Contalbrigo Marco INFN Ferrara Niccolo Cabeo School TMDs

Contalbrigo Marco INFN Ferrara Niccolo’ Cabeo School: TMDs 26 th May, 2010 Ferrara

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

HERa MEasurement of Spin HERA beam @ DESY (27. 6 Ge. V) 27. 6 Ge. V Lepton (Electron/Positron) 920 Ge. V protons Contalbrigo Marco Ferrara: di TMDs Consiglio Sezioneschool Polarised Deep Inelastic Scattering 1 luglio 2009

HERMES @ DESY Self-polarising e+/e- beam: Sokolov-Ternov effect 27. 5 Ge. V (e+/e-) self-polarising <Pb>~ 53± 2. 5 % Pure nuclear-polarised H, D atomic gaseous target ms polarization switching at 90 s time intervals L ~ O(1031) cm-2 s-1 1 H→ <|Pt|> ~ 85 ± 3. 8 % 2 H→ <|P |> ~ 84 ± 3. 5 % t 1 H M. Contalbrigo Ferrara: TMDs school <|Pt|> ~ 74 ± 4. 2 % 5

The HERMES experiment Resolution: Dp/p ~ 1 -2% Dq <~0. 6 mrad Hadron ID in a broad kinematic range [2 -14 Ge. V/c] Electron-hadron separation efficiency ~ 98 -99% kinematic range ~ 7 Ge. V: 1 < Q 2 < 10 Ge. V 2 0. 02 < x < 0. 4 M. Contalbrigo Ferrara: TMDs school 7

SIDIS cross section Distribution Functions (DF) ┴ ┴ g 1 L ┴ M. Contalbrigo ┴ h 1 ┴ Azimuthal moments require careful study of instrumental effects Ferrara: TMDs school 8

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

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 Ferrara: TMDs school 21

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 Ferrara: TMDs school 22

Particle Identification CALO: lead-glass block wall + Preshower: 2 X 0 lead + scintillator TRD: polyethylene fibers as radiator + Xe: CH 4 (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 Ferrara: TMDs school 23

Extracted fluxes M. Contalbrigo Ferrara: TMDs school 24

q. C (rad) The EVT RICH particle ID No ring for p 2 rings for e, 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

The EVT RICH particle ID Expected fractional number of photons hitting NPMT: From MC Poisson probability to have a hit: From DATA with no track 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 r. Qp between most probable and second most probable hypotheses is greater than a certain value M. Contalbrigo Ferrara: TMDs school 26

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 Ferrara: TMDs school 27

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 Ferrara: TMDs school 28

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 Ferrara: TMDs school 30

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 M. Contalbrigo Ferrara: TMDs school correction 31

Polarized analyses Distribution Functions (DF) ┴ ┴ g 1 L ┴ M. Contalbrigo ┴ h 1 ┴ Azimuthal moments require careful study of instrumental effects Ferrara: TMDs school 32

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

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

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

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

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

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 Ferrara: TMDs school 38

2 -D Sivers moments for p± z vs Ph ┴ x vs z M. Contalbrigo Ferrara: TMDs school 39

SIDIS cross section Distribution Functions (DF) ┴ ┴ g 1 L ┴ M. Contalbrigo ┴ h 1 ┴ Azimuthal moments require careful study of instrumental effects Ferrara: TMDs school 41

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

MC tools GMC_trans: Generator implementing models for TMDs and azimuthal moments tuned to reproduce i. e. the observed d. Ph. T/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

MC tools Suppose to have a model for s+and s-, 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

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

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

The multidimensional approach x Q 2 One-dimensional analysis Multi-dimensional analysis Best output for phenomenological models of TMDs M. Contalbrigo Ferrara: TMDs school 47

The multidimensional approach Z x bin=1 x bin=2 x bin=3 x bin=4 x bin=5 ing old unf f f n tio c je pro M. Contalbrigo Ferrara: TMDs school 48

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

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

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

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

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 Analysis : Special algorithms to minimize/correct instrumental effects (ML fits, unfolding, multi-D) evaluate systematic effects (full differential model of the signal) 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

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

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. 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. M. Contalbrigo Ferrara: TMDs school 55

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. 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. 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 4 ); M. Contalbrigo Ferrara: TMDs school 56

Azimuthal moments extraction Distribution Functions (DF) ┴ ┴ g 1 L ┴ M. Contalbrigo ┴ h 1 ┴ Azimuthal moments require careful study of instrumental effects Ferrara: TMDs school 57

Beam dynamic Beam trajectory 2 mm shift at cell center Synchrotron radiation cone 5 k. W emitted power at 50 m. A beam M. Contalbrigo Ferrara: TMDs school 59

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 m. T M. Contalbrigo Ferrara: TMDs school 60

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

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 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 Ferrara: TMDs school 62

The unbinned maximum likelihood M. Contalbrigo Ferrara: TMDs school 63