Proton Structure Functions: Experiments, Models and Uncertainties.

Transcription

1 Proton Structure Functions: Experiments, Models and Uncertainties. S. Glazov, DESY IKTP seminar, July 8.

2 Disclaimer Nothing in this talk should be interpreted as the final knowledge on proton structure. The knowledge is rapidly updated with more experimental data, new theory calculations. A workshop focussed on PDF predictions for LHC physics, PDF4LHC, attempts to summaries current knowledge for the LHC start (next session July 4th, at CERN). Much more information will be given at PDF School organized by the Physics at the Teracale Strategic Helmholtz Alliance: school 8

3 Deep Inelastic Scattering Kinematics of inclusive scattering is determined by Q and Bjorken x. In x scale parameter /3 - equal sharing among quarks. Proton structure for x.5 valence quarks x.5 coupled quark-gluon QCD evolution. Large gluon density. At small x complex dynamics which must obey simple asymptotic solutions (unitarity). DIS scattering experiments at HERA with S = 38 GeV provide A unique tool to study validity of the QCD evolution for a wide range in x and Q. Within the standard QCD evolution, measurement of the proton parton densities. Knowledge of the proton structure is vital for a number of practical applications including pp colliders (LHC). 3

4 HERA, H and ZEUS Current-p [ma] HERA p:.[ma].[h] [GeV] e+:.[ma].[h].[gev] Sun Jul ::5 7 Current-e [ma], Lifetime-e [h] 6 Tau(e) Protons 5 Leptons Thank You HERA R.I.P. 4 Time [h]

5 DIS Event Reconstruction Virtuality: Q = E e E e(+cos θ e ) e e LAr Central Tracker p SpaCal Inelasticity: y = E e( cos θ e ) E e Bjorken x: x = Q /(Sy) p γ invariant mass: jet W = Q ( x)/x Kinematics can be reconstructed using e or hadronic final state. 5

6 PDF determination d σe NC p dxdq = πα Y + xq 4 Leading order relations: (F y F L ± Y ) xf 3 Y + Y + Y ± = ±( y) F xf 3 σ CC = x e q(q(x) + q(x)) = x e q a q (q(x) q(x)) e + p x(ū + c) + x( y) (d + s) x(u + c) + x( y) ( d + s) σ CC e p pp (l l)x x x q(x ) q(x ) Gluon is determined from F scaling violation and from jet cross section. F L = at leading order; proportional to Gluon at higher orders. 6

7 HERA and LHC kinematics x, x are momentum fractions. Factorization theorem states that cross section can be calculated using universal partons short distance calculable partonic reaction. x, = M S exp(±y) Q / GeV Atlas and CMS Atlas and CMS rapidity plateau D Central+Fwd. Jets CDF/D Central Jets H ZEUS NMC BCDMS E665 SLAC x Notation clash: y rapidity (LHC) vs y inelasticity (HERA, Q = Sxy). 7

8 Case study: Higgs production at LHC, SM vs MSSM In SM, b b H is small vs gg H. In MSSM, b b H can be enhanced by tan β Even for MSSM with tan β =, b b H dominates over gg production. production cross section measurement of Higgs is a key ingredient to disentangle new physics scenarios. 8

9 The Measured Cross Sections F i 6 5 x =.5, i = x =.8, i = x =.3, i = 9 x =., i = 8 x =.3, i = 7 x =.5, i = 6 x =.8, i = 5 x =.3, i = 4 H e + p ZEUS e + p BCDMS NMC σ HERA Charged Current H e - p H e + p 94- SM e - p (CTEQ6D) ZEUS e - p ZEUS e + p 99- SM e + p (CTEQ6D) Q = 8 GeV Q = 53 GeV Q = 95 GeV 4 x =., i = 3 x =.3, i = x =.5, i = 3 x =.8, i = x =.3, i = 9 Q = 7 GeV Q = 3 GeV Q = 53 GeV x =., i = 8 x =.3, i = H PDF extrapolation -3 x =.5, i = 6 x =.8, i = 5 x =.3, i = 4 x =.8, i = 3 x =.5, i = x =.4, i = x =.65, i = Q / GeV H Collaboration Q = 95 GeV Q = 7 GeV Q = 3 GeV x HERA data allows to measure xu = x(u + c), xd = x(d + s), xū = x(ū + c), x D = x( d + s), and xg in a single experiment. 9

10 Measurement at low x HERA F Q =.7 GeV 3.5 GeV 4.5 GeV 6.5 GeV 8.5 GeV GeV GeV 5 GeV 8 GeV GeV 7 GeV 35 GeV em F 45 GeV 6 GeV 7 GeV 9 GeV GeV 5 GeV -3-3 ZEUS NLO QCD fit H PDF fit H 96/97 ZEUS 96/97 BCDMS E665 NMC F (x, Q ) shows strong rise as x, the rise increases with increasing Q. To quantify the rise, F = cx λ fit is performed for each Q bin x

11 Sources of Experimental Uncertainty σ r, δl δσr stat, δσ corr syst r uncorr syst δσr Global normalizations arise from luminosity uncertainty δl, global inefficiencies. Affect data sets uniformly. Typical value.5 %. Most serious for PDFs: 3σ shift generates 4.5 6% bias with only 9 units of χ. corr syst Correlated systematic uncertainties, σr arise from misreconstruction of event kinematics, background. Affect groups of experimental points, typically y dependent can change x-shape globally. uncorr syst Uncorrelated systematic uncertainties, σr arise from local efficiencies, miscalibrations. Often the largest source of uncertainty but impact on PDFs is /sqrt(n meas ). Statistical uncertainties, σr stat at HERA are small for x.5 range, become important for high Q, x.

12 Luminosity measurement at HERA Use ep epγ Bethe-Heitler process, detect the scattered photon in a photon tagger m away from the IP. QED prediction with.5% precision (effect of higher orders). Experimental uncertainty dominated by detector acceptance knowledge ( 9 ± %), energy calibration, and beam longitudinal profile. complicated measurement. Ultimate experimental uncertainty: %, uncorrelated H vs ZEUS.

13 Correlated Systematic Uncertainties Data-MC E-scale, percent π J/ψ QED Compton kin. peak E, GeV Example: scattered electron energy E e. Affects y, Q. Calibrated to the electron beam energy using the scattered electron angle and the angle of hadronic final state. Check E e using kinematic peak distribution.% precision. Measure non-linearity with π γγ, J/ψ e + e, QED-Compton ep epγ events. 3

14 Combination of HERA data HERA I e + p Neutral Current Scattering H and ZEUS σ r (x,q ) x=. H PDF ZEUS JETS HERA I (prel.) ZEUS H x=. x=.5 HERA Structure Functions Working Group Average H and ZEUS data before applying QCD analysis. Achieved by fitting σ r values, global normalizations and the correlated systematic uncertainties. Q / GeV Experiments cross calibrate each other: total uncertainties reduced, sometimes better than. 4

15 Combined HERA data σ r (x,q ) x i H and ZEUS Combined PDF Fit x =.3, i= x =.5, i= x =.8, i= x =.3, i=9 x =., i=8 x =.3, i=7 x =.5, i=6 x =.8, i=5 x =.3, i=4 x =., i=3 x =.3, i= x =.5, i= x =.8, i= x =.3, i=9 x =., i=8 HERA I e + p (prel.) Fixed Target HERA I PDF (prel.) x =.3, i=7 x =.5, i=6 x =.8, i=5 x =.3, i=4 x =.8, i=3 x =.5, i= x =.4, i= x =.65, i= Q / GeV HERA data approaches precision of fixed target experiments. Combined data vs theory: stringent test of DGLAP evolution. HERA Structure Functions Working Group April 8 Combination of published H/ZEUS data for CC,NC, e ± p data. χ /dof = 5/599 (over-consistency, conservative uncorr syst δσ red ) 5

16 xf xg (.5) xs (.5) -3 PDFs extraction H and ZEUS Combined PDF Fit HERA I PDF fit (prel.) CTEQ6.M - Q = GeV xu v xd v - x HERA Structure Functions Working Group April 8 xf H and ZEUS Combined PDF Fit xg (.5) xs (.5) -3 HERA I PDF fit (prel.) MRST Sea S and gluon g are far more important at low x. Mind the.5 scale factor for them. - Q = GeV Fit to combined H/ZEUS data returns much more precise xg(x) compared to global fits of CTEQ and MRST: improved data precision and also different data errors treatment. xu v xd v - x HERA Structure Functions Working Group April 8 6

17 xu xd H and ZEUS Combined PDF Fit -3-3 Q =4 GeV - Q =4 GeV - - x - x Model Uncertainties xubar xdbar Q =4 GeV HERA-I PDF(prel.) exp. uncert. model uncert. - Q =4 GeV - - x - Typical functional forms at a starting scale are x HERA Structure Function Working Group April 8 Experimental errors at low x are often smaller compared to model uncertainties: Evolution starting scale, lowest Q in data. Flavour separation at low x, strangeness fraction. Masses of heavy c,b quarks α S value (not in the bands). xf(x) = Ax B ( x) C ( + Dx + Ex +...), additional uncertainty from the choice of the parameterization. 7

18 Model Uncertainties for LHC predictions A study performed by E. Perez and A. Cooper-Sarkar based on HERAPDF.: Different treatment of experimental errors ( Hessian for EP vs Offset for ACS) of the H-ZEUS averaged dataset does not affect uncertainty for W production Significantly smaller errors vs CTEQ 6. estimation. Model uncertainties seem to have larger impact vs experimental precision. 8

19 HERA runs at reduced E p to measure F L H Integrated Luminosity / pb Status: -July-7 electrons positrons low E HERA- Integrated Luminosity / pb - HERA low E p run 5 HERA deliv: 46 GeV 575 GeV H physics: 46 GeV 575 GeV 5 Status: -July-7 HERA Days of running Days since -Jan-7 Last 3 months of HERA operation are dedicated for F L measurement. Luminosity is proportional to E p, from the beam focusing, thus reduced vs nominal 9 GeV run. Successful HERA operation, 3.6 pb and 6.5 pb collected for 46 and 575 GeV run. 9

20 F L measurement challenges 3 events 4 E p = 46 GeV Data MC+BG BG (data) 3 events 3 H Preliminary E e / GeV Θ e / deg 3 events 3 3 events 4 Medium Q region -4-4 Z vtx / cm E-p z / GeV Determination of F L requires measurement at high y E e E e H estimates background directly from data using the measured charge of the electron candidate.

21 F L extraction, y) (x, Q σ r x =.49 x =. Q = 5 GeV x =.6 x =.6 x =.76 x =.5 H Data E p E p H = 9 GeV = 575 GeV E p = 46 GeV Linear fit y / Y + y σ r (y) = F + ( y) F L Linear fit to get F and F L Relative normalization from low y data Data at E p = 575 provides cross check and extends measurement to low x.

22 Average F L by H at medium Q ) (x, Q F L H Data H PDF CTEQ 6.6 MSTW 7 x Q / GeV F L compared to prediction based on H QCD fit to published by H DIS cross section data and global MSTW, CTEQ fits. (DESY-8-53, accepted by Phys. Lett. B)

23 Average FL by H, extended range, preliminary L H Preliminary F ) H PDF CTEQ 6.6 MSTW H (Prelim.).5 = 46, 575, 9 GeV E p (x, Q FL x medium & high Q / GeV Q Extend to higher Q using e scattered in LAr calorimeter. Future: extend to lower Q using Backward Silicon Tracker. Good agreement with theory expectations. 3

24 Jets at Tevatron Gluon density at intermediate and high x is mostly constraint by Tevatron jet measurement. Preliminary CDF Run II analysis based on improved cone algorithm (midpoint). New data from D, with..% jet energy scale uncertainty prefers lower gluon at high x. (Fermilab-PUB-8/34-E, submitted to PRL). data / theory DØ Run II - L =.7 fb y <.4 =.7 R cone NLO scale uncertainty.5. < y < NLO pqcd µ R F T +non-perturbative corrections.4 < y <.8.6 < y <. = µ = p CTEQ6.5M with uncertainties MRST4 5 3 Data Systematic uncertainty.8 < y <.. < y < p (GeV) T Improved precision vs Run-I, lower xg(x). Consistency with Run-I? 4

25 Flavor Decomposition ud _ us _ W + cs _ cd _ -4-4 y du _ su _ W - sc _ dc _ -4-4 y uu _ cc _ Z bb _ dd _ ss _ -4-4 We want to have predictions for W +, W, Z with the main experimental input from F em : u s F em (m W,x (y)) y d c b More important d, s quarks For Z, significant contribution from b. y 5

26 Neutral Current Cross Section and xf 3 HERA xf 3 γz H (prel.) Q =5 GeV xf 3 γz ZEUS (prel.) Q =5 GeV Inclusive SF can be used to study different flavor combinations, for example.. xf 3 = x e q a q (q(x) q(x)) xf 3 γz x - - x H+ZEUS Combined (prel.) Q =5 GeV H PDF ZEUS-JETS PDF - - x Large increase compared to HERA-I of e sample allows to improve precision of the interference structure function xf γz 3 Very difficult measurement at low x for HERA. 6

27 Measurements of heavy flavors F cc _ 4 i H+ZEUS F cc _ (x,q ) x=. i=5 x=.5 i=4 F _ bb 8 i H+ZEUS F bb _ (x,q ) x=. i=5 x=.5 i=4 x=. i=3 x=. i=3 x=.5 i= x=.5 i= x=.3 i= - x=.3 i= - - H HERA I+II 6 e p (prel.) H D ZEUS D MRST4 MRST NNLO CTEQ6HQ 3 x=.3 i= Q /GeV - -3 H HERA I+II 6 e p (prel.) ZEUS (prel.) 39 pb - MRST4 MRST NNLO CTEQ6.5 HVQDIS + CTEQ5F4 3 x=.3 i= Q /GeV Measure F c c and F b b structure functions by tagging the c quarks via D decay or c/b quark using secondary vertex. 7

28 Tevatron input W ± asymmetry W +, W asymmetry analysis is sensitive to u/d momentum ratio at high x: A(y W ) u(x )d(x ) d(x )u(x ) u(x )d(x ) + d(x )u(x ) W Charge Asymmetry CDF Run II Preliminary L = fb - fb data(stat. + syst.) NNLO Prediction(MRST) CTEQ6M PDF Uncertainty Band New technique allows to measure W ± asymmetry directly instead of lepton asymmetry. For y W =.75, x =.6 and x =.64 the measurement compares well with PDF uncertainty. W rapidity 8

29 Tevatron measurements of Z rapidity D publishes a measurement of Z rapidity based on fraction of Run- II data. For D MRST with NNLO corrections describe the data. dσ/dy /σ.. - DØ,.4 fb.3 Z/γ* Rapidity D Run II Data NNLO, MRST Boson Rapidity, y CDF preliminary result can distinguish between different PDF sets. MRST NNLO is worse than CTEQ NLO. 9

30 PDFs for LHC energy scale: LHeC Consider LHC result: σ(h)/σ(z) about 3σ away from SM prediction. New physics or new QCD evolution? Measurement of PDFs close to LHC energy could be performed by 7 GeV 7 GeV ep machine at CERN: LHeC. High luminosity ( fb ): yield of 5 events at GeV. e + and e beams to measure xf 3. Lepton beam polarization (?) for F γz. An attractive machine at its cost. st ECFA-CERN LHeC Workshop -3 Sept 8. 3

31 Experimental data still to come Final analysis of F structure function at low Q < GeV and low x (H). Analysis of σ r at high Q and high x using HERA-II data. Measurement of F L structure function in complete kinematic domain. HERA-II analysis of F c c and F b b. Combination of all HERA data. PDF extraction based on the combined HERA data. Tevatron W asymmetry and Z rapidity with complete statistics. 3

32 Conclusions HERA enables precise determination of PDFs for the LHC kinematic range. DGLAP evolution works very well so far. Precise Tevatron measurements give a preview of what will be possible at LHC. Experimental input for PDFs could be vastly expanded with LHeC. More information will come with finalization of HERA/Tevatron analyzes, combination of H/ZEUS data, measurement of heavy flavors and of F L. 3