Studies of OAM at JLAB Harut Avakian Jefferson

Studies of OAM at JLAB Harut Avakian Jefferson Lab UNM/RBRC Workshop on Parton Angular Momentum , NM, Feb 2005 • Introduction • Exclusive processes • Semi-Inclusive processes • Summary * In collaboration with V. Burkert and L. Elouadrhiri

Parton picture: Longitudinal and transverse variables “long before”

Quark Angular Momentum Sum Rule GPDs Hu, Hd, Eu, Ed provide access to total quark contribution to proton angular momentum. ½ = ½ (Du+Dd+Ds) + Lq + Jg Proton’s spin Jq J q = 1 2 -JG= 1 1 xdx [H q( x , 0 ) + E q( x , 0 )] ò 2 -1 X. Ji, Phy. Rev. Lett. 78, 610(1997) Large x contributions important.

3 D Parton Distributions 0, t x= PDFs fpu(x, k. T), g 1, h 1 dx d 2 k. T Measure momentum transfer to quark GPDs Hpu(x, x, t). . =0 TMD PDFs fpu(x, k. T), Measure momentum transfer to target FFs F 1 pu(t), F 2 pu(t). . Analysis of SIDIS and DVMP are complementary

Form Factor Studies Sachs Form Factors ~9 0% n GE(t)=F 1(t)+t/4 M 2*F 2(t) GM(t)=F 1(t)+F 2(t) More data expected in 2006/2007

Form Factor Studies Use various parameterizations for GPDs to fit the existing form factor data A. Afanasev hep-ph/9910565 Diehl et al, Eur. Phys. J c 39 (2005) M. Guidal et al PRD (2005) Different parameterizations yield different contributions for quarks to the OAM A)Large Ld and small Lu B)Sum of Lu and Ld small Issues: different realistic fits to FFs produce different values for Lq fits done at high t, need to be extrapolated to t→ 0 More observables needed for detailed studies of GPDs and the OAM (RCS, DVMP)

Hard Exclusive Processes and GPDs DVMP DVCS long. only hard gluon hard vertices DVCS – for different polarizations of beam and target provide access to ~ different combinations of GPDs H, H, E DVMP for different mesons is sensitive to flavor contributions ( 0/ + select H, E, for u/d flavors, p, h, K select H, E) Study the asymptotic regime and guide theory in describing HT.

Deeply Virtual Compton Scattering ep->e’p’g DVCS d 4 d. Q 2 dx. Bdtd BH GPD ~ |TDVCS + TBH|2 TBH : given by elastic form factors TDVCS: determined by GPDs Polarized beam, unpolarized target: ~ Ds. LU ~ sinf. Im{F 1 H + x(F 1+F 2)H +k. F 2 E} DVCS Kinematically suppressed BH Unpolarized beam, longitudinal target: ~ Ds. UL ~ sinf. Im{F 1 H+x(F 1+F 2)(H +. . } Kinematically suppressed Unpolarized beam, transverse target: Ds. UT ~ sinf. Im{k 1(F 2 H-F 1 E ) +. . } Kinematically suppressed x = x. B/(2 -x. B ), k = t/4 M 2 • Different GPD combinations accessible as azimuthal moments of the total cross section.

Deeply Virtual Compton Scattering ep→e’p’g Interference responsible for SSA, contain the same lepton propagator P 1( ) as BH Way to access to GPDS GPD combinations accessible as azimuthal moments of the total cross section.

-dependent amplitude BH =0 5. 7 Ge. V =45 =90 DVCS x=0. 25 Strong dependence on kinematics of prefactor f-dependence, at y=ycol P 1(f)=0 Fraction of pure DVCS increases with t and f

DVCS Experiments CLAS at 4. 3 Ge. V HERMES 27 Ge. V A( ) = asin + bsin 2 S. Stepanyan et al. Phys. Rev. Lett. 87 (2001) A. Airapetian et al. Phys. Rev. Lett. 87 (2001)

GPDs from ep->e’p’g Requirements for precision (<15%) measurements of s 2 I and GPDs from DVCS SSA: • Define relation between ALU and s 2 I • effect of other non-0 moments ~5 -10% • effect of finite bins ~10% • Define background corrections • pion contamination ~10% • radiative background • ADVCS <3% at CLAS More relevant when proton is not detected

DVCS event samples 3 event samples(after data quality cuts) 1) ep 0 photons (~2 M events) tight cuts on PID, missing mass MX 2) epg 1 photon in Calorimeter (~150000 events) cut on the direction qg. X<0. 015, 3) epgg 2 photon(p 0) in Calorimeter (~70000 events) cut on the direction qp. X<0. 02, Kinematic coverage of 5. 75 Ge. V(red) and 5. 48(blue) CLAS data sets epg(DVCS) epg(p 0) Angular cut most efficient in separating p 0

p 0 MC vs Data • Exclusive pi 0 production simulated using a realistic MC • Kinematic distributions in x, Q 2, t tuned to describe the CLAS data

p 0 beam SSA cross section Main unknown in corrections of photon SSA are the p 0 contamination and its beam SSA. Use epgg to estimate the contribution of p 0 in the ep and epg samples 1. 6<Q 2<2. 6, 0. 22<x<0. 32 CLAS 5. 7 Ge. V PRELIMINARY Contamination from p 0 photons increasing at large t and x and also at large f. Significant SSA measured for exclusive p 0 s also should be accounted

BH cos moment can generate ~3% sin 2 in the ALU

DVCS SSA kinematic dependences at 5. 7 Ge. V PRELIMINARY Fine binning allows to observe the x and Q 2 dependence ALU for ep->ep[g] sample with -t<0. 5 Ge. V 2 Preliminary data for fully exclusive epg is consistent with the ep data and consistent with GPD base predictions

Dedicated DVCS experiments → Dedicated detection of 3 particles e, p and γ in final state → Firmly establish scaling laws (up to Q 2 ~ 5 Ge. V 2), → if observed, or deviations thereof understood, first significant measurement of GPDs. Large kinematical coverage in x. B and t JLab/Hall A p e e’ γ JLab/CLAS Calorimeter and superconducting magnet within CLAS torus 424 Pb. WO 4 crystals HRS + Pb. F 2 + Plastic scintillator H(e, e’gp) dedicated calorimeters D(e, e’g. N)N

Extraction of GPD H from ALU moment epg ALU/c. LU ~ x(F 1+F 2)H +k. F 2 E ~20% 2<Q 2<2. 4 Ge. V • Red[blue] points correspond to projected ALU [un]corrected for p 0 (bin by bin) • H stands for the ratio of the ALU and prefactor calculated for all events in a bin (averaged over f) • Curves are for a simple model for CFF H (blue) and H+…(red)

Target Spin Asymmetry: t- Dependence Unpolarized beam, longitudinal target: ~ D UL ~ sin Im{F 1 H+x(F 1+F 2)(H +. . } ~ D LL ~ cos Re{F 1 H+x(F 1+F 2)(H +. . } Kinematically suppressed First data available(5 CLAS days), more(60 days) to come at 6 Ge. V Measurements with polarized target will constrain the polarized GPD and combined with beam SSA measurements would allow precision measurement of unpolarized GPDs.

Exclusive ρ meson production: ep → epρ0 CLAS (4. 2 Ge. V) Regge (JML) C. Hadjidakis et al. , PLB 605 GPD (MG-MVdh) CLAS (5. 75 Ge. V) GPD formalism (beyond leading order) describes approximately data for x. B<0. 4, Q 2 >1. 5 Ge. V 2 s An is s y l ro p n s gre i a Two-pion invariant mass spectra Decent description in p. QCD framework already at moderate Q 2

Exclusive p+p- and p+p 0 e p ep π+ π- r 0 e- p e- nr+ π +π 0 r+ Provide access to different combinations of orbital momentum contributions Ju, Jd 0 -> 2 Ju + Jd, + -> Ju - Jd n

Exclusive 0 production on transverse target 2 D ┴(Im(AB*))/p AUT = - |A|2(1 -x 2) - |B|2(x 2+t/4 m 2) - Re(AB*)2 x 2 r 0 A ~ 2 Hu + Hd B ~ 2 Eu + Ed r+ A ~ Hu - Hd B ~ Eu - Ed Eu, Ed needed for angular momentum sum rule. K. Goeke, M. V. Polyakov, M. Vanderhaeghen, 2001 Asymmetry is a more appropriate observable for GPD studies at JLab energies as possible corrections to the cross section are expected to cancel

TMD measurements in SIDIS (g*p→p. X) TMD PDFs related to interference between L=0 and L=1 light-cone wave functions. TMD Process f 1 T┴ ep → ep. X h 1 L┴ ep → ep. X f. L┴ ep → ep. X g┴ ep → ep. X h. L ep → ep. X FF Moment D 1 sin( h- S) ST(q×PT) H 1┴ sin( h- S’) S’=p/2 - h H 1┴ sin( h- S’) S’=p- h D 1 H 1┴ sin h Survive in jet limit Significant beam and target SSA were observed in all listed channels, more data under way

Sivers Effect studies with Transversely polarized target E 06 -010 and E 06 -011 Proposal approved, to study the Sivers function at JLab (Hall-A)

Sivers SSA at CLAS @5. 7 Ge. V Expected precision of the AUT with transversely polarized target Measurement of p 0 AUT at CLAS would allow model independent extraction of the Sivers function Sivers AUT ~ Simultaneous measurement of SIDIS, exclusive , +, w and DVCS asymmetries with a transversely polarized target. p+

Polarized target SSA using CLAS at 6 Ge. V 60 days of CLAS+IC (L=1. 5. 1034 cm-2 s-1) curves, c. QSM from Efremov et al Hunf=-5 Hfav Hunf=-1. 2 Hfav Hunf=0 • Provide measurement of SSA for all 3 pions, extract the Mulders TMD and study Collins fragmentation with longitudinally polarized target • Allows also measurements of 2 -pion asymmetries

Target SSA measurements at CLAS ep→e’p. X p 1 sinf+p 2 sin 2 f W 2>4 Ge. V 2 Q 2>1. 1 Ge. V 2 y<0. 85 CLAS PRELIMINARY 0. 4<z<0. 7 MX>1. 4 Ge. V p 1= 0. 059± 0. 010 p 2=-0. 041± 0. 010 p 1=-0. 042± 0. 015 p 2=-0. 052± 0. 016 p 1=0. 082± 0. 018 p 2=0. 012± 0. 019 PT<1 Ge. V 0. 12<x<0. 48 • Significant SSA measured for pions with longitudinally polarized target • Complete azimuthal coverage crucial for separation of sin , sin 2 moments

ALU x-dependence: CLAS @ 5. 7 Ge. V p+, 0. 5<z<0. 8 Parton distribution g┴(x) is calculated within the same dynamical model of Afanasev, Carlson • Assume k. T is small • Assume NLO corrections small Beam SSA for p 0 may provide a FF independent access to g┴

Measuring the Q 2 dependence of SSA ssinf. LU(UL) ~FLU(UL)~ 1/Q (Twist-3) For fixed x, 1/Q behavior expected Wide kinematic coverage and higher statistics will allow to check the higher twist nature of beam and longitudinal target SSAs

CLAS 12 High luminosity polarized (~80%) CW beam Wide physics acceptance (exclusive, semi-inclusive current and target fragmentation) Wide geometric acceptance 12 Ge. V significantly increase the kinematic acceptance and accessible luminosity Provides new insight into - quark orbital angular momentum contributions - to the nucleon spin - 3 D structure of the nucleon’s interior and correlations - quark flavor polarization

Summary q Current JLab data are consistent with a partonic picture, and can be described by a variety of theoretical models. q High luminosity, polarized CW beam, wide kinematic and geometric acceptance allow studies of exclusive and semi-inclusive processes, providing data needed to constrain relevant 3 D distribution functions (TMDs, GPDs) q Experimental investigation of properties of 3 D PDFs at JLab, complementary to planed studies at HERMES, COMPASS, RHIC, BELLE, GSI, would serve as an important check of our understanding of nucleon structure in terms of quark and gluon properties. ØCLAS 12 Full acceptance, general purpose detector for high luminosity electron scattering experiments, is essential for high precision measurements of GPDs and TMDs in the valence region.