Parton Distributions at a 100 TeV Hadron Collider
Juan RojoCERN, PH Division, TH Unit
Future Circular Colliders Kick-off MeetingGeneva, 14.02.2014
Juan Rojo FCC Kick-off Meeting, Geneva, 14/02/2014
Exploratory first study on the role of Parton Distributions at a Future Circular Collider with CoM of 100 TeV
Concentrate on the basic results, avoid technical details (choice of PDF set etc), and explore the new qualitative features of PDFs at the FCC
Outline of this talk: Kinematic coverage from LHC 14 TeV to FCC 100 TeV PDF luminosities from 14 to 100 TeV New qualitative features of PDF in 100 TeV collisions: top-quark PDFs, LO
small-x PDFs, Electroweak corrections, high-energy BFKL resummation Physics case for polarized collisions at the FCC
2 Juan Rojo FCC Kick-off Meeting, Geneva, 14/02/2014
Kinematic Coverage andPDF Luminosities:
From LHC14 to FCC100
Juan Rojo FCC Kick-off Meeting, Geneva, 14/02/2014
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 FCC Kick-off Meeting, Geneva, 14/02/2014
5
x-1010 -910 -810 -710 -610 -510 -410 -310 -210 -110
( G
eV )
XM
1
10
210
310
410
510
Kinematics of a 100 TeV FCC
y=0y=-4y=-8 y=4 y=8
FCC 100 TeV
LHC 14 TeV
Plot by J. Rojo, Dec 2013Kinematics of a 100 TeV FCC
Juan Rojo FCC Kick-off Meeting, Geneva, 14/02/2014
6
x-1010 -910 -810 -710 -610 -510 -410 -310 -210 -110
( G
eV )
XM
1
10
210
310
410
510
Kinematics of a 100 TeV FCC
y=0y=-4y=-8 y=4 y=8
FCC 100 TeV
LHC 14 TeV
Plot by J. Rojo, Dec 2013Kinematics of a 100 TeV FCC
DY, low-pt jets
W,Z
Higgs, top
2 TeV squarks
20 TeV Z’
Juan Rojo FCC Kick-off Meeting, Geneva, 14/02/2014
7
x-1010 -910 -810 -710 -610 -510 -410 -310 -210 -110
( G
eV )
XM
1
10
210
310
410
510
Kinematics of a 100 TeV FCC
y=0y=-4y=-8 y=4 y=8
FCC 100 TeV
LHC 14 TeV
Plot by J. Rojo, Dec 2013Kinematics of a 100 TeV FCC
x-510 -410 -310 -210 -110 1
]2 [
GeV
2 T /
p2
/ M
2Q
1
10
210
310
410
510
610
710NMC-pdNMCSLACBCDMSHERAI-AVCHORUSFLH108NTVDMNZEUS-H2ZEUSF2CH1F2CDYE605DYE886CDFWASYCDFZRAPD0ZRAPCDFR2KTD0R2CONATLAS-WZ-36pbCMS-WEASY-840PBLHCB-WZ-36pbATLAS-JETS-10
NNPDF2.3 dataset
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
Juan Rojo FCC Kick-off Meeting, Geneva, 14/02/2014
[ GeV ]X M210 310 410
lum
inos
ity ra
tio 1
00 T
eV /
14 T
eV
1
10
210
310
410
510
610
710
810
100 TeV vs 14 TeV PDF Luminosities, NNPDF2.3 NNLO100 TeV vs 14 TeV PDF Luminosities, NNPDF2.3 NNLO
8
Compare the ratio of PDF luminosities between 100 TeV and 14 TeV in different channels as a function of the final state mass
gg lumi ratio For final state masses M < 1 TeV moderate increase in PDF luminosity, between a factor 10 and 100
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
Qualitative similar behavior for other PDF luminosities
Juan Rojo FCC Kick-off Meeting, Geneva, 14/02/2014
New qualitative features of PDFs in 100 TeV collisions
Juan Rojo FCC Kick-off Meeting, Geneva, 14/02/2014
10
At FCC100, the production of 100 GeV particles might require knowledge of PDFs down to x=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-perturbative (Underlying Event, Minimum Bias) we need PDFs down to x=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
x -910 -810 -710 -610 -510 -410 -310
)2x
g ( x
, Q
210
310
410
Small-x NNLO PDFs for FCC studies
NNPDF2.3CT10cteq6MSTW08
Small-x NNLO PDFs for FCC studies
x -910 -810 -710 -610 -510 -410 -310
)2x
u ( x
, Q
210
310
410
Small-x NNLO PDFs for FCC studies
NNPDF2.3CT10cteq6MSTW08
Small-x NNLO PDFs for FCC studies
Juan Rojo FCC Kick-off Meeting, Geneva, 14/02/2014
11
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
x-910 -810 -710 -610 -510 -410 -310 -210 -110 1
0
100
200
300
400
500xg(x,Q), NNPDF23_lo_as_0119_qed.LHgrid members
MembersCentral valueStd. deviation68% c.l.Q = 1.41 GeV
Gen
erat
ed b
y A
PFEL
2.0.
0: V
.Ber
tone
, S.C
arra
zza,
J.R
ojo
(arX
iv:1
310.
1394
)
Juan Rojo FCC Kick-off Meeting, Geneva, 14/02/2014
12
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
]2 [ GeV2Q10 210 310 410
)2xg
(x, Q
0.85
0.9
0.95
1
1.05
1.1
1.15
-2Ratio to NNPDF2.1 GM-VFN, x=10
NNPDF2.1
=3FNNPDF2.1 FFN N
=4FNNPDF2.1 FFN N
-2Ratio to NNPDF2.1 GM-VFN, x=10
]2 [ GeV2Q10 210 310 410
)2 (x
, Q�x
0.7
0.8
0.9
1
1.1
1.2
-2Ratio to NNPDF2.1 GM-VFN, x=10
NNPDF2.1
=3FNNPDF2.1 FFN N
=4FNNPDF2.1 FFN N
-2Ratio to NNPDF2.1 GM-VFN, x=10
missing charm
missing charm
Juan Rojo FCC Kick-off Meeting, Geneva, 14/02/2014
13
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 smaller that all other quark PDFs (charm and bottom are very close to light quark PDFs): should be included in theoretical predictions
x -510 -410 -310 -210 -110
= 1
0 Te
V )
2x
( x, Q
-110
1
10
210
= 6FNNPDF2.3 NNLO N
GluonUpCharmBottomTop
= 6FNNPDF2.3 NNLO N
Juan Rojo FCC Kick-off Meeting, Geneva, 14/02/2014
Gluon PDF
Top PDF
Up quark PDF
14
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
Juan Rojo FCC Kick-off Meeting, Geneva, 14/02/2014
15
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)
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
Evolution equation for the structure function of W bosons
Juan Rojo FCC Kick-off Meeting, Geneva, 14/02/2014
16
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
( GeV )cutWWM
0 1000 2000 3000 4000 5000 6000 7000 8000
(WW
) [Q
CD
] !
(WW
) [Q
CD
+Q
ED
] /
!
0
0.5
1
1.5
2
2.5
WW production @ LHC 100 TeV, 68% CL
qNNPDF2.3 QED, q
qMRST04 QED, q
"" + qNNPDF2.3 QED, q
"" + qMRST04 QED, q
WW production @ LHC 100 TeV, 68% CL
Boughezal, Li, Petriello 2013 Snowmass QCD report
WW at FCC100
(QCD+QED)/QCD
high-mass DY
Juan Rojo FCC Kick-off Meeting, Geneva, 14/02/2014
17
The kinematical coverage of the FCC reaches the small-x region where the usual DGLAP PDF evolution might need to be completed with BFKL high-energy (small-x) resummation
Combining DGLAP and BFKL stabilizes the perturbative expansion of DGLAP evolution at small-x
The theory for DIS known (Altarelli, Ball, Forte 08, Ciafaloni, Colferai, Salam, Stasto 07), more theoretical progress is required for computation of relevant hadronic cross sections at the FCC
Juan Rojo FCC Kick-off Meeting, Geneva, 14/02/2014
DGLAP NNLO
DGLAP+BFKL
gluo
n-gl
uon
DG
LAP
kern
el
18 Juan Rojo FCC Kick-off Meeting, Geneva, 14/02/2014
Crucial milestone for the next years is to produce a global PDF fit which combines NNLO DGLAP evolution with NLL BFKL resummation
This would be a pre-requisite to study the relevance of high-energy resummation at the FCC, specially for benchmark processes like Higgs, W, Z and top production
High-energy resummation affects mostly the gluon PDF, and then feeds to all the quark PDFs
DGLAP NNLO
DGLAP+BFKL
Rat
io g
(x,Q
)/gN
LO(x
,Q)
x=10-4
The Physics Case for Polarized Collisions at the FCC
Juan Rojo FCC Kick-off Meeting, Geneva, 14/02/2014
20
x -210 -110
)2
x q (
x, Q
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
2 GeV4 = 102NNPDF2.3, Q
x g
x u
x d
x s
2 GeV4 = 102NNPDF2.3, Q
x -210 -110
)2
q (
x, Q
#x
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
2 GeV4 = 102NNPDFpol1.1, Q
g #x
u#x
d#x
s#x
2 GeV4 = 102NNPDFpol1.1, Q
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
Juan Rojo FCC Kick-off Meeting, Geneva, 14/02/2014
What are the BSM opportunities for the polarized option of a 100 TeV machine? Polarized beams could provide a useful tool for BSM characterization, where differences in polarized
asymmetries provide a handle on SM vs BSM discrimination
21
Measurement of sign of AL will discriminate between different BSM scenarios (different production modes)
A more precise measurement of AL leads to enhanced discrimination, ie, qq vs gg production mechanisms
Fuks, Proudom, Rojo, Schienbein, in preparation
Juan Rojo FCC Kick-off Meeting, Geneva, 14/02/2014
22
Parton Distributions play a central role at the LHC program, will continue to do so at a 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, PDFs with high-energy resummation
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
Juan Rojo FCC Kick-off Meeting, Geneva, 14/02/2014
23
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
x 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95
)2x
g ( x
, Q
-810
-710
-610
-510
-410
-310
-210
-110
Large-x NNLO PDFs for FCC studies
NNPDF2.3
CT10
MSTW08
Large-x NNLO PDFs for FCC studies
x 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95
)2x
d ( x
, Q
-810
-710
-610
-510
-410
-310
-210
-110
Large-x NNLO PDFs for FCC studies
NNPDF2.3
CT10
MSTW08
Large-x NNLO PDFs for FCC studies
Juan Rojo FCC Kick-off Meeting, Geneva, 14/02/2014
24
Q ( GeV ) 210 310 410
= 6
)F
= 5
) / (
NF
Ratio
( N
0.98
0.99
1
1.01
1.02
1.03
1.04
1.05
1.06-2NNPDF2.3 NNLO, x = 10
GluonUpDown
-2NNPDF2.3 NNLO, x = 10
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
NF=6 vs NF=5
Juan Rojo FCC Kick-off Meeting, Geneva, 14/02/2014
25
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
[ GeV ]X M210 310 410
lum
inos
ity ra
tio 1
00 T
eV /
14 T
eV
1
10
210
310
410
510
610
710
810
100 TeV vs 14 TeV PDF Luminosities, NNPDF2.3 NNLO
GGQGQQbarQQ
100 TeV vs 14 TeV PDF Luminosities, NNPDF2.3 NNLO
Juan Rojo FCC Kick-off Meeting, Geneva, 14/02/2014