Parton Distributions at High Energy Colliders

Transcription

1 Parton Distributions at High Energy Colliders C.-P. Yuan Michigan State University In collaboration with CTEQ-TEA HEP June 6, 2014

2 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 Guzzi Michigan State Univ. Jon Pumplin, Dan Stump, Carl Schmidt, CPY

3 Parton Distribution Functions Needed for making theoretical calculations to compare with experimental data

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5 Deep Inelastic Scattering process

6 Drell Yan Process Naïve parton model QCD improved parton model Factorization Theorem

7 Parton Model h(p1) q W + σ hh W + X = h (P 2 ) X h(p 1 ) = p 1 = x 1 P 1 p 2 = x 2 P 2 q h (P 2 ) σ hh W + X = f,f =q, q 1 0 dx 1 dx 2 { φf/h (x 1 )ˆσ ff φ f /h (x 2)+(x 1 x 2 ) } Partonic Born Cross Section of ff W + The probablility of finding a parton f with fraction x 1 of the hadron h momentum

8 Factorization Theorem σ hh = i,j 1 0 dx 1 dx 2 φ i/h ( x, Q 2 ) H ij ( Q 2 x 1 x 2 S ) φ j/h ( x2,q 2) Nonperturbative, but universal, hence, measurable IRS, Calculable in pqcd Procedure: (1) Compute σ kl in pqcd with k, l partons (not h, h hadron) σ kl = i,j 1 ( dx ( 1dx 2 φ i/k x1,q 2) Q 2 H ij 0 x 1 x 2 S (2) Compute φ i/k,φ j/l in pqcd (3) Extract H ij in pqcd ) φ j/l ( x2,q 2) H ij IRS H ij indepent of k, l same H ij with ( k h, l h ) (4) Use H ij in the above equation with φ i/h,φ j/h

9 Extracting H ij in pqcd Expansions in α s : σ kl = H ij = n=0 n=0 ( αs π ( αs π ) n σ (n) kl ) n H (n) ij φ i/k (x) = δ ik δ (1 x) + n=1 ( αs π ) n φ (n) i/k α s = g2 4π φ (0) i/k (α s =0 Parton k stays itself ) Consequences: H (0) = ff (0) ij ij = Born" suppress "^" from now on H (1) ij = ff (1) ij " ff (0) il ffi (1) l=j + ffi(1) ff(0) k=i kj # Computed from Feynman diagrams process dependent ( ) Computed from the definition of perturbative parton distribution function ( process independent, scheme dependent )

10 NuTev

11 Experimental input (continued) ( ) (DIS jets, heavy quark prod. )

12 Some basics about PDFs Parton Distribution Function f( x,q) Given a heavy resonance with mass Q produced at hadron collider with c.m. energy S What s the typical x value? x Generally, Q S at central rapidity (y=0) Q y Q x1 e and x2 e S S Q x1 x2 2 cosh(y) 1 2 S y x x y : 1 max

13 Kinematics of a 100 TeV SppC J. Rojo: kickoff meeting for FCC at CERN, Feb. 2014

14 Kinematics of Parton variables Predictive power of global analysis of PDFs is based on the renormalization group properties of the universal Parton Distributions f(x,q). QCD (DGLAP) evolution

15 On to a 100 TeV SppC will access smaller x, larger Q 2 currently have no constraints on PDFs for x values below 1E-4 we don t know where at low x, BFKL effects start to become important poor constraints (still) as well for high x PDFs at high masses (Q 2 ), rely on DLAP evolution; we know at large Q 2, EW effects also become important

16 CT10 PDFs NLO NNLO

17 CT10 PDF sets: the naming conventions Two NLO PDF sets, without/with Tevatron Run-2 data on W charge asymmetry A l CT10 NLO does not include CT10W NLO includes 4 p T l bins of D0 Run-2 A l data CT10 and CT10W sets differ mainly in the behavior of d(x, Q)/u(x, Q) at x > 0.1 One NNLO PDF set: only inclusive p T l bins of D0 Run-2 A l (e and µ) data are included that have smallest theory uncertainties The NNLO set is a counterpart of both CT10 NLO and CT10W NLO. It uses only a part of the A l data sample that distinguishes between CT10 NLO and CT10W NLO. C.-P. Yuan (MSU) SUSY 2012, Beijing, China 08/14/2012 6

18 CT10NNLO vs. fitted data F 2 cc (x,q) * i Q 2 = 60 GeV 2 CT10 NNLO CT10 NLO H1 data 2011 Q 2 = 35 GeV 2 Q 2 = 18 GeV 2 Q 2 = 12 GeV 2 i=4 i=3 i=2 0.5 Q 2 = 6.5 GeV 2 i= x i=0 Fits well: 2 N pt

19 CT10 NNLO error PDFs (compared to CT10W NLO) Ratio to reference fit CT10W NLO g(x,q) Q = 2 GeV CT10W NLO CT10 NNLO (prel.)/ct10w NLO x Ratio to reference fit CT10W NLO Ratio to reference fit CT10W NLO u(x,q) Q = 2 GeV CT10W NLO CT10 NNLO (prel.)/ct10w NLO x ub(x,q) Q = 2 GeV CT10W NLO CT10 NNLO (prel.)/ct10w NLO x C.-P. Yuan (MSU) SUSY 2012, Beijing, China 08/14/2012 5

20 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 m q 0), QCD contributions are known only to NLO. (NLO EW contributions, power corrections, other systematic errors may be comparable to NNLO QCD effects.) CT10 NNLO PDFs underwent validation studies for about one year. We identified several types of uncertainties that compete with NNLO QCD contributions. CT10 NNLO and NLO PDFs produce about the same χ 2 /N pt for N pt 2700 data points Shapes of the NNLO PDFs have noticeably evolved compared to NLO as a result of O(α 2 s) contributions, updated electroweak contributions, revised statistical procedures C.-P. Yuan (MSU) SUSY 2012, Beijing, China 08/14/2012 7

21 CT10 NNLO central PDFs, as ratios to NLO, Q=2 GeV (x,q) NLO a (x,q)/f NNLO f a Ratios of CT10 NNLO and CT10W NLO PDFs, Q=2 GeV PRELIMINARY 2 g u u d d s c x 1. At x < 10 2, O(α 2 s) evolution suppresses g(x, Q), increases q(x, Q) 2. c(x, Q) and b(x, Q) change as a result of the O(α 2 s) GM VFN scheme 3. In large x region, g(x, Q) and d(x, Q) are reduced by not including Run-1 inclusive jet data, revised EW couplings, alternative treatment of correlated systematic errors, scale choices. C.-P. Yuan (MSU) SUSY 2012, Beijing, China 08/14/2012 8

22 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.)

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24 u d 7 th CT10 Eigenset s ubar

25 dbar Gluon 7 th CT10 Eigenset d/u dbar/ubar

26 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 F L and F 2 c 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.

27 -1 CMS, L = 4.7 fb at s = 7 TeV Charge asymmetry (b) p T > 35 GeV Data Data is already more precise than current PDF uncertainty. Will help to determine PDFs in small x region. 0.1 NLO FEWZ + NLO PDF, 68% CL CT10 NNPDF23 HERAPDF15 MSTW2008 MSTW2008CPdeut Muon Most useful for determining dbar/ubar. 10

28 Uncertainties on H and ttbar Predictions at the LHC (and update on Intrinsic Charm) Carl Schmidt Michigan State University On behalf of CTEQ-TEA group April 29, 2014 DIS2014, Warsaw, Poland 1

29 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, (2014) 3) Lagrange Multiplier (LM) Uncertainty Analysis on gg->h Dulat et al, arxiv: [hep-ph] 4) Uncertainty Analysis on gg->ttbar 2

30 Intrinsic Charm and CT10IC 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: m c (m c ) = GeV Gao et al, Eur.Phys.J. C73 (2013) 2541 Use m c (pole)=1.3 GeV for this study - some correlation between m c and IC 3) Two model Intrinsic Charm distributions at Q c =1.3 GeV - BHPS valence-like model (Brodsky et al, Phys. Lett. 93B, 451 (1980)) SEA-like model 1 x IC = x c(x,q c )+ c(x,q c ) 0 [ ] dx 3120 BHPS SEA BHPS + T2 SEA + T2 4) 90% CL limits: x IC x IC BHPS SEA 2 F SEA2 BHPS2 SEA BHPS <x> IC 3

31 Intrinsic Charm at LHC c(x) /c(x) Σ p T,Z pb GeV, LHC 14TeV CT10 BHPS1 BHPS2 SEA1 SEA2 IC vs CT10 charm PDF SEA1/BHPS1: x IC = 0.57% SEA2: x IC =1.5% BHPS2: x IC = 2.0% x CT10 PDF unc. Ratios to CT p T,Z GeV pp Zc at LHC may further constrain valence-like model 4

32 CT10 IC at LHC Z ll nb LHC 14 TeV CT10 BHPS1 BHPS2 SEA1 SEA2 top quark pair pb LHC 14 TeV CT10 BHPS1 BHPS2 SEA1 SEA W lν nb Z ll nb W, Z and top production at LHC CT10 IC distributions publicly available 5

33 PDF uncertainties in gg H 1) Most analyses use Hessian Method (n error PDF sets) ( δx) 2 = 1 4 n k=1 ( X(a + k ) X(a k )) 2 - Error sets can be used by anyone for any observable - Assume quadratic and linear dependence of χ 2, X on a k 2) Lagrange Multiplier (LM) method is more robust - Find best fit for each constrained value of observable X - No assumptions on dependence of χ 2, X on a k - Can validate Hessian method - Can display correlations between PDFs and Observable - Must calculate separately for each observable 6

34 Uncertainties in gg H TeV 90% C.L TeV 90% C.L TeV 90% C.L Tier-2 68% C.L H (pb) Tier-2 68% C.L H (pb) Tier-2 68% C.L H (pb) Curves are LM, circles/squares are Hessian Red use χ 2 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

35 Combined PDF+α S Uncertainties Χ 2 T 2 7 TeV Χ 2 T 2 8 TeV T 2 14 TeV Χ Ft ΣH 13.5 ΣH 17.0 ΣH Α S Α S Α S Can include α S uncertainty as contribution to total χ 2 in LM method Use PDF4LHC choice of α S =0.118±0.002 at 90% CL Black curves are 68% and 90% CL contours Hessian method adds α S 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

36 CT10H Extreme Sets T 2 14 TeV Χ Ft ΣH Α S 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+α S uncertainty Useful for efficient gg H analyses 9

37 Sensitivity to Data Sets S LHC (7 TeV) CDF-jet CCFR-dimuon HERA-1 D0-jet ATLAS-WZ S LHC (8 TeV) CDF-jet CCFR-dimuon HERA-1 D0-jet ATLAS-WZ S LHC (14 TeV) CDF-jet HERA-1 CCFR-dimuon D0-jet ATLAS-WZ H (pb) ATLAS-jet -2 ATLAS-jet H (pb) -2-3 ATLAS-jet H (pb) How sensitive are included data sets to value of H? Effective Gaussian Variable S maps cumulative 2 distribution for N pt 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 p T jet, inclusive HERA, CCFR-dimuon HERA more strongly correlated with 14 TeV smaller x CCFR dimuon correlation due to gluon-strange interdependence 10

38 Uncertainties in gg ttbar % 2 2 +T2 68% 0% 68% 90% 2 = = ttbar TeV (102 pb) Same analyses applied to gg ttbar HERA combined data (T2) constrains low values of cross section But T2 less important for combined PDF+α S Hessian and LM consistent 2 +T TeV ttb (102 pb) s CT10 NNLO Hessian PDF Hessian PDF+ s LM PDF LM PDF+ s s =0.116 s =0.118 s = m T (GeV) 7 TeV ttb (102 pb) 11

39 CT10tt extreme sets m t 173 GeV, LHC 7 TeV, CTXX NNLO extreme eigen.sets dσ dp t T pb GeV DiffTop approx NNLO Small dashed band LM method, PDF Αs dashed band CT10NNLO, PDF only dotdashed CT10NNLO center p t T GeV Pairs of CT10tt extreme sets (PDF, PDF+α S ) to be released - for focused ttbar analyses Results provided by DiffTop group (M. Guzzi, K. Lipka, S. Moch) 12

40 CT10tt extreme sets LHC 7 TeV, m t 173 GeV central, CT10NNLO 68 CL CMS data DiffTop mt variation Αs Mz unc. PDF unc. scale unc LHC 7 TeV, m t 173 GeV central, CT10NNLO 68 CL ATLAS data DiffTop mt variation Αs Mz unc. PDF unc. scale unc. data theory data theory P t T GeV P t T GeV CMS data DiffTop LHC 7 TeV, m t 173 GeV central, CTXXextremeeigen.sets PDF Αs unc. 68 CL ATLAS data DiffTop LHC 7 TeV, m t 173 GeV central, CTXXextremeeigen.sets PDF Αs unc. 68 CL data theory data theory P t T GeV P t T GeV 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 p T ) Results provided by DiffTop group (M. Guzzi, K. Lipka, S. Moch) 13

41 Intrinsic Charm Conclusions 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

42 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.

43 Momentum fraction inside proton G t t Solid curves: CT10 NNLO Dashed curves: CT10Top NNLO

44 CT10Top PDFs (Q=2 TeV) t b Top PDF is only a factor of 2 smaller than b PDF

45 CT10Top PDFs (Q=20 TeV)

46 CT10Top PDFs G

47 CT10Top PDFs

48 PDF luminosities dx1dx2 g( x1, M) g( x2, M) ( M) d dy g( x, M) g( x, M) ( M) dm dl dm ( M ) PDF Luminosity y 1 xx 1 2 x 1 ln 2 x2

49 Hard part calculation S ACOT scheme Example: single top production

50 CT10 NNLO update and QED effects in PDFs Carl Schmidt Michigan State University On behalf of CTEQ-TEA group April 29, 2014 DIS2014, Warsaw, Poland 1

51 Motivation 1) Sensitivity to NNLO QCD is at few % level. - QED and Electroweak corrections are now significant. - E.g, QED corrections to pp W + X require order α effects in parton evolution 2) Photon induced processes can be kinematically enhanced. γγ W + W asymptotically ˆ γ γ W + W dσ/dm WW (pb/gev) 1 σ γγ 8πα 2 M W 2 LHC at 14 TeV 3) Last considered in 2004 (MRST) Martin et al., EPJC 39 (2005) Time for more detailed study σ q q LO σ γγ LO σ gg LO M WW (GeV) Bierweiler et al., JHEP 1211 (2012) 093 This talk is an update of CTEQ-TEA activities on this topic. 18

52 Photon PDFs (in proton) 10 1 g 10 1 g xf x,q γ CM c s d u d u xf x,q γ CM γ 0 b c s d u d u γ Q = 3.2 GeV 10 3 Q = 85 GeV γ momentum fraction: p γ (Q) γ ( x,q 0 ) = 0 γ ( x,q 0 ) CM Q = 3.2 GeV 0.05% 0.34% Q = 85 GeV 0.22% 0.51% x Photon PDF can be larger than sea quarks at large x! Initial Photon PDF still significant at large Q. x 8

53 Photon PDF Parametrization Radiative ansatz for initial Photon PDFs (generalization of MRST choice) γ p = α 2π A e 2 u u Pγq u 0 2 ( + A d e dpγq d 0 ) γ n = α 2π A e 2 u u Pγq d 0 2 ( + A d e dpγq u 0 ) where u 0 and d 0 are primordial valence-type distributions of the proton. Assumed approximate isospin symmetry for neutron. Here, we take A u and A d as unknown fit parameters. MRST choice: A q = ln Q ( m q ) Radiation from Current Mass CM We use u 0 = u p u p (x,q 0 ), d 0 = d p d p (x,q 0 ) and reduce the number of parameters further (for initial study) by setting A u = A d = A 0 u 0, d 0 Now everything effectively specified by one unknown parameter: A 0 p 0 γ p γ /P (Q 0 ) (Initial Photon momentum fraction) 7

54 Constraining Photon PDFs 1) Global fitting Isospin violation, momentum sum rule lead to constraints in fit γ We find p 0 can be as large as ~ 5% at 90%CL, much more than CM choice 2) Direct photon PDF probe - DIS with observed photon, ep eγ + X - 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

55 ep eγ + X Subprocess contributions: LL Emission off Lepton line Both quark-initiated and photon-initiated contributions are ~ α 3 if γ(x) ~ α Collinear divergence cancels (in d=4-2ε) by treating as NLO in α with ( ) ε γ bare (x) = γ(x)+ 4π 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, (2006) photon initiated only (MRST), Martin, Roberts, Stirling, Thorne, Eur. Phys. J. C 39, 155 (2005) 10 ε Γ(1+ε) α ( 2π P q γq )(x) (MSbar) e e γ

56 Zeus Experimental Cuts Photon Cuts Lepton Cuts Photon Isolation Cut 4 GeV < E T γ < 15 GeV -0.7 < η γ < 0.9 Also require N 1 forward jet E l! > 10 GeV <θ l! < GeV 2 < Q 2 < 350 GeV 2 Two theoretical approximations to photon isolation implemented: Photon must contain 90% of energy in jet to which it belongs. 1) Smooth isolation (Frixione): E! - Removes fragmentation contribution q < 1 E # 1 cosr & 9 γ % ( for r = Δη 2 2 q! γ + Δϕ! $ 1 cos R ' q γ < R =1 2) Sharp isolation: E q! < 1 E 9 γ for r < R =1 - Requires fragmentation contribution (Use Aleph LO parametrization) 11

57 1) Factorization Scale Theoretical Uncertainties dsêde T g HpbêGeVL dsêdh g HpbL Total QQ LL γ-initiated E T g HGeVL h g ( p γ 0 = 0, Smooth Isolation, 0.5E γ γ T < µ F < 2E T ) Scale dependence of LL contribution reduced drastically compared to photon-initiated alone QQ and LL have different-shaped distributions. LL dominates at large E T γ and small η γ. Can be used to extract photon PDF Scale dependence of QQ and total is still large (LO in α S ) 12

58 Theoretical Uncertainties 2) Isolation Prescription Smooth Sharp dsêde T g HpbêGeVL dsêdh g HpbL E T g HGeVL h g ( p γ 0 = 0, 0.5E Tγ < µ F < 2E Tγ ) 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

59 1) Photon Variables E T γ and η γ Distributions dσ de T Γ pb GeV dσ dη Γ pb p 0 γ = p 0 γ (cm) = 0.29 % p 0 γ = 0.2 % p 0 γ = 0.1 % p 0 γ = 0.0 % E T Γ GeV γ (Smooth Isolation, µ F = 0.5E T ) Best fit for p 0 γ is correlated with choice of isolation and factorization scale µ F. Can obtain excellent fit to shape of distributions for reasonable scale choices. Current Mass ansatz cannot fit shape (prediction too large at large E T γ and small η γ where LL dominates), regardless of scale choice. Η Γ 14

60 Limits on Photon PDF Χ 2 for Npt E T γ E T γ 0.5E T γ 0.35E T γ Χ 2 for Npt E T γ E T γ 0.5E T γ p 0 Γ Smooth Isolation p 0 Γ Sharp Isolation Different χ 2 curves for choice of isolation and scale µ F 90% C.L. for N pt = 8 corresponds to χ 2 = Obtain p γ % at 90 % C.L. independent of isolation prescription (More generally, constrains γ(x) for 10-3 < x < 2x10-2.) Current Mass ansatz has χ 2 > 45 for any choice of isolation and scale 15

61 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 parton of proton, consistent hard part calculations are needed.

62 Backup Slides 17

63 Inclusion of Photon PDFs LO QED + (NLO or NNLO) QCD evolution: dq dt = α s ( 2π P qq q + P qg g) + α 2π e 2 2 q P qq q + e q P qγ γ dg dt = α s ( 2π P gg g + P gq ( q + q) ) dγ dt = α ( P γγ γ + P γq e 2 q ( q + q) ) 2π ( ) Radiative ansatz for initial Photon PDFs (generalization of MRST choice) γ p = α 2π A 2 ue upγq u 0 2 ( + A d e dpγq d 0 ) γ n = α 2π A e 2 u u Pγq d 0 2 ( + A d e dpγq u 0 ) where u 0 and d 0 are primordial valence-type distributions of the proton. Assumed approximate isospin symmetry for neutron. Here, we take A u and A d as unknown fit parameters. ( ) u 0, d 0 t = lnq MRST choice: A q = ln Q 0 m q Radiation from Current Mass - CM 19

64 Inclusion of Photon PDFs (2) Isospin violation occurs radiatively in u and d. To this order in α: u 0, d 0 u n = d p + α 2π A e 2 2 u u A d e d ( ) P qq d 0, d n = u p + α 2π A e 2 2 ( d d A u e u ) P qq u 0 Isospin violation in initial sea and gluon assumed negligible. ( q n = q p, g n = g p ) With this ansatz, number and momentum sum rules automatically satisfied for neutron, for any choice of u 0 and d 0. i.e., p i/p =1 p i/n =1, where p i/h 1 = x f i/h (x) dx 0 Here, assume u 0 = u p u p (x,q 0 ), d 0 = d p d p (x,q 0 ) Also, let A u = A 0 ( 1+δ), A d = A 0 1 δ Expect δ to be small. ( ) Now everything effectively specified by one unknown parameter: A 0 p 0 γ p γ /P (Q 0 ) (Initial Photon momentum fraction) 20

65 Isospin violation d n /u p d n /u p q n q p 1.00 q n q p u n /d p x u n /d p x 1.0 Q=Q 0 =1.3 GeV Q=3.2 GeV Q=85 GeV Γ n Γ p Γ n Γ p γ n /γ p 0.2 γ n /γ p γ ( x,q 0 ) = 0 x x 2 γ ( x,q 0 ) CM 21

66 Constraints on Photon PDFs 1) Global fitting a. Isospin violation effects - come from scattering off nuclei - perturbativity cuts on W 2 generally require x < 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 γ d. Global fit finds p 0 can be as large as ~ 5%, much more than CM choice 2) Direct photon PDF probe - DIS with observed photon, ep eγ + X - Photon-initated subprocess contributes at LO! 22

67 2) Lepton Variables Q 2 and x Distributions dσ dq 2 pb GeV dσ dx pb p 0 γ = p 0 γ (cm) = 0.29 % p 0 γ = 0.2 % p 0 γ = 0.1 % p 0 γ = 0.0 % Q 2 γ (Smooth Isolation, µ F = 0.5E T ) Cannot fit shape for any choice of isolation, scale, or p 0γ. Q 2 and x distributions more sensitive to higher order corrections. (Small Q 2 and x, in particular will receive contributions from more radiation.) Additional cuts on E T γ and η γ make Q 2 and x distributions less inclusive. x 23

68 ETΓ Kinematic Phase Space Η Γ Q 2 GeV GeV 2 < Q 2 < 350 GeV 2 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 Q 2 and x distributions more affected by additional photon cuts. Smallest x bin requires 1 extra parton to satisfy cuts. x Photon Cuts 4 GeV < E T γ < 15 GeV -0.7 < η γ < 0.9 Lepton Cuts E l! > 10 GeV <θ l! <171.8 Use only E t γ and η γ distributions to constrain photon PDF 24

69 Conclusions 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 ep eγ + X p γ % at 90 % C.L. for radiative photon ansatz. Consistent with NNPDF Drell-Yan analysis: Photon PDF smaller than expected? 16