Proton Structure Measurements from HERA

Transcription

1 Proton Structure Measurements from HERA Deep Inelastic Scattering H, ZEUS & HERA ep Collider Data Combination QCD Analyses & HERAPDF. Conclusions Eram Rizvi HepMad - Antananarivo - Madagascar September 5

2 Deep Inelastic Scattering Neutral current scattering Charged current scattering e l(k) ± l(k e ± ) (k), e ± (k) l (kν ),l + (k ) Z/ (q) W ± (q) (p + q) (p + q) (p) (p) p N(p) p N(p) Factorisation in ep collisions: ep!ex = f p!i ˆei!eX f p i = quark / gluon momentum density in proton: parton density function (PDFs) Use factorisation in pp collisions at LHC: Signature Isolated electron/positron pt balanced with hadronic system X pp!x = f p!i ˆi,j!X f p!j Signature No detected lepton (neutrino) pt imbalanced for hadronic system X Eram Rizvi PDFs are not observables - only structure functions are Measuring these cross sections allows indirect access to the universal PDFs fp i HepMad - Antananarivo - September 5

3 Structure Functions ± dσ NC = ddq ± dσ CC = ddq πα G F 4 π Q M W M W +Q Y +! F Y! F 3 y! FL Y + W! ± Y W! ± 3 y! W L ± Y ± = ± ( y)!f (q i + q i )!F 3 (q i q i ) Doant contribution Only sensitive at high Q ~ MZ The NC reduced cross section defined as:!σ ± NC = Q απ Y + d σ ± ddq!f L α s g(,q ) Only sensitive at low Q and high y ±!σ NC ~! F Y Y +! F 3 similarly for pure weak CC analogues: W ±, W 3 ± and W L ± The CC reduced cross section defined as: ± dσ CC σ ± CC = π G F M W + Q M W dσ ± CC ddq = ddq Y W ± + Y W ± 3 y ± W L Eram Rizvi HepMad - Antananarivo - September 5 3

4 HERA Kinematic Plane Q (GeV ) 5 4 HERA Fied Target Eperiments structure doated by valence quark dynamics F 3 HERA data cover wide region of,q 3 F L structure doated by gluon dynamics y= F Q = boson virtuality = fractional momentum of struck quark NC Measurements F doates most of Q reach F3 contributes in EW regime FL contributes only at highest y CC Measurements W and W3 contribute equally WL only at high y Eram Rizvi HepMad - Antananarivo - September 5 4

5 LHC Kinematic Plane (7 TeV) ] ) [GeV Log(Q M = TeV M = TeV M = GeV LHCb = M, 7TeV Q = M ATLAS y = 4 4 LHCb HERA ± e y LHC: largest mass states at large For central production == M= s i.e. M > TeV probes >. Searches for high mass states require precision knowledge at high Z / quantum gravity / susy searches... DGLAP evolution allows predictions to be made High predictions rely on data (DIS / fied target) sum rules behaviour of PDFs as Log() Eram Rizvi HepMad - Antananarivo - September 5 5

6 H and ZEUS Neutral current event selection: High PT isolated scattered lepton Suppress huge photo-production background by imposing longitudinal energy-momentum conservation Kinematics may be reconstructed in many ways: energy/angle of hadrons & scattered lepton provides ecellent tools for sys cross checks Charged current event selection: Large missing transverse momentum (neutrino) Suppress huge photo-production background Topological finders to remove cosmic muons Kinematics reconstructed from hadrons Final selection: ~ 3 events per sample Removal of scattered lepton provides a high stats pseudo-charged current sample Ecellent tool to cross check CC analysis Final selection: ~ 5 events per sample at high Q ~ 7 events for < Q < GeV Eram Rizvi HepMad - Antananarivo - September 5 6

7 HERA Operation HERA-I operation 993- Ee = 7.6 GeV Ep = 8 / 9 GeV s=3 GeV & s=38 GeV L ~ pb - per eperiment HERA-II operation 3-7 Ee = 7.6 GeV Ep = 9 GeV s=38 GeV L ~ 33 pb - per eperiment Longitudinally polarised leptons H Integrated Luosity / pb Status: -July-7 electrons positrons low E HERA- HERA- Low Energy Run 7 Ee = 7.6 GeV Ep = 575 & 46 GeV s=5 GeV & s=5 GeV Dedicated FL measurement 5 5 Days of running Eram Rizvi HepMad - Antananarivo - September 5 7

8 HERA Structure Function Data Summary of HERA-I datasets Combined in HERAPDF. Available since 9 Data Set Range Q Range L e + /e s GeV pb GeV H sv-mb e + p 39 H low Q e + p 39 H NC e + p 3 H CC e + p 3 H NC e p 39 H CC e p 39 H NC HY e p 39 H NC e + p 39 H CC e + p 39 ZEUS BPC e + p 3 ZEUS BPT e + p 3 ZEUS SVX e + p 3 ZEUS NC e + p 3 ZEUS CC e + p 3 ZEUS NC e p 39 ZEUS CC e p 39 ZEUS NC e + p 39 ZEUS CC e + p 39 High Q NC and CC data limited to pb - e + p 6 pb - e p Eram Rizvi HepMad - Antananarivo - September 5 8

9 HERA Structure Function Data ZEUS CC e p 75 pb - EPJ C 6 (9) ZEUS CC e + p 3 pb - 35 EPJ C 7 () ZEUS NC e p 7 pb EPJ C 6 (9) ZEUS NC e + p 35 pb ZEUS-prel- H CC e p 49 pb - Hprelim-9-43 H CC e + p 8 pb - Hprelim-9-43 H NC e p 49 pb - Hprelim-9-4 H NC e + p 8 pb - Hprelim-9-4 ZEUS CC e p 75 pb - EPJ C 6 (9) ZEUS CC e + p 3 pb - 35 EPJ C 7 () ZEUS NC e p 7 pb EPJ C 6 (9) ZEUS NC e + p 35 pb PRD 87 (3) 54 H CC e p 49 pb - H CC e + p 8 pb - H NC e p 49 pb - H NC e + p 8 pb - Up till now HERA-II datasets only partially published } JHEP 9 () 6 HERA-II datasets Combined in HERAPDF.5 (ecept ZEUS NC e + p) R L L = 47.3pb L = 4.4pb P e = (+36. ±.)% P e =( 5.8 ±.7)% L =.3pb L = 8.7pb P e = (+3.5 ±.7)% P e =( 37. ±.7)% Complete the analyses of HERA high Q inclusive structure function data New published data increase L by ~ factor 3 for e + p ~ factor for e p much improved systematic uncertainties Eram Rizvi HepMad - Antananarivo - September 5 9 e p e + p breakdown of HERA-II data samples HERAPDF.

10 HERA Structure Function Data Data Set Grid Q /GeV Grid L e + /e s,q from Ref. from to from to pb GeV equations HERA I E p = 8 GeV and E p = 9 GeV data sets H sv-mb e + p 3, 39,5,6 [] H low Q e + p 3, 39,5,6 [3] H NC e + p 3 7 [4] H CC e + p 3 [4] H NC e p 39 7 [5] H CC e p 39 [5] H NC HY e p 39 [6] H NC e + p 39 7 [6] H CC e + p 39 [6] ZEUS BPC e + p 3 [] ZEUS BPT e + p 3, 7 [] ZEUS SVX e + p 3 [] ZEUS NC e + p 3 9 [3] ZEUS CC e + p 3 [4] ZEUS NC e p 38 8 [5] ZEUS CC e p 38 [6] ZEUS NC e + p 38 8 [7] ZEUS CC e + p 38 [8] HERA II E p = 9 GeV data sets H NC e + p 39, 7 [7] H CC e + p 39 [7] H NC e p 39, 7 [7] H CC e p 39 [7] H NC med Q y e + p 39 [9] H NC low Q y e + p 39 [9] ZEUS NC e + p 38,,8 [] ZEUS CC e + p 38 [] ZEUS NC e p 38 8 [9] ZEUS CC e p 38 [] ZEUS NC noal y e + p 38 [3] ZEUS NC satellite y e + p 38 [3] HERA II E p = 575 GeV data sets H NC high Q e + p 5, 7 [8] H NC low Q e + p 5 [9] ZEUS NC noal e + p 5 [3] ZEUS NC satellite e + p 5 [3] HERA II E p = 46 GeV data sets H NC high Q e + p 5, 7 [8] H NC low Q e + p 5 [9] ZEUS NC noal e + p 5 [3] ZEUS NC satellite e + p 5 [3] H & ZEUS have now published all datasets - HERA-II measurements at high L - reduced s data 4 data sets to be combined: - NC & CC cross sections - e + p and e p scattering - 4 different s values 97 data points in total 37 In some cases 6 measurements combined.45 < Q < 5, GeV 6-7 < <.65 arxiv:56.64 Eram Rizvi HepMad - Antananarivo - September 5

11 H & ZEUS Data Combination Data are combined onto a common,q grid Two grids used: inclusive measurements s=38 GeV fine grid for s=5 & 5 GeV 97 data points 37 combined measurements Data are translated to nearest,q grid point Iterative process using NLO QCD fit to data Use uncombined data in first iteration Then combined data in later iterations No changes after 3 iterations The swimg done iterativaly with our own data. Fractal Fit DGLAP NLO 3. Q weight. Fractal and DGLAP QCD fits were performed with :.5 HERAFitter open source. QCD fit framework, available Q at ( grid,q grid) = model ( grid,q grid ) model( meas,q meas) meas( meas,q meas) Data are also translated outside of region of DGLAP fit validity Q < 3. GeV Use phenomenological fractal model and interpolate to DGLAP region Other phenomenological fits tested negligible differences Averaging of scale factors is performed in dependence on Q. Eram Rizvi HepMad - Antananarivo - September 5

12 H & ZEUS Data Combination i data points j systematic error sources Correlated uncertainties treated multiplicative: size proportional to central averaged value True for normalisation uncertainties Perhaps not true for other uncertainties tot(m, b) = X i [µ i m i ( i,stat µi m i ( P j P i j j b j)] i j b j)+( i,unc m i ) + X j b j µ i = measurement m i = averaged value ɣ i j = correlated relative (%) sys uncertainty on point i from error source j bj = systematic error source strength nuisance parameter left free in fit but constrained no etra degrees of freedom due to additional constraint For HERAPDF. number of correlated error sources j = 69 These include: b/g uncertainty Etra procedural uncertainty included: luosity uncertainty difference between using EM calibration scale additive vs multiplicative had calibration scale correlated uncertainties (ecept normalisation) etc. etra ~.5% uncertainty Are correlated point-to-point within a single measurement Reported in detail in individual publications from eperiments May also be correlated across measurements May also be correlated between H & ZEUS (e.g. had scale & photo-production b/g) Eram Rizvi HepMad - Antananarivo - September 5

13 Entries H & ZEUS Data Combination NC e p Q 3.5 GeV RMS = pull Entries H and ZEUS NC e p 3.5 < Q GeV RMS =.7 a) b) c) pull Entries NC e p < Q 5 GeV RMS = pull Overall χ /ndf = 685 / 6 =.4 Pulls defined for each measurement difference between measured & average values after applying sys shifts bj in units of uncorrelated uncertainty Pulls of the data points should be distributed as a unit Gaussian Entries RMS =.95 - NC e p Entries RMS =.4 + CC e p Entries RMS =.97 - CC e p Each measurement channel shows pull centred on zero & unit width d) e) f) pull pull pull Entries pulls of the systematic sources bj RMS = systematic pull Eram Rizvi HepMad - Antananarivo - September 5 3

14 Combined NC Cross Sections σ r, NC.8 e + p H and ZEUS + HERA NC e + p.5 fb.6 =..4 =.. s = 38 GeV ZEUS HERA II ZEUS HERA I H HERA II H HERA I σ r, NC. e p H and ZEUS =.8 HERA NC e p.4 fb s = 38 GeV ZEUS HERA II ZEUS HERA I H HERA II H HERA I =.8.8 = =.8.6 =.3.4 =.8 =.8 =.8.4 =.5.. = Q /GeV 3 4 Q /GeV Figure 4: The combined HERA data for the inclusive NC e + p reduced cross sections as a function of Q for si selected values of compared to the individual H and ZEUS data. The individual measurements are displaced horizontally for better visibility. Error bars represent the total uncertainties. only 6 bins shown here factor more data than HERA-I data sets NC e + p data systematically limited χ / ndf = 687 / 6 high precision reached over large kinematic range better than.3% Q < 4 GeV 77 Eram Rizvi HepMad - Antananarivo - September 5 4

15 Combined CC Cross Sections σ r, CC +.5 Q = 3 GeV e + p H and ZEUS Q = 5 GeV Q = GeV Q = 5 GeV σ r, CC 3 Q = 3 GeV e p H and ZEUS Q = 5 GeV Q = GeV Q = 5 GeV.5.6 Q = GeV Q = 3 GeV Q = 5 GeV Q = 8 GeV Q = GeV Q = 3 GeV Q = 5 GeV Q = 8 GeV Q = 5 GeV - Q = 3 GeV HERA CC e + p.5 fb Bj s = 38 GeV ZEUS HERA II ZEUS HERA I H HERA II H HERA I Q = 5 GeV - Q = 3 GeV HERA CC e p.4 fb Bj s = 38 GeV ZEUS HERA II ZEUS HERA I H HERA II H HERA I Figure : The combined HERA data for the inclusive CC e + p reduced cross sections Figure as 4: a The combined HERA data for the inclusive CC e p reduced cross section function of for the different values of Q compared to the individual H and function ZEUS of for the different values of Q compared to the individual H and Z data. The individual measurements are displaced horizontally for better visibility. Error data. bars The individual measurements are displaced horizontally for better visibility. Erro represent the total uncertainties. Large improvement in statistical limitations represent of individual the total uncertainties. data sets from H & ZEUS Eram Rizvi HepMad - Antananarivo - September 5 5

16 PDF Etractions from Data Parameterise PDFs at arbitrary starting scale Q Perturbative QCD evolution equations allows PDFs to be detered at any other scale Q Calculate theory cross section at given,q of measurement Compare data & theory via χ function Minimise χ function with respect to PDF parameters ~ iterations Eram Rizvi HepMad - Antananarivo - September 5 6

17 HERAPDF. HERAPDF. &.5 Combine NC and CC HERA-I data from H & ZEUS Complete MSbar NLO fit NLO: standard parameterisation with parameters NNLO HERAPDF.5 with 4p HERAPDF. Include additional NC and CC HERA-II combined data Complete MSbar NLO and NNLO fit NLO & NNLO fits require5 parameters f (,Q ) = A B ( ) C (+ D + E ) g u v d v U D g U = u + c D = d + s U = u + c D = d + s g() = A g B g ( ) C g, u v () = A uv B uv ( ) C u v d v () = A dv B dv ( ) C d v, Ū() = A Ū B Ū ( ) CŪ, D() = A D B D ( ) C D. ( + Euv ), eters, A A A, are constrained by the qu HERAPDF. & NLO HERAPDF.5 g() = A g B g ( ) C g A g B g ( ) C g, ( u v () = A uv B uv ( ) C u v + Euv ), d v () = A dv B dv ( ) C d v, Ū() = A Ū B Ū ( ) CŪ ( + DŪ ), D() = A D B D ( ) C D. HERAPDF. Apply momentum/counting sum rules: B U = B D d u v = d d v = s = f s D strange sea is a fied fraction f s of D at Q Sea = (U + D) d (u v + d v + U + D + g) = A U = A D ( f s ) ensures u d as Q =.9 Q = 3.5 or GeV α s (M z ) = Eram Rizvi HepMad - Antananarivo - September 5 7

18 HERAPDF. g() = A g B g ( ) C g A g B g ( ) C g, ( u v () = A uv B uv ( ) C u v + Euv ), d v () = A dv B dv ( ) C d v, Ū() = A Ū B Ū ( ) CŪ ( + DŪ ), D() = A D B D ( ) C D. fied or constrained by sum-rules parameters set equal but free NC structure functions F = 4 U + Ū 9 + D + D 9 F 3 u v + d v CC structure functions W = (U + D), W+ = (U + D) W3 = (U D), W+ 3 = (D U), Additional parameters: heavy quark masses Mc and Mb are optimised fs =.4 compromise value between unsuppressed (fs =.5) and default strange sea from dimuon data tot(m, b) = X i [µ i m i ( i,stat µi m i ( P j P i j j b j)] i j b j)+( i,unc m i ) + X j b j + X i ln i,unc m i + i,stat µi m i i,unc µ i + i,stat µ i modified χ definition includes ln term to account for likelihood transition to χ after error scaling Eram Rizvi HepMad - Antananarivo - September 5 8

19 HERAPDF. Uncertainties Eperimental Uncertainties Hessian method uses 4 eigenvector pairs Standard definition Δχ = for 68% CL error bands Model Assumptions Variation of charm and bottom quark masses Mc, Mb Variation of Q imum cut used on input data Q Variation of strange quark fraction fs Parameterisation Uncertainties Variation of Q Variation of fit using additional 5th parameter Variation Standard Value Lower Limit Upper Limit Q [GeV ] Q [GeV ]HiQ M c (NLO) [GeV] M c (NNLO) [GeV] M b [GeV] f s α s (MZ ).8 µ f [GeV].9.6. αs(mz ) is fied but series of PDFs provided scanning large range in value:. to.3 Eperimental uncertainties also checked using RMS spread of 4 replica fits Eram Rizvi HepMad - Antananarivo - September 5 9

20 NC Cross Sections σ r, NC i =.5, i= =.8, i= =.3, i=9 =., i=8 =.3, i=7 =.5, i=6 H and ZEUS gluon splitting positive scaling violations at low Neutral Current e ± p =.8, i=5 =.3, i=4 =., i=3 =.3, i= HERA NC e p.4 fb HERA NC e + p.5 fb s = 38 GeV Fied Target HERAPDF. e p NLO =.5, i= =.8, i= HERAPDF. e + p NLO =.3, i=9 =., i=8 =.3, i=7 =.5, i=6 =.8, i=5 =.3, i=4 =.8, i=3 =.5, i= Precision.3% for Q < 4 GeV factor reduction in error wrt HERA-I Statistics limited at higher Q and high Etended reach at high compared to H preliary data This region is the sweet spot High precision with long Q lever arm -range relevant for Higgs production Combination of high Q data HERA- and HERA-II - =.4, i= Larger HERA-II luosity improved precision at high / Q - gluon radiation negative high scaling violations =.65, i= Q / GeV HERAPDF. provides good description Eram Rizvi HepMad - Antananarivo - September 5 +

21 High Q NC & CC Cross Sections Neutral Current e ± p H and ZEUS Charged Current e ± p H and ZEUS σ r, NC 3 HERA s = 38 GeV NC e + p.5 fb NC e p.4 fb HERAPDF. NLO s = 38 GeV NC e + p NC e p =. (575) =.3 (4) =.5 (7) =.8 (7) =.3 (8) σ r, CC HERA HERAPDF. NLO s = 38 GeV s = 38 GeV CC e + p.5 fb CC e + p CC e p.4 fb CC e p =.8 (5) =.3 (3) =.3 (7) =.8 () =.8 (7) =.3 () =.5 (6) =.5 () - =.4 () =.65 =.4 (.) Q / GeV 75: The combined HERA data for the inclusive NC e + p and e p reduced cross sections nction of Q for selected values of at s = 38 GeV with overlaid predictions of PDF. NLO. The bands represent the total uncertainties ofthepredictions. Q / GeV Eram Rizvi HepMad - Antananarivo - September Difference in NC at high for e + and e is due to F3 and Z boson echange valence quarks CC e + p suppressed at high due to (-y) helicity suppression of quarks at high y,q & fied CC e p unaffected as helicity suppression applies to anti-quarks HERAPDF. describes high data well for both NC and CC channels

22 Valence quarks and F3 Z γ F 3 H and ZEUS Q = GeV - HERA fb HERAPDF. NLO.5 At high Q F3 arises due to Z effects enhanced e - cross section wrt e + Difference is F3 Sensitive to valence PDFs - F! 3 = Y + (!σ Y NC!F 3 (q i q i )!σ + γ Z NC ) a e χ Z F Measure integral of F3 ɣz - validate sumrule: d F γz 3 (, Q = 5 GeV )=..34 ±.9(stat).57(stat) ±.7(syst).57(syst) ± ± LO integral predicted to be 5/3 + O(αS/π) Eram Rizvi HepMad - Antananarivo - September 5

23 High Q CC Cross Sections σ r, CC Electron scattering d σ CC ddq = G F π Q = 3 GeV M W M W + Q (u + c) + ( y) (d + s ) H and ZEUS Q = 5 GeV Q = GeV Q = 5 GeV σ r, CC + d + σ CC ddq = G F π.5.5 Q = 3 GeV Positron scattering M W M W + Q (u + c ) + ( y) (d + s) H and ZEUS Q = 5 GeV Q = GeV Q = 5 GeV Q = GeV Q = 3 GeV Q = 5 GeV Q = 8 GeV.6 Q = GeV Q = 3 GeV Q = 5 GeV Q = 8 GeV Q = 5 GeV Q = 3 GeV HERA CC e p.4 fb s = 38 GeV HERAPDF. NLO Q = 5 GeV Q = 3 GeV HERA CC e + p.5 fb s = 38 GeV HERAPDF. NLO Combination of high Q CC data (HERA-I+II) Improvement of total uncertainty Doated by statistical errors CC e+ data provide strong dv constraint at high Precision limited by statistics: typically 3-7% HERA-I precision of -5% for e+p Provide important flavour decomposition information Figure 38: The combined HERA inclusive CC e + p reduced cross sections at s = with overlaid predictions from HERAPDF. NLO. The bands represent the total unc Eram Rizvi HepMad - Antananarivo on the predictions. - September

24 HERAPDF. (NLO Fit) f.8 H and ZEUS HERAPDF. NLO uncertainties: eperimental model parameterisation µ f = GeV u v u.5.5 µ f = GeV H and ZEUS c.5.5 µ f = GeV HERAPDF. NLO uncertainties: eperimental model parameterisation.6 HERAPDF.AG NLO g (.5) d v d.5 µ f = GeV s.5 µ f = GeV. S (.5) : The parton distribution functions u v, d v, S = (Ū + D)andgof HERAPDF. µ f = GeV.Thegluonandseadistributionsarescaleddownbyafactorof. The ental, model and parameterisation uncertainties are shown. The dotted lines Figure represent : The flavour breakdown of the sea distribution of HERAPDF. NLO at µ f DF.AG NLO with the alternative gluon parameterisation, see Section 6.8. GeV.Shownarethedistributionsū, d, c and s together with their eperimental, mo and parameterisation uncertainties. The fractional uncertainties are also shown Eram Rizvi HepMad - Antananarivo - September 5 4

25 u v g u v / u v(herapdf.) HERAPDF. Comparison to Other PDFs µ = GeV f HERAPDF. NLO MMHT4 NLO CT NLO NNPDF3. NLO - - H and ZEUS - - d v S Eram Rizvi HepMad - Antananarivo - September H and ZEUS Comparison µ = GeV f of HERAPDF. vs MMHT4, NNPDF3., CT (others use only HERA- combined data) HERAPDF. NLO 3 Differences MMHT4 at NLOhigh CT NLO (68% CL) New HERA combined data improve precision at high, Q NNPDF3. NLO HERAPDF uses proton target data only no nucleon / deuterium data Softer gluon at high d v / d v(herapdf.) u v / u v(herapdf.) g / g(herapdf.) µ = GeV f HERAPDF. NLO MMHT4 NLO CT NLO (68% CL) NNPDF3. NLO - - d v / d v(herapdf.) H and ZEUS S / S(HERAPDF.) Figure 5: The parton distribution functions u v, d v, S = (Ū + D)andgo NLO at µ f = GeV compared to those of MMHT4 [36], CT [38]andN The top panel shows the distribution with uncertainties only forherapdf panel shows the PDFs normalised to HERAPDF. and with uncertainties for a 3

26 7.4 HERAPDF.Jets HERAPDF. Jets Data on jet production were included in the analysis as described in Section 6.. Thisinclusion was first used to validate the choice of α s (MZ ) =.8 for HERAPDF by investigating the dependence of the χ Inclusive jet + s of the HERAPDF pqcd fits on α charm cross sections in ep s (MZ collisions ). Three χ scans vs. the value of α s (MZ are )wereperformedatnloforthreevaluesofq sensitive to g and.theresultisdepictedinthetoppanel αs NLO of Fig. 65. A distinct imum at α s (MZ ).8 is observed, which is basically independent of Q 4 Separate.Thisvalidatesthechoiceofα s(mz ) =.8 for HERAPDF. NLO. Scans at NLO and NNLO wereh also& performed ZEUS measurements for fits to inclusive data are only. added The middle and bottom panels of Fig. to HERAPDF. 65 show that these scans HERAPDF.-Jets yielded similar shallow χ dependences and the ima were strongly dependent on the Q. This demonstrates that the inclusive data alone cannot constrain α H and ZEUS s (MZ )reasonably. f 7.4. PDFs and measurement of α s (M Z ).8 g HERAPDF. NLO = GeV µ f χ - χ a) χ - χ χ - χ H and ZEUS The χ of the HERAPDF.Jets fit with free α s (M c) Z )isthesameasforthefitwithfied α s (MZ ) =.8, see Table. Thisisagainduethefactthatthevalueofα s(mz )obtainedfrom the parton fit is very distribution close to functions the value previously α u v, d v, S fied. = (Ū The strong + D)andg coupling ofconstant HERAPDF. obtained is s (M Z ) Value of αs detered from DIS data: GeV compared to those of HERAPDF.HiQ NLO on logarithmic (top)and α s (MZ) =.83 ±.9(ep) ±.5(model/parameterisation) Consistent with world average scales. The bands represent the total uncertainties. Figure 65: χ = χ χ vs. α s(mz ) for pqcd fits with different Q using data on ±.(hadronisation) inclusive, (scale) charm. Competitive with other NLO deterations and jet production at NLO, (b) inclusive ep scattering only at NLO and The uncertainty on α s (M inclusive ep scattering only at NNLO. Z Eram Rizvi )duetoscaleuncertaintieswasevaluatedbyvaryingtherenormalisation and factorisation scales by a factor of two, both separately and simultaneously, HepMad - Antananarivo - September 5 6 and 4 inclusive + charm + jet data, Q = 3.5 GeV inclusive + charm + jet data, Q = GeV inclusive + charm + jet data, Q = GeV NLO The PDFs resulting from a fit with free α s (MZ ), HERAPDF.Jets, and from a fit 4with fied HERAPDF.HiQ NLO α s (MZ ) =.8 are shown in Fig. 66. A full uncertainty analysis was performed in both cases, including model and parameterisation uncertainties aswellasadditionalhadronisation.6 S uncertainties on the jet data. The PDFs are very similar, because the HERAPDF.Jets fit with free α s (MZ )yieldsavaluewhichisveryclosetothevalueusedforthefitwith fied α s(mz ). The jet data detere the value of α s (MZ ) very well in the HERAPDF.Jets fit. Thus, the u v b) uncertainty.4on α s (MZ )inthisfitdoesnotsignificantlyincreasetheuncertaintyonthegluon PDF with respect to the fit with α s (MZ )fied. Thedifference in the α s(mz )freefitismostly due to etra uncertainty cog from the hadronisation corrections. The PDFs. from the HERAPDF.Jets d v fit with α s (MZ ) =.8 fied are also very similar to the standard PDFs from HERAPDF. NLO. This is demonstrated in Fig. 67. Thisisagain the result of the choice of α s (MZ ) =.8 for HERAPDF. which is also the preferred value for HERAPDF.Jets. Consequently, there is only a small reduction of the uncertainty on the gluon distribution observed for HERAPDF.Jets. inclusive data only, Q = 3.5 GeV inclusive data only, Q = GeV inclusive data only, Q = GeV NNLO inclusive data only, Q inclusive data only, Q = 3.5 GeV inclusive data only, Q = GeV inclusive data only, Q = GeV

27 Conclusions Electroweak symmetry breaking H and ZEUS ) (pb/gev dσ/dq - HERA NC e p.4 fb HERA NC e p.5 fb - HERAPDF. NC e p + HERAPDF. NC e p H / ZEUS completed their final SF measurements New HERA-II data provide tighter constraints at high / Q These data provide some of the most stringent constraints on PDFs -5 y <.9 s = 38 GeV HERA CC e p.4 fb HERA CC e p.5 fb - HERAPDF. CC e p + HERAPDF. CC e p Stress-test of QCD over 4 orders of mag. in Q DGLAP evolution works very well HERA data provide a self-consistent data set for complete flavour decomposition of the proton Final combination of HERA data completed HERAPDF. QCD fit at NLO & NNLO Q / GeV Eram Rizvi HepMad - Antananarivo - September 5 7

28 Backup Eram Rizvi HepMad - Antananarivo - September 5 8

29 HERAPDF HERAPDF. Combine NC and CC HERA-I data from H & ZEUS Complete MSbar NLO fit NLO: standard parameterisation with parameters αs =.76 (fied in fit) desy-9-58 g u v d v U D f (,Q ) = A B ( ) C (+ D + E ) g U = u + c D = d + s U = u + c D = d + s HERAPDF.5 Include additional NC and CC HERA-II data Complete MSbar NLO and NNLO fit NLO: standard parameterisation with parameters HERAPDF.5f NNLO: etended fit with 4 parameters g() = A g B g ( ) C g, u v () = A uv B uv ( ) C u v d v () = A dv B dv ( ) C d v, Ū() = A Ū B Ū ( ) CŪ, D() = A D B D ( ) C D. H--4 / ZEUS-prel--8 ( + Euv ), eters, A A A, are constrained by the qu s = f s D strange sea is a fied fraction f s of D at Q Apply momentum/counting sum rules: d (u v + d v + U + D + g) = d u v = d d v = Parameter constraints: Buv = Bdv BUbar = BDbar sea = (Ubar +Dbar) Ubar = Dbar at = Q =.9 GeV (below m c ) Q > 3.5 GeV -4 < <.65 Fits performed using RT-VFNS Eram Rizvi HepMad - Antananarivo - September 5 9

30 F Structure Function H and ZEUS ~ F.6.4 Q = 6.5 GeV Q = GeV Q = GeV HERA NC e + p.5 fb s = 38 GeV HERAPDF. NLO..8 Q = GeV Eram Rizvi HepMad - Antananarivo - September 5 3

31 Optimisation of Heavy Quark Masses χ - χ χ - χ H and ZEUS NLO NNLO M c /GeV χ - χ χ - χ NLO H and ZEUS NNLO M b /GeV Eram Rizvi HepMad - Antananarivo - September 5 3

32 HERAPDF. HiQ (Q > GeV ) χ /d.o.f ACOT NLO, F L O(α s ) FONLL-B NLO, F L O(α s ) RTOPT NLO, F L O(α s ) b) a).5 FF3B NLO, F L O(α s ) FF3A NLO, F L O(α s ) H and ZEUS Q /GeV Figure : The dependence of χ /d.o.f. on Q for HERAPDF. fits using a) the RTOPT [83], FONNL-B [9], ACOT [9] andfied-flavour(ff) schemesatnloandb) thertoptand FONNL-B/C [9] schemesatnloandnnlo.thef L contributions are calculated using matri elements of the order of α s indicated in the legend. The number of degrees of freedom drops from 48 for Q =.7GeV to 3 for the noal Q = 3.5 GeV and to 868 for Q = 5 GeV. χ /d.o.f FONLL-B NLO, F L O(α s ) FONLL-C NNLO, F L O(α s ) RTOPT NLO, F L O(α s ) RTOPT NNLO, F L O(α s 3 ) b) Q /GeV Eram Rizvi HepMad - Antananarivo - September 5 3

33 f HERAPDF. (NLO vs NNLO Fit) H and ZEUS µ f = GeV f f H and ZEUS H and ZEUS µ µ f f HERAPDF. NLO HERAPDF. NLO NNLO HERAPDF. NNLO = GeV = GeV.8 HERAPDF. NNLO uncertainties: eperimental model parameterisation u v g (.5) g (.5) S (.5) S (.5) d v d v u v u v.6.4 g (.5) HERAPDF.AG NNLO d v f f g g - - H and ZEUS H and ZEUS µ µ f f HERAPDF. NLO HERAPDF. NLO NNLO - - = GeV = GeV. S (.5) S S HERAPDF. NNLO u v.4 u v : The parton distribution functions u v, d v, S = (Ū + D)andgof HERAPDF at µ f Eram = Rizvi GeV. The gluon and sea distributions are scaled HepMad down - Antananarivo by a factor. - September The d v d v

34 HERAPDF. Variants HERAPDF Q [GeV ] χ d.o.f. χ /d.o.f. NLO HiQ NLO NNLO HiQ NNLO AG NLO HiQ AG NLO AG NNLO HiQ AG NNLO NLO FF3A NLO FF3B Jets α s (MZ )fied Jets α s (MZ )free Table : The values of χ per degree of freedom for HERAPDF. and its variants. Eram Rizvi HepMad - Antananarivo - September 5 34