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Double Helicity Asymmetry for Charged Pion + Jet Production in P+P Collisions at Fa=200-Gev at STAR James Prewitt Hays-Wehle

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Double Helicity Asymmetry for Charged Pion + Jet Production in P+P Collisions at Fa=200-Gev at STAR James Prewitt Hays-Wehle Double Helicity Asymmetry for Charged Pion + Jet Production in p+p collisions at fa=200-GeV MASSACHU T TIU at STAR APR 6 by James Prewitt Hays-Wehle B.S., Physics, Carnegie Mellon University (2006) Submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY February 2013 @ Massachusetts Institute of Technology 2013. All rights reserved. 7 Author.............................of .Physic f epartment of .P.hysi .c s December 12, 2012 . C ertified by ........................... .. Richard G. Milner Professor of Physics; Director, aboratory for Nuclear Science Ttesis Su pervisor Accepted by ................. John W. Belcher Associate Department Head for Education i q Double Helicity Asymmetry for Charged Pion + Jet Production in p+p collisions at vs=200 GeV at STAR by James Prewitt Hays-Wehle Submitted to the Department of Physics on January 25, 2013, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract Inclusive measurements from polarized proton-proton collisions at RHIC have con- strained Ag, the polarized gluon distribution function of the proton. Correlation observables, such as this pion+jet measurement, allow for reconstruction of initial parton kinematics and are thus sensitive to the x dependence of Ag. By measuring charged pions opposite a jet, this particular measurement can be sensitive to the fla- vor of the struck parton. This measurement, which is dominated by the quark-gluon subprocess, can be divided into terms proportional to AuAg and AdAg. The rela- tively larger quark polarization amplifies the measured asymmetry thereby enhancing the statistical power. This thesis presents the result of the mid-rapidity pion+jet lon- gitudinal double spin asymmetry analysis from 10.6 pb- 1 of luminosity collected in the 2009 200 GeV p+p run. Thesis Supervisor: Richard G. Milner Title: Professor of Physics; Director, Laboratory for Nuclear Science 3 4 Acknowledgments I owe a great deal of thanks to many people without whom this work could never have been done. Firstly, to my advisor Richard Milner, for guiding and supporting me through three different projects during my graduate studies. To all the members of the RHIC-Spin group. I've had mentoring and guidance from Bernd Surrow and Joe Seele, but I've learned just as much from my fellow students Chris Jones, Matthew Walker, Michael Betancourt, Will Leight, and Ross Corliss, who all provided insight, expertise, and camaraderie. Outside of the group, I value the friendships that I've had at MIT. Most notably Shawn, Parthi, Rachel, and Dan, but also many others. I would never have made it to, or through, grad school if it were not for the love and support of my family. Lastly and most importantly, to my fiancee Teesa, who has been with me through every step of this thesis and has been my greatest motivation to finish it. 5 THIS PAGE INTENTIONALLY LEFT BLANK 6 Contents 1 Introduction and Overview 15 1.1 History ........ ................................... 16 1.2 The Spin of the Proton .. .. .. .. .. .. ... .. .. .. .. .. 20 1.3 Measuring Gluon Polarization . ... .. .. .. .. .. .. .. .. .. 22 1.3.1 Factorization .. ... .. .. ... .. .. .. ... .. .. .. 24 1.3.2 Fragm entation . .. .. .. .. ... .. .. .. .. .. .. .. 26 1.4 The Analysis Channel .. .. .. .. .. .. .. .. .. .. .. ... 27 1.4.1 P ions .. .. ... .. .. ... .. .. ... .. .. ... .. .. 27 1.4.2 Jets .. .. .. .. ... .. .. .. .. .. .. .. .. ... .. 28 1.4.3 Charged Pion and Jet Correlations .. .. .. .. .. ... .. 28 2 Experimental Setup 31 2.1 The Relativistic Heavy Ion Collider . .. .. ... .. .. .. ... .. 31 2.1.1 Making Polarization . .. .. ... .. .. .. ... .. .. .. 33 2.1.2 Maintaining Polarization .. .. .. .. .. .. .. .. .. .. 33 2.1.3 Measuring Polarization . .. .. .. .. .. .. .. .. .. .. 34 2.2 The Solenoidal Tracker at RHIC . .. .. .. .. .. .. .. .. .. 35 2.2.1 The Time Projection Chamber . .. .. .. .. .. .. .. .. 36 2.2.2 The Barrel Electromagnetic Calorimeter .. ... .. ... 37 2.2.3 The Beam Beam Counters and Zero Degree Calorimeters . 37 3 Event Finding and Counting 39 3.1 Event Structure ....... .............................. 39 7 3.2 Triggering ........ .. .. .. ... .. ... .. .. ... .. .. 4 0 3.3 Tracking and Vertexing . .. .. .. .. .. .. .. .. .. .. - -- 4 1 3.3.1 Jet-Finding . .. .... .. .. .. .. ... .. .. .. .. .. 43 3.4 Pion Identification ... .. ..... .. ... .. .. .. ... .. 4 3 4 ALL Analysis 47 4.1 Statistical Uncertainty .. .. .. .. .. ... .. .. .. ... .. 48 4.1.1 M ultiplicity . .. .. .. .. .. .. .. .. .. .. .. .. 48 4.2 Jet Energy .. .. .. .. .. .. .. .. .. .. .. - --- .. - 49 4.2.1 Jet Simulation ... .. .. ... .. .. .. ... .. .. .. 50 4.2.2 Jet Unfolding .. .. .. .. .. .. ... ... ... ... .. 50 4.3 Background Subtraction .. .. .. ... .. ... ... ... ... .. 55 4.4 Relative Luminosity . .. .. .. .. .. .. .. .. ... .. .. .. 57 4.4.1 Accidental and Multiple Coincidence Corrections . .. .. .. 58 4.4.2 Relative Luminosity Uncertainties .. .. ... .. .. ... 59 4.4.3 False Asymmetries .. .. .. .. ... .. .. .. ... .. 59 4.5 Polarization . .. .. .. .. ... .. .. .. .. .. ... .. .. .. 61 4.5.1 Beam Transverse Component . .. .. .. .. .. ... .. 62 4.6 Summary of Statistical Uncertainties . .. .. ... .. .. ... 62 4.7 Summary of Systematic Uncertainties . .. .... .... ..... 63 5 Results and Conclusions 65 5.1 Theory and Comparison . .. .. .. .. .. .. .. .. .. 65 5.2 Agreement with Previous Results . .. .. .. .. .. .. .. 67 5.3 Future Measurements . .. .. .. .. .. .. .. .. .. .. 70 A Comparison of Data to Simulation 73 B Additional Tables and Graphs 77 B.1 Unfolding Matrices .. .. .. .. .. .. .. .. .. .. .. .. .. 77 B.2 Correlation of x and z with track PT . .. .. .. .. .. .. .. .. 79 B.3 Ratio of yields binned in z. .. .. .. .. .. .. .. .. .. .. .. 79 8 List of Figures 1-1 Diagram of a Deep Inelastic Scattering event. An electron carrying four-momentum k transfers a virtual photon with momentum q = k -k' to a parton carrying a fraction x of the proton's momentum P. The inelastic final state particles are denoted as X. .. .. .. .. .. .. 17 1-2 World DIS data from both fixed target and collider experiments show Bjorken scaling: the invariance of the form factor F2 with respect to Q2.[4] At sufficiently low x the contributions of gluons and sea-quarks violate the scaling law, but this was not discovered until later experi- m ents. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 18 1-3 Gell-Mann's "Eightfold Way" shows SU(3) flavor symmetry in baryons. This particular irreducible representation includes the Q-, a particle predicted by Gell-Mann's quark theory before it was discovered. [6] . 20 1-4 The EMC polarized DIS experiment probed into low x, where the measured quark polarization was not compatible with the Ellis-Jaffe predictions. [8] .. .. .. .. .. .. .. .. .. .. .. .. 22 1-5 Bounds placed on polarized PDFs, including Ag(x). This is a global fit to both scaling violations in polarized Deep Inelastic Scattering and previous polarized proton measurements. [9] The yellow and green 2 2 bands represent the AXy2 = 1 and Ax /X - 2 uncertainties, respectively. 23 9 1-6 Diagram of a hard scattering event in a proton-proton collision, labelled by important quantities. The diagram shows inclusive production of a hadron, h. This thesis measures events where h represents a charged pion. In the case of a r+, there is a high probability that fa and fb represent a gluon and an up quark. ................... 25 1-7 The dependence of subprocess fractions on PT and z.[10] Quark+gluon dominates in this kinematic regime, but especially at high x and z. 29 2-1 Schematic of RHIC accelerator complex. Protons start their journey at the Polarized H- source before moving through the Linac, Booster, AGS and finally RHIC. .... ............ .......... 32 2-2 The STAR detector. Important subsystems, such as the Time Projec- tion Chamber and Barrel Electromagnetic Calorimeter, are labeled. 35 3-1 Jet+pion production in a proton-proton collision. Such an event often contains two jets in opposition and many pions within those jets. All charged pions are included in this analysis provided they are opposite a jet. ......... ....................... .... 40 3-2 The likelihood of a vertex ranking for an example event.[25] ..... 42 3-3 For a given momentum higher than MIP (such as the range indicated by the dashed red line), dE/dx corresponds to particle mass.[2] The momentum range where particles can be identified by this method is approximately 1-20 GeV/c .. ............ .......... 45 4-1 Multiplicity of 7r+ for each z bin (left) and x bin (right). Pions in a given event should frequently fall into the same x bin, but rarely into the sam e z bin. .... ........ ........ ....... ... 49 4-2 The joint distribution of reconstructed jet PT and true jet PT. .... 51 4-3 An unfolding matrix and its effect: the unfolding matrix for 7r+ binned in z (left) and the associated reconstructed (red) and unfolded (blue) distributions (right). ........ ........... 53 10 4-4 The unfolding matrix for - binned in x (left) and the associated reconstructed (red) and unfolded (blue) distributions (right). The di- agonality of the matrix suggests the NLO approximation (Equation 1.10) is valid. ... .... .... .... .... .... ... .... 54 4-5 A simultaneous fit of distributions in no,, for all particle species and both charges. ... .... .... .... .... .... ... .... 55 4-6 The single-spin false asymmetries as a function of run number. ... 60 4-7 The like-
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