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Tom Danielson University of Wisconsin – Madison

A Measurement of Multijet Production in Low- x Bj Deep Inelastic Scattering with ZEUS at HERA. Tom Danielson University of Wisconsin – Madison. Study of Partons. Particle Scattering Study charge & magnetic moment distributions Scattering via probe exchange Wavelength

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Tom Danielson University of Wisconsin – Madison

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  1. A Measurement of Multijet Production in Low-xBjDeep Inelastic Scattering with ZEUS at HERA Tom Danielson University of Wisconsin – Madison

  2. Study of Partons • Particle Scattering • Study charge & magnetic moment distributions • Scattering via probe exchange • Wavelength • Special Case : Deep Inelastic Scattering • High energy lepton transfers momentum to a nucleon via probe h : Plank’s Constant Q: related to momentum of photon

  3. Naïve Quark Parton Model e(k) e(k’)  *(q)  Jet p(P) • Scattering on proton is sum of elastic scattering on all of the proton’s constituents (partons) • Point-like Partons • Structure Functions: quantify distribution of partons and their momentum • Parton Density Functions (PDF) • Must be extracted from experimental structure function measurements Bjorken Scaling: Only x dependence x = fraction of momentum carried by quark

  4. QCD Theory • Gluons: vector colored bosons carry strong force • Gluons produce quark and gluon pairs • Quarks gain transverse momentum • Gluon-driven increase in F2 Bjorken Scaling Violation: Fi(x) Fi(x,Q2) Observation of QCD effects  Small x

  5. e±p scattering mediated by g, Z0 (Neutral Current) W± (Charged Current) Deep Inelastic Scattering Squared center-of-mass energy of ep system Exchange boson virtuality (negative squared 4-mom. of exchange boson) Fractional proton momentum carried by struck quark (QPM) Fraction of electron energy transferred to proton in proton rest frame Kinematics relation

  6. Neutral Current (NC) DIS Cross Section • Express NC cross section in terms of DIS kinematics and proton structure • F2, FL, F3 → proton structure functions • F2 → interaction between transversely polarized photon and partons • FL → interaction between longitudinally polarized photon and partons • xBjF3 → parity violating term from Z0exchange • fi(x,Q2) → Parton density functions (PDFs) • Extracted from fits to structure function measurements

  7. Perturbative QCD and Splitting Functions      lepton S S S photon  gluon quark • DIS cross sections expressed as series expansion in as • Splitting functions give probability quark or gluon to split into parton pair • Leading Order quark and gluon splitting diagrams shown

  8. QCD evolution: Described by DGLAP equations Done by perturbative resummations over diagrams DGLAP Leading Log: Sum over diagrams contributing ln(Q2) terms Double Leading Log: Sum over ln(Q2) ln(1/x) terms BFKL: Sum over diagrams contributing ln(1/x) terms CCFM: Splitting functions with non-Sudakov form factors kt factorization interpolates between DGLAP, BFKL QCD Parton Evolution Splitting Functions

  9. Kinematic Coverage of Colliders LHC Tevatron HERA • HERA: e±p • 0.1 < Q2 < 20000 GeV2 • 10-6 < xBj < 0.9 • CM energy 300 – 318 GeV2 • Tevatron: pp • 2000 < Q2 < 250000 GeV2 • 10-2 –10-3 < xBj < 0.9 • CM Energy 1.8 – 1.96 TeV • LHC: pp • 100 < Q2 < 108 GeV2 • 10-6 < xBj < 0.9 • CM Energy 14 TeV (startup) • HERA coverage in x similar to LHC • ~2 orders of magnitude lower in x than Tevatron

  10. Evolving PDFs to LHC • Are extracted PDFs usable in the LHC kinematic range? • (10-6 < x < 1) • Account for low-x effects • Saturation • Multiple interactions • Does DGLAP evolution work sufficiently to extrapolate? • Gluon contribution dominant at low x

  11. Testing QCD Parton Evolution: Multijets Jets in DIS Boson-Gluon Fusion (BGF) QCD Compton • Partons not experimentally observed • Colorless hadrons form through hadronization • Collimated “spray” of particles → Jets • Dijets • Produced from Boson-Gluon Fusion, QCD Compton processes • Leading-Order diagrams O(a1s) • Direct coupling to gluon

  12. Testing Parton Evolution: Jets at low xBj increasing η • Study QCD evolution schemes with jets at low xBjin DIS • DGLAP • Leading Log: Strong ordering in kT, ordering in x • Double Leading Log: Strong ordering in kT, and x • well tested over large range of Q2 • BFKL: sums over ln(1/x) terms • Strong ordering in x, but not ordered in kT • More energetic forward jets • Jets from hard scatter less correlated in energies, angles • CCFM: kT factorization • Approaches BFKL for low xBj, DGLAP for high Q2 • angular ordering (instead of kTordering) • uses unintegrated parton densities

  13. Testing Parton Evolution: Jets at low xBj • Study QCD evolution schemes with jets at low xBjin DIS • DGLAP • Leading Log: Strong ordering in kT, ordering in x • Double Leading Log: Strong ordering in kT, and x • well tested over large range of Q2 • BFKL: sums over ln(1/x) terms • Strong ordering in x, but not ordered in kT • More energetic forward jets • Jets from hard scatter less correlated in energies, angles • CCFM: kT factorization • Approaches BFKL for low xBj, DGLAP for high Q2 • angular ordering (instead of kTordering) • uses unintegrated parton densities Applicability range of evolution approaches

  14. HERA Accelerator at DESY • Beam energies • Proton energies • 820 GeV (1992 – 1997) • 920 GeV (1998 – 2007) • 460, 575 GeV (2007) • Facilitated FL Measurement • 27.5 GeV e- or e+ • 300 – 318 GeV Center-of-Mass Energy • Equivalent to ~30 TeV fixed target • 220 bunches • Not all filled • Crossings every 96 ns • Typical beam currents • Proton: 100 mA • Electron: 40 mA • Instantaneous luminosity • ~5 x 1031cm-2s-1 HERMES H1 H1 ZEUS HERA-B DESY Hamburg, Germany

  15. ZEUS Detector x z ZEUS coordinate system p 920 GeV MUON CAL CTD y e+ 27.5 GeV Multi-purpose detector Characterizes energy, direction and type of particles in the final state

  16. ZEUS Calorimeter h = 0.0q = 90o h = -0.75q = 129.1o h = 1.1q = 36.7o h = 3.0q = 5.7o e p FCAL BCAL RCAL Hadronic Cells Electromagnetic Cells • Alternating layers of depleted uranium and plastic scintillator • Sampling Calorimeter • Most energy absorbed by DU • Compensating • Equal hadronic and electromagnetic response • Segmented • 3 Sections (FCAL, RCAL, BCAL) • Divided further into modules, cells • 2 PMTs/cell • Energy resolutions (test beam) • Electromagnetic: 18% / √E • Hadronic: 35% / √E • Timing Resolution • ~1 – 2 ns • 99.7% solid angle coverage • (-3.5 < h< 4.0) h = -ln(tan(q/2))

  17. Central Tracking Detector (CTD) • Drift chamber inside 1.43 T solenoid • Angular coverage: 15o < q < 164o (-1.96 < h < 2.04) • Organization • 16 azimuthal sectors • 9 concentric superlayers • 8 radial layers superlayer • 32 – 96 cells per superlayer • Resolutions • Transverse momentum s/pT = [(0.005pT)2 + (0.0016)2]1/2 • Vertex resolution • longitudinal (z): 4mm • transverse (x-y): 1mm Superlayers Sectors

  18. ZEUS Trigger • 10 MHz crossing rate, 100 kHz Background rate, 10Hz physics rate • First level: Use data subset: 10 MHz → 500 Hz • Pipelined without deadtime • Global and regional energy sums • Isolated m and e+ recognition • Basic tracking information • Second level: Use all data: 500 Hz → 100 Hz • Calorimeter timing cuts • Tracking, vertex information • Simple physics filters • Third level: Use full reconstruction information: • 100 Hz → 10 Hz • Full event information • Refined jet and electron finding • Complete tracking algorithms • Advanced physics filters

  19. ZEUS Event Reconstruction • Vertex: Use CTD tracks fit to 5-parameter Helix model • Calorimeter • Use cell position, magnitude of PMT pulse, timing of PMT pulse • Island formation: Cells merged based on location and size of energy deposits • e-/e+: SINISTRA95 Neural Network electron finder • Use electromagnetic islands as input • Require corresponding CTD track if island within CTD acceptance region • Output: list of electron candidates with associated probabilities • Use most probable candidate as DIS electron • Energy Flow Objects (EFOs) • Combine track and calorimeter information for hadrons • CTD has better angular resolution than CAL • CTD has better energy resolution at low energy than CAL

  20. Kinematic Reconstruction Four measured quantities: EH, gH, E‘e, qe. Only two independent quantities. Reconstruction methods used: Electron method, Jacquet-Blondel Methods have different resolutions over different kinematic regions gH qe

  21. Jet FindingHadronic Center of Mass Frame • Select a frame to optimize multijet finding • Single jet event • Struck quark rebounds parallel to frame’s z-axis • Zero transverse energy (ET) • Dijet event • Jets balanced in ET at leading order • Equivalent to Breit Frame, apart from longitudinal boost • Used in other ZEUS analysis • HCM frame used to compare to results from H1 collab.

  22. Jet Reconstruction – Energy Scale • Calorimeter response calibrated using Uranium background • Methods for finding jet scale uncertainty • 1: Use single jet DIS event • Scattered electron, jet balanced in momentum • Predict jet energy from scattered electron energy, compare rel. diff. • 2: Use MC to correct for energy loss from inactive material • Correct jets from MC and data to hadron level • Compare using tracking information in cone around jets • Jet energy scale uncertainty • ± 1% for ET > 10 GeV, ± 3% otherwise • ± 1% → ~5% uncertainty in s • 41% of dijets • ± 3% → ~15% uncertainty in s • 59% of dijets Jet energy scale uncertainty as function of hLAB

  23. Jet Trigger – Cone Algorithm R • Used in higher level trigger selection • Maximize ET of hadrons in cone of fixed size • Construct seeds from energy deposits in cells • Iterate until stable cone found • Merge overlapping cones according to scheme • For the jet: • Issues with older cone algorithms • Overlapping jets and soft radiation between jets • Seed – Energy threshold • Infrared unsafe – s → ∞ as seed threshold → 0

  24. Jet Reconstruction – kt Algorithm • kt: In ep transverse momentum with respect to beam line • For every object i and every pair of objects i, j calculate • di = (ET,i)2 → Distance to beam line in momentum space • dij = min{E2T,i,E2T,j}[(Dh)2 + (Df)2]→ Distance between objects • Combine all di, dijinto set • Calculate min{di,dij} for each object and pair of objects • If minimum of set corresponds to di → Object for ditaken as jet • If minimum of set corresponds to dij→ Combine objects i and j • Advantages • No seed required and no overlapping jets • Suitable for beyond-NLO pQCD calculations

  25. Leading Order Monte Carlo • MC events + detector simulation • to compare with the data • to correct data for detector effects • ARIADNE v4.10 • Color Dipole Model (CDM) • Gluons emitted from color field between quark-antiquark pairs • Gluons not necessarily kt ordered (BFKL-like) • Supplemented with boson-gluon fusion processes • LEPTO v6.5.1 • Matrix Element + Parton Shower (MEPS) • Parton cascade: approximate higher orders in LO calc • Decreasing virtuality (q2) as cascade progresses • Radiated gluons kt-ordered (DGLAP) • Both use Lund String Model to simulate hadronization CDM MEPS

  26. Next-to-Leading-Order (NLO) pQCD Calculations • NLOjet: Inclusion of single gluon emission in dijet, trijet final states • Terms of up to O(a2s) (O(a3s)) included for dijet (trijet) calculations • One-loop corrections for virtual particles • Correction for 3rd (4th) parton in final state (soft/collinear gluon emissions) • Calculations do not include parton showering, hadronization • Corrections taken from MC • Scale dependences • Renormalization scale: scale for evaluating as • Factorization scale: scale at which PDFs are evaluated Programs for DIS • DISENT • MEPJET • DISASTER++ • NLOJET++ (used)

  27. Application of NLOjet Calculations Scales: • Varied simultaneously by factors 4, ¼ for theoretical uncertainty • Renormalization scale uncertainty estimates contributions from higher-order terms PDF set: CTEQ6M Hadronization corrections from LEPTO For certain jet phase space, O(as3) calculations possible for dijets

  28. Low xBj DIS Multijet Sample • Data: 1998-2000 electron and positron: 82.2 pb-1

  29. Triggering Efficiency • Trigger selection → well-reconstructed event • Trigger rate, efficiency affected by bandwidth, storage limits • Low-Q2 trigger ~100% efficient, but prescaled • Enhance low-Q2 efficiency of trigger selection with medium-Q2, dijet and prescaled low-Q2 trigger • ~80% overall efficiency at low Q2 with combined trigger chain Low Q2 Low Q2 (prescaled) Medium Q2 Dijet Total

  30. Low-xBj Dijets vs. Ariadne ZEUS 82 pb-1 ARIADNE Discard Kinematic variables well-described by Ariadne Jet variables reasonably well-described 6% Excess jets at High ET included in systematics Level of agreement similar to other ZEUS multijet analyses

  31. Low-xBj Dijets vs. Lepto ZEUS 82 pb-1 LEPTO Kinematic variables reasonably well-described by Lepto High-ET excess reduced to ~2%

  32. Low-xBj Trijets vs. Ariadne ZEUS 82 pb-1 ARIADNE Trijet variables reasonably well-described by Ariadne Excess jets at High ET included in systematics

  33. Low-xBj Trijets vs. Lepto ZEUS 82 pb-1 LEPTO Trijet variables reasonably well-described by Lepto High-ET excess reduced

  34. Systematic Uncertainties • Kinematic and jet cuts: +/- Ariadne resolutions • Jet energy scale variation • Difference between Ariadne and Lepto acceptance correction • Largest uncertainties from • Lepto instead of Ariadne: 5 – 10 % • Sometimes larger • Jet energy scale: 5 – 15 % • Cut on E1,2T,HCM: 5 – 10 % for jet correlations • Cut on E3T,HCM for trijet sample: 5 – 10 %

  35. ZEUS Dijet, Trijets vs. xBj • Test DGLAP-based calculations from NLOjet for inclusive cross sections, ratios • Dijet, trijet cross sections both well-described. • Measure cross section ratios → cancel theoretical uncertainties • Ratios also well-described, esp. at low xBj

  36. Jet Correlations • Inclusive cross sections well-described by NLOjet calculations • Examine correlations between two highest ET,HCM jets for non-DGLAP effects Separation in h of two hardest jets Difference in ET,HCM of two hardest jets Magnitude of vector sum of jet pT Scaled magnitude of vector difference of jet pT Separation in f of two hardest jets

  37. Separation in h of two hardest jets Dijets Trijets • NLOjet calculations describe h correlations • Description of data independent of xBj • Higher-order terms not needed to describe dijet h correlations

  38. Dijets:Mag. of Vector Sum of pT from Jet 1,2 • |SpT| sensitive to parton evolution, gluon radiation • |SpT| = 0 without gluon radiation • NLOjet calculations at O(as2) do not describe dijet data at low xBj • NLOjet calculations at O(as3) describe data, even at low xBj • Higher order terms important at low xBj • Allows for more gluon emission

  39. Trijets: Mag. of Vector Sum of pT from Jet 1,2 • Expand study of |SpT| by examining trijets • Higher order measurement (O(as2) at LO) • NLOjet calculations at O(as3) describe the data • Better description at higher values of xBj • Higher-order NLO calculations not available • Effect much less pronounced than for dijets vs. O(as2) NLOjet calculations

  40. Dijets: Scaled Mag. of Vec. Difference of Jet pT • |DpT|/(2 ETjet1) sensitive to parton evolution, gluon radiation • |DpT|/(2 ETjet1) = 1 without gluon radiation • NLOjet calculations at O(as2) do not describe dijet data at low xBj • NLOjet calculations at O(as3) describe data, even at low xBj • Higher order terms important at low xBj • Allows for more gluon emission

  41. Dijets:Separation in f of Two Hardest Jets • |Df| sensitive to parton evolution, gluon radiation • |Df| = p without gluon radiation • NLOjet calculations at O(as2) do not describe dijet data at low xBj • NLOjet calculations at O(as3) describe data, even at low xBj • Higher order terms important at low xBj • Allows for more gluon emission

  42. Trijets: Separation in f of Two Hardest Jets • Expand study of |Df| by examining trijets • Combine first two bins in |Df| to reduce stat., systematic errors • NLOjet calculations at O(as3) describe the data • Slightly better description at higher values of xBj • Higher-order NLO calculations not available • Large theoretical uncertainties

  43. ZEUS 2,3-jet Azimuthal Correl. vs. Q2, xBj Dijets Trijets • |Df*| < 2p/3 → high-ET forward jet • Measurements sensitive both to angular correlations, forward jets • NLOjet calculations at O(as3) describe dijet, trijet data, even at low xBj • Dijets at low xBj: O(as3) calcs for dijets ~ 10 x O(as2) calcs

  44. H1 Trijet Results vs. NLOjet • Parton evolution for multijet events examined: • Angular correlations • Normalized jet energies • For • Inclusive trijet • Trijet with 1, 2 forward jets Inclusive Trijets • Inclusive trijet data generally well-described by NLOjet calculations at O(as3) • Data above calculations at low xBj

  45. Summary: Low-xBj Dynamics at HERA • Dijet, trijet correlations at ZEUS measured at small xBj(10-2 < xBj < 10-4) • Dijet, trijet pT and azimuthal correlations most sensitive to gluon radiation, parton evolution • Higher-order terms important at low Q2, xBj • Effects more pronounced for dijets • Higher-order calculations up to 10x larger at very small xBj • Correlations well-described by NLOjet calcs. • Cross sections in xBj, correlations in h well-described by NLOjet calcs. • Less sensitive to parton evolution scheme • DGLAP evolution with current PDFs safe to (x ~ 10-4) • O(as2) calcs not good enough for entire dijet phase space. Need O(as3).

  46. ZEUS inclusive forward jets: Expect more forward jets with BFKL, CCFM at low xBj LEPTO (DGLAP) consistently below measurements CASCDE (CCFM) inconsistent in description of data Better description from J2003 set 2 than set 1 ARIADNE (CDM, ~BFKL) gives best overall description H1 dijet azimuthal correlations: Expect broader Df* spectrum from BFKL, CCFM CASCADE with J2003 pdf set describes data at higher xBj CASCADE predictions dependent on unintegrated gluon PDF All models fail to describe Df* at low xBj Other ZEUS and H1 Results:Leading-Order Models

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