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HERMES A nalysis T echniques

HERMES A nalysis T echniques. Contalbrigo Marco INFN Ferrara. Niccolo ’ Cabeo School: TMDs 26th May, 2010 Ferrara. Moving out of collinearity. X. Semi-inclusive. Semi-inclusive. Inclusive. TMDs ( x ,z, P h ,Q 2 ). PDFs (x ,z,Q 2 ). SFs (x,Q 2 ). T.

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HERMES A nalysis T echniques

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  1. HERMES Analysis Techniques Contalbrigo Marco INFN Ferrara Niccolo’ Cabeo School: TMDs 26th May, 2010 Ferrara

  2. Moving out of collinearity X Semi-inclusive Semi-inclusive Inclusive TMDs (x,z,Ph ,Q2) PDFs(x,z,Q2) SFs (x,Q2) T Transverse momentum dependent partondistri. Spin-Orbit effects Parton distributions Flavor sensitivity Structure functions (unpolarized, helicity) Sum over quark charges Rich and Involved phenomenology !! M. Contalbrigo 2 Ferrara: TMDs school

  3. TheExperiment

  4. Contalbrigo Marco Consiglio di Sezione 1 luglio 2009 HERaMEasurementof Spin HERA beam @ DESY (27.6 GeV) Polarised Deep Inelastic Scattering 27.6 GeV Lepton (Electron/Positron) 920 GeV protons Ferrara: TMDs school

  5. HERMES @ DESY <Pb>~ 53±2.5 % Self-polarisinge+/e- beam: Sokolov-Ternov effect 27.5 GeV (e+/e-) self-polarising Pure nuclear-polarised H,D atomic gaseous target ms polarization switching at 90s time intervals L ~ O(1031) cm-2 s-1 1H→<|Pt|> ~ 85 ±3.8 % 2H→<|Pt|> ~ 84 ±3.5 % 1H <|Pt|> ~ 74 ±4.2 % M. Contalbrigo 5 Ferrara: TMDs school

  6. The HERMES experiment Hadron ID in a broad kinematic range [2-14 GeV/c] Resolution: Dp/p ~ 1-2% Dq<~0.6 mrad Electron-hadron separation efficiency ~ 98-99% kinematic range ~ 7 GeV: 1 < Q2 < 10 GeV2 0.02 < x < 0.4 M. Contalbrigo Ferrara: TMDs school 7

  7. SIDIS cross section g1L h1 Distribution Functions (DF) ┴ ┴ ┴ ┴ ┴ Azimuthal moments require careful study of instrumental effects M. Contalbrigo 8 Ferrara: TMDs school

  8. Experimental artefacts  Particle mis(identification)  Acceptance effects Radiative corrections  Detector smearing M. Contalbrigo 9 Ferrara: TMDs school

  9. ParticleIdentification

  10. Particle Identification To identify a lepton one requires PID (ratio of probabilities) greater than a certain value For each track the conditional probability that the track is a lepton (hadron) given detector response is related via the Bayes’ theorem to the probability a lepton (hadron) causes the signal and the prior (flux of particles) The PID can be rewritten as M. Contalbrigo 21 Ferrara: TMDs school

  11. Particle Identification Defined by combining the responses of all the (independent) PID detectors D Measured by placing very restrictive cuts to other PID detectors to isolate a very clean sample of a particular particle type M. Contalbrigo 22 Ferrara: TMDs school

  12. Particle Identification CALO: lead-glass block wall + Preshower: 2 X0 lead + scintillator TRD: polyethylene fibers as radiator + Xe:CH4 (90:10) proportional chambers Is the ratio between the hadron and lepton fluxes impinging onto the detector The fluxes were computed in an iterative procedure starting from uniform case (lepton flux = hadron flux) by comparing resulting lepton/hadron yields with assumed fluxes. M. Contalbrigo 23 Ferrara: TMDs school

  13. Extracted fluxes M. Contalbrigo 24 Ferrara: TMDs school

  14. The EVT RICH particle ID qC (rad) No ring for p 2 rings for e,p 1 ring for k,p Dual radiator Ring Imaging Cerenkov To avoid inefficiency related to track spatial position (azimuthal angles) Likelihood based on full event topology M. Contalbrigo Ferrara: TMDs school 25

  15. The EVT RICH particle ID Expected fractional number of photons hitting NPMT: From DATA with no track From MC Poisson probability to have a hit: Likelihood for a Combined Particle Type Hypothesis with observed hit pattern (1 or 0 for each PMT) : Take the most probable hypothesis if the ratio rQp between most probable and second most probable hypotheses is greater than a certain value M. Contalbrigo 26 Ferrara: TMDs school

  16. RICH P-matrices Identified hadron vector True hadron fluxes P: probability that a track of true tipe ht is identified as type hi M. Contalbrigo 27 Ferrara: TMDs school

  17. RICH unfolding Identified hadron vector True hadron fluxes Truncated to account for only Identified hadrons Event weighting procedure: Each identified hadron is assigned a weight given by the appropriate elements of P-1. The sum run over all the identified tracks, and ht(hi)j labels the identified type of track j. M. Contalbrigo 28 Ferrara: TMDs school

  18. Acceptance

  19. Detector acceptance Lepton Virtual Photon Hadrons Partial coverage in phi at a given detected event kinematics Acceptance introduce azimuthal modulations in the measured yields ! M. Contalbrigo 30 Ferrara: TMDs school

  20. Detector acceptance Detector acceptance and efficiency cancel out in spin asymmetries thanks to the rapid target spin flipping This is not the case for binned quantities systematics This is not the case for unpolarised modulations correction M. Contalbrigo 31 Ferrara: TMDs school

  21. Polarized analyses g1L h1 Distribution Functions (DF) ┴ ┴ ┴ ┴ ┴ Azimuthal moments require careful study of instrumental effects M. Contalbrigo 32 Ferrara: TMDs school

  22. The unbinned maximum likelihood M. Contalbrigo Ferrara: TMDs school 33

  23. The unbinned maximum likelihood The event distribution and probability density distribution for target polarization distribution All terms In a binned analysis residual acceptance dependencebecause ofintegrated quantities (acceptance/efficiency does not factorize) systematics M. Contalbrigo Ferrara: TMDs school 34

  24. The unbinned maximum likelihood All terms Rapid cycling of the target spin states is crucial ! M. Contalbrigo 35 Ferrara: TMDs school

  25. Full-differential physical model The full kinematicdependenceof the Collins and Siversmoments on is evaluated from the real data through a fit of the full set of SIDIS eventsbased on a Taylor expansion on : e.g.: acceptance effects vanish model assumptions minimized Extraction: Testing the method: The extracted azimuthal moments and are folded with the spin-independent cross section (known!) in 4 and within the HERMES acceptance : M. Contalbrigo Ferrara: TMDs school 36

  26. Testing the method with MC Small effectwith model extracted fromDATA systematic error Arbitrary input model Standard extraction method New extraction method The method works nicely at MC level! Blue: within acceptance Black: in 4 M. Contalbrigo Ferrara: TMDs school 37

  27. Physics results Sivers is different from zero !! Statistics: three projections of the same data set ! Systematics: extracted asymmetry versus model at average kinematics M. Contalbrigo 38 Ferrara: TMDs school

  28. 2-D Siversmomentsforp± x vs z zvs Ph ┴ M. Contalbrigo 39 Ferrara: TMDs school

  29. RadiativeCorrections

  30. SIDIS cross section g1L h1 Distribution Functions (DF) ┴ ┴ ┴ ┴ ┴ Azimuthal moments require careful study of instrumental effects M. Contalbrigo 41 Ferrara: TMDs school

  31. Radiative and Instrumental smearing Radiative effects: vertex corrections and real photon radiation by the lepton Instrumental effects: multiple scattering and external bremsstrahlung Measured Smearing: true DIS but with biased kinematics Background: fake DIS (i.e. elastic events) or true DIS outside kinematic limits Generated M. Contalbrigo 42 Ferrara: TMDs school

  32. MC tools GMC_trans: • Generator implementing models for TMDs and azimuthal moments • tuned to reproduce i.e. the observed dPhT/dz distribution •  no radiative effects up to now Pythia: • Sophisticated generator of the unpolarized cross-section •  tuned to the HERMES kinematics (multiplicities) • polarization dependence is introduced a-posteriori • randomly sort the spin state with probability defined by a given asymmetry model M. Contalbrigo Ferrara: TMDs school 43

  33. MC tools Suppose to have a model for s+ands-, or equivalently for A Polarized case: divide the unpolarized sample into two subsamples by randomly choosing the spin state following s+ and s- probabilities Unpolarized case: select a subsamples by randomly choosing the events following one of the two probability M. Contalbrigo Ferrara: TMDs school 44

  34. The unfolding of radiative effects procedure Probability that an event generated with kinematics wis measured with kinematics w’ Includes the events smeared in from outside kinematic limits Accounts for acceptance (Sii<1), radiative and smearing effects depends only on instrumental and radiativeeffects (known quantities) is a relative quantity: “no” model dependence Introduces a model dependence Needs a proper normalization M. Contalbrigo Ferrara: TMDs school 45

  35. The unfolding of radiative effects procedure Remove systematics but introduce statistical correlations Typical inflation of the statistical errors for the diagonal elements of the covariance matrix The covariance matrix provides the full statistical power of the measurement (correlations should be taken into account) The correction is averaged over the bin M. Contalbrigo Ferrara: TMDs school 46

  36. The multidimensional approach x Q2 One-dimensional analysis Multi-dimensional analysis Best output for phenomenological models of TMDs M. Contalbrigo Ferrara: TMDs school 47

  37. The multidimensional approach x bin=1 x bin=2 Z x bin=3 x bin=4 x bin=5 f f f f f unfolding projection M. Contalbrigo Ferrara: TMDs school 48

  38. The method of least squares M. Contalbrigo 49 Ferrara: TMDs school

  39. Linear Least Squares hj(xi)=1 (V non-diagonal): weighted average (of correlated quantities) h(xi)=(1, cos<fi>, cos<2fi>), V,y after unfolding: unpolarizedazimuthal moments M. Contalbrigo 50 Ferrara: TMDs school

  40. Unfolding + linear regression Method 1 Method 2 FIT of the measured yields FIT of the unfolded yields Linear regression Linear regression C-1EXP is diagonal: 1 matrix inversion 3 large matrix inversions M. Contalbrigo 51 Ferrara: TMDs school

  41. Physics results Different from zero result !! Clear dependence on hadron charge !! Projections of a full-differential result ! Only possible thanks to the large unpolarised statistics accomulated M. Contalbrigo Ferrara: TMDs school 52

  42. Conclusions TMDs analyses required special care Event Reconstruction: Account for beam and scattered particles bending in target holding field Account for full event topology in particle ID Special algorithms to minimize/correct instrumental effects (ML fits, unfolding, multi-D) evaluate systematic effects (full differential model of the signal) Analysis : Statistics matters: number of bins in a multi-dimensional analysis number of constrained terms in a full-differential model M. Contalbrigo Ferrara: TMDs school 53

  43. Systematic error Tracking: • Different tracking algorithms •  alternative correction methods for bending inside the transverse magnet • standard tracking and improved version with refined Kalmann filter implementation, • accounting for all B fields, misalignments and providing goodness of fit estimator. M. Contalbrigo Ferrara: TMDs school 54

  44. Systematic error Misalignment: • Monte Carlo study comparing • different beam position and slopes within ranges estimates • by special alignment runs (dipole off); •  detector aligned and misaligned geometry, the latter from • survey measurements of the sub-detector positions; • indicator: top versus bottom detector halve response comparison. Tracking: • Different tracking algorithms •  alternative correction methods for bending inside the transverse magnet • standard tracking and improved version with refined Kalmann filter implementation, • accounting for all B fields, misalignments and providing goodness of fit estimator. M. Contalbrigo Ferrara: TMDs school 55

  45. Systematic error Misalignment: • Monte Carlo study comparing • different beam position and slopes within ranges estimates • by special alignment runs (dipole off); •  detector aligned and misaligned geometry, the latter from • survey measurements of the sub-detector positions; • indicator: top versus bottom detector halve response comparison. Tracking: • Different tracking algorithms •  alternative correction methods for bending inside the transverse magnet • standard tracking and improved version with refined Kalmann filter implementation, • accounting for all B fields, misalignments and providing goodness of fit estimator. Acceptance/Resolution: • Monte Carlo study comparing • reconstructed azimuthal moments with physical model in input • to the simulation (evaluated at the average kinematics or integrated in 4p); M. Contalbrigo Ferrara: TMDs school 56

  46. Azimuthal moments extraction g1L h1 Distribution Functions (DF) ┴ ┴ ┴ ┴ ┴ Azimuthal moments require careful study of instrumental effects M. Contalbrigo 57 Ferrara: TMDs school

  47. Online Issues

  48. Beam dynamic Beam trajectory 2mm shift at cell center Synchrotron radiation cone 5 kW emitted power at 50 mA beam M. Contalbrigo 59 Ferrara: TMDs school

  49. HERMES Transverse Target Field The holding magnetic field is required to inhibit depolarization mechanism by effectively decoupling the electrons and nucleons magnetic moments while providing the target spin direction. Due to the RF fields induced by the bunched HERA beam, depolarization resonances could happen between different hyperfine states at certain B values. The magnetic flux density has to be stabilized within 0.18 mT M. Contalbrigo 60 Ferrara: TMDs school

  50. B Field drifts with Temperature The magnetic flux density decreased with time due to the increasing temperature of the main yoke, pole and pole tips, affecting the magnetic permeability of the material (magnet is off during beam injection) Automatic compensating system added: pair of correcting coils to the main coils Before After Additional correction coils mounted into the cell to increase spatial uniformity of the field M. Contalbrigo Ferrara: TMDs school 61

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