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The Electron Ion Collider (EIC)

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The Electron Ion Collider (EIC) 7/18/16 EIC Lecture 2 at NNPSS 2016 at MIT 1 The Electron Ion Collider (EIC) Abhay Deshpande Lecture 2: What do we need polarized beams? Nucleon Spin Structure: What’s the problem? 2. Quantum Chromodynamics: The Fundamental Description of the Heart of Visible Matter Sidebar 2.6: Nucleon Spin: So Simple and Yet So Complex The simple fact that the proton carries spin 1/2, quark spins to account for most of the proton’s spin measured in units of Planck’s famous constant, is but were quite surprised when experiments at CERN exploited daily in thousands of magnetic resonance and other laboratories showed that the spins of all imaging images worldwide. Because the proton is a quarks and antiquarks combine to account for no more composite system, its spin is generated from its quark than about 30% of the total. This result has led nuclear 7/18/16 EIC Lecture 2 at NNPSS 2016 at MIT and gluon constituents. Physicists’ evolving appreciation scientists2. Quantum to address Chromodynamics: the more daunting The Fundamental challenges2 Description of the Heart of Visible Matter of how the spin might be generated, and of how much involved in measuring the other possible contributions to we have yet to understand about it, is an illustrative the spin illustrated in Figure 1. The gluons also have an Thecase study nucleon of how seemingly simple spin properties of visible intrinsic spin (1 unit) and might be “polarized” (i.e., might matter emerge from complex QCD interactions. have a preferential orientation of their spins along or puzzle…. opposite the proton spin). And just as the earth orbits Quarks are also spin 1/2 particles, and at any given around the sun while simultaneously spinning about its moment an individual quark may spin in the same or own axis, the quarks and gluons in a proton could have Stheince opposite direction1988.. of its proton host, respectively, orbital motion that would also contribute to the overall making a positive or negative contribution to the total proton spin. proton spin. Physicists originally expected the sum of Figure 2.15: Te increased coverage (colored bands) over existing experiments (point symbols) that EIC polarized electron-proton collisions will provide in parton momentum fraction and resolving power. Figure 1: A schematic view of the proton and its potential spin contributions. Figure 2.14: Te projected reduction in the uncertainties of the net gluon and net quark spin contributions to the proton’s spin for EIC electron So how much of the spin comes from the spin of gluons? xmin indicated on the horizontal axis. For each dataset, The first important constraints have come from recent the uncertaintiesenergies of 5 (red) grow and 20 significantly (yellow) GeV. at low x as the 1 1 min measurements at RHIC, which provides the world’s contributions have not been directly measured there. first and= only polarized⌃ proton+ ∆ colliderG +capabilityLQ at + LG Tomographic Images of the Proton high2 energy.2 There, the STAR and PHENIX experiments In a significantDeep inelastic breakthrough, scattering (DIS)the RHIC experiments results tocarried date out at EIC collision rates will provide for the first time 3D have used the polarized quarks in one proton as a (light blue band in Figure 2) indicate that the gluon spins ? ? images of gluons in the proton’s internal landscape. Of scattering probe to reveal that the gluons in the other do indeed have a non-negligible orientation preference for xparticular above 5%. interest But they are tell exclusive us very measurements, little about whether where proton are indeed polarized. Just as critical has been the one detects an outgoing meson in coincidence with the development of the theoretical framework to integrate the much more abundant lower-momentum gluons may scattered electron with sufcient resolution to confirm the RHIC measurements into a global QCD analysis to reinforce or counterbalance this preference. This leaves that the proton has been left intact by the scattering constrain both quark and gluon spin preferences. Results a large uncertainty in the total gluon spin contribution, process. For example, the detection of exclusive J/ of those analyses are shown in Figure 2. indicated at the left edge of the plot, which can be reducedmeson by productionanalysis of wouldanticipated provide RHIC unprecedented polarized maps The protons at RHIC move at nearly the speed of light, proton(Figure data 2.17)(the showingdarker blue how band). the gluons However, are distributed this still and each quark and gluon inside carries a fraction x wouldin spaceleave thewithin overall a plane uncertainty perpendicular at a level to the that parent proton’s motion. These particular maps encode vital of the proton’s overall momentum. The widths of the remains larger than the entire proton spin itself. Only Figure 2.16: A simulation based on projected EIC data of the transverse colored bands in Figure 2 illustrate the uncertainties in an EICinformation, (yellow band) inaccessible can uniquely without settle the howEIC, onmuch the of amount motion preferences of an up sea quark within a proton moving out of the summed spin of all gluons that carry more than a the overallof proton spin spin is contributedassociated withby the the spins gluons’ of quarks,orbital motion. the page, with its spin pointing upward. Te color code indicates the probability of fnding the up quarks. fraction xmin of the proton’s momentum, with the value of antiquarks, and gluons combined. Proton Spin at the EIC and Lattice QCD with such detailed EIC measurements of proton spin The ability of LQCD calculations to reproduce many structure as the images and distributions in Figures 2.16 features of the hadron spectrum is a testimony to striking 36 and 2.17. Such comparisons will not only bring deep recent advances in our treatment of quark and gluon insight into the origin of the spin but will also shed light interactions from first principles. An important recent on the role the abundant gluons play in generating the breakthrough in LQCD methodology now provides the proton’s mass and confining quarks and gluons inside promise of precision future comparisons of theory the proton. 34 7/18/16 EIC Lecture 2 at NNPSS 2016 at MIT 3 A brief history of nucleon spin: “Crisis” à “Puzzle” 7/18/16 EIC Lecture 2 at NNPSS 2016 at MIT 4 Some equations… Assume only γ* exchange • Lepton Nucleon Cross Section Nucleon spin Lepton spin • Lepton tensor Lµν affects the kinematics (QED) • Ηadronic tensor Wµν has information about the hadron structure 5332 D. ADAMS et al. 56 target. Both inclusive and semi-inclusive data were obtained, and polarized H and D targets will be used in the future. In this paper, we present SMC results on the spin- p p dependent structure functions g1 and g2 of the proton, ob- 5332 tained from data takenD. ADAMS in 1993et with al. a polarized butanol tar- 56 get. First results from these measurements were published in target. Both inclusive and semi-inclusiveRefs. data⌦9, were 10͔. We obtained, use here the same data sample, but present and polarized H and D targets will bea used more in refined the future. analysis; in particular, the influence of the radiative corrections on the statistical error on the asymmetry 5332 In this paper, we present SMC resultsD. on ADAMS the spin-et al. 56 dependent structure functions g p andisg p nowof properly the proton, taken ob- into account, resulting in an observ- 1 able2 increase of this error at small x, and we allow for a Q2 tained from data taken in 1993 with a polarized butanolp tar- target. Both inclusive and semi-inclusive data wereevolution obtained, of the g1 structure function as predicted by pertur- FIG. 1. Lepton and nucleon kinematic variables in polarized get. First results from these measurementsbative were QCD. published SMC has in also published results on the deuteron lepton scattering on a fixed polarized nucleon target. and polarized HRefs. and⌦9, D 10 targets͔. We use will here be the used same in data the sample, future. but presentd structure function g1 ⌦11–13͔ and on a measurement of In this paper,a more we refined present analysis; SMC in results particular, onsemi-inclusive the the influence spin- cross of section the asymmetries ⌦14͔. For a test of The spin-dependent part of the cross section can be writ- radiative correctionsp on the statisticalp error on the asymmetry d ten in terms of two structure functions g and g which dependent structure functions g1 and g2 of thethe proton, Bjorken ob- sum rule, we refer to our measurement of g1 . 1 2 tained from datais nowtaken properly in 1993 taken with into a polarized account, resulting butanolThe paper in tar- an is organizedobserv- as follows. In Sec. II we review describe the interaction of lepton and hadron currents. When able increase of this error at small x, andthe theoretical we allow background. for a Q2 The experimental setup and the the lepton spin and the nucleon spin form an angle ␺, it can get. First results from these measurementsp weredata-taking published procedure in are described in Sec. III. In Sec. IV we be expressed as ⌦16͔ evolution of the g1 structure function as predicted by pertur- FIG. 1. Lepton and nucleon kinematic variables in polarized Refs. ⌦9, 10͔. We use here the same data sample,discuss but present the analysis of cross section asymmetries, and in Sec. bative QCD. SMC has also published results on the deuteron lepton scattering on a fixed polarized nucleon target.⌬⌅⇤cos ␺⌬⌅ ⌅sin ␺ cos ⌬⌅ , ⇥2.4⇧ a more refined analysis; in particular,d the influenceV we give of the evaluation of the spin-dependent structure ⇥ ' structure function g ⌦11–13͔ and on a measurementp of p 1 function g and its first moment.
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