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Bernd L öhr, DESY

DIFFRACTION AT HERA. The HERA Collider and the Experiments Luminosity and its Measurement Kinematics of Deep-Inelastic (DIS) and Diffractive Reactions Diffraction in High-Energy Particle Scattering Regge Phenomenology versus pQCD Exclusive Vectormeson Production and

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Bernd L öhr, DESY

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  1. DIFFRACTION AT HERA The HERA Collider and the Experiments Luminosity and its Measurement Kinematics of Deep-Inelastic (DIS) and Diffractive Reactions Diffraction in High-Energy Particle Scattering Regge Phenomenology versus pQCD Exclusive Vectormeson Production and Deeply-Virtual Compton Scattering (DVCS) Inclusive Diffraction and Diffractive Structure Functions Exclusive Diffractive Reactions: Jets and Heavy Quarks Page 1 Bernd Löhr, DESY

  2. 27.5 GeV 920 GeV The HERA Collider Electron - proton collisions electrons protons This corresponds to an electron energy in a fixed-target experiment of Ee = 26952 GeV Bernd Löhr, DESY Page 2

  3. The H1 Experiment HERA I Configuration Tracking : protons backward Liquid-Argon calorimeter : EM section : protons HAC section : electrons Bernd Löhr, DESY Page 3

  4. A rear view of the H1 detector Bernd Löhr, DESY Page 4

  5. The ZEUS Experiment Tracking : HERA I Configuration backward Uranium-scintillator- calorimeter : protons EM section : protons electrons HAC section : Bernd Löhr, DESY Page 5

  6. protons The ZEUS detector seen from above electrons Bernd Löhr, DESY Page 6

  7. The Concept of Luminosity Proton and electron beams are not continuous but they consist of bunches. Typically 180 proton bunches and electron bunches collided. Individual bunches from each beam collide What is the probability that a given process happens ? reaction rate ; (instantaneous) luminosty [cm-2s-1] cross section ; The luminosity can be calculated from HERA parameters: -number of electrons/protons in the i-th bunch -beam revolution frequency ; where: - transverse size of interaction region [cm-2] L = integrated luminosity Cross section: Bernd Löhr, DESY Page 7

  8. Measurement of the Luminosity Measure the rate of a process whose cross-section is well known: initial state radiation final state radiation Bremsstrahlung in e- collisions or Bethe-Heitler process proton proton Measure energy and rate of bremsstrahlung photons in specialized photon detector under very small angles w.r.t. the electron beam ZEUS interaction point p- beam very well known cross-section photon detector e-- beam (universal) integrated luminosity, for all cross-section calculations about 100m away from interaction point Bernd Löhr, DESY Page 8

  9. From Optical Diffraction to High Energy Particle Scattering High energetic elastic scattering Optical diffraction Generalization in high energy particle interactions : Diffraction is the exchange of an object with vacuum quantum numbers. Hypothetical object : Pomeron IP double dissociation double Pomeron exchange single dissociation elastic Bernd Löhr, DESY Page 9

  10. Kinematics of DIS and Diffraction Inclusive nondiffr. DIS events : center of mass energy squared virtuality, size of the probe - proton cms energy squared x: fraction of the proton carried by the struck parton y: inelasticity, fraction of the electron momentum carried by the virtual photon Diffractive DIS events : mass of the diffractive system x For diffractive events in addition 2 variables k k’ four-momentum transfer squared at the proton vertex q = k - k’ momentum fraction of the proton carried by the Pomeron fraction of the Pomeron momentum which enters the hard scattering Bernd Löhr, DESY Page 10

  11. DIS- and Diffractive Events Inclusive DIS events : Considerable energy flow in the very forward direction Diffractive DIS events : Large rapidity gap in forward direction k k’  ln tan(2) Pseudo-Rapidity • is the angle w.r.t. proton direction. Bernd Löhr, DESY Page 11

  12. Regge Phenomenology vs. pQCD Regge Phenomenology Peripheral (soft) processes e’ e X R I =Reggeon trajectory I P, R I P =Pomeron trajectory I p P’ t Diffraction shrinkage From fit to hadronic data : (Donnachie, Landshoff) 0.16 Bernd Löhr, DESY Page 12

  13. Diffractive DIS in pQCD In pQCD the simplest way to describe the exchange of vacuum quantum numbers is the exchange of a colour neutral system of two gluons. This is realized in the colour dipole picture. + + The wave function of the incoming virtual photon can be calculated from QED. The outgoing wave function might be known for some exclusive Final states, like e.g. vector mesons. higher orders Bernd Löhr, DESY Page 13

  14. Exclusive Vectormeson Production I VDM+Regge * VM VM Shrinkage ; p P’ pQCD r r2 small if Q2 large or MV large * z VM 1-z Ryskin : p P’ and fast rise with W no or little shrinkage Do pQCD models describe the data ? Which variables can provide a hard scales ? Bernd Löhr, DESY Page 14

  15. PHP Exclusive Vectormeson Production II DIS Bernd Löhr, DESY Page 15

  16. Can the Vectormeson Mass be a Hard Scale ? I Photoproduction ; Q2=0 The w-dependence of the “light” vector-meson ( r, w, f )production is described by Regge phenomenology For higher mass vector mesons the rise of the production cross section with W gets steeper. This indicates the onset of hard diffractive scattering Bernd Löhr, DESY Page 16

  17. Can the Vectormeson Mass be a Hard Scale ? II Photoproduction : Q2=0 Shrinkage W dependence d=0.74 from H1 alone [GeV] 50 100 200 W[GeV] pQCD models can describe photoproductionof J/Y mesons. Still some shrinkage seen in J/Y photoproduction but compatible with pQCD models. Bernd Löhr, DESY Page 17

  18. Can Q2 be a Hard Scale ? I r-electroproduction -electroproduction For r –production the W-dependence gets steeper with Q2. ZEUS . J/Y The rise with W is essentially independent of Q2 for production pQCD models can describe exclusive production Bernd Löhr, DESY Page 18

  19. Can Q2 be a Hard Scale ? II Slopes of the t-distributions The b-slope of r-production decreases with Q2. At high Q2 it reaches the value of -production. The b-slope of -production is independent of Q2 . It is a hard process already at Q2 =0. Q2 provides a hard scale Bernd Löhr, DESY Page 19

  20. Can |t| be a Hard Scale ? I Complication : at high |t|, the vector-meson production proceeds predominantly through proton-dissociative processes. e’ e VM Low mass MY : particles of system Y disappear undetected through the beampipe hole in the detector. High mass MY: a fraction of the particles from system Y are detected in the calorimeter. Y p t Within experimental uncertainties : vertex factorization holds . We have to assume vertex factorization : The ratio should not depend on Q2. Bernd Löhr, DESY Page 20

  21. Can |t| be a Hard Scale ? II Ivanov et al. pQCD models Bartels et al. not exponential at high |t|, predicted by pQCD models. t-dependence of p-dissociative vector-meson production can be described by pQCD models. Large |t| may provide a hard scale to apply pQCD. Bernd Löhr, DESY Page 21

  22. The Pomeron Trajectory I e’ e Measure W-dependence separately for different t-bins Pomeron trajectory VM I P p P’ t IP(t)= IP(0)+’•t 1.198 + 0.115.t DIS r 1.14 + 0.04.t r photoproduction 1.096+0.125.t F photoproduction 1.081+0.158.t Soft pomeron (DL) 1.08+.25.t Bernd Löhr, DESY Page 22

  23. The Pomeron Trajectory II Slope of the Pomeron trajectory at higher |t| : depends on t However : for high |t| , proton diffractive processes dominate. In Regge language : is not linear in t Bernd Löhr, DESY Page 23

  24. Decay Matrix Density and Ratio of Longitudinal to Transverse Cross-Section for roProduction The rois a spin 1 particles. It decays into two pions: ro -> p++p-. The angular distribution ofthe decay particles p+ and p-isdescribed by a function of 3 angles: In total 15 density matrix elements describe the decay angular distribution, which depend on the helicity amplitudes for spin non-flip, single spin-flip, and double spin-flip: T00, T01, T10, T11, T1-1 ; Notation: S-channel helicity conservation Only non-flip amplitudes T00and T11are non-zero Bernd Löhr, DESY Page 24

  25. Measured Decay Matrix Elements for roProduction I If S-channel helicity conservation (SCHC) is valid only the following matrix elements should be different from zero: Bernd Löhr, DESY Page 25

  26. Measured Decay Matrix Elements for roProduction II If S-channel helicity conservation is valid only the following spin density matrix elements should be zero: r100 = r111 = r500 = r511 = 0 At very small |t| SCHC holds, as |t| grows SCHS is increasingly violated. A pQCD based model (I.Royen and J.Cudell) is able to describe the SCHC violation. Bernd Löhr, DESY Page 26

  27. Ratio of longitudinal to transverse cross-section A virtual photon has two polarization states: transverse: helicity 1 (normal light) longitudinal: helicity 0 (only for Q2>0) Ratio of longitudinal to transverse cross-section is function of the photon virtuality: If SCHS holds -> D=0. R is qualitatively described by pQDC models Bernd Löhr, DESY Page 27

  28. Deeply Virtual Compton Scattering I DVCS Bethe-Heitler Bethe-Heitler processes lead to the same final state Difficult to disentangle experimentally Interference between QCD and QED gives access to DVCS-QCD amplitude : x - skewedness Interference term can be derived from asymmetries, e.g. Beam-Spin-Asymmetry: Probably cleanest test of pQCD , no hadrons in the final state. Generalized parton distributions GPD -> information on transverse distribution of partons Bernd Löhr, DESY Page 28

  29. Deeply Virtual Compton Scattering II s ~ Wd Q2 = 8 GeV2 : d = 1.0 DVCS is a hard process NLO-QCD calculations can describe DVCS qualitatively, magnitude of the predicted cross-section depends on used parton-density functions Bernd Löhr, DESY Page 29

  30. Deeply Virtual Compton Scattering III t-dependence of DVCS measured at several Q2 and W values For Q2> 5 GeV2: b ~ 5 -6 GeV-2 Compatible with b values for hard production of vector mesons Bernd Löhr, DESY Page 30

  31. Summary of Exclusive Vectormeson Production • A high vectormeson mass provides a hard scale. • Photoproduction of r, w, f is described by sof Pomeron exchange, • whereas J/Y photoproduction is a hard process, it can be described by pQCD models. • Vectormeson production at high Q2 is a hard process, pQCD can be applied. • The vertex factorization holds. • Vectormeson production at high |t| is a hard process. • The |t|-n dependence is in agreement with pQCD expectations. • The Pomeron trajectory for r, f photoproduction is compatible with the • soft Pomeron trajectory : and shrinkage is observed. • DIS r and J/Y trajectories are not compatible with a soft Pomeron, • little shrinkage is observed. • pQCD based models are able to describe the features of exclusive hard-production • of vector mesons Bernd Löhr, DESY Page 31

  32. Summary of Deeply Virtual Compton Scattering • At high Q2 the W-dependence of the DVCS cross-section • and the slope of the t-distribution are compatible with a • hard production process • DVCS described in terms of generalized parton distributions (GPD) • which contain information on transverse distributions of partons in • the proton. • Recently high statistics measurements of DVCS by H1 became available • for electron-proton and positron-proton scattering. • It is, however, still along way before one can extract GPDs. • Apologies to HERMES ! The HERMES experiment have measured DVCS to • a larger extent, also beam-spin asymmetries. These data are typically at • Q2 of 1-2 GeV2. It is not really clear whether pQCD is already applicable • at these low Q2. Bernd Löhr, DESY Page 32

  33. Definition of Inclusive Diffraction Model of a resolved pomeron Colour dipole model e’ e e’ e no colour exchange, vacuum quantum numbers no colour exchange, vacuum quantum numbers P’ p P’ p Definition of inclusive diffractive scattering: • The quantum numbers of the vacuum are exchanged • between the proton and the virtual photon. • (The proton stays intact.) Attention: different definitions of diffractive cross-sections, proton dissociative events are (partially) included or not. Bernd Löhr, DESY Page 33

  34. Inclusive Diffraction I Diffractive/proton dissociative scattering in the parton picture : Two additional variables e’ e Momentum fraction of the proton carried by the Pomeron MX ß W xIP Large rapidity gap Momentum fraction of the Pomeron carried by the struck quark MY p t There is no method available to measure directly inclusive diffractive cross-sections Experimentally there are three different methods used to select diffractive events : 1.Detection of outgoing proton : includes reggeon exchange 2. Large rapidity gap : includes reggeon exchange and proton dissociation into small mass 3. MX – method : includes proton dissociation into small mass Bernd Löhr, DESY Page 34

  35. The Proton Detection Method 1.) Detection of outgoing proton ( H1,ZEUS) The ZEUS Leading Proton Spectrometer LPS Z=96 m diffractive peak Proton-beam direction S4+S5+S6 : vertical spectrometer Silicon strip detectors xL= 1-xIP S1+S2+S3 : horizontal spectrometer Fraction of initial proton momentum carried by the diffractive proton Z=26 m Detection of the diffractive proton is the only method to measure the t-distribution Advantage: no proton dissociaton Disadvantage: small acceptance possible Reggeon contributions Bernd Löhr, DESY Page 35

  36. The Rapidity Gap Method min . No tracks or energy deposits in calorimeter for rapidities greater than maxor at angles less than min. H1 LEPTO : nondiffractice MC-simulation Requiring a rapidity gap Dh (e.g. hmax<2) in the events removes most of the nondiffractive contribution. mostly diffractive This is equivalent to restrict measurements to low xIP. Advantage: large acceptance -> high statistics Disadvantage: contains contributions from nondiffractive and proton dissociative reactions and Reggeon contributions hmax Bernd Löhr, DESY Page 36

  37. The MX-Method (I) Non diffractive events Rapidity Uncorrelated particle emissionbetween incoming p-direction and scattered quark. Property of a produced particle Idealised rapidity distribution Length of rapidity distribution is given by cms-energy Rapidity gap as a statistical fluctuation Poisson distr. for Dy in nondiffractive events Bernd Löhr, DESY Page 37

  38. x< 0.1 The MX-Method (II) Experimentally at high energies and not too low MX with This follows also from a triple Regge model Cortousy of K.Goulianos t-averaged Bernd Löhr, DESY Page 38

  39. The MX-Method (III) Nondiffractive + diffractive contributions Two approaches for fit to the data D is the diffractive contribution 1.) take D=const.for a limited range in ln M2X Fit slope b, c and D for 2.) take D from a BEKW-model (see later) parametrization which describes the measured data. This is an iterative procedure. Determine diffractive events by subtracting nondiffractive events from measured data bin by bin as calculated from fitted values b and c. Advantage: no nondiffractive contribution large acceptance -> high statistics Disadvantage: contains contribution from proton dissociation Both approaches give the same results Bernd Löhr, DESY Page 39

  40. Diffractive Cross-Section and Diffractive Structure Functions sizeable only at high y, can safely be neglected in the range of HERA measurements. If t is not measured, i.e. integrated over and anlogously H1 uses , ZEUS neglects the longitudinal part and uses Bernd Löhr, DESY Page 40

  41. Diffractive DIS Factorization In the same way as for DIS, diffractive deep inelastic cross sections can be expressed as a convolution of diffractive parton densities with a deep inelastic cross section. diffractive parton distribution function (dpdf) number density of a parton i in the proton under the condition that it undergoes a diffractive reaction dpdfs at fixed t and xIP evolve with Q2 according to DGLAP hard universal DIS cross section DDIS factorization rigorously proven: Collins ; Berera, Soper ; Trentadue, Veneziano dpdfs are universal for all hard diffractive processes Bernd Löhr, DESY Page 41

  42. Regge-Factorization Regge theory originally developed for eleastich 2-body scattering Extension to inclusive diffraction: Triple-Regge formalism This expression allows the decomposition into a flux factor and a cross section: Based on the triple-Regge formalism the diffractive parton distribution functions are factorized accordingly: with This Regge- or vertex-factorization cannot be proven in pQCD Bernd Löhr, DESY Page 42

  43. Separation of Pomeron from Reggeon Contributions Results obtained with LPS/FPS method and the LRG method may contain nondiffractive contributions from Reggeon exchanges. They are fitted by a sum of Pomeron and Reggeon contributions. From the fit the Pomeron contribution can be extracted. is taken from a parametrization of the pion structure function The fluxes are normalized according to: with Fitted values are and , the normalization of the Reggeon contribution Other parameters, like , are also fitted or taken from other measurements. Bernd Löhr, DESY Page 43

  44. QCD DGLAP Fits In a picture where the Pomeron has a partonic structure (Ingelmann-Schlein Model) can be interpreted as the Pomeron structure function Pomeron structure function expressed as a sum of universal Pomeron parton distribution functions : Pomeron pdfs obey DGLAP evolution Parametrization at a starting value Q02as : z is the longitudinal momentum fraction of the parton entering the hard sub-process. z = b for lowest order quark-parton modell process, 0 < b < z for higher order processes. A DGLAP fit and the Regge fit are usually carried out simultaneously Bernd Löhr, DESY Page 44

  45. Results from Proton Detection Method H1: Forward Proton Spectrometer (FPS) ZEUS: Leading Proton Spectrometer (LPS) combined Regge and DGLAP fit Regge fit at two t-values --- extrapolation to nonmeasured Q2 ..... Pomeron contribution only Bernd Löhr, DESY Page 45

  46. Comparison FPS with LPS data Fair agreement in shape between the FPS and LPS results Both datasets have systematic uncertainties from the beam divergence H1: +/- 10% ZEUS: +12%/-10% They are not shown in the figures. Bernd Löhr, DESY Page 46

  47. H1 LRG Results DGLAP fit to H1 data Regge fit to ZEUS data Both data show qualitatively the same features Data contain contributions from proton dissociation Bernd Löhr, DESY Page 47

  48. Comparison between H1 and ZEUS LRG Results Good agreement in shape The ZEUS data are normalized to the H1 data Reason : The H1 dataset and the ZEUS dataset contain different amounts of proton dissociation. The data are not corrected for that. Bernd Löhr, DESY Page 48

  49. Comparison between H1 FPS and LRG Results The LRG data contain contributions from proton dissociation up to masses of 1.6 GeV. The FPS data are multiplied by a factor 1.23 such that they correspond to the LRG data Bernd Löhr, DESY Page 49

  50. H1 DPDF Fits Singlet Structure function Gluon structure function Differences between fit A and fit B For both fits only data with Q2>8.5 GeV2 have been used. Aq, Bq, Cqare always fitted Qo2 = 1.75 GeV2 Fit A: Bgis set to zero Qo2 = 2.5 GeV2 Fit B: Bg, Cgis set to zero For fit A the fraction of exchanged momentum carried by gluons in the range 0.0043<z<0.8 is around 70% throughout the studied Q2 range. For fit B it is a little less but compatible with fit A. The gluon density is only weakly constraint by the data Bernd Löhr, DESY Page 50

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