This talk is intended as a brief overview of the Jefferson Lab program to study the multi-dimensional structure of the nucleon in coordinate and momentum space. The experimental program is extensive and given the available space only selected samples can be discussed

Burkert, V. D.

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DOI 10.1393/ncc/i2013-11565-7Colloquia: QCDN12IL NUOVO CIMENTO Vol. 36 C, N. 5 Settembre-Ottobre 2013The Jefferson Lab 12GeV program on nucleon structureV. D. BurkertJefferson Lab - Newport News, VA 23606, USAricevuto il 18 Aprile 2013Summary. — This talk is intended as a brief overview of the Jefferson Lab pro-gram to study the multi-dimensional structure of the nucleon in coordinate andmomentum space. The experimental program is extensive and given the availablespace only selected samples can be discussed.PACS 13.40.Gp – Electromagnetic form factors.PACS 13.60.Fz – Elastic and Compton scattering.PACS 13.60.Le – Meson production.PACS 13.88.+e – Polarization in interactions and scattering.1. – IntroductionThe science program at the JLab 12GeV upgrade is very broad and encompassesfour major directions: 1) exploring the multi-dimensional quark structure of the nucleon,2) probing hadron confinement through the search for gluonic excitations, 3) studyingnucleon modifications and QCD in nuclei, and 4) performing precision measurements offundamental symmetries as a probe of physics beyond the Standard Model. A broaderoverview can be found in [1]. Over 70% of all approved experiments focus on the studyof nucleon structure, and I am restricting this presentation on selected topics of thoseexperiments.While much is known about the charge and current distribution in transverse im-pact parameter space through elastic form factor measurements, and quark distributionfunctions have been determined from deep inelastic inclusive measurements, there arestill challenges in reaching kinematic domains where a single quark carries much of thenucleons momentum. Other frontiers have opened up with the possibility to access themulti-dimensional quark-gluon structure as expressed through the generalized parton dis-tributions (GPD) and the transverse momentum distributions (TMDs), which representthe 3D structure in transverse space and longitudinal momentum, and in 3D momentumspace, respectively. These new avenues of research can be explored with much higherprecision than has been achieved before using the 12GeV cw beam of the JLab upgrade.Also, the high luminosity available will allow scientists to explore the regime of extremequark momentum with precision, where a single quark carries 80% or more of the pro-ton’s total momentum. In this presentation a brief overview is given of some of thec© Societa` Italiana di Fisica 259260 V. D. BURKERT00.10.20.30.40.50.60.70.80.910 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x*F2n / F2pSU(6)d/u = 1/5d/u = 0W* > 2.0 GeVW* > 1.8 GeV00.10.20.30.40.50.60.70.80.910 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1x*d / uSU(6)d/u = 1/5d/u = 0W* > 2.0 GeVW* > 1.8 GeVFig. 1. – Projected CLAS12 data for the ratio F2n/F2p and d(x)u(x) from experiment [2]. Thesystematic errors are given by the area near the horizontal axis. The yellow band shows theuncertainty of current data due to uncertainties in the nuclear corrections.experimental studies planned to obtain a much improved understanding of the complexstructure of the nucleon.The JLab 12GeV upgrade project includes the energy-doubling of the cw electronaccelerator to 12GeV, the construction of a new experimental Hall D for meson spec-troscopy, and major equipment upgrades in the existing Hall B and Hall C. Hall A willkeep the existing pair of high-resolution spectrometers, and will house major user drivenexperimental equipment, e.g. for experiments at the precision frontier, and to search forphysics beyond the Standard Model. A major part of the experimental program on thenucleon will initially be done in Hall B with the new CLAS12 detector and with themagnetic spectrometer pair in Hall C [1].2. – Inclusive structure functions and parton distributionsPolarized and unpolarized structure functions of the nucleon offer insights into thespin-averaged and spin-dependent parton distribution functions. One uncharted area istheir behavior in the kinematic limit x → 1 where contributions from the virtual sea ofquark-antiquark pairs are suppressed, making this region simpler to model, and pQCDcan make absolute predictions. Experimentally, the large x domain is hard to studybecause cross sections are kinematically suppressed. First forays into the large x domainbecame possible at JLab energies of up to 6GeV [3-6]. The necessity to extend theprogram to larger x makes this one of the cornerstones of the JLab 12GeV upgradephysics program. The polarized parton distribution functions have not been determinednearly as well and more precise data especially on structure function g1(x,Q2) are neededto determine the polarized gluon density as a function of x.2.1. Valence quark structure and flavor dependence at large x. – The unpolarizedstructure function F2p(x) has been mapped out in a large range of x leading to preciseknowledge of the quark distribution u(x). The corresponding structure function F2n(x)of the neutron is well-measured only for x < 0.5 as nuclear corrections are not wellcontrolled at large x. A new technique tested recently with CLAS was shown to be veryeffective in reducing the nuclear corrections [3]. The experiment detects the low-energyspectator proton in the reaction en(ps) → epsX. Measurement of ps for momenta aslow as 70MeV/c and at large angles minimizes the nuclear corrections at large x. Thetechniques will be used at 12GeV to accurately determine the ratio d/u to larger xvalues. Figure 1 shows the projected data for Fn2 (x)/Fp2 (x) and d(x)/u(x). A dramaticimprovement is achieved at large x.THE JEFFERSON LAB 12GeV PROGRAM ON NUCLEON STRUCTURE 261Fig. 2. – Projected results on Ap1 in DIS (left). The four different symbols in the left panelrepresent four different Q2 ranges. The statistical uncertainty is given by the error bars whilethe systematic uncertainty is given by the shaded band. The right panel shows the improvementon ΔG(x) (red line) using Ap1 from DIS only. The blue line includes information from Ap1 withSIDIS from π+, π− and kaons collected in the same experiment.2.2. Spin structure functions and parton distributions. – A new experiment [7] willstudy polarized parton distribution functions at large x. Using standard detection equip-ment, a redesigned longitudinally polarized target NH3 (ND3) target adapted to CLAS12will allow high-precision measurements. The left panel in fig. 2 shows the expected pre-cision for the helicity asymmetry Ap1(x).2.3. Global analysis of polarized parton distributions. – The large window that willopen up in the DIS domain with the 12GeV upgrade will permit constraints of global fitsto improve our knowledge of the polarized parton distributions. JLab data at lower ener-gies had already unique impact at large x. The improvements from the 12GeV upgradeare also significant at low and moderate x, noticeably for the polarized gluon distributionΔG which is still much poorer defined compared to the quark spin distributions. If theQ2 dependence of the structure function gp1(x,Q2) is well measured the polarized gluondistribution ΔG(x) may be extracted as can be seen from the expressionΔg1(x,Q2)pQCD =12Nf∑qe2q[(Δq + Δq¯)⊗(1 +αs(Q2)2πδCq)+αs(Q2)2πΔGδCGNf].The right panel in fig. 2 shows the impact on the NLO analyses of the polarized gluondistribution using the evolution equation [8]. The data will not only reduce the errorband on ΔG, but will likely allow a more detailed modeling of its x-dependence.3. – Generalized parton distributionsThe GPDs describe the simultaneous distribution of particles with respect to bothtransverse coordinate and longitudinal momentum. GPDs allow us to quantify how theorbital motion of quarks in the nucleon contributes to the nucleon spin — a question ofcrucial importance to our understanding of the dynamics underlying nucleon structure.262 V. D. BURKERTFig. 3. – Projected data with error bars for the beam spin asymmetry ALU for the DVCS-BHinterference for experiment [13].The mapping of the nucleon GPDs through deeply virtual exclusive processes such asDVCS, are key objectives of the JLab 12GeV upgrade. Through certain moments, GPDsencode information on the angular momentum distribution of the quarks, their mass-energy distribution, and their pressure and force distribution [9]. For example, the quarkangular momentum form factor Jq(t) of the nucleon is given by the 2nd moment oftwo GPDs: Jq(t) =∫ +1−1 dxx[Hq(x, ξ, t) + Eq(x, ξ, t)]. At JLab energies GPDs can bebest accessed through measurement of cross sections and polarization asymmetries ofdeeply virtual Compton scattering (DVCS). For example, the beam helicity-dependentcross section is given in leading twist as σLU ≈ sinφ[F1(t)H + ξ(F1 + F2)H˜]dφ, whereφ is the azimuthal angle between the electron scattering plane and the hadronic plane.Similar expressions with different sensitivity relate to longitudinal and transverse targetpolarization asymmetries.First generation DVCS experiments carried out at JLab [10] and DESY [11] yieldedpromising results in terms of the applicability of the handbag mechanism to probe GPDs,and first information on GPDs H(xB , t) and H˜(xb, t) was extracted from these data [12].The 12GeV upgrade offers much improved possibilities for accessing GPDs, in termsof kinematic reach and precision. Figure 3 shows an example of projected data forthe polarized beam asymmetry at 12GeV upgrade. Measurements of unpolarized crosssections and of all 3 polarization asymmetries will allow for the separate determinationof GPDs H, H˜ and E in the same kinematics. Through a Fourier transformation thet-dependence of GPD H and GPD E can be used to determine the quark distribution intransverse impact parameter space: ρX(x,	bT ) =∫d2ΔT(2π)2 [H(x, 0, t)− E(x,0,t)2M ∂∂by ]e−iΔTbT .Projected results for ρX(x,	bT ) on a transversely polarized proton are shown in fig. 4.4. – Transverse momentum dependent parton distributions and SIDISSemi-inclusive deep inelastic scattering (SIDIS), when a hadron is detected in coinci-dence with the scattered electron allows for “flavor tagging”, and provides more directaccess to contributions from different quark species. In addition, SIDIS give access toTHE JEFFERSON LAB 12GeV PROGRAM ON NUCLEON STRUCTURE 263Fig. 4. – Quark densities for different xB in a transversely polarized proton target from proposedexperiment [14]. The upper row shows the shrinkage of the transverse charge densities withincreasing xB . The bottom row is the contribution of the E GPD only, and shows the emergenceof a flavor dipole due to a separation of the positive and negative charge densities.the transverse momentum distributions of quarks, that are not accessible in inclusivescattering. Azimuthal distributions of final state particles in SIDIS processes give accessto the orbital motion of quarks and play an important role in the study of the nucleonTMDs. The TMDs contain structural information that is complementary to the GPDs,and encode the quark spin distributions in 3D momentum space. TMDs describe tran-sitions of a nucleon with one polarization in the initial state to a quark with anotherpolarization in the final state. They can be accessed through measurement of SIDIS-0.1-0.0500.050.15 10e p  e'   XQ2 (GeV2)AUUcos2-0.1-0.0500.050.10 1 2+-0PT (GeV)Fig. 5. – The cos 2φ moment (Boer-Mulders asymmetry) for pions as a function of Q2 (left) andPT (right) with CLAS12 at 11GeV for 2000 hours of running.264 V. D. BURKERTprocesses using unpolarized, longitudinally polarized, and transversely polarized nucleontargets. Extraction of TMDs generally requires knowledge of the quark fragmentationfunctions. Several of the TMDs are related to wave function overlap of L = 0 andL = 1 Fock states of the nucleon and relate to the real and imaginary parts of the corre-sponding interference terms. For example, the TMDs f⊥1T and h⊥1 (known as the Siversand Boer-Mulders functions), are related to the imaginary part of the interference ofwave functions for different orbital momentum states, and describe unpolarized quarksin the transversely polarized nucleon and transversely polarized quarks in the unpolar-ized nucleon, respectively. The most simple mechanism that can lead to a Boer-Muldersfunction is a correlation between the spin of the quarks and their orbital angular momen-tum. Examples of expected uncertainties [15] for the Boer-Mulders asymmetry Acos 2φUUare presented in fig. 5.5. – ConclusionsThe JLab energy upgrade is well matched to an exciting scientific program aimedat studies of the complex nucleon structure in terms of the GPDs and TMDs. Theyprovide fundamentally new insights in the complex multi-dimensional structure of thenucleon. In addition, the high precision afforded by the high luminosity and the largeacceptance detectors, and the development of novel techniques to measure scattering offnearly free neutrons, will enable the exploration of phase space domains with extremeconditions that could not be studied before. The CLAS12 detector will play a crucialrole in exciting program.∗ ∗ ∗This work was supported in part by the U.S. Department of Energy. The JeffersonScience Associates, LLC, operates Jefferson Lab under contract DE-AC05-060R23177.REFERENCES[1] Dudek J. et al., Eur. Phys. J. A, 48 (2012) 187.[2] Bueltman S. et al., http://www.jlab.org/exp prog/proposals/06/PR12-06-113.pdf.[3] Baillie N. et al. (CLAS Collaboration), Phys. Rev. Lett., 108 (2012) 199902.[4] Zheng X. et al., Phys. Rev. C, 70 (2004) 065207.[5] Dharmawardane V. et al., Phys. Lett. B, 641 (2006) 11.[6] Bosted P. et al., Phys. Rev. C, 75 (2007) 035203.[7] Kuhn S. et al., http://www.jlab.org/exp prog/proposals/06/PR12-06-109.pdf.[8] Leader E., Sidorov S. and Stamenov D., Phys. Rev. D, 75 (2007) 074027.[9] Goeke K. et al., Phys. Rev. D, 75 (2007) 094021.[10] Stepanyan S. et al., Phys. Rev. Lett., 87 (2001) 182002; Girod F. X. et al., Phys. Rev.Lett., 100 (2008) 162002; Chen S. et al., Phys. Rev. Lett., 97 (2006) 072002; GavalianG. et al., Phys. Rev. C, 80 (2009) 035206; Munoz-Camacho C. et al., Phys. Rev. Lett.,97 (2006) 262002.[11] Airapetian A. et al., Phys. Rev. Lett., 87 (2001) 182001.[12] Guidal M., Phys. Lett. B, 689 (2010) 156.[13] Sabatie F. et al., http://www.jlab.org/exp prog/proposals/06/PR12-06-119.pdf.[14] Elouadrhriri L. et al., http://www.jlab.org/exp prog/proposals/12/PR12-12-010.pdf.[15] Avakian H. et al., http://www.jlab.org/exp prog/proposals/07/PR12-07-107.pdf.

The Jefferson Lab 12 GeV program on nucleon structure

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The Jefferson Lab 12 GeV program on nucleon structure

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