Outline: Introduction Quantum ChromoDynamics (QCD) Jet algorithms Tests of QCD QCD analyses at HERA extraction of the proton PDFs

Transcription

1 Outline: Introduction Quantum ChromoDynamics (QCD) Jet algorithms Tests of QCD QCD analyses at HERA etraction of the proton PDFs

2 Etraction of the proton PDFs Etraction Etractionof of the proton protonpdfs PDFs

3 QCD analyses 3 NC DIS processes are a testing ground of pqcd and allow a direct determination of α s and the ppdfs To do a QCD analysis: The PDFs depend on α s need to assume a value of α s (M Z ) the quark densities can be determined from fits to inclusive DIS data the gluon density can be determined from scaling violations in inclusive DIS cross sections testing of the resulting parametrisations of the PDFs can be performed with jet production cross sections Etraction of α s depends on the PDFs need to assume PDFs and determination should be made from ervables that have a small dependence on the PDFs (eg ratios of ervables) For a precise measurements of α s need small eperimental uncertainties (eg ratios) and small theoretical uncertainties (need NLO calculations) jet production in NC DIS particularly suited for precise determination of α s... or perform a simultaneous determination of α s and the PDFs

4 NLO QCD fit to determine the proton PDFs 3 NLO DGLAP equations were used to fit simultaneously the high-precision data on NC e + p DIS and fied target data at larger to obtain the ppdfs Fied-target data were used to gain information on the valence distributions and the flavour composition of the sea, and to constrain the fit at high (BCDMS, NMC, E665, CCFR) The precision data provide information on the gluon and quark densities at low The kinematic range covered by the data input to the fits is and.5 Q 3 GeV The fits have been performed within the framework of the NLO DGLAP evolution equations These equations yield the quark and gluon momentum distributions at all values of Q provided they are input as functions of at some scale Q : the input scale was chosen to be Q = 7 GeV

5 NLO QCD fit to determine the proton PDFs 3 The PDFs were parametrised at Q = 7 GeV by the form p p ( ) p 3( + p 4 + p5 ) so that the distributions are either or singular as, and tend to as The parton momentum distributions that were parametrised are: u valence: u v (u ū); d valence: d v (d d) total sea: S ( d + ū + s + c); gluon: g difference between d and u sea contributions: ( d ū) Impose number and momentum sum rules: (g + Σ) d = ; d v d = ; u v d = (Σ = S + u v + d v ) Some parameters were fied, so that there are free parameters in the fit when α s is fied to α s (M Z ) =.8 (current world average) The DGLAP evolution equations were written in terms of quark-flavour singlet and non-singlet distributions and the gluon distribution The definition of the χ was: χ = [F i (p, s) Fi meas ] (σ i i,stat + σ i,unc ) + s j j where F i (p, s) = Fi NLO (p) + j s j syst ij

6 Results of the NLO QCD fit 33 Q =.7 GeV 3.5 GeV 4.5 GeV 6.5 GeV 8.5 GeV GeV GeV 5 GeV em F -log () 5 =6.3E-5 =. =.6 =.53 =.4 =.5 =.63 =.8 =.3 NLO QCD fit tot. error 96/97 BCDMS 4 =. =.3 E665 NMC em F 8 GeV GeV 7 GeV 35 GeV 3 =.5 =.8 =.3 =. 45 GeV 6 GeV 7 GeV 9 GeV =.3 =.5 =.8 GeV 5 GeV =.3 =.8 =.5 NLO QCD fit tot. error 96/97 BCDMS E665 NMC =.4 = Q (GeV ) The fit gives an ecellent description of the high-precision and fied-target data

7 Results of the NLO QCD fit 34 Comparison of the high-q NC and CC e + p and e p data (not included in the fit) and the fit to low-q NC e + p data.5.5 Q = GeV 5 GeV 35 GeV 45 GeV GeV 8 GeV GeV 5 GeV Q =8 GeV 53 GeV 95 GeV 7 GeV NLO QCD fit tot. error 3 GeV 53 GeV σ NC.8 GeV 3 GeV 5 GeV 8 GeV σ CC GeV GeV 3 GeV - NLO QCD fit tot. error GeV 7 GeV 3 GeV CC e - p 98/99 CC e + p NC e - p 98/99 NC e + p 96/ These high-q data are very well described by the fit - - -

8 Results of the NLO QCD fit 35 Parton distribution functions at Q = GeV using the PDF parameters etracted from the fit to and fied-target data Very good precision: total uncertainties dominated by systematics f S(.5) NLO QCD fit CTEQ 6M MRST g(.5) Q = GeV d v u v - - f (a) S(.5) NLO QCD fit α s (M Z ) =.8 tot. error uncorr. error g(.5) Q = GeV d v u v - - Etracted PDFs compared to the latest distributions from MRST and CTEQ analyses The differences between these sets of PDFs are compatible with the size of the uncertainties on the PDFs

9 Results of the NLO QCD fit 36 Valence distributions u v and d v etracted from the fit as a function of for different Q values The high- behaviour of these distributions is constrained by the fied-target data u V Q = GeV u valence GeV NLO QCD fit d V Q = GeV d valence GeV NLO QCD fit GeV tot. error (α s free) GeV tot. error (α s fied) uncorr. error (α s fied) GeV tot. error (α s free) GeV tot. error (α s fied) uncorr. error (α s fied) The u-valence distribution is much better determined than the d-valence since structure-function data from the fied-target eperiments are dominated by the u quark

10 Results of the NLO QCD fit 37 Etracted sea and gluon distributions as a function of for different Q values The uncertainty in the sea distribution is less than 5% for Q.5 GeV and 4 < < The gluon distribution is determined to within % for Q > 5 GeV and 4 < < The sea distribution rises at small The distribution rises steeply at low for Q 5 GeV but at lower Q the low- gluon shape is flatter Comparison of the shapes of the gluon and the sea distributions: for Q 5 GeV, the gluon becomes much larger than the sea, but for lower Q the sea continues to rise at low, whereas the gluon is suppressed f 6 Q = GeV 4-3 S S S NLO QCD fit g 7 GeV tot. error (α s free) g GeV g S S.5 GeV GeV tot. error (α s fied) g uncorr. error (α s fied) S g GeV g

11 Results of the NLO QCD fit 38 g (a) Etracted gluon distribution as a function of Q for different values of =. =. The scaling violations of the gluon distribution at small are clearly seen reflection of the singular behaviour of the P gq and P gg splitting functions as 5 NLO QCD fit tot. error (α s -free) tot. error (α s -fied) The tendency of the gluon distribution to become negative at low and low Q indicates that pqcd could be inadequate to describe this regime scale too low for perturbation theory =. 5 =. 3 4 Q (GeV )

12 New determination of the proton PDFs 39 Conventional ervables used in the fits to determine the ppdfs: inclusive measurements of deep inelastic ln scattering Advantages: inclusive (only final-state lepton is tagged) no QCD corrections associated to the final-state signature (lepton!) no hadronisation corrections associated to the final-state signature (lepton!) Disadvantages: the gluon distribution contributes indirectly through higher-order terms Observables based on jets have hardly been used (ecept jet production in p p at TeVatron by CTEQ) large QCD corrections and hadronisation corrections That s the past! NOW there are measurements of jet cross sections at HERA: in good agreement with pqcd predictions directly sensitive to the gluon density in the proton small eperimental and theoretical uncertainties

13 Determination of PDFs using structure function and jet data 3 σ ~ NC Q =.7 GeV 8.5 GeV 8 GeV 45 GeV GeV 3.5 GeV GeV GeV 6 GeV 5 GeV GeV GeV 7 GeV 7 GeV -JETS tot. uncert. 6.5 GeV 5 GeV 35 GeV 9 GeV NC e p low-q NC DIS high-q NC DIS σ ~ NC Q = GeV - 65 GeV GeV GeV GeV 8 GeV 3 GeV GeV GeV GeV 5 GeV 3 GeV GeV 5 GeV 8 GeV - -JETS tot. uncert. + NC e p NC e p NC e p σ ~ CC Q = 8 GeV 7 GeV 95 GeV - 53 GeV 3 GeV 7 GeV - 95 GeV -JETS tot. uncert. 53 GeV 3 GeV + CC e p CC e p CC e p high-q CC DIS Determination of the ppdfs using inclusive measurements of NC and CC DIS e ± p in a large level arm of and Q < <.65,.7 < Q < 3 GeV and measurements of jet cross sections in NC DIS and γp collisions from only (pb/gev) B dσ/de T,jet (pb/gev) jet dσ/de T Jets NC DIS -JETS tot. uncert. incl. jet DIS Jet energy scale uncert. 5 < Q < 5 GeV 5 ( ) 5 < Q < 5 GeV 4 ( ) 5 < Q < GeV 3 ( ) < Q < GeV ( ) < Q < 5 GeV ( ) Q > 5 GeV ( ) γ >.75 -JETS Jets γp jet <η <.4 jet -< η < ( ) jet <η < -< η jet < (.5) tot. uncert. B E T,jet -< η jet, < (.) Sufficient sensitivity to determine the ppdfs within a single eperiment! (GeV) dijet γp Jet energy scale uncert. jet <η <.4 jet < η < ( ) jet, < η < (.) jet, < η <.4 ( ) jet E T (GeV)

14 Inclusive jet cross sections in NC DIS at Q > 5 GeV 3 Measurement of inclusive jet cross sections in the kinematic region defined by Q > 5 GeV and.7 < cos γ <.5 for jets with E jet T,B > 8 GeV and < ηjet B <.8 Jets identified using the longitudinally invariant k T cluster algorithm in the Breit frame Small eperimental uncertainties: jet energy scale (±% for E jet T ±5% on the cross sections > GeV) Small parton-to-hadron corrections: < 5% for Q > 5 GeV (ecept for lowest-e jet T,B point) Very good agreement with NLO QCD (O(α s )) calculations (DISENT) Small theoretical uncertainties: higher-order terms: ±5% hadronisation: < % Inclusive jet cross sections in NC DIS Breit frame provide direct sensitivity to the gluon density in the proton with small eperimental and theoretical uncertainties dσ/de B T,jet (pb/gev) Jet energy scale uncertainty NLO QCD: (corrected to hadron level) α s (M Z )=.75 DISENT MRST99 (µ R =E B T,jet ) DISENT MRST99 (µ R =Q) 5 < Q < 5 GeV ( 5 ) 5 < Q < 5 GeV ( 4 ) 5 < Q < GeV ( 3 ) < Q < GeV ( ) < Q < 5 GeV ( ) Q > 5 GeV ( ) E B T,jet (GeV)

15 Dijet photoproduction 3 Measurements of dijet photoproduction provide direct sensitivity to α s and gluon density in proton However, resolved processes are also sensitive to both the quark and gluon densities in the photon Photon structure: information on quark densities from F γ in e+ e : gluon density poorly constrained! To suppress the dependence on the γpdfs: measurements restricted to the region where direct processes dominate Observable to separate the contributions from resolved and direct processes: the fraction of the photon s energy participating in the production of the dijet system γ = E jet i E T e ηjet i γ i= Direct-process-enriched region: γ >.75 F γ (Q,udsc) / α OPAL (. < <.6) AMY (.3 < <.8) JADE (. < <.) DELPHI prl. (.3 < <.8) TPC (.3 < <.6) TOPAZ (.3 < <.8) ALEPH (. < <.6) L3 prl. (.3 < <.8) PLUTO (.3 < <.8) TASSO (. < <.8).5.5 GRV LO (. < <.9) GRV LO (.3 < <.8) GRV LO (. < <.6) SaSD (. < <.6) HO (. < <.6) ASYM (. < <.6) Q [GeV ]

16 Dijet photoproduction cross sections for γ >.75 Measurement of dσ/de jet, T for dijet events with E jet,() T >4() GeV, <η jet <.4 and γ >.75 in the kinematic region Q < GeV and 34<W γp < 77 GeV Jets identified using the longitudinally invariant k T cluster algorithm in the laboratory frame Small eperimental uncertainties: jet energy scale (±% for E jet T ±5% on the cross sections > GeV) Small parton-to-hadron corrections: < % (ecept at the edges of phase space) Very good agreement with NLO QCD (O(α s )) calculations (Friione & Ridolfi) Small theoretical uncertainties: higher-order terms: ±% hadronisation: 3% Dijet cross sections in photoproduction provide direct sensitivity to the gluon density in the proton with small eperimental and theoretical uncertainties dσ/de T jet (pb/gev) < η jet < - < η jet < (.5) - < η jet, < (.) γ > NLO (GRV) HAD NLO (AFG) HAD Jet energy scale uncertainty < η jet <.4 - < η jet < ( ) < η jet, < (.) < η jet <.4 < η jet < ( ) < η jet, <.4 ( ) jet E T (GeV)

17 Determination of the proton PDFs 34 Parametrization of the proton PDFs: u valence (u V ), d valence (d V ), gluon (g), total sea (S) and = ( d ū) at Q = 7 GeV by the functional form: f() = p p ( ) p 3( + p 4 ) Constraints on the parameters {p i }: momentum and number sum rules: p,g, p,uv, p,dv no sensitivity to difference on low- behaviour of u and d valence: p,uv = p,dv no sensitivity to flavour structure of light-quark sea: fi p i, consistent with Gottfried sum rule and Drell-Yan data suppression of strange sea in accordance with dimuon data from CCFR-NuTeV Results of fit not sensitive to reasonable variations of these assumptions possibility to etract a flavour-averaged sea distribution from data alone! Heavy quarks: variable flavour-number scheme of Roberts and Thorne free parameters (+α s when free; otherwise α s (M Z ) =.8) Evolution of the PDFs with the energy scale: DGLAP equations at NLO (MS scheme)

18 Inclusion of jet cross sections in a fit of the proton PDFs 35 In contrast with the evaluation of the structure functions from the evolved PDFs, the calculation of jet cross sections at NLO requires much more CPU time: O() hours per PDF set unaffordable in a fit of the proton PDFs Deconvolution of the PDFs and α s from the matri elements in the calculations construction of grids such that the calculations for the jet cross sections can be performed sufficiently fast and accurately O( second) per PDF set! σ jet (bin i)= f a (ξ k, Q j ) αn s (Q j ) G i,a,n,ξ k,q j n=, a=q, q,g j k G i,a,n,ξk,q grid of weights in the ( = ξ, Q ) plane for a given bin of the j cross section (i), parton species (a) and order (n) typical size in (ξ, Q ) Jet-cross-section calculations can be performed for ANY PDF set and ANY value of α s in a fast way and with an accuracy better than.5%

19 Determination of the proton PDFs 36 Data sets used in the fit (577 data points): structure function measurements: reduced double differential cross sections in and Q : NC e ± p DIS CC e ± p DIS jet cross section measurements: inclusive jet production in NC DIS dijet production in γp collisions Kinematic region: <<.65,.7<Q <3 GeV W > GeV Full account of correlated eperimental uncertainties using the offset method A good description of the data is obtained: χ = 47 for 577 data points σ ~ NC Q =.7 GeV 8.5 GeV 8 GeV 45 GeV GeV GeV GeV GeV 6 GeV 5 GeV GeV GeV 7 GeV 7 GeV - - -JETS tot. uncert. 6.5 GeV 5 GeV 35 GeV 9 GeV - + NC e p Low-Q NC DIS e + p data vs -JETS fit

20 High-Q NC and CC DIS e ± p data vs -JETS fit 37 High-Q NC DIS e ± p High-Q CC DIS e ± p σ ~ NC.5 Q = GeV 5 GeV 35 GeV 45 GeV σ ~ CC Q = 8 GeV 53 GeV 95 GeV.5 -JETS tot. uncert GeV 8 GeV GeV 5 GeV GeV 3 GeV 53 GeV.8 GeV 3 GeV 5 GeV 8 GeV GeV GeV 3 GeV - - -JETS tot. uncert GeV 7 GeV 3 GeV + CC e p CC e p CC e p NC e p NC e p NC e p

21 Jet cross sections vs -JETS fit 38 Inclusive Jet Production in NC DIS e + p Q > 5 GeV, E B T,jet > 8 GeV (pb/gev) B dσ/de T,jet JETS tot. uncert. incl. jet DIS Jet energy scale uncert. 5 < Q < 5 GeV 5 ( ) 5 < Q < 5 GeV 4 ( ) 5 < Q < GeV 3 ( ) < Q < GeV ( ) < Q < 5 GeV ( ) (pb/gev) jet dσ/de T Dijet Production in γp collisions > 4 () GeV γ >.75 E jet,() T 6 γ >.75 -JETS tot. uncert jet <η <.4 jet -< η < ( ) dijet γp Jet energy scale uncert. jet <η <.4 jet < η < ( ) jet, < η <.4 ( ) - > 5 GeV ( ) Q B E T,jet (GeV) -4-5 jet, jet <η < jet -< η < (.5) jet, < η < (.) -< η < (.) jet E T (GeV)

22 Valence distributions 39 Precision of the valence quark distributions at high- not as well constrained as in global PDF fits which include fied-target DIS data but competitive and advantage of being free from heavy-target corrections, higher twists and isospin-symmetry assumptions f - - d v Q = GeV u v Q = GeV tot. uncert. uncorr. uncert. Q = GeV -JETS fit d v u v Q = GeV - d v u v d v u v

23 Gluon and sea distributions 3 f Q = GeV -JETS fit S Q =.5 GeV g S Precision of the gluon and sea distributions at low-: as well determined as in global PDF fits which make use of HERA data at higher-: the uncertainty of the gluon has been reduced by the addition of jet data S g Q = 7 GeV uncorr. uncert. tot. uncert. g S Q = GeV g Q = GeV Q = GeV 3 g g S S

24 Gluon and sea distributions 3 -. Model uncertainties in PDFs: variation of Q in the range 4<Q < GeV modification ( + p 4 ) ( + p 5 ).5 in parameterisations of valence quarks choice of constraints in parameterisation of sea tighter cuts on jet data; E jet -.5 T,B > GeV in NC DIS and E jet T > 7 GeV in γp -. parton-to-hadron corrections to jet cross sections residual uncertainty due to photon PDFs used in the dijet calculations (AFG GRV) Effects much smaller than the eperimental uncertainties Fractional Difference u v S Q - = 4 GeV - Q = GeV change cuts on jet data. v d Q = GeV g - change sea param. - change valence param. GRV photon PDF

25 Improving the gluon distribution: jet data 3 Comparison of gluon distributions from fits with and without jet data no significant change of the shape: no tension between jet and inclusive data the jet cross sections constrain the gluon density in the range..4 Sizeable reduction of the gluon uncertainty eg from 7% to % at =.6 and Q = 7 GeV similar reduction by a factor of two in the mid- region over the full Q range gluon fractional error Q = GeV Q = 7 GeV Q = GeV Q =.5 GeV without jet data with jet data Q = GeV Q = GeV

26 Future improvements to PDFs etraction 33 New sets of data awaiting inclusion in the fits: Combined H+ reduced cross sections in NC and CC DIS Inclusive-jet and dijet cross sections in NC DIS at high Q Optimised dijet cross sections in photoproduction Inclusive-jet cross sections in CC DIS HERA I e + p Neutral Current Scattering - H and HERA I e - p Charged Current Scattering - H and σ r (,Q ) i =.3, i= =.5, i= =.8, i= =.3, i=9 =., i=8 =.3, i=7 =.5, i=6 =.8, i=5 =.3, i=4 =., i=3 =.3, i= =.5, i= =.8, i= =.3, i=9 =., i=8 =.3, i=7 =.5, i=6 =.8, i=5 HERA I (prel.) Fied Target H PDF -JETS =.3, i=4 =.8, i=3 =.5, i= =.4, i= =.65, i= NC e Q p DIS data / GeV CC e p DIS data σ r (,Q ) HERA Structure Functions Working Group Q = 3 GeV Q = 5 GeV Q = GeV Q = 5 GeV Q = GeV Q = 3 GeV Q = 5 GeV - Q = 3 GeV - Q = 5 GeV - HERA I (prel.) H PDF -JETS Q = 8 GeV - HERA Structure Functions Working Group

27 Future improvements to PDFs etraction 34 New sets of data awaiting inclusion in the fits: Combined H+ reduced cross sections in NC and CC DIS Inclusive-jet and dijet cross sections in NC DIS at high Q Optimised dijet cross sections in photoproduction Inclusive-jet cross sections in CC DIS ξ = Bj ( + M jj L = 8 pb L dσ/de jet T,B(pb/GeV) - - (8 pb - ) inclusive jets 5 < Q < 5 GeV 5 < Q < 5 GeV (ξ) (pb) dσ/dlog 3 5 < Q < 5 GeV 5 < Q < 5 GeV Q ) = 9 pb jet energy scale uncertainty 5 < Q < GeV < Q < GeV < Q < 5 GeV 4 NLO (CTEQ6) inclusive-jet NC DIS µ R = (E jet T,B) µ R = Q µ R =Q + (E T,B ) Q > 5 GeV 4 E jet T,B(GeV) 5 < Q < GeV < Q < 5 GeV log (ξ) < Q < GeV log (ξ) NLO (CTEQ6) C had cos(γ had jet() E T,Breit jet - < η Breit - prel. (9 pb ) jet energy scale uncertainty ) <.65 > (8) GeV <.5 dijet NC DIS µ R µ R µ =E R T =Q +E T =Q

28 Future improvements to PDFs etraction New sets of data awaiting inclusion in the fits: Combined H+ reduced cross sections in NC and CC DIS Inclusive-jet and dijet cross sections in NC DIS at high Q Optimised dijet cross sections in photoproduction Inclusive-jet cross sections in CC DIS NLO uncertainty < Q < 5 GeV inclusive jets 5 < Q < 5 GeV NLO uncertainty. -.. dijets 5 < Q < 5 GeV 5 < Q < 5 GeV gluon fraction (CTEQ6).8.6 dijets (log ξ = -.5) 35 inclusive jets ( < E jet T,B < 4 GeV) < Q < GeV < Q < GeV < Q < 5 GeV 3 4 Q > 5 GeV PDF (CTEQ6) µ R scale 3 4 E jet T,B (GeV) NLO uncertainty < Q < GeV < Q < GeV < Q < 5 GeV log ξ log ξ PDF (CTEQ6) µ R scale NLO uncertainty gluon fraction Q (GeV )

29 γ Future improvements to PDFs etraction 36 (pb) dσ/d p New sets of data awaiting inclusion in the fits: Combined H+ reduced cross sections in NC and CC DIS Inclusive-jet and dijet cross sections in NC DIS at high Q Optimised dijet cross sections in photoproduction Inclusive-jet cross sections in CC DIS jet jet < η <, < η < 3 jet,jet E T > 5, 5 GeV High- γ p (pb) dσ/d p jet jet < η <, < η < 3 jet,jet E T >, 5 GeV 5 High- γ p )/(dσ/d γ (d(σ + σ)/d ) γ )/(dσ/de T ) (d(σ + σ)/de.4 T..8 γ 4 6 E T.75 (GeV) p = E jet E p L = 8 pb (gluon))/(dσ/d γ (dσ/d γ ) γ (dσ/de T (gluon))/(dσ/de T ) T eηjet γ E T (pb) dσ/d p jet, < η < jet,jet E T > 3, 5 GeV High- 3 γ p (pb) dσ/d p 5 5 dijets in PHP jet jet - < η <, < η < jet,jet E T >, 5 GeV - 8 pb NLO (AFG4) HAD NLO (CJK) HAD Jet ES uncertainty 5 High- 4 γ p )/(dσ/d p (d(σ + σ)/d ).4 p..8 Low- γ p 3 )/(dσ/d p (d(σ + σ)/d ) (GeV).4 High- γ p. Total theor. uncertainty µ uncertainty R most diff. γpdf (CJK) Proton PDF unc p NLO uncertainty (gluon))/(dσ/d p (dσ/d p ) Low- γ Proton Photon (AFG4) Photon (CJK) p 3 )(gluon)/(dσ/d p (dσ/d p ) High- γ p gluon fraction

30 Future improvements to PDFs etraction 37 New sets of data awaiting inclusion in the fits: Combined H+ reduced cross sections in NC and CC DIS Inclusive-jet and dijet cross sections in NC DIS at high Q Optimised dijet cross sections in photoproduction Inclusive-jet cross sections in CC DIS L = 36 pb e p e p W W ν u proton remnant ν d proton remnant d u Jet dσ/d (pb) Jet E jet T > 4 GeV < η jet <.5 Q > GeV y <.9 inclusive-jet CC DIS CC e p 8 pb CC e + p 79 pb NLO inclusive jets theoretical uncertainty e + p CTEQ6 (e - p) CTEQ6 (e + p) MRST (e - p) MRST (e + p) scale uncertainty e - p PDF uncertainty hadronization uncertainty inclusive jets NLO uncertainty - - Good description of data by NLO QCD calculations Theoretical uncertainties dominated by PDF uncertainty measured cross sections can help to constrain further u and d PDFs