parton distributions at high energy...

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:

��

��

��

��

��

��

��

��

�

��

��

suppress "^" from now on

process dependent

process independent, scheme dependent

� �

��

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

1.6

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


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



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


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.


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.

parton distributions at high energy...

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