assignments of the pentaquarks are 5/2+
for the
Pc(4450)+
and 3/2−
for the Pc(4380)+
(Aaij et al., 2015b). So far, these are the
only five-quark states observed in an experiment. This concludes our overview of
the current experimental situation.
In parallel with the experimental discoveries, a large theoretical activity has gone
into the interpretation of the new particles. To be sure, nobody has challenged
the validity of Quantum Chromodynamics (QCD) or has invoked the presence of
new types of fundamental constituents. Rather, the existence of different pictures
in the interpretation of the data reflects the remarkable ignorance about the exact
solutions of nonperturbative QCD. Different interpretations call into play different
approximations, or different regimes of the basic QCD force, to arrive at seemingly
contradictory pictures. Thus, the pieces of this new dynamical puzzle will have to
be put together painstakingly, and it is conceivable that there are more than a single
template which QCD seems to be making use of in the dynamics of these exotic
hadrons.
The most conventional explanation of the exotic states is in terms of kinematic
effects due to the opening of new channels (also trademarked as cusps). While it is a
logical possibility, it is less likely to hold sway to accommodate all or most of these
hadrons. This is due to the unconventional dynamics required in this scenario to
produce narrow structures as cusps, like the X(3872), and the fact that the phase of
the charged state Z±
(4430) and of at least one pentaquark resonance, Pc(4450)+
,
measured by the LHCb, become 90◦
at the peak, which is a telltale signature of
a Breit-Wigner resonance. Thus, with more data, this scenario can be checked by
doing an Argand analysis of the decay amplitudes in question.
It is more likely that hadron spectroscopy finds itself at the threshold of a new
era, and in anticipation thereof, three dynamical models of the X,Y,Z, and Pc
hadrons have been put forward in the current literature as viable explanations.

10 Introduction
We briefly review them later in this chapter, and will discuss them in more detail in
the subsequent chapters of this book.
The first picture goes under the name compact tetraquarks, which are bound
states of color nonsinglet diquark-antidiquarks, tightly bound by gluons, very much
along the same lines as colored quark-antiquark pairs are bound into color-neutral
mesons. This view then opens a secondary layer of compact hadrons in QCD,
which, in principle, are even more numerous than the quark-antiquark mesons. The
tetraquark picture relies as a guiding framework on the nonrelativistic Constituent
Quark Model, which gives quite accurate picture of the conventional qq̄ and qqq
mesons and baryons, including charmed and beauty hadrons. The starting point is
the attraction within a color antisymmetric quark pair, which arises in perturbative
QCD due to one gluon exchange and in nonperturbative QCD due to instanton inter-
action. This makes diquarks and antidiquarks the basic units to build X,Y,Z, and Pc
hadrons, with mass splittings due to spin-spin interactions and orbital momentum
excitation.
The rekindled interest in tetraquarks is mostly data driven, as they provide a
template for the newly found quarkonium-like states, both neutral and charged.
Prior to this, for a long time, tetraquarks were banished from the observable hadron
spectrum by field-theory arguments. In particular, their reputation as bona fide
hadrons was tarnished by a theorem due to Sidney Coleman, which stated that
tetraquark correlation functions for N → ∞ (N is the number of colors) reduce to
disconnected meson-meson propagators (Coleman, 1980). Hence, according to this
argument, they do not exist as poles in the scattering amplitudes. Lately this large-N
argument has been put to question by Steven Weinberg (2013b) and by others. They
noted that the existential issue for tetraquarks is not so much the dominance of the
disconnected diagrams in the N → ∞ limit. Indeed, if the connected tetraquark
correlation functions do develop poles for finite N, it does not matter much that
the residue is not of leading order for N → ∞. After all, it was observed, meson-
meson interactions do vanish as well in this limit, and we do not believe that mesons
are free particles. The catch could rather be that the decay widths increase in the
large-N limit, making these states undetectable. By explicit examination one sees,
however, that, once tetraquark correlation functions are properly normalized, the
decay rates do indeed vanish as N → ∞, reassuring that there is no prima facie
field-theoretic argument against their existence and visibility. This is the line of
argument which we will pursue here in this book at some length.
There is no evidence of a diquark structure in light baryons, such as neutron
and proton. In particular, data on deep inelastic scattering on a proton, such as at
HERA, can be analyzed in terms of quarks and gluons without the need of invok-
ing diquarks. However, heavy-light baryons with a single heavy quark (Qqq) do
admit an interpretation as heavy quark-light diquark systems (Lichtenberg, 1975;

Introduction 11
Ebert et al., 2011; Chen et al., 2015a). Very much along these lines, the five narrow
excited c states , discovered recently by LHCb (Aaij et al., 2017a), and confirmed
by Belle (Yelton et al., 2017), can be accommodated as an excited css quark-
diquark system in a P state with well-defined quantum numbers (Karliner and
Rosner, 2017c). While suggestive, the diquark interpretation of the excited c
states is by no means unique. Experimental confirmation of the quantum numbers
will certainly be a boost to the heavy quark-diquark interpretation of the excited
c states.
The spectrum of the excited doubly charmed baryons was likewise worked out
long ago in the relativistic quark-diquark picture (Ebert et al., 2002). The first of
these, a doubly charmed baryon ++
cc = ccu, has been discovered recently by the
LHCb collaboration (Aaij et al., 2017c) in the decay mode ++
cc → +
c K−
π+
π+
,
having a mass 3621.40±0.78 MeV, in agreement with theoretical predictions (Kar-
liner and Rosner, 2014). This can be interpreted as a cc color-antitriplet diquark
bound by QCD attractive forces to a color-triplet light quark (in this case a u quark)
to yield a color-singlet double-charm baryon. More such doubly-heavy baryons
QQq, with Q = c,b and q = u,d,s should follow. Thus, it seems that there is a
prima facie case that the single heavy baryons Qqq
, as well as the double heavy
baryons QQq, can be classified in the spectroscopic sense as heavy quark–light
diquark and heavy diquark–light quark systems, respectively.
It is therefore natural to anticipate that also the double-heavy tetraquarks QQq̄q̄
,
consisting of a heavy diquark QQ and a light antidiquark q̄q̄
, and their charge
conjugates (Q̄Q̄qq
), also exist. Arguments for the stability of such tetraquarks
against strong interactions in the heavy quark limit date back to the initial epoch
of this field (Ader et al., 1982; Carlson et al., 1988; Manohar and Wise, 2000),
reviewed recently (Richard, 2016). There has been a surge of theoretical interest in
stable tetraquarks ever since the discovery of the ++
cc , which we discuss at some
length in this book.
The second dynamical model studied in quite some detail is that of hadronic
molecules, loosely bound together by the exchange of pions and other light mesons.
This model has received a lot of interest due to the proximity in mass of several
of the X, Y, and Z hadrons to a number of meson-antimeson thresholds, such
as (DD̄ ), (D D̄ ), . . . in the charmonium sector, and (BB̄ ), (B B̄ ), . . . in bot-
tomonium. In the case of X(3872), the DD̄ threshold is so close that, using the
formula which gives the radius of the bound states in terms of the binding energy,
R ∼ 1/
√
2MDEb, one would deduce a surprisingly large value of R in the order of
several fermis.
Molecular models are predicated on ideas borrowed from nuclear physics, such
as the Deuteron viewed as a bound state molecule of neutron and proton, and go
quite far in explaining some of the decay characteristics of the exotic hadrons.

12 Introduction
This has made the nuclear physics community working on low-energy hadron
physics very excited about them. However, it is through their hadronic production
cross sections at the Tevatron and now at the LHC that the underlying dynamics
will be put to a stringent test. In particular, their production rates at large transverse
momenta will be quite revealing and we expect that also the heavy ion collision
experiment ALICE at the LHC may contribute in their understanding.
There are yet other options available, called hybrids, consisting of a charm-
anticharm, or beauty-antibeauty, quark pair in a color-octet mode and a color-octet
gluon, or a light quark-antiquark pair in a color-octet configuration, bound to yield
an overall color-singlet hadron.
Finally, to complete this list, also the hadro-quarkonium picture has been pro-
posed, in which a cc̄ or bb̄ state is surrounded by light quark matter.
Thus far, no smoking gun signature has been found to distinguish the different
interpretations. Perhaps, this could indicate that these models are, after all, different
but complementary descriptions of the same QCD underlying reality. One feature
that may distinguish between the compact tetraquark vis-à-vis the other models is
the fact that the latter are expected to lead to incomplete flavor multiplets, due to
the sensitivity to the mass differences involved of the forces related to pion and
other low energy, color singlet, mesons. Incomplete isospin multiplets are, by the
way, frequent in nuclear physics. On the other hand, complete flavor multiplets
are expected for tetraquarks, as is the case for the mesons and baryons described
by (1.1). Despite their ubiquitous nature, candidate tetraquark states are still rather
sparse, and the key question is: Will the situation remain patchy, with an exotic
hadron popping up randomly, or will the multiplets based on a symmetry principle
fill up as statistics and better resolutions add up?
These ideas are confronted not only by experiments, but are being studied along
different theoretical lines: potential models, heavy quark effective theories, chiral
perturbation theory, QCD sum rules and, above all, using lattice QCD. A compre-
hensive discussion of these methods will stretch the size of this book much beyond
its intended scope and readership. Also, many of these techniques have not yet
matured. However, we shall review selected applications of these techniques to
specific processes, with emphasis on lattice QCD.
The aim of this book is to summarize the current data on exotic hadrons and
confront them with the dynamical models listed earlier in the chapter. Our main
emphasis is on illustrating the underlying dynamics rather than providing a precise
quantitative description of the observed phenomena, as this field is still in a devel-
opment stage and in many cases a dynamical theory is still lacking. On the other
hand, ever since the discovery of the X(3872), scientific activity in this field has
been both intense and multifarious, spanning over a period well over a decade, and

Introduction 13
we think that it is a useful exercise to take stock of the situation and put together
various theoretical scenarios in a coherent way.
With several ongoing experimental facilities operating and a couple of more in
the offing, this field is expected to transform, from mostly exploratory, which is
currently the case, to a quantitative discipline in a decade from now.
We hope the present book may provide a useful introduction to the theoretical
and experimental physicists who want to get into this promising and fascinating
field.

2
XYZ and Pc Phenomenology
2.1 Charmonium Taxonomy
We start by recalling some standard terminology for the anticipated charmonia and
unanticipated charmonia-like states, employed throughout the book. Charmonia are
cc̄ bound states in QCD, similar to the positronium in QED, and, likewise, they are
characterized by the following quantum numbers:
• total cc̄ spin=S,
• orbital angular momentum=L,
• total angular momentum=J,
• radial excitation quantum number=n.
The generic state is indicated with the spectroscopic notation: n 2S+1
LJ . The lowest
lying, S and P wave charmonia are given more colloquial names
1 1
00 = ηc(1S)
1 3
01 = ψ(1S) = J/ψ
2 3
01 = ψ(2S) = ψ
1 3
1J = χJ,c(1P ), J = 0,1,2
1 1
11 = hc(1P ). (2.1)
Similar notations are used for the bb̄ states: the 1 3
01 state is called ϒ(1S), and
the radial excitations are labelled as ϒ(nS) (n = 2,3,...).
Unanticipated charmonia are usually indicated as X, Y and Z mesons, according
to the following terminology
• X, neutral, positive parity mesons, typically seen in J/ψ + pions, JPC
=
0++
, 1++
, 2++
, e.g., X(3872).
• Y: neutral, negative parity mesons, seen in e+
e−
annihilation with or without the
initial state radiation (ISR), therefore JPC
= 1−−
, e.g., Y(4260).
14

• Z: charged/neutral, typically positive parity, with manifest four valence quarks,
seen to decay in J/ψ + π, hc(1P ) + π, χc(1P ) + π; eg. Z(4430), where hc(1P )
and χc(1P ) are the P -wave quark spin singlet and triplet states, respectively,
see (2.1).
The XYZ nomenclature is at variance with the notation adopted for these states
in the Particle Data Group (PDG) (Patrignani et al., 2016) - a potential source of
confusion in some cases.
2.2 Hidden cc̄ Exotics
Table 2.1 lists the exotic states with their main characteristics (masses, decay
widths, and JPC
quantum numbers), which we shall discuss in detail in this book.
In this chapter, we concentrate on a few of them, which we have picked to illustrate
their exotic nature, and to briefly review the kind of theoretical models that have
been proposed to accommodate them.
Table 2.1 A summary of the exotic XYZ mesons and the exotic baryons Pc
discussed in this book. Most entries are from the tables in PDG (Patrignani et al.,
2016), though not their notations for the exotic states. Parameters for the four
J/ψφ states, X(4140), X(4274), X(4500), and X(4700) are taken from the LHCb
paper (Aaij et al., 2017b). With a slight abuse of notation, we attribute to the
charged XYZ states the C eigenvalue of their neutral isospin partner.
State M (MeV) (MeV) JPC
X(3872) 3871.68 ± 0.17 1.2 1++
Z±
c (3900) 3891.2 ± 2.3 40 ± 8 1+−
Z±
c (4020) 4022.9 ± 2.8 7.9 ± 3.7 1+−
Y(4260) 4263+8
−9 95 ± 14 1−−
Y(4360) 4361 ± 13 95 ± 14 1−−
Z±
c (4430) 4458 ± 15 166+37
−32 1+−
X(4140) 4146.5 ± 4.5 83 ± 21 1++
X(4274) 4273.3 ± 8.3 56 ± 11 1++
X(4500) 4506 ± 11 92 ± 21 0++
Y(4660) 4664 ± 12 48 ± 15 1−−
X(4700) 4704 ± 10 120 ± 31 0++
Z±
b (10610) 10607.2 ± 2.0 18.4 ± 2.4 1+−
Z±
b (10650) 10652.2 ± 1.5 11.5 ± 2.2 1+−
Pc(4380)± 4380 ± 8 ± 29 205 ± 18 ± 86 JP = 3/2−
Pc(4450)± 4449.8 ± 1.7 ± 2.5 39 ± 5 ± 18 JP = 5/2+

16 XYZ and Pc Phenomenology
X(3872). First observed in 2003 by Belle (Choi et al., 2003) in the decays of
the B mesons, the neutral X(3872) was later confirmed by BaBar (Aubert et al.,
2005b), and by hadron collider experiments (Acosta et al., 2004; Abazov et al.,
2004; Chatrchyan et al., 2013; Aaij et al., 2013a). It was also found in the radiative
decay of another exotic particle Y(4260) (see Table 2.1.)
Y(4260) → γ X(3872), (2.2)
and was observed to be promptly produced in pp(p̄) collisions.
The X(3872) has JPC
= 1++
quantum numbers, confirmed with a high degree
of precision. This resonance has some enigmatic features:
1. Its charged partners have not been observed, so far.
2. Its mass is almost perfectly fine-tuned with the D0
D̄0∗
threshold, with m(X) −
M(D∗0
) − m(D0
) = 0.1 ± 0.18 MeV (Patrignani et al., 2016).
3. It decays into J/ψ ρ and J/ψ ω with almost the same branching fraction.
4. It is a considerably narrow resonance, its width being 1 MeV.
5. It is very close in mass to the JPC
= 1+−
Zc(3900) resonance, discussed below.
The absolute neutrality of the X(3872), which seems to be the case experi-
mentally at the time of this writing, does not speak loud for it to be a a compact
four-quark structure, as it is indeed the case for some other exotic mesons, such
as Z(4430), Zc(3900), and Zc(4020). On the other hand a more complex quark
structure is called for because a pure charmonium should not appreciably decay by
violating isospin, due to the very small u and d quark masses.
The spectacular vicinity to the D0
D̄0∗
threshold is often used to suggest that
the X(3872) could be a D0
D̄0∗
loosely bound molecule. However, it is produced
in hadronic collisions with a stiff transverse momentum (pT (X)) distribution – a
feature not seen for other bonafide hadronic molecules, such as Deuterium. A way
out of this is presumably provided by the presence of a substantial cc̄ component in
its Fock space. We discuss these aspects in Chapter 4.
As for the width of the X(3872), its experimental measurement is still a chal-
lenge; a loosely bound molecule should be as broad as the shortest lived of its
constituents, the D∗
in the case of X(3872), with the charged D∗
width of the order
of 100 keV. This remains to be tested.
Y(4260). A charmonium-like state was discovered by BaBar (Aubert et al.,
2005a) with a mass of around 4.26 GeV in the initial state radiation process
e+
e−
→ γISR J/ψ π+
π−
, JPC
= 1−−
. (2.3)
The measured mass by BaBar was 4259 ± 8+2
−6 MeV and the width was deter-
mined as 88 ± 23+6
−4 MeV. This state was confirmed by Belle (Abe et al., 2006).

Figure 2.1 The J/ψπ+π− invariant mass distribution in inclusive production in
pp collisions at
√
s = 7 TeV from LHCb. The two peaks are from ψ(3.77) and
X(3872), the latter also shown in inset. Figure reprinted with thanks from (Aaij
et al., 2012b).
However, the mass was measured to be 2.5σ higher than the one measured by
BaBar, and the width was 50 % higher. It is tentatively called Y(4260).
Additional confirmation of the Y(4260) came from CLEO-c (He et al., 2006),
also using the ISR technique, and by BESIII (Ablikim et al., 2017b), by a precise
measuremet of the cross section e+
e−
→ J/ψπ+
π−
, scanning at the center-of-
mass energies from 3.77 to 4.60 GeV. BES III data, however, suggest the possible
presence of two resonances under the nominal 4260 peak, see Chapter 9.
The current world average of the Y(4260) mass and its width are given in
Table 2.1. The production cross section of Y(4260) is small, with the present world
average ee × B(Y(4260) → J/ψπ+
π−
) = 9.2 ± 1.0 eV (Patrignani et al., 2016),
where ee is the decay width (Y(4260) → e+
e−
). No evidence of the Y(4260)
has so far been found in B decays. It is not seen in the prompt production processes
in proton(antiproton)–proton collisions either.
CLEO-c also reported a evidence for a second decay channel (Coan et al., 2006)
Y(4260) → J/ψπ0
π0
, confirmed by Belle, and the ratio of the two branching frac-
tions was determined as B(Y(4260) → J/ψπ0
π0
)/B(Y(4260) → J/ψπ+
π−
)
0.5. This implies that the isospin of the ππ system must be zero, i.e., IG
= 0+
.
This is completely different from that of X(3872), where the ππ sytem has I = 1,
with JPC
= 1−−
. Also, the π+
π−
mass distribution in Y(4260) → J/ψπ+
π−
exhibits an f0(980) signal, with JPC
= 0++
. This is also completely different from

80
70
(a)
Events
/
(0.020
GeV/c
2
)
60
50
40
30
20
10
0
m(J/ψπ+π-)(GeV/c2)
3.8 4 4.2 4.4 4.6 4.8 5 5.2 5.4
Figure 2.2 The J/ψπ+π− invariant mass distribution from 3.74 to 5.5 GeV,
showing the Y(4260) resonance, measured in e+e− annihilation with the initial-
state-radiative events at PEPII asymmetric collider with the BaBar detector at
center-of-mass energy
√
s = 10.54 and 10.58 GeV (Lees et al., 2012). Reprinted
with permission from [J.P. Lees et al. (BABAR Collaboration), Phys. Rev. D86,
051102, 2018; http:/dx.doi.org/10.1103/PhysRevD.86.051102]. Copyright (2012)
by the American Physical Society.
the X(3872) in which the π+
π−
exhibits a ρ signal. Thus, in contrast to X(3872),
the Y(4260) does not violate isospin in the decay.
The Y(4260) has been discussed in the literature as a hybrid [cc8g] (Close and
Page, 2005) with a color octet cc pair bound to a valence type gluon. However,
recently there is evidence that the Y(4260) decays also to hcπ+
π−
(Ablikim et al.
(2017a)), which would imply a spin flip of the heavy quark system. If this decay
is confirmed by another measurement, an interpretation of the Y(4260) as a hybrid
would be strongly disfavored. On the other hand, comparable rates to the spin-0 cc̄
and spin-1 cc̄ states can be accommodated in the tetraquark picture, which allows
to have both spin-0 and spin-1 components in the Fock space of Y(4260).
Y(4260) is also a candidate for a tetraquark state (Maiani et al., 2014; Ali et al.,
2018a). This hypothesis will be taken up at some length in Chapter 9, together
with the other observed JPC
= 1−−
exotic states. This includes the state Y(4630),
measured in the ISR process
e+
e−
→ γISR
+
c
−
c (2.4)
by Belle (Pakhlova et al., 2008). Y(4630) is presumably the same state as the
Y(4660), seen in the decay Y(4660) → ψ
π+
π−
, listed in Table 2.1. It is a

Events
/
20
MeV
mΛc
+
Λc
–
[GeV]
4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3
40
30
20
10
0
Figure 2.3 Invariant mass m +
c
−
c
distribution in the process e+e− → γISR
+
c
−
c
showing the signal of Y(4630), measured by Belle (Pakhlova et al., 2008).
Reprinted with permission from [G. Pakhlova et al. (Belle Collaboration), Phys.
Rev. Lett. 101, 172001, 2008; http:/dx.doi.org/10.1103/PhysRevLett.101.172001].
Copyright (2008) by the American Physical Society.
candidate for the much sought-after baryonium states as the first example of the
charmed baryonium formed by four quarks (Cotugno et al., 2010).
The general pattern that the most natural decay of a tetraquark state, if allowed
by phase space and other quantum numbers, is in a pair of baryon-antibaryon, is
anticipated also in the string-junction picture of the multiquark states (Rossi and
Veneziano, 2016), and in the holography inspired stringy hadron (HISH) perspec-
tive (Sonnenschein and Weissman, 2016). A corollary of this picture is that the
tetraquark states, very much like the qq̄ mesons, are expected to lie on a Regge
trajectory, and predictions about a few excited states in the ss̄, cc̄, and the bb̄ are
available in the literature (Sonnenschein and Weissman, 2016).
The Regge behavior of the excited tetraquark states, if confirmed experimentally,
would underscore the fundamental difference anticipated between the tetraquarks
and other competing scenarios, such as the kinematic cusps and hadron molecules,
for which the Regge trajectories are not foreseen.
Z±
(4430). The first clearly multiquark resonance observed was the Z±
(4430),
claimed by Belle in 2007 (Choi et al., 2008), but confirmed only in 2014 by the
LHCb collaboration (Aaij et al., 2014c) in the channel
B̄0
→ K−
(ψ
π+
). (2.5)

Figure 2.4 Argand plot for the Z±(4430) (left) and the ψπ± invariant mass
(right) proving the resonant nature of this state. Figure reprinted with thanks from
LHCb (Aaij et al., 2014c).
A clear peak is seen in the ψ
π±
invariant mass as shown in Fig. 2.4. The minimum
quark content of this resonance is cc̄ud̄ - a four-quark state. LHCb also reported a
measure of the phase of the resonant amplitude, showing an Argand plot with the
typical Breit–Wigner circle, the phase going through 900
at the peak, also shown in
this figure. The spin parity determined by LHCb is JP
= 1+
. The current mass and
decay width of Z±
(4430) are (Patrignani et al., 2016)
M = 4458 ± 15 MeV; = 166+37
−32 MeV (2.6)
In the tetraquark interpretation (Maiani et al., 2005, 2007; Liu et al., 2008), the
resonant ψ
π+
state, identified as Z(4430)±
, comes about by the interplay of the
weak b → cc̄s decay and uū pair creation from the vacuum. The s quark from
the weak decay makes a K−
with the ū quark from the vacuum. The remaining u
and d̄ quarks (spectator quark in B0
meson), together with the cc̄ pair, constitute
the valence content (cc̄ud̄) of the (ψ
π+
) resonance. The corresponding Feynman
diagram for the generic decay B → K(ψ(2S)π) is shown below.
This diagram admits as well the configuration in which Z±
(4430) is a bound
state of D∗
(2010)D̄1(2420), whose threshold is close to the Z±
(4430) mass. The
charm meson pair then rescatters into ψ
π+
, thus Z±
(4430) could be a threshold
effect (Rosner, 2007). Considering the possibility that Z±
(4430) is an S-wave state
of the D∗
and D̄1 would yield JP
= 0−
,1−
,2−
as possible quantum numbers. With
its spin-parity now determined to be JP
= 1+
, the D∗
(2010)D̄1(2420) bound state
hypothesis is ruled out.
A variation on the theme is the so-called “cusp effect” (Bugg, 2008a), arising
from the deexcitation of the D∗
(2010)D̄1(2420) pair into lower-mass D-meson
states. This hypothesis has been put forward often in the context of the XYZ states.
However, the phase motion of a cusp is distinguishable from that of a Breit–Wigner,

Figure 2.5 The generic weak decay diagram for B → K + ψ + π.
B D(∗)+
D(∗)–
b
q´ q´
c
(a)
s
q
s
(b)
D–
s
D+
p+
D*0
B0
K
–
J/ψ
(c)
Ds
D∗+
p+
D0
B0
K
–
J/ψ
∗-
Figure 2.6 Feynman diagram for B decays into radially excited D−
s meson, (a),
followed by the rescattering process DD∗ → ψπ+, (b), (c). Figure reprinted with
thanks from (Pakhlov and Uglov, 2015).
in that for a cusp, the imaginary part of the S-wave amplitude is a step function near
the threshold. The Argand diagram for Z±
(4430) in Fig. 2.4 does not support this
phase motion.
Another model based on rescattering of the charmed mesons involves a yet
to be discovered meson D−
s , whose mass is predicted in the range (2600–2650)
MeV (Pakhlov and Uglov, 2015). The mechanism is illustrated by the triangle
diagrams in Fig. 2.6. While the peaking structure in this hypothesis is still due
to the rescattering effects, the amplitude of the Z±
(4430) now carries a phase

due to the intermediate D−
s resonance. The resulting phase looks very similar
to a Breit–Wigner, albeit with a clockwise phase motion as one moves along the
width of the structure (Pakhlov and Uglov, 2015). Since the clockwise and counter-
clockwise phase (for a Breit–Wigner) motions are experimentally not distinguished,
this hypothesis is consistent with the data. Of course, one has to find the putative
D−
s in the right mass range.
In the meanwhile, the J/ψπ±
mode of Z±
(4430) has also been measured
(Chilikin et al., 2014). From all the experimental facts, one concludes that the
preferred option for Z±
(4430) is to be a genuine resonance with spin-parity
JP
= 1+
.
All the observations of Z+
(4430) are made so far in the (ψ
,J/)π+
K−
decay
modes of the B̄0
. To understand its nature, it is essential to confirm its existence in
another production process, such as in proton–proton collisions at the LHC and/or
in photoproduction. While it is difficult to be quantitative about the production
cross section for the former, the latter has been estimated in the process γp →
Z+
(4430)n → ψ
π+
n (Liu et al., 2008), on the basis of γ −ψ
mixing and charged
pion exchange. The ψ
π+
mode is preferred over the J/ψπ+
due to the larger
coupling.
In 2013 another resonance, the Zc(3900), was observed simultaneously by BES
III (Ablikim et al., 2013a) and by Belle (Liu et al., 2013), as a decay product of the
Y(4260)
Y(4260) → π+
(J/ψ π−
) (2.7)
with Y(4260) being itself a tetraquark resonance candidate with a cc̄ quark pair
in its valence. The (J/ψ π−
) resonance, dubbed Zc(3900), has again a minimal
valence quark content of four, and1
JPC
= 1+−
.
The Zc(3900) appears in the three states of charge, and the same occurs for
Z
c(4020), another, slightly heavier JPC
= 1+−
resonance, also found in BES III
data in the decay:
Z
c(4020) → hc(1P ) + π (2.8)
and also unequivocally exotic.
There are three other unanticipated charged resonances reported in Fig. 1.1,
that however need confirmation: Z(4050) and Z(4250), seen to decay in χc1(1P )
and attributed JP
= 0+
, and Z(4200), seen to decay in J/ψπ+
with possible
JP
= 1+
.
1 The charge conjugation quantum number, C, cannot be assigned to a charged meson; we give here the charge
conjugation of the neutral partner, which is seen to decay in J/ψ + π0 and therefore has C = −1; the same
convention is adopted for the other Z mesons.

Figure 2.7 The J/ψπ+ invariant mass distribution from BESIII e+e− annihi-
lation data taken near the peak of Y(4260) (Ablikim et al., 2013a). Reprinted
with permission from [M. Ablikim et al. (BESSIII Collaboration), Phys. Rev. Lett.
110, 252001, 2013; http:/dx.doi.org/10.1103/PhysRevLett.110.252001]. Copy-
right (2013) by the American Physical Society.
X(4140), X(4274), X(4500), X(4700). The Z states considered have all a
valence quark composition of the type: cc̄qq̄
. If we assume they have the same
internal color configuration and fix the internal spin configurations, each of these
states would belong to a SU(3)flavour nonet made by the same valence quarks, with
q,q
= u,d,s. A structure with valence composition cc̄ss̄, named X(4140), was
first observed in 2009 by CDF (Aaltonen et al., 2009) in the decay
B → K (J/ψ φ) (2.9)
In 2016, the LHCb Collaboration reported (Aaij et al., 2017b) the observation
of four J/ψ φ structures, X(4140), X(4274), X(4500), X(4700). The width of
X(4140) observed by LHCb is considerably larger than the one reported by CDF.
The structures seen by LHCb can be fitted with single Breit–Wigner resonances
with: JPC
= 1++
, for X(4140), X(4274) and JPC
= 0++
, for X(4500), X(4700)
and will be discussed later, in Chapter 7.
2.3 Hidden bb̄ Exotics
No neutral or charged Xb has been observed so far. A hidden bb̄ candidate state
Yb(10890) with JPC
= 1−−
was discovered by Belle in 2007 (Chen et al., 2008)
in the process e+
e−
→ Yb(10890) → (ϒ(1S),ϒ(2S),ϒ(3S))π+
π−
just above

Figure 2.8 The J/ψφ invariant mass distribution from LHCb. The separate reso-
nance contributions are also shown. Figure reprinted with thanks from LHCb (Aaij
et al., 2017b).
the ϒ(5S)2
. The interpretation that Yb(10890) is possibly a different state than the
canonical bb̄ radial bound state ϒ(5S) was mainly triggered by the circumstance
that the branching ratios measured in the dipionic transitions are two orders of
magnitude larger than anticipated from similar dipionic transitions in the lower
ϒ(nS) states and in the ψ
. This can be judged from the partial decay widths
(Yb(10890) → ϒ(nS)π+
π−
) (270,400,250) keV, for n = 1,2,3, compared
to (ϒ(4S) → ϒ(1S)π+
π−
) 1.7 keV (Patrignani et al., 2016). Moreover,
the dipion invariant mass distribution in the decay Yb(10890) → ϒ(1S)π+
π−
is marked by the presence of the resonances f0(980) and f2(1270) (Chen et al.,
2008). The corresponding distributions in the lower mass quarkonia decays are
well understood in terms of the QCD multipole expansion, as discussed later in
Chapter 13. The dipionic decay rates, and decay distributions in Yb(10890) require
a different mechanism. The state Yb(10890) was interpreted as a JPC
= 1−−
P-wave
tetraquark (Ali et al., 2010a,b).
The current status of Yb(10890) is, however, unclear. Subsequent to its discovery,
Belle undertook high-statistics scans to measure the ratios Rbb̄ and Rϒ(nS)π+π−
as functions of the e+
e−
center-of-mass energy
√
s. They are shown in Fig. 2.9
and Fig. 2.10, respectively. The two masses, M(5S)bb̄ measured through Rbb̄,
and M(Yb), measured through Rϒ(nS)π+π− , now differ by slightly more than 2σ,
2 This state is called ϒ(10860) by the Paricle Data Group, though its mass is listed as M = 10889.9+3.2
−2.6 MeV.

Figure 2.9 The ratio Rb = σ(e+e− → bb̄)/σ(e+e− → μ+μ−) in the Y(10860)
and Y(11020) region. The components of the fit are depicted in the lower part
of the figure: total (solid curve), constant |Aic|2 (thin), |Ac|2 (thick): for ϒ(5S)
(thin) and ϒ(6S) (thick): |f |2 (dot-dot-dash), cross terms with Ac (dashed),
and two-resonance cross term (dot-dash). Here, Ac and Aic are coherent and
incoherent continuum terms, respectively (Santel et al., 2016). Reprinted with
permission from [D. Santel et al. (BELLE Collaboration), Phys. Rev. D93, 011101,
2016; http:/dx.doi.org/10.1103/PhysRevD.93.011101]. Copyright (2016) by the
American Physical Society.
M(5S)bb̄ − M(Yb) = −9 ± 4 MeV. From the mass difference alone, these two
could very well be just one and the same state, namely the canonical ϒ(5S) - an
interpretation adopted by the Belle collaboration (Santel et al., 2016). In particular,
the current data shows no other structures apart from the ϒ(5S) and ϒ(6S) in the
Rbb̄ scan.
Despite this, an excess of events around
√
s ∼ 10.77 GeV is visible in the
Rϒ(nS)π+π− scan, as can be seen in Fig. 2.10. If confirmed, this state has the same
signature as that of the putative tetraquark state Yb(10890), namely a JPC
= 1−−
state decaying into ϒ(nS)π+
π−
with a significant branching fraction (Ali et al.,
2010a,b). More data and/or a refined analysis of the current scan are called for to
establish (or rule out) this state. It is crucial to also reanalyse the Rbb̄-scan data in
this energy region to establish (or rule out) a similar structure as is visible in the
Rϒ(nS)π+π− scan data.
It is pertinent to remark that the spectrum of the P -wave charmonia-like states
is rich, as can be seen from Table 2.1, and discussed later in this book. In the
tetraquark interpretation of the Y states, a similar rich spectrum is anticipated in

Figure 2.10 The ratio Rϒ(nS)π+π− = σ(e+e− → ϒ(nS)π+π−)/σ(e+e− →
μ+μ−) in the Y(10860) and Y(11020) region. Figure from Belle (Santel et al.,
2016). Reprinted with permission from [D. Santel et al. (BELLE Collaboration),
Phys. Rev. D93, 011101, 2016; http:/dx.doi.org/10.1103/PhysRevD.93.011101].
the bb̄ sector. The candidate Y(10.77) could be the lowest lying state in this part
of the spectrum. As data taking starts in 2019 by Belle-II at the refurbished KEK
e+
e−
facility, dedicated runs in the ϒ(5S) and ϒ(6S) region should be one of their
top priorities.
The charged states Z±
b (10610) and Z±
b (10650). In ϒ(10860) decays, Belle
observed two new states with masses m = 9898.3 ± 1.1+1.0
−1.1 MeV and m =
10259.8 ± 0.6+1.4
−1.0 MeV, respectively (Adachi et al., 2012). These new states are
widely accepted to represent the conventional bottomonium states hb (11
P1, 1+−
)
and hb (21
P1, 1+−
). In a second step, the observation of the hb(1P ) and the hb(2P )
also enabled the study of their specific production mechanism in ϒ(5S) decays,
i.e., are they produced according to phase space or are there any intermediate
resonances? Surprisingly, both the hb(1P )π+
π−
and hb(2P )π+
π−
final states
contain a large fraction of hb(nP)π±
resonances.
In addition to the hb(nP)π±
, the ϒ(nS)π±
were also investigated. In fact, all five
final states show two intermediate resonances, which, being similar to the Z states

Figure 2.11 Charged pion recoil mass for ϒ(5S)→ϒ(1S)π+π− (left),
ϒ(5S)→ϒ(2S)π+π− (center) and ϒ(5S)→ϒ(3S)π+π− (right). The Zb and
Z
b states are labelled (Bondar et al., 2012). Reprinted with permission from
[A. Bondar et al. (BELLE Collaboration), Phys. Rev. Lett. 108, 122001, 2012;
http:/dx.doi.org/10.1103/PhysRevLett.108.122001]. Copyright (2012) by the
American Physical Society.
in charmonium, were given the names Zb (or Zb(10610)) and Z
b (or Zb(10650)),
shown in Table 2.1. The resonances Z±
b (10610), Z±
b (10650) lie very close in mass
to where expected on the basis of simple quark mass considerations — and very
close to the B(∗)
B̄∗
thresholds. Also, the neutral partner has been found in the
meanwhile (Patrignani et al., 2016). As these two resonances are charged, they
cannot be bottomonium states. Figure 2.11 shows the recoil mass for ϒ(1S)π±
,
ϒ(2S)π±
and ϒ(3S)π±
.
Fits were performed using two Breit–Wigner shapes with different masses and
widths. For ϒ(5S)→ϒ(nS)π+
π−
, an S-wave Breit–Wigner shape was assumed, as
the ϒ states have the same quantum numbers. For the transitions ϒ(5S)→hb(nP )
π+
π−
, a P -wave Breit–Wigner shape was adopted due to the change of the heavy
quark (bb) spin by one unit. Strong interaction phases φi were included into the fit
functions by exp(iφi) terms for the different signals i. Table 2.2 shows the fitted
masses, widths and their statistical significance. Fitting with two Breit–Wigner
shapes with a relative phase, the result is that the phases in ϒ(nS) and hb(nP ) final
states seem to be shifted by 180◦
. Interestingly, the Zb is very close to the B0∗
B
±
threshold and the Z
b to the B0∗
B
∗±
threshold. Mass differences with respect to the
thresholds are only +2.6 MeV and +2.0 MeV, respectively. Both mass differences
are positive and thus indicate no binding energy in the system, although m and
the errors in the mass determination of 2.0 MeV and 1.5 MeV are of the same order
of magnitude.
An angular analysis was performed by Belle as well. In particular (a) the angle
between the charged pion π1 and the e+
from the ϒ decay and (b) the angle between
the plane (πi,e+
) and the plane (π1,π2) turned out to be useful. All distributions
turned out to be consistent with JP
=1+
, while all other quantum numbers were
disfavored at typically ≥3σ level. Thus, it is likely that the Zb and the Z
b carry the
same spin and parity as the X(3872).

Table 2.2 Measured masses and widths (in MeV) of the charged Zb and Z
b states
by Belle. Reprinted with permission from [D. Santel et al. (BELLE Collaboration),
Phys. Rev. D93, 011101, 2016; http:/dx.doi.org/10.1103/PhysRevD.93.011101].
ϒ(1S)π+π− ϒ(2S)π+π− ϒ(3S)π+π− hb(1P )π+π− hb(2P )π+π−
m(Zb(10610)) 10611±4±3 10609±2±3 10608±2±3 10605±2+3
−1 10599+6
−3
+5
−4
(Zb(10610)) 22.3±7.7+3.0
−4.0 24.2±3.1+2.0
−3.0 17.6±3.0±3.0 11.4+4.5
−3.9
+2.1
−1.2 13.0+10
−8
+9
−7
m(Zb(10650)) 10657±6±3 10651±2±3 10652±1±2 10654±3+1
−2 10651+2
−3
+3
−2
(Zb(10650)) 16.3±9.8+6.0
−2.0 13.3±3.3+4.0
−3.0 8.4±2.0±2.0 20.9+5.4
−4.7
+2.1
−5.7 19±7+11
−7
There are numerous attempts to explain the Zb states, e.g., as coupled channel
effects (Danilkin et al., 2012), cusp effect (Bugg, 2011), or tetraquarks (Ali et al.,
2012; Karliner and Lipkin, 2008). A particular attempt was made (Bondar et al.,
2011) to explain the states along with the anomalous observations in hb production.
The ansatz is to interpret the new resonances as B0∗
B
±
and B0∗
B
∗±
molecular
states, and to form 1+
states based upon the quantum number from the angular
distribution tests.
For the Zb(10610), a neutral partner has been observed, pointing to an isospin
triplet. Principally, in case of sufficiently precise experimental mass resolution,
this would allow tests of different quark contents, e.g. [bbud] or [bbdu] for the
charged Zb and [bbuu] or [bbdd] for the neutral Zb. However, so far the measured
masses are compatible within the errors, with 10609±4±4 MeV for the neutral
Zb (Krokovny et al., 2013) and 10607.2±2.0 for the charged Zb (Bondar et al.,
2012).
2.4 The Charged Pentaquarks P ±
c (4350) and P±
c (4450)
The last two entries in Table 2.1 are the charged pentaquarks, which were observed
in b baryon decays by LHCb (Aaij et al., 2015b)
b → K−
(J/ψ p). (2.10)
The Dalitz plot projections are shown in Fig. 2.12. Indeed there are significant
structures in the K−
p mass spectrum that differ from phase space expectations,
and there is also a peak in the J/ψp mass spectrum.
The leading order Feynman diagrams for b → J/ψp ∗
, and for b →
K−
P +
c , where P +
c is a possible state that decays into J/ψp, are shown below in

2.4 The Charged Pentaquarks P±
c (4350) and P±
c (4450) 29
Figure 2.12 Invariant mass of (a) K−p and (b) J/ψp combinations from b →
J/ψK−p decays. The solid (red) curve is the expectation from phase space. The
background has been subtracted. Figure reprinted with thanks from LHCb (Aaij
et al., 2015b).
b
u
d
b
u
d
c
u
d
s
u
u
c
s
u
d
c
c
(a) (b)
Λ
∗
J/ψ
K–
P+
c
Λ0
b
Λ0
b
Figure 2.13 Feynman diagrams for (a) 0
b → J/ψ ∗ and (b) 0
b → P+
c K−
decay. Figure reprinted with thanks from LHCb (Aaij et al., 2015b).
Fig. 2.13 (a) and (b), respectively. In the latter, a uū quark pair is produced from
the vacuum, which together with the rest of the quarks and an antiquark from the
weak decay of the 0
b rearrange themselves as K−
P +
c state(s).
Their masses, decay widths, and preferred JP
quantum numbers are given in
Table 2.1. The exotic nature of the pentaquarks, dubbed as Pc, is very clear, as it is
the case for the Zcs and Zbs.

3
Color Forces and Constituent Quark Model
In a seminal paper of the mid sixties, Han and Nambu proposed a Yang–Mills theory
of strong interactions among quarks, based on the SU(3) color symmetry (Han
and Nambu, 1965). The Han–Nambu model was quite different from QCD in that
quarks with the same flavor and different colors could have different electric charge,
leading to electrically charged gluons, later excluded by deep inelastic scatter-
ing data. The strong and electroweak interaction gauge groups did not commute
among themselves, unlike in the Standard Theory. However, in a world with strong
interactions only, electric charges do not matter and many features of Han–Nambu
theory have been incorporated in QCD, including the hypothesis that quarks and
antiquarks would bind exclusively in color singlets and that color non singlets
would be unobservable, i.e., color confinement.
These ides already emerge at the very simple level of color forces mediated by a
single gluon exchange.
3.1 Color Forces in the One-Gluon Approximation
Consider two quarks interacting through the exchange of one virtual gluon as in
Fig. 3.1. Similar considerations can be done for a quark–antiquark system.
The interaction energy of the two quarks is proportional to the matrix element
of the product T a
ij T a
IJ . We consider the general case where the two initial/final state
particles are respectively in the color representations R1 and R2, so that
H = const. × T a
R1
⊗ T a
R2
≡ const. × T R1 ⊗ T R2 . (3.1)
To decide wether there is attraction or repulsion between two initial quarks in some
color configuration, say for example (1,3)–(3,1), the final quarks in Fig. 3.1 must
be in the same color configuration: we have to diagonalize T R1 ⊗ T R2 and read the
eigenvalue of the corresponding color “channel.”
30

3.1 Color Forces in the One-Gluon Approximation 31
Figure 3.1 One-gluon exchange interaction.
The Hamiltonian is a color singlet and takes constant values over states in the
irreducible color representations of the Clebsch-Gordan decomposition:
R1 ⊗ R2 = S1 ⊕ S2 ⊕ S3 . . . , (3.2)
that is
T R1 ⊗ T R2 =

i=1,n
1
2
λ(Si,R1,R2)1Si, (3.3)
where 1R is the identity matrix of dimension D(R). We define the quadratic
Casimir in the representation R
T R · T R = CR1R, (3.4)
and obtain λ from the square of the generators
T R1⊗R2 ≡ (T R1 ⊗ 1R2 + 1R1 ⊗ T R2 ), (3.5)
leading to
2T R1 ⊗ T R2 =

T R1⊗R2
2
− T 2
R1
⊗ 1R2 − 1R1 ⊗ T 2
R2
. (3.6)
Since

T R1⊗R2
2
=

T S1⊕S2⊕···
2
= CS1 1S1 ⊕ CS2 1S2 ⊕ · · · , (3.7)
the result is1
λ(Si,R1,R2) ≡ CSi − CR1 − CR2 . (3.8)
The parameter λ in (3.8) is like the product of charges in an abelian theory – we
get repulsion or attraction according to λ 0 or λ 0.
The SU(3)color representations in (3.8), are those of the individual quark or anti-
quark, namely the fundamental representations 3 or 3̄, respectively, and that of the
1 using
1R1
⊗ 1R2
= 1S1
⊕ 1S2
⊕ · · ·

32 Color Forces and Constituent Quark Model
inital (= final) quark–quark or quark–antiquark state, which are to be found in the
Clebsch–Gordan decompositions
quark − quark
3 ⊗ 3 = 3̄ ⊕ 6, (3.9)
quark − antiquark
3 ⊗ 3̄ = 1 ⊕ 8. (3.10)
The representations in (3.9) correspond to the antisymmetric and symmetric com-
ponents of the product 3 ⊗ 3, respectively; those in (3.10) correspond to the singlet
and octet (or regular) representations.
For future applications, we report in Table 3.1 Casimir coefficients and λ values
in SU(N), for the representations appearing in quark–quark and quark–antiquark
channels.
One sees from the last column of the table that there is attraction in the color
singlet qq̄ and in the antisymmetric qq channel, repulsion in the others.
The Han–Nambu argument, assumed in QCD as well, is that the self-interaction
of a color nonsinglet state would (presumably) be infinite and that finite energy
states would be obtained only when color charges are completely screened, that is
when quark and antiquarks arrange themselves in color singlet configurations. This
is what is meant by quark confinement.
The pattern of attraction and repulsion summarized in Table 3.1 suggests that:
• a quark and an antiquark bind in color singlet mesons,
• diquarks (color 3̄) may be significant subunits which either bind to a single quark,
to form a color singlet baryon, or to an antidiquark, to form a color singlet
tetraquark meson.
Table 3.1 Quadratic Casimir for the fundamental, the two index symmetric and
antisymmetric and the regular representations in color SU(N), N ≥ 2 (complex
conjugate representations have the same Casimir). In the last column, the coeffi-
cient of the interaction energy for quark–quark and quark–antiquark systems, in
the one-gluon exchange approximation.
Representation dimension CR λ(R,R1,R2)
Fundamental N (N2 − 1)/(2N) −−
q − q Antisymmetric N(N − 1)/2 (N + 1)(N − 2)/N −(N + 1)/N 0
q − q Symmetric N(N + 1)/2 (N − 1)(N + 2)/N (N − 1)/N 0
q − q̄ Singlet 1 0 −(N2 − 1)/N 0
q − q̄ Regular N2 − 1 N 1/N 0

3.2 New Hadrons 33
A simple Casimir calculation in SU(3)color. The generators of 3 are the eight
Gell–Mann matrices:
T a
=
1
2
λa
, Tr(T a
T b
) =
1
2
δab
, a = 1,2, . . . ,8, (3.11)
and we find immediately:
C3 =
1
3
Tr(T · T ) =
4
3
. (3.12)
The generators of the 3̄ are T̄ = −T T
and C3̄ = C3 as expected. The values
of the Casimir of representations in (3.9, 3.10) are found by subtraction. We give
explicitly the case of the 6 representation. The generators in the (reducible) product
3 ⊗ 3 are
T 3⊗3 = T 3 ⊗ 1 + 1 ⊗ T 3, (3.13)
and
Tr(T 3⊗3 · T 3⊗3) = 18 C3 = 3 C3̄ + 6 C6,
where in the latter we use
T a
3⊗3 = T a
3̄
⊕ T a
6 , (3.14)
whence
C6 =
10
3
. (3.15)
Obviously, C1 = 0 and we leave to the reader to find C8 = 3.
The above method is easily generalized to SU(N) by replacing the Gell–Mann
matrices with the N2
− 1, N × N hermitian and traceless matrices with the same
normalization condition.
3.2 New Hadrons
At the nonperturbative level, we may describe color binding as due to color strings
that go from quarks (color charge 3) to antiquarks (color charge 3̄). With three
colors, we have the further possibility that three such strings join together in a single
vertex, due to the fact that the product 3 ⊗ 3 ⊗ 3 contains the singlet representation.
Mesons and baryons realize both types of binding, as illustrated in Fig. 3.2.
Starting from these, new allowed structures are obtained by the substitution
q̄ → [qq], (3.16)
where bracket indicates a diquark in color antisymmetric configuration, a 3̄ of
color (we discuss below flavor and spin configurations). The structures obtained

q q q
q
q
meson baryon
Figure 3.2 The substitution (3.16) transforms a qq̄ meson into a qqq baryon.
antibaryon
pentaquark
P+
→ (cc) + (uud) = J/Ψ + p
tetraquark
dibaryon ???
c
c
c
u
u
u
u
u
d
d
d
Figure 3.3 Successive substitutions (3.16) applied to q̄q̄q̄ antibaryons generate
tetraquarks, pentaquarks and dibaryons.
by making successive substitutions2
on the structures of Fig. 3.2 are illustrated in
Fig. 3.3.
The compact tetraquark model, discussed later in Chapter 7, associates unex-
pected charmonia and bottomonia as well as the observed pentaquarks with
tetraquark and pentaquark configurations in Fig. 3.3. The existence of configu-
rations with baryon number B = 2, a color bound version of the deuteron called
dibaryon, is a yet untested prediction.
It seems a reasonable possibility that tetraquarks, pentaquarks and dibaryons
make the next layer of hadron spectroscopy following the first layer made by the
Gell–Mann–Zweig baryons and mesons, Fig. 3.2.
We expect many tetraquarks, pentaquarks and dibaryons since color strings
may have radial and orbital excitations. In a relativistic picture, tetraquarks would
have to be on rising Regge trajectories, due to the confining nature of QCD forces
(Sonnenschein and Weissman, 2016).
2 Perhaps, it is appropriate to stress that, for the moment, we are unable to determine theoretically if the new
configurations are stable or at least semistable, so as to correspond to visible hadron resonances. Hints that this
may be so for hadrons involving doubly heavy diquarks will be discussed in Chapter 15

3.2 New Hadrons 35
The parities of X, Y, Z mesons and pentaquarks, give already some evidence
for the existence of orbital excitations in multiquark states, when compared to the
parities of qq̄ mesons and qqq baryons.
The lowest lying X and Z have positive parities, as expected for S-wave diquark–
antidiquark pair. Y states are higher in mass and have negative parities, as appro-
priate to diquark–antidiquarks in P -wave. This is the opposite of what happens in
normal mesons, where the lowest lying S-wave states (π, ρ) have negative parity
and the first orbital, P -wave, excitations (A1, A2, f2, etc.) have positive parity.
Normal baryons in S-wave have only quarks, hence positive parity, with the first
excitations, e.g., N(1520), with negative parity, corresponding to one unit of orbital
momentum. For pentaquarks, the preferred fit indicates opposite parity for the two
states, with some preference of negative parity for the lighter one, in agreement
with the presence of c̄ antiquark, and positive parity for the next state, presumably
one of the first orbital excitations (more details are given in Chapter 10).
A quite different pattern would be followed by meson-meson molecules,
supposed to be bound by short range forces, generated by color singlet meson
exchange. If bound at all, molecules are expected to have a limited spectrum, in
particular no orbital excitations.
The nonrelativistic Constituent Quark Model. Color string forces produce an
overall spin-independent potential that confines quarks inside a definite volume
(bag), with some wave functions ψ(x1,x2,x3). QCD interactions affect as well
the mass of the valence quarks. Seen with probes of large momentum, as in deep
inelastic scattering, light quarks appear as bare, essentially massless, spin 1/2
fermions. At low momentum transfer, i.e., large space-time scales, masses are
renormalized to larger values almost universal, between mesons and baryons, as
indicated by the ratio between baryon to meson masses, which is not far from
3:2, e.g., mp/mρ ∼ 1.25, m/mK∗ ∼ 1.33 ( for a recent analysis of effective quark
masses in mesons and baryons see (Karliner et al., 2017)). To describe hadron
masses, Sakharov and Zeldovich (Zeldovich and Sakharov, 1967), formulated
in 1967 the nonrelativistic Constituent Quark Model (CQM) whereby the quark
hamiltonian inside a hadron is made by mass terms, one for each valence quark, and
residual spin–spin interactions. As we shall see, the model meets with considerable
success in describing meson and baryon masses with few phenomenological
parameters, including quark masses approximately equal in the two hadron
families.
De Rujula, Georgi, and Glashow (De Rujula et al., 1975) in 1975 revisited CQM
in the light of QCD, with the aim of obtaining realistic predictions of the properties
of charmed mesons, yet to be discovered, see also (Gasiorowicz and Rosner, 1981).
Also in this case, the model met with considerable success, with many predictions

verified a posteriori, such as the very small width of D∗
, due to extreme nearness
of D∗
mass to Dπ threshold.
Application of the nonrelativistic CQM to the tetraquark spectrum is considered
in (Maiani et al., 2005, 2014).
In this Section we first review the essentials of the CQM and then illustrate
the derivation of mass formulae for mesons and baryons with Charm and Beauty,
c, b = 0,1, with the aim of extracting the values of the phenomenological param-
eters involved, quark masses and spin–spin couplings. A comparison of the values
of the parameters with QCD expectation is provided at the end.
Spin–spin interactions. Residual quark–quark or quark–antiquark interactions
produce color-magnetic, spin–spin, forces of the form
Hij =
g2
m1m2
(T 1 · T 2) s1 · s2 δ(3)
(x1 − x2). (3.17)
T are the color charges, s and m quark spin and mass, g the QCD coupling and
the form is derived from the non relativistic limit of QCD.
If quarks i,j are in a given color representation R, the formula simplifies to
Hij = 2κij si · sj, (3.18)
κij = λ(R) ×
g2
mimj
|ψ(0)|2
. (3.19)
λ(R) is the color factor introduced in (3.8) where, for brevity, we understand
the dependence from the quark or antiquark color representations and the total
Hamiltonian is:
H =

i
mi +

ij
2κij sj · sj . (3.20)
For light quarks, the Hamiltonian can be expanded to first order in the small mass
difference, m = ms − mq (q = u,d).
There are two sources of SU(3)flavor symmetry breaking. One is the mass differ-
ence in the first term of (3.20). But there is another, first order, contribution obtained
by expanding in m the spin–spin Hamiltonian (3.19). The first term simply counts
the number of strange quarks in the hadron, while the second gives rise to the
so-called D-term in the mass formula of the baryons, which is crucial to split 0
and 0
masses.
If one assumes the overlap probabilty, |ψ(0)|2
, to be the same for hadrons in
the same multiplet, which is correct in the exact SU(3)flavor limit, spin-spin cou-
plings are inversely proportional to the constituent masses. Going further, assuming
equality of the meson and baryon overlap probabilities would give κij the status

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