Joshua G. Rubin University of Illinois SPIN 2008 October 9, 2008 Joshua G. Rubin University of Illinois SPIN 2008 October 9, 2008 The new  q(x) at HERMES

Joshua Rubin - SPIN October 9, 20082/18 Var.Description SIDIS Requirements x Light Cone Momentum Fraction of Parton Q2Q2 Negative Squared Photon Momentum Q 2 > 1 GeV 2 W2W2 Final State Invariant Mass W 2 > 10 GeV 2 pTpT Hadron transverse momentum w.r.t. q-vector ZhZh Energy Fraction carried by Hadron h 0.2 < z h < 0.8 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 - SPIN October 9, 20083/18  q(x) and How to Measure it LO expression: Experimental Asymmetry: (A || and A 1 are related by depolarization and kinematic factors) How can we get at  q(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 with semi-inclusive analysis The semi-inclusive version of A 1 : Take advantage of the hadrons!

Joshua Rubin - SPIN October 9, 20084/18 To jog the memory... “The Long Paper” A. Airapetian et al. Phys. Rev., D71:012003, 2005 Highlights  First ever 5-flavor  q(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. z h, p h┴  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. Though the reanalysis is not complete, it has already yielded new results!

Joshua Rubin - SPIN October 9, 20085/18 New Dimensions! (z h and p h┴ )

Joshua Rubin - SPIN October 9, 20086/18 Low-zMid-zHigh-z Low-p h ┴ Leading Mid-p h ┴ Standard High-p h ┴ Remnant Highest energy hadron & fewest string breaks Lowest energy hadrons & most string breaks Each x-bin can be divided into z and p h┴ dimensions... z and p h┴ yield information about the fragmentation process... What’s interesting about semi-inclusive kinematic variables? We’re looking at two features of this extended binning: 1.Quark-hadron correlations can be enhanced in the purity-based extraction of  q(x) by identifying leading quark and remnant containing hadrons. Work in progress... 2.A 1 ( p h┴ ) is interesting in itself! It yields information about the fragmentation p T and intrinsic k T. New result! We’re looking at two features of this extended binning: 1.Quark-hadron correlations can be enhanced in the purity-based extraction of  q(x) by identifying leading quark and remnant containing hadrons. Work in progress... 2.A 1 ( p h┴ ) is interesting in itself! It yields information about the fragmentation p T and intrinsic k T. New result!

Joshua Rubin - SPIN October 9, 20087/18 What is p h┴ of a final state hadron good for? M. Anselmino, A. Efremov, A. Kotzinian, and B. Parsamyan Phys.Rev.D74:074015,2006. p h┴ is interesting, but complicated! It is a convolution of fragmentation p T (string breaks) and intrinsic k T (PDFs) Any flavor dependence of k T unknown Important for transverse momentum dependences (TMDs) x and p h┴ are not completely independent variables… apparent p h┴ dependence can result from different in each p h┴ bin. Construct Assume Recent theoretical work: Calculate

Joshua Rubin - SPIN October 9, 20088/18 P   P   d   d   d  K d  K A 1 (x, p h┴ ) – New Result! No significant p h┴ dependence observed Binned in x and p h┴ to hold more constant within an x-bin. Points fit with and without p h┴ dependant term:

Joshua Rubin - SPIN October 9, 20089/18 Addressing Error Bar Inflation: Covariance and Smoothness

Joshua Rubin - SPIN October 9, /18 The bin-to-bin unfolding procedure used in the long  q(x) paper for A 1 (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 Born Bins (j) Kinematic Unfolding and the Interpretation of Uncertainties When A 1 is fit with a smooth function and statistical covariance is taken into account (blue band), inflated uncertainties are reduced. Published asymmetries from HERMES long  q(x) paper fit with: A 1 h (x) = C 1 + C 2 x

Joshua Rubin - SPIN October 9, /18 Fits to the Quark Polarizations Helicity densities fitted with x  q(x) = C 1 x c2 (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 - SPIN October 9, /18 A More Robust Calculation of the Purity Matrix Systematic

Joshua Rubin - SPIN October 9, /18 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  2 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  2 minimum was not addressed at the time.

Joshua Rubin - SPIN October 9, /18 22 parj a parj b Best MC Tune   min   min +C 1. Scan  2 surface around best Monte Carlo tune. Fit with quadratic Polynomial. 2. Find 68% contour. Based on two factors: Height of 68% of d-dimensional Gaussian Distribution. The height of  2 minimum to accommodate model imperfection. PDG does something like this. 3. Compute  q(x) along contour: The maximum deviation of  q(x) from the best tune is the 68% uncertainty! Correlating MC tune and  q(x) systematic uncertainty 68% Contour  q(x) Purities

Joshua Rubin - SPIN October 9, /18 What locations on the 68% contour should be sampled? (J. Pumplin et al., JHEP 07 (2002) 012) This problem is similar to fitting global PDF parameterizations… Models typically have correlated parameters. What do those guys do?! Look at CTEQ. 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 68% Contour Extract  q(x) where uncorrelated parameter vectors cross 68% certainty contour. The greatest deviations represent  q(x) tune systematic uncertainty.

Joshua Rubin - SPIN October 9, /18 Blue ellipses represent 68% contour Colored lines represent uncorrelated parameter directions Blue ellipses represent 68% contour Colored lines represent uncorrelated parameter directions Jetset/Lund  2 surface in Fragmentation Parameter Basis Scan the  2 surface around the best Monte Carlo tune. Correlations are quite clear between parameters Generate and diagonalize the matrix of 2 nd derivatives to find linear combinations that are uncorrelated The real thing…

Joshua Rubin - SPIN October 9, /18 Revised  q(x) uncertainty estimate u d u d s x Published  q(x) total systematic Published  q(x) MC systematic Difference between  q(x) on 68% contour along Hessian vectors and at the  2 minimum. We can move the gray estimate down to the highest colored point! In most bins, the tune- related systematic can be greatly reduced.

Joshua Rubin - SPIN October 9, /18 Concluding Remarks A 1 (p h┴ ) -- A first look at this interesting quantity – No dependence was observed. –Can we differentiate sources of p h┴ ? Can we learn something about flavor- dependence of intrinsic k T ? Can we learn something meaningful about fragmentation? Fits will compliment the new  q(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 - SPIN October 9, /18 Backup slides…

Joshua Rubin - SPIN October 9, /18

Joshua Rubin - SPIN October 9, /18 Studies on transverse spin effects at Jlab From: Harut Avakian, “Studies on transverse spin effects at Jlab”, QCD Structure of the Nucleon June 12-16, 2006, Rome What do we know about A 1 (p h┴ ) so far? CLAS sees clear p h┴ dependence of A 1 Some care was taken to correct for the varying x- dependence in in each p h┴ - bin. CLAS result is at a significantly lower W and higher x than HERMES