Introduction Combined Cross Sections & QCD Fits NC & CC Cross Section Measurements F L Summary Novel Measurements of Proton Structure at HERA Katie Oliver University of Oxford On behalf of the H1 and ZEUS collaborations Rencontres de Moriond QCD and High Energy Interactions 19th March 20 Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 1 / 17
Introduction Combined Cross Sections & QCD Fits NC & CC Cross Section Measurements F L Summary HERA, H1 and ZEUS HERA collided protons with longitudinally polarized e ± H1 and ZEUS were multi-purpose collider detectors at HERA 0.5 fb 1 luminosity taken by each experiment H1 Integrated Luminosity / pb -1 Status: 1-July-2007 400 300 200 electrons positrons low E HERA-2 HERA-1 HERA Energies p beam: 920 GeV e ± beam: 27.5 GeV Centre of mass energy: 318 GeV 0 0 0 500 00 1500 Days of running Mean polarization: 30-40% Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 2 / 17
Introduction Combined Cross Sections & QCD Fits NC & CC Cross Section Measurements F L Summary Kinematics & Deep Inelastic Scattering Probing power of the lepton: Q 2 = q 2 = (k k ) 2 = sxy Bjorken scaling variable, the fraction of the proton s momentum carried by the struck quark x = Q2 2p.q Neutral current exchange of γ or Z Charged current exchange of W ± Inelasticity, the energy fraction transferred from the lepton in the proton s rest frame y = p.q p.k Centre of mass energy squared: s = (p + k) 2 Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 3 / 17
Introduction Combined Cross Sections & QCD Fits NC & CC Cross Section Measurements F L Summary Neutral Current Cross Sections Unpolarised neutral current reduced cross section σ e± p NC Y ± 1 ± (1 y) 2 = xq4 1 d 2 σ(e ± p) 2πα 2 Y + dxdq 2 = F 2 Y xf 3 y 2 F L Y + Y + Structure functions at Leading Order F 2 (q + q) Dominant contribution xf 3 (q q) Contributes at high Q 2 (γz interference) F L = 0 Zero at Leading Order Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 4 / 17
Introduction Combined Cross Sections & QCD Fits NC & CC Cross Section Measurements F L Summary Charged Current Cross Sections Charged current reduced cross section σ(e p) CC = (1 P e ) [u + c + (1 y) 2 (d + s)] σ(e + p) CC = (1 + P e ) [u + c + (1 y) 2 (d + s)] Linear polarisation dependence Electron (positron) data is sensitive to u (d) valence quark Probes flavour structure of the proton Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 5 / 17
Introduction Combined Cross Sections & QCD Fits NC & CC Cross Section Measurements F L Summary HERA-I Inclusive Cross Section Combination H1 & ZEUS have combined inclusive cross sections from HERA I data ( 115 pb 1 per experiment) Combination procedure: 1 Swim all points to a common Q 2 x grid 2 Move 820 GeV data to 920 GeV p-beam energy 3 Calculate average values and uncertainties 4 Evaluate procedural uncertainties Data combination uses χ 2 minimisation method Overall precision is improved χ 2 /NDF = 637/656 Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 6 / 17
Introduction Combined Cross Sections & QCD Fits NC & CC Cross Section Measurements F L Summary QCD Fits NC and CC reduced cross sections are the main input used to determine Parton Distribution Functions (PDFs) by performing QCD Fits Measure σ for polarised data Obtain F 2, xf 3 and extract the PDFs: q(x, Q 2 ), q(x, Q 2 ), g(x, Q 2 ) Proton PDFs are an important input for LHC physics Evolve PDFs to the LHC kinematic region with DGLAP equations Only need to evolve in Q 2 since HERA x range is comparable to that of LHC Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 7 / 17
Introduction Combined Cross Sections & QCD Fits NC & CC Cross Section Measurements F L Summary HERAPDF1.0 Combined HERA-I data are the sole input in determination of a new set of PDFs with small experimental uncertainties: HERAPDF1.0 Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 8 / 17
Introduction Combined Cross Sections & QCD Fits NC & CC Cross Section Measurements F L Summary Combined Data With HERAPDF1.0 HERA-I data: Good sensitivity at low Q 2 BUT limited statistical precision at high Q 2 HERA-II data not yet included: further improvement possible! JHEP01 (20) 9 Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 9 / 17
Introduction Combined Cross Sections & QCD Fits NC & CC Cross Section Measurements F L Summary Charged Current & Neutral Current at HERA-II Higher statistics improved precision Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 / 17
Introduction Combined Cross Sections & QCD Fits NC & CC Cross Section Measurements F L Summary High Q 2 NC Cross Sections I Eur. Phys. J. C 62 (2009) 625-658 H1prelim-09-042 σ e± p NC F 2 Y Y + xf 3 and x F ( ) 3 = Y+ 2Y σ e p σ e+ p x 3 (2u v + d v ) Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 11 / 17
Introduction Combined Cross Sections & QCD Fits NC & CC Cross Section Measurements F L Summary High Q 2 NC Cross Sections II Polarization asymmetry provides a direct measure of EW effects: NC parity violation observed at EW scale A ± = P + e 2 P e ( σ ± (P e + ) σ ± (Pe ) ) σ ± (P e + ) + σ ± (Pe ) Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 12 / 17
Introduction Combined Cross Sections & QCD Fits NC & CC Cross Section Measurements F L Summary High Q 2 CC Cross Sections I H1prelim-09-043 Eur. Phys. J. C 61 (2009) 223-235 Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 13 / 17
Introduction Combined Cross Sections & QCD Fits NC & CC Cross Section Measurements F L Summary F L I At NLO, F L α s xg(x, Q 2 ). F L contributes at high y, low Q 2 F L has not previously been measured directly: gluon density was derived from scaling violations in F 2 Direct F L measurement requires measurement of the reduced cross sections at same x and Q 2 but different y Q 2 = sxy different y different s different beam energies Low Q 2 NC reduced cross section σ e± p NC = F 2(x, Q 2 ) y 2 Y + F L (x, Q 2 ) At given x and Q 2 : F 2 is the intercept at y-axis, F L is the negative slope Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 14 / 17
Introduction Combined Cross Sections & QCD Fits NC & CC Cross Section Measurements F L Summary F L II NEW: ZEUS and H1 combination σ r σ r 1.5 1.4 1.3 1.2 1.1 1 0.9 0.8 0.7 1.5 1.4 1.3 1.2 1.1 1 0.9 0.8 H1 and ZEUS Q 2 =24GeV 2 Q 2 =32GeV 2 Q 2 =60GeV 2-3 -2 x Q 2 =80GeV 2-3 -2 x HERA prel. Q 2 =45GeV 2 E p =920 GeV E p =575 GeV E p =460 GeV Q 2 =1GeV 2 HERAPDF1.0 σ r 920 σ r 575 σ r 460-3 -2 x HERA Inclusive Workging Group March 20 σ r (x,q 2,y) 1.4 1.2 1 0.8 1.4 1.2 1 0.8 Q 2 =1 GeV 2 X=0.00205 X=0.00290 0.5 1 X=0.00229 X=0.00334 0.5 1 H1 and ZEUS X=0.00256 X=0.00444 HERA prel. E p =920 GeV E p =575 GeV E p =460 GeV Linear fit HERA Inclusive Workging Group March 20 0.5 1 y 2 /(1+(1-y) 2 ) E p (GeV) s (GeV) L (pb 1 ) 920 318 21.6 575 251 6.2 460 225 12.4 Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 15 / 17
Introduction Combined Cross Sections & QCD Fits NC & CC Cross Section Measurements F L Summary x F L III F L 0.4 0.2 0-0.2 0.000059 0.000087 0.000128 0.000168 0.000231 0.000324 0.000404 0.000534 0.000641 HERA preliminary HERAPDF1.0 H1 and ZEUS 0.000855 0.001215 0.001599 0.002113 2 Q 2 / GeV 2 F L is extracted in region: 2.5 < Q 2 < 800 GeV 2 A new and important input to QCD 0.002927 0.003795 0.005420 0.006843 0.0099 0.012250 0.020170 0.026220 0.032270 HERA Inclusive Workging Group March 20 Published: Combined: H1: Phys. Lett. B665 (2008) 139-146 H1prelim--043 ZEUS: Phys. Lett. B682 (2009) 8-22 ZEUS-prel--001 Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 16 / 17
Introduction Combined Cross Sections & QCD Fits NC & CC Cross Section Measurements F L Summary Summary A lasting legacy of HERA is a far greater understanding of the structure of the proton H1 and ZEUS will continue to combine data to achieve greater precision HERA data is necessary for precise predictions at the LHC Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 17 / 17
Back-Up Slides Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 1 / 26
HERA: Polarised Lepton Beam e beam becomes transversely polarized through emission of synchrotron radiation Spin rotators were installed during the HERA upgrade to obtain longitudinal polarization at both IPs Mean (lumi weighted) polarization achieved: 30-40% Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 2 / 26
H1 Hermetic - 4π detector Tracking: Central drift chamber Silicon Microvertex detector Liquid-argon calorimeter (LAr) Rear lead-scinitillator (SPACAL) µ chambers Optimised for precision measurement of the scattered electron Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 3 / 26
ZEUS Hermetic - 4π detector Tracking: Central Tracking Detector (CTD), a cylindrical drift chamber Silicon Microvertex detector (MVD) (HERA-II) Compensating uranium scintillator calorimeter (UCAL) µ chambers Optimised for precision measurement of the hadronic final state Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 4 / 26
F L : H1 Comparison To Theory Curves ) 2 (x, Q F L 1 H1 Data H1 PDF 2000 CTEQ 6.6 MSTW 07 x 0.00028 0.00037 0.00049 0.00062 0.00093 0.0014 0.0022 0.0036 0.5 0 20 40 60 80 2 2 Q / GeV Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 5 / 26
F L : ZEUS Comparison To Theory Curves -4 5-3 ZEUS -3 2-3 3 x 4-3 F L 0.7 ZEUS MSTW08 NLO 0.6 0.5 ZEUS-JETS CTEQ6.6 MSTW08 NNLO KW Dipole (b-sat) TW Resummed 0.4 0.3 0.2 0.1 0 2 20 30 40 50 60 70 80 90 Q 2 (GeV 2 ) Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 6 / 26
F L : Indirect Measurement Low Q 2 reduced cross section σ NC Derivative method: σ NC = F 2 (Q 2, x) y 2 Y + F L (x, Q 2 ) d σ d ln y Q 2 df 2 d ln y Q 2 2y 2 (2 y) Derivative dominated by F L term at high y Shape method: σ fit = cx λ y 2 Y + F L Y 2 + Shape driven by kinematic factor rather than F L F L Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 7 / 26
F 2 & F 3 Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 8 / 26
Charged Current & Neutral Current Events CC Event: Large missing transverse momentum (p T ) due to neutrino NC Event: High p T isolated scattered electron/positron and balanced total p T Final selection: 3 events per sample Final selection: 5 events per sample Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 9 / 26
Neutral Current Event Selection High p T isolated scattered electron/positron and balanced total p T Suppress photoproduction background: conserve longitudinal energy-momentum: δ = E p z 2E e Final selection: 5 events per sample Kinematic reconstruction: angle and energy of scattered electron Q 2 el = 2E e E e(1 + cos θ e ) y el = 1 E e 2E e (1 cos θ e ) x el = Ee E p E e (1+cos θe) 2E e E e(1 cos θ e) Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 / 26
Charged Current Event Selection Large missing transverse momentum (p T ) due to neutrino Suppress dominant background (photoproduction) Topological finders to remove cosmic muons Final selection: 3 events per sample Kinematic reconstruction from hadrons (Jacquet-Blondel) δ = ( i E i pz) i pt 2 = ( ) 2 ( ) 2 i pi x + i pi y y JB = δ 2E e x JB = p 2 T sy JB (1 y JB ) Q 2 JB = sx JBy JB Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 11 / 26
High Q 2 NC and CC Cross Sections NC and CC high Q 2 cross sections are measured very precisely over many orders of magnitude in Q 2 Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 12 / 26
High Q 2 CC Cross Sections II σ e± p CC (P e) = (1 ± P e )σ e± p CC (P e = 0) Tests chiral nature of the SM Do not constrain linear fit to zero at P e = +1 (P e = -1) for electrons (positrons) Assume non-zero cross section due to a right-handed W boson (W R ) Derive lower limit on mass of W R assuming: g L = g R Light ν R Electron Positron H1 186 GeV 208 GeV ZEUS 180 GeV Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 13 / 26
ZEUS & H1 Combination Method Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 14 / 26
Combination Method: χ 2 µ i Measured value at point i γj i Relative correlated systematic δ i, stat Relative statistical uncertainty δ i, uncor Relative uncorrelated systematic uncertainty m i Prediction for measurement Shifts of correlated error sources b j Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 15 / 26
Combination Method: Procedural Uncertainties Additive vs multiplicative nature of the error sources typically below 0.5% A study of the possible correlated systematic uncertainties between H1 and ZEUS was performed: Identified 12 possible uncertainties of common origin Compared 212 averages taking all pairs as correlated/uncorrelared in turn Mostly negligible except for: 1 Correlated systematic uncertainty for the photoproduction background (few % at high-y) 2 Correlated systematic uncertainty for the hadronic energy scale (at the per mille level) Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 16 / 26
Combination Method: Uncertainties 1402 points are combined to 741 unique cross section measurements χ 2 /NDF = 637/656 1 systematic errors from the experimental considerations 3 procedural systematic errors Overall precision: 3 < Q 2 < 500 GeV: 2% precision 20 < Q 2 < 0 GeV: 1% precision Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 17 / 26
Combination Method: Cross-Calibration Several correlated systematic uncertainties are reduced considerably for the averaged result: Uncertainty on H1 calorimeter energy scale reduced by 55% Uncertainty on ZEUS γp background reduced by 65% Different reconstruction methods similar systematic sources influence cross sections differently as a function of Q 2 and x Requiring agreement at all Q 2 and x constrains systematics In some regions, one experiment has better precision The less precise measurement is fitted to the more precise one Reduction in correlated systematic uncertainty Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 18 / 26
PDF Details Scheme: Thorne-Roberts VFNS Evolution: QCDNUM Order: NLO Q0 2 1.9 GeV 2 f s 0.31 Renormalisation scale: Q 2 Factorisation scale: Q 2 Qmin 2 3.5 GeV 2 α S (M W ) 0.1176 M c 1.4 GeV 4.75 GeV M b Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 19 / 26
PDF Experimental Uncertainties Uncorrelated uncertainties: Statistical errors Point-to-point uncorrelated uncertainties: e.g statistical errors due to MC simulations Are added in quadrature to the statistical errors Correlated uncertainties: Point-to-point correlated uncertainties: e.g. electromagnetic and hadronic energy scale calibration often common for CC and NC for a given experiment and run period Overall normalisation uncertainty: Correlated for all data points for a given experiment and run period Correlations between H1 and ZEUS: H1 and ZEUS use similar analyses methods Largest from γp background and hadronic energy scales Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 20 / 26
PDF Model Uncertainties Numerical values used for the central fit are varied Difference between the nominal fit and fits corresponding to model variations are added in quadrature Total model uncertainty Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 21 / 26
PDF Parametrisation Uncertainties 1 Variation in Q0 2 (starting scale) 2 Negative gluon contribution at low-x is allowed 3 B uv B dv for u v and d v parametrisations: xu v (x) = A uv x Bu v (1 x) Cu v (1 + E uv x 2 ) xd v (x) = A dv x B dv (1 x) C d v 4 Variation in number of terms in the polynomial: xf (x) = Ax B (i x) C (1 + ɛ (x) + Dx + Ex 2 ) Envelope representing the maximum deviation at each x value is constructed to represent the parametrisation uncertainty Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 22 / 26
HERAPDF1.0: Comparison to Other PDFs xf 1 2 2 Q = GeV xf 1 2 2 Q = GeV 0.8 0.8 xg ( 0.05) HERAPDF1.0 xg ( 0.05) HERAPDF1.0 0.6 CTEQ6.6 90% CL 0.6 MSTW08 90% CL 0.4 xu v 0.4 xu v xs ( 0.05) xs ( 0.05) 0.2 xd v 0.2 xd v 0-4 -3-2 -1 1 x 0-4 -3-2 -1 1 x Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 23 / 26
ZEUSfit09: Adding High Q 2 NC and CC Polarised e p Data The ZEUS-JETS PDF was modified by incorporating: 1 high-q 2 NC polarised e p data: Eur. Phys. Journal C 62 (2009) 625-658) 2 high-q 2 CC polarised e p data: Eur. Phys. Journal C 61 (2009) 223-235) fractional uncertainty 0 0.2 0.4 0.6 0.8 1 0.6 xu v 2 2 Q = GeV 0.4 0.2 0-0.2-0.4-0.6 0 0.2 0.4 0.6 0.8 1 0.6 0.4 0.2 0-0.2-0.4-4 -0.6-4 xs -3-3 -2 ZEUS fit - (CC/NC e p) -2-1 -1 ZEUS 0 0.2 0.4 0.6 0.8 1 2 xd v 1.5 1 0.5 0-0.5-1 -1.5-2 0 0.2 0.4 0.6 0.8 1 0.8 0.6 0.4 0.2-0 -0.2-0.4-0.6-4 -0.8-4 xg -3-3 -2 ZEUS-JETS PDF -2-1 -1 x Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 24 / 26
ZEUSfit09: Adding High Q 2 CC Polarised e + p Data In addition, high-q 2 CC polarised e + p data was added (ZEUS-prel-09-002) fractional uncertainty 0 0.2 0.4 0.6 0.8 1 0.6 xu v 2 2 Q = GeV 0.4 0.2 0-0.2-0.4-0.6 0 0.2 0.4 0.6 0.8 1 0.6 0.4 0.2 0-0.2-0.4-4 -0.6-4 xs -3-3 -2 ZEUS fit ± - (CC e p/nc e p) -2-1 -1 ZEUS 0 0.2 0.4 0.6 0.8 1 2 xd v 1.5 1 0.5 0-0.5-1 -1.5-2 0 0.2 0.4 0.6 0.8 1 0.8 0.6 0.4 0.2-0 -0.2-0.4-0.6-4 -0.8-4 xg -3-3 -2 ZEUS fit - (CC/NC e p) -2-1 -1 x Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 25 / 26
ZEUSfit09: Adding High Q 2 NC and CC Polarised e p and High Q 2 CC Polarised e + p Data The ZEUS-JETS PDF was modified by incorporating: 1 high-q 2 NC polarised e p data: Eur. Phys. Journal C 62 (2009) 625-658 2 high-q 2 CC polarised e p data: Eur. Phys. Journal C 61 (2009) 223-235 3 high-q 2 CC polarised e + p data: ZEUS-prel-09-002 fractional uncertainty 0 0.2 0.4 0.6 0.8 1 0.6 xu v 2 2 Q = GeV 0.4 0.2 0-0.2-0.4-0.6 0 0.2 0.4 0.6 0.8 1 0.6 0.4 0.2 0-0.2-0.4-4 -0.6-4 xs -3-3 -2 ZEUS fit ± - (CC e p/nc e p) -2-1 -1 ZEUS 0 0.2 0.4 0.6 0.8 1 2 xd v 1.5 1 0.5 0-0.5-1 -1.5-2 0 0.2 0.4 0.6 0.8 1 0.8 0.6 0.4 0.2-0 -0.2-0.4-0.6-4 -0.8-4 xg -3-3 -2 ZEUS-JETS PDF -2-1 -1 x Katie Oliver (University of Oxford) Novel Measurements of Proton Structure at HERA 19th March 20 26 / 26