Parton Distributions Functions and Electroweak Physics James Stirling IPPP, University of Durham Precision predictions for  (W),  (Z) at hadron colliders QED-improved parton distributions Isospin violation and the NuTeV sin 2  W “anomaly” (with Alan Martin, Dick Roberts and Robert Thorne)

ICHEP042 the QCD factorization theorem for hard-scattering (short- distance) inclusive processes: where X=W, Z, H, high-E T jets, SUSY sparticles, … and Q is the ‘hard scale’ (e.g. = M X ), usually  F =  R = Q, and  is known to some fixed order in pQCD and pEW (or to all orders in some LL approximation) ^ ^  precision QCD at hadron colliders what limits the precision? the order of the perturbative expansion the uncertainty in the input parton distribution functions example LHC  σ pdf  ±3%,  σ pt  ± 2% →  σ theory  ± 4% whereas for gg→H :  σ pdf <<  σ pt

ICHEP043 longer Q 2 extrapolation smaller x

ICHEP044   forward W, Z, dijet… production at LHC samples small and high x but no acceptance, no triggers?!

ICHEP045 examples of ‘precision’ phenomenology W, Z productionjet production NNLO QCD NLO QCD

ICHEP046 σ(W) and σ(Z) : precision predictions and measurements at the Tevatron and LHC the pQCD series appears to be under control the EW corrections are known and can in principle be included (see below) with sufficient theoretical precision, these ‘standard candle’ processes can be used to measure machine luminosity  4% total error (MRST 2002)

ICHEP047 LHCσ NLO (W) (nb) MRST ± 6 (expt) CTEQ6205 ± 8 (expt) Alekhin02215 ± 6 (tot) similar partons different Δχ 2 different partons the rapidity distributions dσ/dy are also known to NNLO  matching to experimental acceptance however… Anastasiou et al. hep-ph/ hep-ph/

ICHEP048 Djouadi & Ferrag, hep-ph/ the differences between pdf sets needs to be better understood!

ICHEP049 why do ‘best fit’ pdfs and errors differ? different data sets in fit – different subselection of data – different treatment of exp. sys. errors different choice of – tolerance to define   f i (CTEQ: Δχ 2 =100, Alekhin: Δχ 2 =1) – factorisation/renormalisation scheme/scale – Q 0 2 – parametric form Ax a (1-x) b [..] etc – α S – treatment of heavy flavours – theoretical assumptions about x→0,1 behaviour – theoretical assumptions about sea flavour symmetry – evolution and cross section codes (removable differences!) → see ongoing HERA-LHC Workshop PDF Working Group

ICHEP0410 small MRST and CTEQ differences largely understood, see hep-ph/ mainly: CTEQ gluon at Q 0 2 required to be positive at small x means g CTEQ > g MRST there, also  2 = 50 (MRST), 100 (CTEQ) ALEKHIN gluon smaller at high x (no Tevatron jet data in fit) and different content of sea at small x from different assumptions about ubar-dbar as x  0 and (ii) ratio of strange to non-strange pdfs. Also  2 = 1 allowed by use of smaller overall data set.

ICHEP0411 ratio of W – and W + rapidity distributions x 1 =0.52 x 2 = x 1 =0.006 x 2 =0.006 ratio close to 1 because u  u etc. (note: MRST error = ±1½%) – sensitive to large-x d/u and small x u/d ratios Q. What is the experimental precision? –– d  (W - ) d(x 1 ) u(x 2 ) + u(x 1 ) d(x 2 ) + … = d  (W + ) u(x 1 ) d(x 2 ) + d(x 1 ) u(x 2 ) + … LHCW - /W + MRST CTEQ60.75 Alekhin020.74

ICHEP0412   bb  Z contribution to Z LHC Note: much smaller effect at Tevatron

QED effects in pdfs QED corrections to DIS include: included in standard radiative correction packages (HECTOR, HERACLES) Note: C int finite as m q  0 De Rujula, Petronzio, Savoy-Navarro 1979 Krifganz, Perlt 1988 Bluemlein 1990 Spiesberger 1994 Roth, Weinzierl 2004

ICHEP0414 above QED corrections are universal and can be absorbed into pdfs, exactly as for QCD singularities, leaving finite (as m q  0 ) O(α) QED corrections in coefficient functions relevant for electroweak correction calculations for processes at Tevatron & LHC, e.g. W, Z, WH, … (see e.g. U. Baur et al, PRD 59 (2003) )

ICHEP0415 QED-improved DGLAP equations at leading order in α and α S where momentum conservation:

ICHEP0416 effect on valence quark evolution: effect on quark distributions negligible at small x where gluon contribution dominates DGLAP evolution at large x, effect only becomes noticeable (order percent) at very large Q 2, where it is equivalent to a shift in α S of  α S  dynamic generation of photon parton distribution isospin violation: u p ( x) ≠ d n ( x) first consistent global pdf fit with QED corrections included (MRST 2004)

proton neutron  R - iso valence difference MRST 2004

ICHEP0418 first measurement of  p ( x, Q 2 ) ? e p ZEUS: “Observation of high E T photons in deep inelastic scattering”, hep-ex/  s = 318 GeV, Q 2 > 35 GeV 2, E e > 10 GeV o <  e < o 5 < E T  < 10 GeV, -0.7 <   < 0.9  (ep  e  X) = 5.64  0.58 (stat.)  (syst.) pb prediction using MRST2004 QEDpdfs:  (ep  e  X) = 6.2 pb

ICHEP0419 sin 2  W from N 3  difference

ICHEP0420 Conclusion: uncertainties in detailed parton structure are substantial on the scale of the precision of the NuTeV data – consistency with the Standard Model does not appear to be ruled out at present

ICHEP0421 summary more work needed to establish true theoretical error on the predictions for  (W),  (Z) at LHC: target is < 5% pdf sets with O (α) QED effects are now available and allow pEW corrections at hadron colliders to be consistently included details of hadron structure can effect NuTeV measurement of sin 2  W

extra slides

23 perturbative generation of s(x) ≠ s(x) P us (x) ≠ P us (x) at O(α S 3 ) Quantitative study by de Florian et al hep-ph/   x(s-s)  pQCD <   cf. from global pdf fit (Olness et al, hep-ph/ ,3)   <  x(s-s)  fit < partial explanation of NuTeV sin 2  W “anomaly”? note!

ICHEP0424 x dependence of f i (x,Q 2 ) determined by ‘global fit’ to deep inelastic scattering (H1, ZEUS, NMC, …) and hadron collider data F 2 (x,Q 2 ) =  q e q 2 x q(x,Q 2 ) etc DGLAP equations

ICHEP0425 pdfs from global fits Formalism NLO DGLAP MSbar factorisation Q 0 2 functional Q 0 2 sea quark (a)symmetry etc. Who? Alekhin, CTEQ, MRST, GKK, Botje, H1, ZEUS, GRV, BFP, … Data DIS (SLAC, BCDMS, NMC, E665, CCFR, H1, ZEUS, … ) Drell-Yan (E605, E772, E866, …) High E T jets (CDF, D0) W rapidity asymmetry (CDF) N dimuon (CCFR, NuTeV) etc. f i (x,Q 2 )   f i (x,Q 2 ) α S (M Z )

ICHEP0426 (MRST) parton distributions in the proton Martin, Roberts, S, Thorne

ICHEP0427 uncertainty in gluon distribution (CTEQ) then  f g →  σ gg→X etc.

ICHEP0428 solid = LHC dashed = Tevatron Alekhin 2002 pdf uncertainties encoded in parton-parton luminosity functions: with  = M 2 /s, so that for ab→X

ICHEP0429 Djouadi & Ferrag, hep-ph/ Higgs cross section: dependence on pdfs

ICHEP0430 Djouadi & Ferrag, hep-ph/

ICHEP0431 MRST: Q 0 2 = 1 GeV 2, Q cut 2 = 2 GeV 2 xg = Ax a (1–x) b (1+Cx 0.5 +Dx) – Ex c (1-x) d CTEQ6: Q 0 2 = 1.69 GeV 2, Q cut 2 = 4 GeV 2 xg = Ax a (1–x) b e cx (1+Cx) d

ICHEP0432 with dataset A in fit, Δχ 2 =1 ; with A and B in fit, Δχ 2 =? ‘tensions’ between data sets arise, for example, – between DIS data sets (e.g.  H and N data) – when jet and Drell-Yan data are combined with DIS data tensions within the global fit?

ICHEP0433 CTEQ α S (M Z ) values from global analysis with Δχ 2 = 1, 100

ICHEP0434 extrapolation errors theoretical insight/guess: f ~ A x as x → 0 theoretical insight/guess: f ~ ± A x –0.5 as x → 0

ICHEP0435 differences between the MRST and Alekhin u and d sea quarks near the starting scale ubar=dbar

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ICHEP0437 Note: high-x gluon should become better determined from Run 2 Tevatron data Q. by how much? Note: CTEQ gluon ‘more or less’ consistent with MRST gluon

ICHEP0438 comparison with existing approximate NNLO fits? (MRST, Alekhin) exact NNLO splitting functions are very close to approximate splitting functions (van Neerven, Vogt) based on moments & known small- and large-x behaviours… … and therefore the corresponding pdfs are almost identical Note: –the full NNLO pdf fit awaits calculation of the inclusive high E T jet cross section at NNLO –including NNLO (splitting & coefficient functions) gives a slight improvement in overall fit quality, and reduction in α S (M Z ) from to 0.116

ICHEP0439 ratio of MRST2001 NLO and ‘NNLO’ parton distributions

ICHEP0440 summary of NNLO collider calculations p + p → jet + X * ; in progress p + p → γ + X ; in principle, subset of the jet calculation but issues regarding photon fragmentation, isolation etc p + p → QQbar + X ; requires extension of above to non- zero fermion masses p + p → (γ*, W, Z) + X * ; van Neerven et al, Harlander and Kilgore corrected (2002) p + p → (γ*, W, Z) + X differential rapidity distribution * ; Anastasiou, Dixon, Melnikov (2003) p + p → H + X ; Harlander and Kilgore, Anastasiou and Melnikov (2002-3) Note: knowledge of processes * needed for a full NNLO global parton distribution fit

ICHEP0441 pdfs from global fits Formalism LO, NLO, NNLO DGLAP MSbar factorisation Q 0 2 functional Q 0 2 sea quark (a)symmetry etc. Who? Alekhin, CTEQ, MRST, GGK, Botje, H1, ZEUS, GRV, BFP, … Data DIS (SLAC, BCDMS, NMC, E665, CCFR, H1, ZEUS, … ) Drell-Yan (E605, E772, E866, …) High E T jets (CDF, D0) W rapidity asymmetry (CDF) N dimuon (CCFR, NuTeV) etc. f i (x,Q 2 )   f i (x,Q 2 ) α S (M Z )

ICHEP0442 summary of DIS data + neutrino FT DIS data Note: must impose cuts on DIS data to ensure validity of leading-twist DGLAP formalism in the global analysis, typically: Q 2 > GeV 2 W 2 = (1-x)/x Q 2 > GeV 2

ICHEP0443 typical data ingredients of a global pdf fit

ICHEP0444 recent global fit work H1, ZEUS: ongoing fits for pdfs + uncertainties from HERA and other DIS data Martin, Roberts, WJS, Thorne (MRST): updated `MRST2001' global fit (hep-ph/ ); LO/NLO/‘NNLO’ comparison (hep-ph/ ); pdf uncertainties: from experiment (hep-ph/ ) and theory (hep- ph/ ) Pumplin et al. (CTEQ): updated ‘CTEQ6’ global fit (hep-ph/ ), including uncertainties on pdfs; dedicated study of high E T jet cross sections for the Tevatron (hep-ph/ ); strangeness asymmetry from neutrino dimuon production (hep-ph/ ) Giele, Keller, Kosower (GKK): restricted global fit, focusing on data- driven pdf uncertainties (hep-ph/ ) Alekhin: restricted global fit (DIS data only), focusing on effect of both theoretical and experimental uncertainties on pdfs and higher-twist contributions (hep-ph/ ); updated and including ‘NNLO’ fit (hep-ph/ )

ICHEP0445 HEPDATA pdf server Comprehensive repository of past and present polarised and unpolarised pdf codes (with online plotting facility) can be found at the HEPDATA pdf server web site: … this is also the home of the LHAPDF project

ICHEP0446 pdfs with errors…. CTEQ gluon distribution uncertainty using Hessian Method output = best fit set + 2N p error sets “best fit” parameters Hessian Matrix

ICHEP0447 Djouadi & Ferrag, hep-ph/

ICHEP0448 Djouadi & Ferrag, hep-ph/

ICHEP0449 MRST: Q 0 2 = 1 GeV 2, Q cut 2 = 2 GeV 2 xg = Ax a (1–x) b (1+Cx 0.5 +Dx) – Ex c (1-x) d CTEQ6: Q 0 2 = 1.69 GeV 2, Q cut 2 = 4 GeV 2 xg = Ax a (1–x) b e cx (1+Cx) d

ICHEP0450 with dataset A in fit, Δχ 2 =1 ; with A and B in fit, Δχ 2 =? ‘tensions’ between data sets arise, for example, – between DIS data sets (e.g.  H and N data) – when jet and Drell-Yan data are combined with DIS data tensions within the global fit? pictures from W-K Tung

ICHEP0451 CTEQ α S (M Z ) values from global analysis with Δχ 2 = 1, 100

ICHEP0452 extrapolation errors theoretical insight/guess: f ~ A x as x → 0 theoretical insight/guess: f ~ ± A x –0.5 as x → 0

ICHEP0453 differences between the MRST and Alekhin u and d sea quarks near the starting scale ubar=dbar

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ICHEP0456 contours correspond to ‘ experimental’ pdf errors only; shift of prediction using CTEQ6 pdfs shows effect of ‘theoretical’ pdf errors ±2% ±3%

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ICHEP0459 as small x data are systematically removed from the MRST global fit, the quality of the fit improves until stability is reached at around x ~ (MRST hep-ph/ ) Q. Is fixed–order DGLAP insufficient for small-x DIS data?! Δ = improvement in χ 2 to remaining data / # of data points removed

ICHEP0460 the stability of the small-x fit can be recovered by adding to the fit empirical contributions of the form... with coefficients A, B found to be O(1) (and different for the NLO, NNLO fits); the starting gluon is still very negative at small x however

ICHEP0461 the ‘conservative’ pdfs (blue lines) do not describe the very low x DIS data not included in the fit MRST, hep-ph/

ICHEP0462 the change in the NLO and NNLO gluons when DIS data with x < are removed from the global fit MRST, hep-ph/

ICHEP0463 comparison of the standard MRST and ‘conservative’ NNLO pdfs MRST, hep-ph/ no data in fit

ICHEP0464

ICHEP0465 (LO) W cross sections at the Tevatron and LHC using (NLO) partons from MRST, CTEQ and Alekhin TevatronB.σ(W) (nb) MRST CTEQ62.10 Alekhin LHCB.σ(W + ) (nb)B.σ(W) (nb)W + /W – MRST CTEQ Alekhin

ICHEP0466 flavour decomposition of W cross sections at hadron colliders recall that the only constraint on very small x quarks from inclusive DIS (F 2 ep ) data is on the combination 4/9 [u+c+ubar+cbar] + 1/9 [d+s+dbar+sbar]

ICHEP0467 differences between the MRST, CTEQ and Alekhin strange quarks near the starting scale

ICHEP0468 NNLO precision phenomenology predictions calculated (MRST 2002) using ‘old’ approximate two- loop splitting functions width of shows uncertainty from P (2) (biggest at small x) this uncertainty now removed, NNLO prediction unchanged  4% total error (MRST 2002)