Parton Distributions at a 100 TeV Hadron Collider

Parton Distributions
at a 100 TeV Hadron Collider
Juan Rojo
CERN, PH Division, TH Unit
Future Circular Colliders Meeting
CERN, 27.01.2014
Juan Rojo

FCC Meeting, CERN, 27/01/2014

Very exploratory ﬁrst study on the role of Parton Distributions at a Future
Circular Collider with CoM of 100 TeV
Concentrate on the basic features, avoid technical details
Study both main physics issues, and also tools available for FCC 100 TeV
studies from the PDF point of view
Outline of this talk:
Kinematic coverage from LHC 14 TeV to FCC 100 TeV
PDF luminosities from 14 to 100 TeV
Tools for FCC PDF studies: large-x PDFs, top PDF, LO small-x PDFs ...
PDFs with Electroweak corrections
Physics case for polarized collisions at the FCC

2

Juan Rojo


Kinematic Coverage and
PDF Luminosities:
From LHC14 to FCC100

Juan Rojo


At Born level, for the production of a particle at rapidity y with mass M, the PDFs are evaluated at

Going from Ecm=14 TeV to Ecm=100 TeV, for a given M and y knowledge of PDFs at smaller x is
required:
x1,20( S=100 TeV ) = 0.14 x1,20( S=14 TeV )
In addition, for ﬁxed M, the increased range in y allows to prove even further smaller x
Conversely, ﬁxing x1,20 and y, the increased center of mass energy implies that higher masses will
be probed:
M( S=100 TeV ) = 7.14 M( S=14 TeV )
But recall that hadronic cross-sections fall as 1/M2 so this is not how BSM mass reach scales!
Some consequences:
For Higgs and SM probes (tt, W, Z), PDFs will be proved (at least) one order of magnitude
smaller x
For possible new high-mass particles of mass M, large-x PDFs (required at 14 TeV) turn into
medium-x PDFs (at 100 TeV), not only leading to larger cross-sections but with less uncertainties
For small masses M, a completely new kinematical range opens that has never been explored
4

Juan Rojo


Kinematics of a 100 TeV FCC
Plot by J. Rojo, Dec 2013

105

FCC 100 TeV

MX ( GeV )

104

LHC 14 TeV

3

10

102

10
y=-8
1 -10
10

5

-9

10

Juan Rojo

y=-4
-8

10

10-7

y=0
-6

10

-5

10
x

y=4
10-4

y=8

-3

10

10-2

10-1



105

20 TeV Z’

FCC 100 TeV

MX ( GeV )

104

2 TeV squarks

LHC 14 TeV

3

10

Higgs, top
102

W,Z
DY, low-pt jets

10
y=-8
1 -10
10

6

-9

10

Juan Rojo

y=-4
-8

10

10-7

y=0
-6

10

-5

10
x

y=4
10-4

-3

10

y=8
10-2

10-1


NNPDF2.3 dataset


105

107

NMC-pd
NMC
SLAC
BCDMS

6

5

10

LHC 14 TeV

103

HERAI-AV
CHORUS
FLH108

Q2 / M2 / p2 [ GeV2 ]
T

MX ( GeV )

10

FCC 100 TeV

104

ZEUS-H2
ZEUSF2C
H1F2C

104

102

NTVDMN

DYE605
DYE886
CDFWASY

3

10

CDFZRAP
D0ZRAP
CDFR2KT
D0R2CON

102
10

ATLAS-WZ-36pb
CMS-WEASY-840PB
LHCB-WZ-36pb
ATLAS-JETS-10

y=-8
1 -10
10

-9

10

y=-4
-8

10

10-7

y=0
-6

10

-5

10
x

y=4
10-4

-3

10

y=8
10-2

10-1

10
1 -5
10

10-4

-3

10

x

10-2

10-1

Compare kinematical coverage to that of the NNPDF2.3 set:
Current PDF determinations have essentially no constraints for x < 10-4
The region of masses for M>1 TeV also unconstrained: rely on DGLAP evolution extrapolation
Poor constraints on high-x PDFs, relevant for high masses M
For M > 10 GeV, constraints from HERA only available for x > 10-3
Global PDF ﬁts rely on QCD evolution, but EW effects will be required in multi-TeV region

7

Juan Rojo


1

Compare the ratio of PDF luminosities between 100 TeV and 14 TeV in different channels as a
function of the ﬁnal state mass

100 TeV vs 14 TeV PDF Luminosities, NNPDF2.3 NNLO

PDF luminosity ratio 100 TeV / 14 TeV

108
107

For ﬁnal state masses M < 1 TeV
moderate
increase
in
PDF
luminosity, between a factor 10 and
100

6

10

105
104

For M > 1 TeV, much steeper
increase (since 14 TeV lumis
damped by large-x PDFs), up to a
factor 108 for M = 10 TeV

103
102
10
1

8

gg lumi ratio

Qualitative similar behavior for
other PDF luminosities
102

Juan Rojo

10

3

MX [ GeV ]

104


100 TeV vs 14 TeV PDF Luminosities, NNPDF2.3 NNLO

PDF luminosity ratio 100 TeV / 14 TeV

108
107
106

GG
QG
QQbar
QQ

105
104
103
102
10
1

102

10

3

MX [ GeV ]

104

Gluon-initiated processes grow faster than quark initiated from 14 to 100 TeV
Very large PDF uncertainties affect QQbar luminosities since large-x antiquarks poorly
known
Using these results, it is possible to estimate how the cross-sections for different processes
will increase when going from 14 TeV to 100 TeV
9

Juan Rojo


PDF tools for
100 TeV FCC studies

Juan Rojo


We need to make sure that PDFs behave properly when used in the context of FCC 100
TeV studies and simulations
FCC studies will probe PDFs at very large-x and large Q: make sure that all modern sets
extrapolated properly in this region
FCC studies of non-perturbative physics such as Underlying Event and important
processes like quarkonium production require PDFs down to very small values of x
For M > 2 TeV, the top quark is essentially a massless quark: need PDFs which include a
top quark PDF t(x,Q). Missing the top PDF also affects DGLAP evolution indirectly

11

Juan Rojo


High-mass production at FCC will probe PDFs at very high-x, we want to make sure that available PDF
sets properly extrapolate in this region
Michelangelo reported some weeks ago that using CTEQ at very large x returns zero
I have tried using LHAPDF5.9.0 with CT10, MSTW08 and NNPDF2.3. Consider only central PDF sets
(ignore for the time being PDF uncertainties), for Q = 10 TeV
Large-x PDFs seems to behave properly at very large-x, though MSTW08 extrapolation has a peculiar
behavior, at least using the LHAPDF library
Note substantial differences for d(x,Q) at high-x
Large-x NNLO PDFs for FCC studies

Large-x NNLO PDFs for FCC studies

NNPDF2.3

10-1

10-1

CT10
-2

CT10
-2

10

MSTW08

-3

10

MSTW08

-3

10

x d ( x, Q2)

10

x g ( x, Q2)

NNPDF2.3

10-4

10-4

10-5

10-5

10-6
10-7

10-7

10-8
0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95
x

12

10-6

10-8
0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95
x

Juan Rojo


At FCC100, the production of 100 GeV particles might require knowledge of PDFs down to 1e-6, 1e-7,
depending on acceptance
For other processes, both perturbative (low mass Drell-Yan, Quarkonium production, low pt photons
and jets) and non-perturvative (Underlying Event, Minimum Bias) we need PDFs down to 1e-8, 1e-9
Compare various PDFs at very small x out of the box using LHAPDF5.9.0: small-x PDFs frozen between
1e-6 and 1e-8 depending on the PDF set

Small-x NNLO PDFs for FCC studies

NNPDF2.3
CT10
cteq6
MSTW08

2

103

102

10-9

13

NNPDF2.3
CT10
cteq6
MSTW08

104
x u ( x, Q2)

104
x g ( x, Q )

Small-x NNLO PDFs for FCC studies

103

102

10-8

10-7

Juan Rojo

10-6
x

10-5

10-4

10-3

10-9

10-8

10-7

10-6
x

10-5


10-4

10-3

This is not a fundamental problem: is easy enough to provide a extrapolation down to very small-x ...
... but this extrapolation must be driven by theory + methodology, since no data available
The NNPDF2.3LO set can be extrapolated down to 1e-9 using the neural network extrapolation: huge
PDF uncertainties, but central values turn out to have a reasonable behavior
NNPDF2.3LO PDF set is already available as standalone code in Pythia8, where there is an ongoing
tuning effort. Torbjorn has been using it to provide UE predictions for FCC ﬁnding reasonable results
xg(x,Q), NNPDF23_lo_as_0119_qed.LHgrid members

500

Members
Generated by APFEL2.0.0: V.Bertone, S.Carrazza, J.Rojo (arXiv:1310.1394)

Central value
Std. deviation

400

68% c.l.
Q = 1.41 GeV

300
200
100
0
-9
10
14

Juan Rojo

-8

10

10-7

-6

10

-5

10

x

10-4

-3

10

10-2

10-1

1


In the Variable-Flavor-Number (VFN) scheme, heavy quark PDFs for charm and bottom are generated
radiatively from the gluon PDF

For very high-mass production at a 100 TeV FCC, the top quark can be considered as approximately
massless, and thus we need to generate a top quark PDF t(x,Q) just as we have a charm and bottom PDF
Note that missing the top PDF also feeds back into all other PDFs due to the different DGLAP evolution
Ratio to NNPDF2.1 GM-VFN, x=10-2

Ratio to NNPDF2.1 GM-VFN, x=10-2

1.15

missing charm

1.1

NNPDF2.1

1.2

NNPDF2.1 FFN NF=3
1.1

NNPDF2.1 FFN NF=4

x (x, Q 2)

xg (x, Q2)

1.05

1

1

0.9

0.95

NNPDF2.1
NNPDF2.1 FFN NF=3

0.9

missing charm

0.8

NNPDF2.1 FFN NF=4
0.85

102
Q 2 [ GeV 2 ]

10

15

Juan Rojo

3

10

104

0.7
10

102
Q 2 [ GeV 2 ]

3

10


104

Currently, only the NNPDF Collaboration provides sets with top quark PDF included (as well as sets in
the other VFN schemes, NF=3, NF=4 and NF=5)
At 10 TeV, the top quark PDF t(x,Q) is only a factor 2/3 smaller that all other quark PDFs (charm and
bottom are very close to light quark PDFs): should be included in theoretical predictions

x PDF ( x, Q2 = 10 TeV )

NNPDF2.3 NNLO NF = 6

102

10

1

10-1 -5
10
16

Gluon
Up
Charm
Bottom
Top

Juan Rojo

10-4

-3

10

x

10-2

10-1


At 10 TeV, the top quark PDF t(x,Q) is only a factor 2/3 smaller that all other quark PDFs (charm and
bottom are very close to light quark PDFs): should be included in theoretical predictions
The missing contribution from t(x,Q) also feeds back to the gluon PDF: up to 4% differences due to the
missing top quark PDF

NNPDF2.3 NNLO, x = 10-2
1.06

1.04

F

Ratio ( N = 5 ) / ( N = 6 )

1.05

Gluon
Up
Down

NF=6 vs NF=5

1.03

F

1.02
1.01
1
0.99
0.98
102

17

Juan Rojo

3
Q10GeV )
(

104


Parton Distributions and
QED/Electroweak Corrections

Juan Rojo


As mentioned in the case of top quark, when Q >> mt it makes sense computationally to resum
large collinear-like logarithms into a top PDF

With a similar motivation, it might be efﬁcient to resum multiple initial state emissions of W and Z
bosons into the corresponding parton distributions, FW(x,Q), FZ(x,Q)
The analogous of DGLAP evolution equations in QCD can be derived in the electroweak sector of
the Standard Model, but the resulting equations are very different (Ciafaloni and Comelli,
2002,2005)
The purely electroweak evolution equations must be supplemented with the QED evolution
equations and the determination of the photon PDF
(x,Q2) from experimental data
(NNPDF2.3QED)

An important difference between QED and EW evolution is that in the later case W and Z boson
PDFs are always generated dynamically, while there is an intrinsic photon PDF in the proton
19

Juan Rojo


The analogous of DGLAP evolution equations in QCD can be derived in the electroweak sector of
the Standard Model, but the resulting equations are very different (Ciafaloni and Comelli, 2002,2005)
Evolution equation for the structure function of W bosons

No numerical implementation of EW evolution equations exist. Very different ﬂavor/coupling
structure as compared to QCD evolution equations
In addition, EW must be combined with pure QED evolution, and then combined with QCD into
a complete set of Standard Model PDF evolution equations
Could this be of relevance at the LHC, and not only at FCC?

20

Juan Rojo


Once QED corrections to PDFs are taken into account, photon-initiated contributions are relevant
at the LHC, could be even more the case at the FCC
Many examples, like photon-initiated corrections substantially modify the lepton pt in high-mass
Drell-Yan
They also induce substantial uncertainties for high-mass WW production, up to 100%
More FCC-speciﬁc studies required

WW production @ LHC 100 TeV, 68% CL

high-mass DY

σ(WW) [QCD+QED] / σ(WW) [QCD]

2.5

2

WW at FCC100

1.5

1

NNPDF2.3 QED, qq
0.5

(QCD+QED)/QCD

MRST04 QED, qq
NNPDF2.3 QED, qq + γ γ
MRST04 QED, qq + γ γ

0
0

21

Boughezal, Li, Petriello 2013
Juan Rojo

1000

2000

3000

4000
5000
Mcut ( GeV )
WW

6000

7000

Snowmass QCD report

8000

The Physics Case for
Polarized Collisions at the FCC

Juan Rojo


What are the BSM opportunities for the polarized option of a 100 TeV machine?
While likely not required for discovery, polarized beams could provide a useful tool for BSM
characterization, where differences in polarized asymmetries provide a handle on SM vs BSM
discrimination
Phenomenology implications explored in the context of in Bozzi, Fuks, Klasen 04, Debove, Fuks,
Klasen 08. Here just brieﬂy motivate the idea in a general context. Benjamin will give a more
complete talk next meeting about BSM opportunities with polarized beams.
NNPDF2.3 dataset

NNPDF polarized
104

107

NMC-pd

NNPDF unpolarized

SLAC

EMC
SMC

6

10

CHORUS

103

FLH108
ZEUS-H2
ZEUSF2C
H1F2C

104

DYE605
DYE886
CDFWASY

3

10

CDFZRAP
D0ZRAP
CDFR2KT

STAR-jets 09 (prel.)
PHENIX-jets

E155
COMPASS-D
COMPASS-P

2

10

T

Q2 / M2 / p2 [ GeV2 ]
T

NTVDMN

Q2/M2/p2 [GeV 2]

5

10

STAR-jets

E154

HERAI-AV

STAR-W± (prel.)

E143

BCDMS

COMPASS-OC

SMClowx

NMC

HERMES97
HERMES

D0R2CON

2

10

10

ATLAS-WZ-36pb
CMS-WEASY-840PB
LHCB-WZ-36pb
ATLAS-JETS-10

10
1

1 -5
10

-3

10-4

-3

10

x

10-2

10-1

1

10

10-2

10-1

x

Polarized PDFs are affected by much larger uncertainties than unpolarized PDFs
due to reduced dataset and kinematical coverage
23

Juan Rojo


NNPDF2.3, Q2 = 104 GeV2
0.8

0.8

xg

0.7

0.6

xd
xs

0.5

2

x ∆ q ( x, Q )

0.5

x∆g
x∆u
x∆d
x∆s

0.7

xu

0.6
x q ( x, Q2)

NNPDFpol1.1, Q2 = 104 GeV2

0.4
0.3
0.2

0.4
0.3
0.2

0.1

0.1

0

0

-0.1

-0.1

10-2

10-1
x

10-2

10-1
x

Different qualitative behaviors of PDFs wrt unpolarized PDFs
Polarized PDFs smaller than unpolarized due to positivity condition

and suppressed at small-x due to different DGLAP splitting functions
Only asymmetries which involve high-x polarized PDFs (ﬁnal states with large invariant mass)
will be large enough to be accessible experimentally
24

Juan Rojo


Fuks, Proudom, Rojo, Schienbein,
in preparation

Measurement of sign of AL will discriminate between different BSM scenarios (different production modes)
25

A more precise measurement of AL leads to enhanced discrimination, ie, qq vs gg production mechanisms

Parton Distributions play a central role at the LHC program, will continue to do so at a
potential Future Circular Collider at 100 TeV
Many new qualitative features of PDFs need to be studied: top PDF, PDFs at very large-x,
PDFs with electroweak corrections
It will be useful to provide speciﬁc PDF sets for FCC studies, with suitable extrapolations at
very small and very large-x as well as to a very large Q2 (and include top PDF)
A polarized mode of the FCC might provide a unique way of characterizing BSM dynamics
uncovered in unpolarized collisions

2

The future?

x PDF ( x, Q = 10 TeV )

NNPDF7.4 N3LO, HERA+LHC+FCC
102

10

1

10-1 -7
10

26

Juan Rojo

Gluon
Up
Charm
Bottom
Top

10-6

10-5

10-4 x 10-3

10-2

10-1

Parton Distributions at a 100 TeV Hadron Collider

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