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C.-P. YuanMichigan State University
Parton Distributions at High Energy Colliders
In collaboration with CTEQ-TEA
HEP seminar@PKUJune 6, 2014
CTEQ‐TEA group
• CTEQ – Tung et al. (TEA) in memory of Prof. Wu‐Ki Tung, who established
CTEQ Collaboration in early 90’s
• Current members:Sayipjamal Dulat (Xinjiang Univ.)Tie‐Jiun Hou (Academia Sinica, Taipei)Southern Methodist Univ. ‐‐ Pavel Nadolsky, Jun Gao, Marco GuzziMichigan State Univ. ‐‐ Jon Pumplin, Dan Stump, Carl Schmidt, CPY
Parton Distribution Functions
Needed for making theoretical calculations to compare with
experimental data
Deep Inelastic Scattering process
Drell‐Yan Process
• Naïve parton model• QCD improved parton model• Factorization Theorem
Parton Model
σhh′→W+X =
h(P1)
h′(P2)
q
W+
X
=
h′(P2)
h(P1)
p1 = x1P1
p2 = x2P2
q
σhh′→W+X =∑
f,f ′=q,q̄
∫ 10 dx1dx2
{φf/h (x1) σ̂ff ′φf̄ ′/h′ (x2) + (x1 ↔ x2)
}
The probablility of finding a ”parton” f with
fraction x1 of the hadron h momentum
Partonic ”Born”
Cross Section of ff′ → W+
Factorization Theorem
σhh′ =∑
i,j∫ 10 dx1dx2 φi/h
(x, Q2
)Hij
(Q2
x1x2S
)φj/h′
(x2, Q
2)
Nonperturbative,but universal,hence, measurable
IRS, Calculablein pQCD
Procedure:
(1) Compute σkl in pQCD with k, l partons
(not h, h′ hadron)
σkl =∑i,j
∫ 1
0dx1dx2 φi/k
(x1, Q
2)Hij
(Q2
x1x2S
)φj/l
(x2, Q2
)
(2) Compute φi/k, φj/l in pQCD
(3) Extract Hij in pQCD
Hij IRS ⇒ Hij indepent of k, l
⇒ same Hij with(k → h, l → h′)
(4) Use Hij in the above equation with φi/h, φj/h′
Extracting Hij in pQCD
• Expansions in αs:
σkl =∞∑
n=0
(αs
π
)nσ(n)kl αs =
g2
4π
Hij =∞∑
n=0
(αs
π
)nH
(n)ij
φi/k (x) = δikδ (1 − x) +∞∑
n=1
(αs
π
)nφ(n)i/k
↑φ(0)i/k (αs = 0 ⇒ Parton k “ stays itself ”)
• Consequences:
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suppress "^" from now on
process dependent
process independent, scheme dependent
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NuTev
Experimental input (continued)
( )
(DIS jets, heavy quark prod. …)
Some basics about PDFs• Parton Distribution Function • Given a heavy resonance with mass Q produced at hadron collider with c.m. energy
• What’s the typical x value?at central rapidity (y=0)
• Generally,
S
( ,Q)f x
QxS
1 2y yandQ Qx e x e
S S
1 2 2 cosh(y)Qx xS
1 2max : 1y x x
Kinematics of a 100 TeV SppC
• J. Rojo: kickoff meeting for FCC at CERN, Feb. 2014
Kinematics of Parton variables
QCD (DGLAP)evolutionPredictive power of
global analysis of PDFs is based on the renormalization group properties of the universal Parton Distributions f(x,Q).
On to a 100 TeV SppCwill access smaller x, larger Q2
currently have no constraints on PDFsfor x values below1E-4
we don’t know whereat low x, BFKL effects start tobecome important
poor constraints (still) as well for high x PDFs
at high masses (Q2), rely on DLAP evolution; we know at large Q2,EW effects also become important
CT10 PDFs
• NLO
• NNLO
CT10 PDF sets: the naming conventions� Two NLO PDF sets, without/with Tevatron Run-2 data on W
charge asymmetry A`
CT10 NLO does not includeCT10W NLO includes
4 pT` bins of D0 Run-2 A` data
⇒ CT10 and CT10W sets differ mainly in the behavior ofd(x,Q)/u(x,Q) at x > 0.1
� One NNLO PDF set: only inclusive pT` bins of D0 Run-2 A`(e and µ) data are included that have smallest theoryuncertainties
� The NNLO set is a counterpart of both CT10 NLO and CT10WNLO. It uses only a part of the A` data sample thatdistinguishes between CT10 NLO and CT10W NLO.
C.-P. Yuan (MSU) SUSY 2012, Beijing, China 08/14/2012 6
CT10NNLO vs. fitted data
8
0
0.5
1
1.5
2
2.5
3
0.0001 0.001 0.01
F 2cc (x
,Q) +
0.5
* i
x
Q2 = 6.5 GeV2
i=0
Q2 = 12 GeV2
i=1
Q2 = 18 GeV2
i=2
Q2 = 35 GeV2
i=3
Q2 = 60 GeV2
i=4
CT10 NNLOCT10 NLO
H1 data 2011
2 N pt 2950 26411.11Fits well:
CT10 NNLO error PDFs (compared to CT10W NLO)
0.4
0.6
0.8
1
1.2
1.4
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1.8
10-5 10-4 10-3 0.01 0.02 0.05 0.1 0.2 0.5 0.9
Rat
io to
ref
eren
ce f
it C
T10
W N
LO
x
g(x,Q) Q = 2 GeV
CT10W NLOCT10 NNLO (prel.)/CT10W NLO
0.4
0.6
0.8
1
1.2
1.4
1.6
10-5 10-4 10-3 0.01 0.02 0.05 0.1 0.2 0.5 0.9
Rat
io to
ref
eren
ce f
it C
T10
W N
LO
x
u(x,Q) Q = 2 GeV
CT10W NLOCT10 NNLO (prel.)/CT10W NLO
0.4
0.6
0.8
1
1.2
1.4
1.6
10-5 10-4 10-3 0.01 0.02 0.05 0.1 0.2 0.5 0.9
Rat
io to
ref
eren
ce f
it C
T10
W N
LO
x
ub(x,Q) Q = 2 GeV
CT10W NLOCT10 NNLO (prel.)/CT10W NLO
C.-P. Yuan (MSU) SUSY 2012, Beijing, China 08/14/2012 5
Striving for NNLO accuracy in the PDFs� So far, only “partial NNLO” global fits exist. For some fitted
processes (inclusive jet production, CC DIS with mq 6= 0),QCD contributions are known only to NLO. (NLO EWcontributions, power corrections, other systematic errorsmay be comparable to NNLO QCD effects.)
� CT10 “NNLO” PDFs underwent validation studies for aboutone year. We identified several types of uncertainties thatcompete with NNLO QCD contributions.
� CT10 NNLO and NLO PDFs produce about the sameχ2/Npt ≈ 1.05− 1.10 for Npt ' 2700 data points
� Shapes of the NNLO PDFs have noticeably evolvedcompared to NLO as a result of O(α2
s) contributions,updated electroweak contributions, revised statisticalprocedures
C.-P. Yuan (MSU) SUSY 2012, Beijing, China 08/14/2012 7
CT10 NNLO central PDFs, as ratios to NLO, Q=2 GeV
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
x -510 -410 -310 -210 0.1 0.2 0.5 0.7 1
(x,Q)
NLO
a(x,
Q)/f
NNLO
af
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
guuddsc
Ratios of CT10 NNLO and CT10W NLO PDFs, Q=2 GeV
PRELIMINARY
1
2
3
1. At x < 10−2, O(α2s) evolution suppresses g(x,Q), increases q(x,Q)
2. c(x,Q) and b(x,Q) change as a result of the O(α2s) GM VFN scheme
3. In large x region, g(x,Q) and d(x,Q) are reduced by not includingRun-1 inclusive jet data, revised EW couplings, alternative treatment ofcorrelated systematic errors, scale choices.
C.-P. Yuan (MSU) SUSY 2012, Beijing, China 08/14/2012 8
CT10 NNLO PDFs• PDF error bands
– u and d PDFs are best known– currently no constraint for x below 1E‐4– large error for x above 0.3– larger sea (e.g., ubar and dbar) quark uncertainties in large x region
– with non‐perturbative parametrization form dependence in small and large x regions
• PDF eigensets– useful for calculating PDF induced uncertainty – sensitive to some special (combination of) parton flavor(s).
(e.g., eigenset 7 is sensitive to d/u or dbar/ubar; hence, W asymmetry data at Tevatron and LHC.)
7th CT10Eigenset
u d
subar
7th CT10Eigenset
dbar Gluon
d/u dbar/ubar
CT10, CT14, and LHC data
• We have since included early (7 TeV) LHC data: Atlas W/Z production and asymmetry at 7 TeV, Atlas single jet inclusive, CMS W asymmetry,
HERA FL and F2c
• More flexible parametrization – gluon, d/u at large x and both, d/u and dbar/ubar at small x, strangeness, and s - sbar.
• Improvements modest so far, but expectation from ttbar, W/Z, Higgs, etc.
10|Muon |
0 0.5 1 1.5 2
Cha
rge
asym
met
ry
0.05
0.1
0.15
0.2
0.25
NLO FEWZ + NLO PDF, 68% CLCT10NNPDF23HERAPDF15MSTW2008MSTW2008CPdeut
> 35 GeVT
(b) p
Data
= 7 TeVs at -1CMS, L = 4.7 fb
Data is already more precise than current PDFuncertainty.
Will help to determine PDFs in small x region.
Most useful for determining dbar/ubar.
Uncertainties on H and ttbar Predictions at the LHC (and update on Intrinsic Charm)
Carl Schmidt Michigan State University
April 29, 2014 DIS2014, Warsaw, Poland
On behalf of CTEQ-TEA group
1
Outline 1) Update of CTEQ-TEA activities discussed this morning
CT10 update, MetaPDFs, photon PDF, etc. 2) Update of Intrinsic Charm Analysis
Dulat et al, PRD 89, 073004 (2014)
3) Lagrange Multiplier (LM) Uncertainty Analysis on gg->H Dulat et al, arXiv:1309.0025[hep-ph]
4) Uncertainty Analysis on gg->ttbar
2
Intrinsic Charm and CT10IC
3
1) Update of CTEQ6.5 IC study from 2007 to CT10NNLO - includes combined H1 and ZEUS data, HERA inclusive charm
2) Recent CT10 global analysis study of charm quark mass:
Gao et al, Eur.Phys.J. C73 (2013) 2541 Use mc(pole)=1.3 GeV for this study - some correlation between mc and IC
3) Two model Intrinsic Charm distributions at Qc=1.3 GeV - BHPS valence-like model (Brodsky et al, Phys. Lett. 93B, 451 (1980)) - SEA-like model
4) 90% CL limits:
BHPS
SEA
mc (mc ) =1.15−0.12+0.18 GeV
2960
3000
3040
3080
3120
3160
0 0.01 0.02 0.03
r2 F
<x>IC
BHPS1
BHPS2SEA1
SEA2
BHPSSEABHPS + T2SEA + T2
xIC≤ 0.025
xIC≤ 0.015
xIC= x c(x,Qc )+ c (x,Qc )[ ]
0
1∫ dx
Intrinsic Charm at LHC
4
c(x)
/c(x)
x
IC vs CT10 charm PDF
pp → Zc at LHC may further constrain valence-like model
!Σ
!pT ,Z!pb"GeV#, LHC 14TeV
CT10BHPS1BHPS2SEA1SEA2
10#3
10#2
10#1
1
Ratios to CT10CT10 PDF unc.
100 200 300 400 5000.60.81.01.21.41.61.82.0
pT ,Z !GeV#SEA1/BHPS1: SEA2: BHPS2:
xIC= 0.57%
xIC=1.5%
xIC= 2.0%
CT10 IC at LHC
5
!!""!!
""!!
LHC !14 TeV"! CT10 " BHPS1 ! BHPS2 " SEA1 ! SEA2
21.0 21.5 22.0 22.5 23.0 23.52.05
2.10
2.15
2.20
2.25
2.30
W##$!lΝ" !nb"
Z!ll"!nb"
!!""
!!
""!!
LHC !14 TeV"! CT10 " BHPS1 ! BHPS2 " SEA1 ! SEA2
2.05 2.10 2.15 2.20 2.25 2.30
920
940
960
980
1000
Z!ll" !nb"topquarkpair!pb"
W, Z and top production at LHC CT10 IC distributions publicly available
PDF uncertainties in gg→H
6
1) Most analyses use Hessian Method (n error PDF sets)
- Error sets can be used by anyone for any observable - Assume quadratic and linear dependence of χ2, X on ak
2) Lagrange Multiplier (LM) method is more robust
- Find best fit for each constrained value of observable X - No assumptions on dependence of χ2, X on ak - Can validate Hessian method - Can display correlations between PDFs and Observable - Must calculate separately for each observable
δX( )2 = 14
X(ak+ )− X(ak
− )( )2
k=1
n
∑
Uncertainties in gg→H
• Curves are LM, circles/squares are Hessian • Red use χ2 • Blue add Tier-2 penalty to ensure no specific experiment is too badly fit • Allowed Tolerance is 100 at 90% CL
• Small differences in asymmetries, but in general the two methods agree well for this observable
7
3180
3200
3220
3240
3260
3280
3300
3320
42 43 44 45 46 47
r2
mH (pb)
14 TeV90% C.L.
68% C.L.
r2
r2 + Tier-2 3180
3200
3220
3240
3260
3280
3300
3320
16.2 16.6 17 17.4 17.8
r2
mH (pb)
8 TeV90% C.L.
68% C.L.
r2
r2 + Tier-2 3180
3200
3220
3240
3260
3280
3300
3320
13.1 13.6
r2
mH (pb)
7 TeV90% C.L.
68% C.L.
r2
r2 + Tier-2
Combined PDF+αS Uncertainties
• Can include αS uncertainty as contribution to total χ2 in LM method • Use PDF4LHC choice of αS=0.118±0.002 at 90% CL • Black curves are 68% and 90% CL contours
• Hessian method adds αS and PDF uncertainties in quadrature • Hessian and LM agree well for Higgs cross section (despite non-quadratic
behavior, especially obvious at 14 TeV) • For instance 90% CL uncertainties at 14 TeV (% of central value):
• LM: +5.2/-5.2 Hessian: +5.4/-5.0 8
!!
ΧFt2 "T2 !14 TeV"ΧFt2 "T2 !14 TeV" "
""
"
0.116 0.117 0.118 0.119 0.12042
43
44
45
46
47
ΑS
ΣH!!
Χ2"T2 !8 TeV"Χ2"T2 !8 TeV"
0.116 0.117 0.118 0.119 0.12016.0
16.5
17.0
17.5
18.0
ΑS
ΣH
!!
Χ2"T2 !7 TeV"Χ2"T2 !7 TeV"
0.116 0.117 0.118 0.119 0.12012.5
13.0
13.5
14.0
14.5
ΑS
ΣH
CT10H Extreme Sets
• PDF sets that give extreme values of Higgs cross section at 90% CL are publically available as CT10H sets
• Shown on contour plot as Red squares • PDF uncertainly only or PDF+αS uncertainty
• Useful for efficient gg→H analyses
9
!!
ΧFt2 "T2 !14 TeV"ΧFt2 "T2 !14 TeV" "
""
"
0.116 0.117 0.118 0.119 0.12042
43
44
45
46
47
ΑS
ΣH
Sensitivity to Data Sets
•How sensitive are included data sets to value of H ?•“Effective Gaussian Variable” S maps cumulative 2 distribution for Npt onto
cumulative Gaussian distribution• +1,+2,+3,… equivalent to that many sigma deviations• Negative values correspond to anomalously well-fit data
•Most strongly correlated data: high pT jet, inclusive HERA, CCFR-dimuon• HERA more strongly correlated with 14 TeV—smaller x• CCFR dimuon correlation due to gluon-strange interdependence
10
-3
-2
-1
0
1
2
3
4
12.8 13 13.2 13.4 13.6 13.8 14
S
H (pb)
LHC (7 TeV)
CDF-jet
CCFR-dimuon
HERA-1
D0-jetATLAS-WZ
ATLAS-jet-3
-2
-1
0
1
2
3
4
16.3 16.7 17.1 17.5 17.9S
H (pb)
LHC (8 TeV)CDF-jet
CCFR-dimuon
HERA-1
D0-jet
ATLAS-WZ
ATLAS-jet-3
-2
-1
0
1
2
3
4
42 43 44 45 46
S
H (pb)
LHC (14 TeV)
CDF-jet
CCFR-dimuonHERA-1
D0-jet
ATLAS-WZ
ATLAS-jet
Uncertainties in gg→ttbar
• Same analyses applied to gg→ttbar • HERA combined data (T2) constrains low values of cross section • But T2 less important for combined
PDF+αS • Hessian and LM consistent
11
r2
m7 TeVttbar (102 pb)
6r2 = 100.0
6r2 = 36.96
0% 68%68% 90%90%
r2
r2+T2
2880
2900
2920
2940
2960
2980
3000
1.60 1.70 1.80 1.90
m7 TeVttb (10 2 pb)
r2+T2300029902980297029602950294029302920291029002890
0.116 0.117 0.118 0.119 0.12_s
1.50
1.60
1.70
1.80
1.90
2.00
m7T
eVttb
(1
02 pb)
mT (GeV)
CT10 NNLOHessian PDFHessian PDF+_sLM PDFLM PDF+_s_s=0.116_s=0.118_s=0.120
1.50
1.60
1.70
1.80
1.90
2.00
2.10
2.20
168 169 170 171 172 173 174 175 176
CT10tt extreme sets
• Pairs of CT10tt extreme sets (PDF, PDF+αS) to be released
- for focused ttbar analyses
Results provided by DiffTop group (M. Guzzi, K. Lipka, S. Moch) 12
0 100 200 3000.0
0.2
0.4
0.6
0.8
1.0
1.2
ptT !GeV"
dΣ#dpt T
!pb#GeV"
mt"173 GeV, LHC 7 TeV, CTXX NNLO extreme eigen.sets
DiffTop approx NNLOSmall#dashed band " LM method, PDF$Αs
dashed band " CT10NNLO, PDF onlydotdashed CT10NNLO $center%
CT10tt extreme sets
• Comparison with CMS (left) and ATLAS (right) data • Hessian top, LM extreme sets bottom • Extreme sets useful if highly correlated with inclusive ttbar (note high pT)
Results provided by DiffTop group (M. Guzzi, K. Lipka, S. Moch) 13
0 100 200 300 4000.80
0.85
0.90
0.95
1.00
1.05
1.10
1.15
1.20
PtT !GeV"
data#theo
ryLHC 7 TeV, mt!173 GeV $central%, CT10NNLO 68"CL
! CMS data#DiffTop mt variationΑs$Mz% unc.PDF unc.scale unc.
0 100 200 300 4000.80
0.85
0.90
0.95
1.00
1.05
1.10
1.15
1.20
PtT !GeV"
data#theo
ry
LHC 7 TeV, mt!173 GeV $central%, CTXX extreme eigen.sets! CMS data#DiffTop
PDF " Αs unc. 68$ CL
0 100 200 300 4000.80
0.85
0.90
0.95
1.00
1.05
1.10
1.15
1.20
PtT !GeV"
data#theo
ry
LHC 7 TeV, mt!173 GeV $central%, CT10NNLO 68"CL
! ATLAS data#DiffTop mt variationΑs$Mz% unc.PDF unc.scale unc.
0 100 200 300 4000.80
0.85
0.90
0.95
1.00
1.05
1.10
1.15
1.20
PtT !GeV"data#theo
ry
LHC 7 TeV, mt!173 GeV $central%, CTXX extreme eigen.sets! ATLAS data#DiffTop
PDF " Αs unc. 68$ CL
Conclusions • Intrinsic Charm
• Limits on valence-like and sea-like IC • CT10IC PDFs available for further study • LHC will probe further
• Lagrange Multiplier Uncertainty analysis • Less dependent on assumptions than Hessian analysis • Allows study of data correlations with particular observable • Test of Hessian results
• Consistent with Hessian results for both Higgs and ttbar • CT10H extreme sets available for focussed studies
(CT10tt extreme sets to come)
14
Top quark as a parton
• For a 100 TeV SppC, top mass (172 GeV) can be ignored; top quark, just like bottom quark, can be a parton of proton.
• Top parton will take away some of the momentum of proton, mostly, from gluon (at NLO).
• Need to use s‐ACOT scheme to calculate hard part matrix elements, to be consistent with CT10 PDFs.
Momentum fraction inside proton
G
t
t
Solid curves: CT10 NNLODashed curves: CT10Top NNLO
CT10Top PDFs(Q=2 TeV)
Top PDF isonly a factorof 2 smaller than b PDF
t b
CT10Top PDFs(Q=20 TeV)
CT10Top PDFs
G
CT10Top PDFs
PDF luminosities1 2 1 2
2
1 2
2
( , ) ( , ) ( )
( , ) ( , ) ( )
( )
dx dx g x M g x M M
d dy g x M g x
dLdM
M M
dM M
PDF Luminosity
1 2
1
2
x x
1y ln2
xx
Hard part calculation
• S‐ACOT scheme• Example: single‐top production
CT10 NNLO update and QED effects in PDFs
Carl Schmidt Michigan State University
April 29, 2014 DIS2014, Warsaw, Poland
On behalf of CTEQ-TEA group
1
Motivation 1) Sensitivity to NNLO QCD is at few % level.
- QED and Electroweak corrections are now significant. - E.g, QED corrections to require order α effects in parton evolution
2) Photon induced processes can be kinematically enhanced. asymptotically
3) Last considered in 2004 (MRST) Martin et al., EPJC 39 (2005) 155.
- Time for more detailed study. This talk is an update of CTEQ-TEA activities on this topic.
18
σ̂ γγ ≈ 8πα2M
W
2γγ→W+W
−
γ
γ
W+
W −
δQCD/10
δgg
δγγ
δEW
MWW(GeV)
δ(%)
600550500450400350300250200
20
10
0
−10
−20
−30
σggLO
σγγLO
σqq̄LO
Tevatron
MWW(GeV)
dσ/dMWW(pb/GeV)
600550500450400350300250200
1
0.1
0.01
0.001
0.0001
10−5
10−6
10−7
δQCD/10
δgg
δγγ
δEW
MWW(GeV)
δ(%)
1000900800700600500400300200
20
10
0
−10
−20
−30
σggLO
σγγLO
σqq̄LO
LHC at 8 TeV
MWW(GeV)
dσ/dMWW(pb/GeV)
1000900800700600500400300200
1
0.1
0.01
0.001
0.0001
10−5
10−6
10−7
δQCD/10
δgg
δγγ
δEW
MWW(GeV)
δ(%)
200018001600140012001000800600400200
20
10
0
−10
−20
−30
σggLO
σγγLO
σqq̄LO
LHC at 14 TeV
MWW(GeV)
dσ/dMWW(pb/GeV)
200018001600140012001000800600400200
1
0.1
0.01
0.001
0.0001
10−5
10−6
10−7
Bierweiler et al., JHEP 1211 (2012) 093
pp→W + X
Photon PDFs (in proton)
8
Q = 3.2 GeV 0.05% 0.34% Q = 85 GeV 0.22% 0.51%
pγ (Q) γ x,Q0( ) = 0 γ x,Q0( )CM
γ momentum fraction:
γ0
γ0 γCM
γCM
g g
u u d d
c c b
s s d d
uu
Q = 3.2 GeV Q = 85GeV
Photon PDF can be larger than sea quarks at large x!
Initial Photon PDF still ← significant at large Q.
10!3 10!2 10!1 100
10!3
10!2
10!1
100
101
x
xf!x,Q2
"
10!3 10!2 10!1 100
10!3
10!2
10!1
100
101
x
xf!x,Q2
"
Photon PDF Parametrization “Radiative ansatz” for initial Photon PDFs (generalization of MRST choice)
where u0 and d0 are “primordial” valence-type distributions of the proton. Assumed approximate isospin symmetry for neutron. Here, we take Au and Ad as unknown fit parameters. MRST choice: “Radiation from Current Mass” – CM We use and reduce the number of parameters further (for initial study) by setting Now everything effectively specified by one unknown parameter:
7
γ p=α
2πAueu
2 Pγq u0+ A
ded
2 Pγq d0( )
γ n =α
2πAueu
2 Pγq d0+ A
ded
2 Pγq u0( )
Aq = ln Q0
2mq
2( )
u0, d0
Au = Ad = A0
u0= u
p≡ u
p(x,Q
0), d
0= d
p≡ d
p(x,Q
0)
A0 ⇔ p0γ ≡ pγ /P (Q0 ) (Initial Photon momentum fraction)
Constraining Photon PDFs 1) Global fitting
• Isospin violation, momentum sum rule lead to constraints in fit • We find can be as large as ~ 5% at 90%CL,
much more than CM choice
2) Direct photon PDF probe - DIS with observed photon, - Photon-initiated subprocess contributes at LO, and no larger background with which to compete - But must include quark-initiated contributions consistently - Treat as NLO in α, but discard small corrections, suppressed by α γ(x).
9
p0γ
ep→ eγ + X
Subprocess contributions: LL Emission off Lepton line Both quark-initiated and photon-initiated contributions are if Collinear divergence cancels (in d=4-2ε) by treating as
NLO in with QQ Emission off Quark line Has final-state quark-photon collinear singularity
QL Interference term Negligible < about 1% (but still included)
Previous calculations: quark-initiated only – (GGP) Gehrmann-De Ridder, Gehrmann, Poulson, PRL 96, 132002 (2006)
photon initiated only – (MRST), Martin, Roberts, Stirling, Thorne, Eur. Phys. J. C 39, 155 (2005) 10
ep→ eγ + X
γ (x) ~α~α 3
α γ bare (x) = γ (x)+4π( )
ε
εΓ(1+ε)
α
2πPγq q( )(x) (MSbar)
eγ
e’
Zeus Experimental Cuts
Also require N ≥ 1 forward jet Two theoretical approximations to photon isolation implemented: 1) Smooth isolation (Frixione):
- Removes fragmentation contribution
2) Sharp isolation:
- Requires fragmentation contribution (Use Aleph LO parametrization) 11
4 GeV < ETγ < 15 GeV
-0.7 <ηγ < 0.9
E !ℓ > 10 GeV139.8° <θ !ℓ <171.8°10 GeV2 <Q2 < 350 GeV2
Photon Cuts Lepton Cuts Photon Isolation Cut Photon must contain 90% of energy in jet to which it belongs.
E !q < 19 Eγ
1− cosr1− cosR#
$%
&
'( for r = Δη !q γ
2 +Δϕ !q γ2 < R =1
E !q < 19 Eγ for r < R =1
Theoretical Uncertainties 1) Factorization Scale
( , Smooth Isolation, ) • Scale dependence of LL contribution reduced drastically compared to
photon-initiated alone • QQ and LL have different-shaped distributions. LL dominates at large ET
γ and small ηγ . Can be used to extract photon PDF
• Scale dependence of QQ and total is still large (LO in αS) 12
4 6 8 10 12 14
0.2
0.5
1.0
2.0
5.0
10.0
ETg HGeVL
dsêdE Tg
HpbêGeVL
-0.5 0.0 0.50
5
10
15
20
hg
dsêdhgHpbL
Total QQ LL γ-initiated
p0γ = 0 0.5ET
γ < µF < 2ETγ
Theoretical Uncertainties 2) Isolation Prescription
( , ) • Difference between two isolation prescriptions is about same size as scale
uncertainty • Smooth prescription gives larger predictions. In principle, should give smaller. • Uncertainty in fragmentation function, and higher order effects in both
prescriptions are major sources of difference. • Use both prescriptions as measure of uncertainty in prediction. 13
Smooth Sharp
p0γ = 0 0.5ETγ < µF < 2ETγ
4 6 8 10 12 14
0.5
1.0
2.0
5.0
ETg HGeVL
dsêdE Tg
HpbêGeVL
-0.5 0.0 0.50
5
10
15
20
25
hg
dsêdhgHpbL
Distributions 1) Photon Variables ET
γ and ηγ
(Smooth Isolation, ) • Best fit for p0
γ is correlated with choice of isolation and factorization scale µF. • Can obtain excellent fit to shape of distributions for reasonable scale choices. • “Current Mass” ansatz cannot fit shape (prediction too large at large ET
γ and small ηγ where LL dominates), regardless of scale choice.
14
µF = 0.5ETγ
p0γ = p0
γ (cm) = 0.29 % p0γ = 0.2 %
p0γ = 0.1 %
p0γ = 0.0 %
4 6 8 10 12 14
0.5
1.0
2.0
5.0
ETΓ !GeV"
dΣ#dE TΓ
!pb#GeV"
!0.5 0.0 0.50
5
10
15
20
25
ΗΓdΣ!dΗΓ "p
b#
Limits on Photon PDF
Smooth Isolation Sharp Isolation • Different χ2 curves for choice of isolation and scale µF • 90% C.L. for Npt = 8 corresponds to χ2 = 13.36 • Obtain independent of isolation prescription
(More generally, constrains γ(x) for 10-3 < x < 2x10-2.)
• “Current Mass” ansatz has χ2 > 45 for any choice of isolation and scale 15
0.00 0.05 0.10 0.15 0.20 0.25 0.300
20
40
60
80
p0Γ
Χ2forN
pt#8
0.00 0.05 0.10 0.15 0.20 0.25 0.300
20
40
60
80
p0Γ
Χ2forN
pt#8 0.35ET
γ
0.5ETγ ET
γ 2ETγ 2ET
γ ET
γ 0.5ET
γ
p0γ ≤ 0.14% at 90 % C.L.
Summary
• PDFs have larger uncertainties in both small x and large x regions.
• PDFs will be further determined by LHC data.• Photon can be treated as a parton inside proton.
• In a 100TeV SppC, top quark can be a partonof proton, consistent hard part calculations are needed.
Backup Slides
17
Inclusion of Photon PDFs LO QED + (NLO or NNLO) QCD evolution:
“Radiative ansatz” for initial Photon PDFs (generalization of MRST choice)
where u0 and d0 are “primordial” valence-type distributions of the proton. Assumed approximate isospin symmetry for neutron. Here, we take Au and Ad as unknown fit parameters. MRST choice: “Radiation from Current Mass” - CM
19
dq
dt=αs
2πPqqq+P
qg g( )+
α
2πeq
2 Pqqq+ e
q
2 Pqγ γ( )
dg
dt=αs
2πPgg g+P
gq q+ q( )∑( )
dγ
dt=α
2πPγγ γ +
Pγq eq
2q+ q( )∑( )
γ p=α
2πAueu
2 Pγq u0+ A
ded
2 Pγq d0( )
γ n =α
2πAueu
2 Pγq d0+ A
ded
2 Pγq u0( )
Aq = ln Q0
2mq
2( )
u0, d0
t = lnQ2
Inclusion of Photon PDFs (2) Isospin violation occurs radiatively in u and d. To this order in α:
Isospin violation in initial sea and gluon assumed negligible.
With this ansatz, number and momentum sum rules automatically satisfied for neutron, for any choice of u0 and d0 .
i.e., , where
Here, assume
Also, let Expect δ to be small.
Now everything effectively specified by one unknown parameter:
20
un= d
p+α
2πAueu
2− Aded
2( ) Pqq d 0 , dn= u
p+α
2πAded
2− Aueu
2( ) Pqq u0
pi/P∑ =1 ⇒ pi/N∑ =1
qn= q
p, g
n= g
p( )
Au= A
01+δ( ), A
d= A
01−δ( )
A0 ⇔ p0γ ≡ pγ /P (Q0 ) (Initial Photon momentum fraction)
u0= u
p≡ u
p(x,Q
0), d
0= d
p≡ d
p(x,Q
0)
u0, d0
pi/h = x fi/h (x)0
1∫ dx
Isospin violation
21 γ x,Q02( )CMγ x,Q0
2( ) = 0
γn/γp γn/γp
dn/up dn/up
un/dp un/dp Q=Q0=1.3 GeV Q=3.2 GeV Q=85 GeV
0.0 0.2 0.4 0.6 0.8
0.96
0.98
1.00
1.02
1.04
x
qn!qp
0.0 0.2 0.4 0.6 0.80.0
0.2
0.4
0.6
0.8
1.0
x
Γn!Γp
0.0 0.2 0.4 0.6 0.8
0.96
0.98
1.00
1.02
1.04
x
qn!qp
0.0 0.2 0.4 0.6 0.80.0
0.2
0.4
0.6
0.8
1.0
x
Γn!Γp
Constraints on Photon PDFs 1) Global fitting
a. Isospin violation effects - come from scattering off nuclei - perturbativity cuts on W2 generally require x < .2-.4 - constraints likely to be small (MRST)
b. Momentum sum rule - momentum carried by photon leaves less for other partons - constrains momentum fraction of photon (upper bound)
c. Otherwise, O(α) corrections to hadronic processes are small d. Global fit finds can be as large as ~ 5%, much more than CM choice
2) Direct photon PDF probe
- DIS with observed photon, - Photon-initated subprocess contributes at LO !
22
p0γ
ep→ eγ + X
Distributions 2) Lepton Variables Q2 and x
(Smooth Isolation, ) • Cannot fit shape for any choice of isolation, scale, or p0
γ. • Q2 and x distributions more sensitive to higher order corrections.
(Small Q2 and x, in particular will receive contributions from more radiation.)
• Additional cuts on ETγ and ηγ make Q2 and x distributions less inclusive.
23
µF = 0.5ETγ
p0γ = p0
γ (cm) = 0.29 % p0γ = 0.2 %
p0γ = 0.1 %
p0γ = 0.0 %
10 20 50 100 200
0.01
0.02
0.05
0.10
0.20
0.50
1.00
Q2
dΣ!dQ2 "
pb!GeV
2 #
2! 10"4 5! 10"4 0.001 0.002 0.005 0.010 0.020
100
200
500
1000
2000
5000
xdΣ!dx"pb
#
Kinematic Phase Space
• Dashed lines show kinematic bins • Red region allowed for “photon + lepton + 0 additional partons”
(LO photon-initiated kinematics) • Red plus Blue region allowed for “photon + lepton + anything” • Q2 and x distributions more affected by additional photon cuts. • Smallest x bin requires ≥1 extra parton to satisfy cuts.
Use only Etγ and ηγ distributions to constrain photon PDF 24
!0.5 0.0 0.5 1.0
4
6
8
10
12
14
ΗΓ
E TΓ
0.000 0.005 0.010 0.015 0.020 0.0250
50
100
150
200
250
300
350
x
Q2 !GeV
"2
4 GeV < ETγ < 15 GeV
-0.7 <ηγ < 0.9
E !ℓ > 10 GeV139.8° <θ !ℓ <171.8°10 GeV2 <Q2 < 350 GeV2
Photon Cuts
Lepton Cuts
Conclusions
16
• CT1X update in progress • New LHC data, New parametrizations, …
• Other CTEQ-TEA activities
• Benchmarking, MetaPDFs • Intrinsic Charm, Lagrange Multiplier uncertainties in Higgs, ttbar
(this afternoon)
• Photon PDF • Strong constraint from • for radiative photon ansatz.
• Consistent with NNPDF Drell-Yan analysis: Photon PDF smaller than expected?
ep→ eγ + X
p0γ ≤ 0.14% at 90 % C.L.