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The new D q(x) at HERMES

The new D q(x) at HERMES. Joshua G. Rubin University of Illinois SPIN 2008 October 9, 2008. Deep-Inelastic Scattering and DIS Kinematics at HERMES. 27.6 GeV positron beam on deuterium gas target ~ 53% Beam Polarization ~ 82% Target Polarization. Thanks Halzen & Martin!.

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The new D q(x) at HERMES

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  1. The newDq(x) at HERMES Joshua G. Rubin University of Illinois SPIN 2008 October 9, 2008

  2. Deep-Inelastic Scattering and DIS Kinematics at HERMES • 27.6 GeV positron beam on deuterium gas target • ~ 53% Beam Polarization • ~ 82% Target Polarization Thanks Halzen & Martin! Joshua Rubin - SPIN2008 - October 9, 2008

  3. Dq(x) and How to Measure it Experimental Asymmetry: (A|| and A1 are related by depolarization and kinematic factors) LO expression: How can we get at Dq(x) then?! Purity is probability that hadron h came from quark flavor q.  Use correlation between struck quark and observed hadrons to flavor-tag events Extract quark contributions withsemi-inclusive analysis Take advantage of the hadrons! The semi-inclusive version of A1: Joshua Rubin - SPIN2008 - October 9, 2008

  4. To jog the memory... “The Long Paper” • Highlights • First ever 5-flavor Dq(x) extraction • 9 x-bins for valence quarks, 7 for sea quarks • Rigorous unfolding procedure developed which removes detector and radiative smearing without assuming smoothness Room for Improvement • Overlooked low-momentum deuterium data • Semi-inclusive kinematic dimensions unexplored. i.e. zh, ph┴ • Bin-to-bin correlations and absence of smoothness assumption causes apparent error bar inflation • An attempt was made to overestimate the difficult-to-compute purity matrix systematic uncertainty. It was hoped that the subject could be revisited with more rigor. A. Airapetian et al. Phys. Rev., D71:012003, 2005 Though the reanalysis is not complete, it has already yielded new results! Joshua Rubin - SPIN2008 - October 9, 2008

  5. New Dimensions! (zh and ph┴) Joshua Rubin - SPIN2008 - October 9, 2008

  6. What’s interesting about semi-inclusive kinematic variables? Each x-bin can be divided into z and ph┴dimensions... Highest energy hadron & fewest string breaks Lowest energy hadrons & most string breaks z and ph┴ yield information about the fragmentation process... • We’re looking at two features of this extended binning: • Quark-hadron correlations can be enhanced in the purity-based extraction of Dq(x) by identifying leading quark and remnant containing hadrons. Work in progress... • A1(ph┴) is interesting in itself! It yields information about the fragmentation pT and intrinsic kT. • New result! Joshua Rubin - SPIN2008 - October 9, 2008

  7. What is ph┴of a final state hadron good for? • ph┴is interesting, but complicated! • It is a convolution of fragmentation pT(string breaks) and intrinsic kT(PDFs) • Any flavor dependence of kT unknown • Important for transverse momentum dependences (TMDs) • x and ph┴are not completely independent variables… apparent ph┴ dependence can result from different <x> in each ph┴bin. Recent theoretical work: • M. Anselmino, A. Efremov, A. Kotzinian, and B. Parsamyan • Phys.Rev.D74:074015,2006. Calculate Construct Assume Joshua Rubin - SPIN2008 - October 9, 2008

  8. A1(x, ph┴ ) – New Result! • Binned in xandph┴to hold <x> more constant within an x-bin. • Points fit with and without ph┴ dependant term: No significant ph┴ dependence observed Joshua Rubin - SPIN2008 - October 9, 2008

  9. Addressing Error Bar Inflation: Covariance and Smoothness Joshua Rubin - SPIN2008 - October 9, 2008

  10. Kinematic Unfolding and the Interpretation of Uncertainties Published asymmetries from HERMES long Dq(x) paper fit with: A1h (x) = C1 + C2 x Born Bins (j) • The bin-to-bin unfolding procedure used in the long Dq(x) paper for A1(x): • Corrects radiative and detector smearing by tracking MC event bin migration • Makes no assumption of smoothness • Side-effect: • Statistical errors correlated and considerably larger than those of raw asymmetry When A1 is fit with a smooth function and statistical covariance is taken into account (blue band), inflated uncertainties are reduced. Joshua Rubin - SPIN2008 - October 9, 2008

  11. Fits to the Quark Polarizations • Helicity densities fitted with xDq(x) = C1 xc2 (1-x)c3 • Data points have rigorous model-independent uncertainties (and associated covariance) • Fits give a more reasonable impression of the true statistical significance of the data taking into account covariance and (reasonably) assuming smooth physics • Statistical covariance is crucial when interpreting data. Fit uncertainty can be overestimated without including covariance (pink band). Fit central values are affected as well. • Do utilize provided covariance info when interpreting data! (Simulated data points for illustrative purposes only!) Joshua Rubin - SPIN2008 - October 9, 2008

  12. A More Robust Calculation of the Purity Matrix Systematic Joshua Rubin - SPIN2008 - October 9, 2008

  13. Tuning JETSET, the Fragmentation Monte Carlo • Purity matrices, which encode the correlation between struck quark flavor and observed hadron type, are generated using a JETSET Monte Carlo. • JETSET is an implementation of the Lund-string phenomenological fragmentation model based on ~12 tunable parameters. • These parameters are tuned by minimizing a c2 comparison of MC to data multiplicities. • In the existing publication, the systematic uncertainty related to this tune was conservatively overestimated by comparing several tunes that poorly describe multiplicities in the HERMES kinematic regime. This was a major source of uncertainty in the publication. • The (unlikely) possibility of correlated parameters creating an ambiguous c2 minimum was not addressed at the time. Joshua Rubin - SPIN2008 - October 9, 2008

  14. Correlating MC tune and Dq(x) systematic uncertainty Purities Dq(x) 1. Scanc2 surface around best Monte Carlo tune. Fit with quadratic Polynomial. 68% Contour Best MC Tune • 2. Find 68% contour. Based on two factors: • Height of 68% of d-dimensional Gaussian Distribution. • The height of c2 minimum to accommodate model imperfection. PDG does something like this. c2 c2min+C c2min parj b parj a 3. ComputeDq(x) along contour: The maximum deviation of Dq(x) from the best tune is the 68% uncertainty! Joshua Rubin - SPIN2008 - October 9, 2008

  15. What locations on the 68% contour should be sampled? 68% Contour This problem is similar to fitting global PDF parameterizations… Models typically have correlatedparameters.What do those guys do?! Look at CTEQ. (J. Pumplin et al., JHEP 07 (2002) 012) • A & B are correlated parameters. The minimum in one depends on the location of the other • Compute Hessian matrix of second derivatives to find uncorrelated directions Extract Dq(x) where uncorrelated parameter vectors cross 68% certainty contour. The greatest deviations represent Dq(x) tune systematic uncertainty. Joshua Rubin - SPIN2008 - October 9, 2008

  16. The real thing… • Scan the c2 surface around the best Monte Carlo tune. • Correlations are quite clear between parameters • Generate and diagonalize the matrix of 2nd derivatives to find linear combinations that are uncorrelated Jetset/Lund c2 surface in Fragmentation Parameter Basis • Blueellipses represent 68% contour • Coloredlines represent uncorrelated parameter directions Joshua Rubin - SPIN2008 - October 9, 2008

  17. Revised Dq(x) uncertainty estimate u Published Dq(x) total systematic d PublishedDq(x) MC systematic Difference between Dq(x) on 68% contour along Hessian vectors and at the c2 minimum. u d We can move the gray estimate down to the highest colored point! In most bins, the tune-related systematic can be greatly reduced. s x Joshua Rubin - SPIN2008 - October 9, 2008

  18. Concluding Remarks • A1(ph┴ ) -- A first look at this interesting quantity • No dependence was observed. • Can we differentiate sources ofph┴ ? Can we learn something about flavor-dependence of intrinsic kT? Can we learn something meaningful about fragmentation? • Fits will compliment the new Dq(x) data: • Unfolded data points provide assumption-free presentation of the data, but suffer from apparent inflation of error bars and statistical covariance. • The addition of fit curves give a more reasonable impressions of statistical significance • Improved fragmentation model tune uncertainty • Uncertainty appears to be considerably smaller than published • Robust Hessian approach properly handles correlated parameters Joshua Rubin - SPIN2008 - October 9, 2008

  19. Backup slides… Joshua Rubin - SPIN2008 - October 9, 2008

  20. Joshua Rubin - SPIN2008 - October 9, 2008

  21. What do we know about A1(ph┴) so far? From: Harut Avakian, “Studies on transverse spin effects at Jlab”, QCD Structure of the Nucleon June 12-16, 2006, Rome CLAS sees clear ph┴ dependence of A1 • Some care was taken to correct for the varying x-dependence in in each ph┴ -bin. • CLAS result is at a significantly lower W and higher x thanHERMES Joshua Rubin - SPIN2008 - October 9, 2008

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