Studies of OAM at JLAB

Transcription

1 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

2 Parton picture: Longitudinal and transverse variables long before

3 Quark Angular Momentum Sum Rule GPDs H u, H d, E u, E d provide access to total quark contribution to proton angular momentum. Proton s spin ½ = ½ (Δu+Δd+Δs) + L q + J g J q J q = 1 2 J G = xdx [ H q ( x, ξ,0) + E q ( x, ξ,0) ] 1 X. Ji, Phy.Rev.Lett.78,610(1997) Large x contributions important.

4 3D Parton Distributions TMD PDFs f pu (x,k T ), GPDs H pu (x,ξ,t).. Measure momentum transfer to quark d 2 k T ξ=0,t=0 dx Measure momentum transfer to target PDFs f pu (x,k T ), g 1, h 1 FFs F 1pu (t),f 2pu (t).. Analysis of SIDIS and DVMP are complementary

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

6 Form Factor Studies Use various parameterizations for GPDs to fit the existing form factor data A.Afanasev hep-ph/ Diehl et al, Eur.Phys.J c39 (2005) M.Guidal et al PRD (2005) Different parameterizations yield different contributions for quarks to the OAM A)Large L d and small L u B)Sum of L u and L d 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,DVCS,DVMP)

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

8 Deeply Virtual Compton Scattering ep->e p γ DVCS GPD BH d 4 σ dq 2 dx B dtdφ ~ T DVCS + T BH 2 T BH : given by elastic form factors T DVCS : determined by GPDs Polarized beam, unpolarized target: ~ Δσ LU ~ sinφim{f 1 H + ξ(f 1 +F 2 )H +kf 2 E} dσ/dt (nb/gev 4 ) DVCS 6 GeV 27 GeV 200 GeV Kinematically suppressed Unpolarized beam, longitudinal target: ~ Δσ UL ~ sinφim{f 1 H+ξ(F 1 +F 2 )(H +.. } Kinematically suppressed Unpolarized beam, transverse target: Δσ UT ~ sinφim{k 1 (F 2 H-F 1 E ) +.. } Kinematically suppressed t(gev 2 ) ξ = x B /(2-x B ),k = t/4m 2 BH Different GPD combinations accessible as azimuthal moments of the total cross section.

9 Deeply Virtual Compton Scattering ep e p γ s I I A xb s1 LU y BH c0 8 Ky ( 2 y ) Im H ~ Δ = λ Way to access to GPDS [ F H ( F F ) F Ε ] x 2 B x B M Interference responsible for SSA, contain the same lepton propagator P 1 (φ) as BH 2 GPD combinations accessible as azimuthal moments of the total cross section.

10 φ-dependent amplitude 2 Q t y col = = 2 Q xt 2 2 t Q ( Q 2xME y = col 2 ( Q 2ME ) x ) BH φ=0 5.7 GeV φ=45 φ=90 DVCS x=0.25 Strong dependence on kinematics of prefactor φ-dependence, at y=y col P 1 (φ)=0 Fraction of pure DVCS increases with t and φ

11 DVCS Experiments CLAS at 4.3 GeV HERMES 27 GeV Α(φ) = αsinφ + βsin2φ S. Stepanyan et al. Phys. Rev. Lett. 87 (2001) A. Airapetian et al. Phys. Rev. Lett. 87 (2001)

12 GPDs from ep->e p γ Requirements for precision (<15%) measurements of s 2 I and GPDs from DVCS SSA: Define relation between A LU 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

13 DVCS event samples 3 event samples(after data quality cuts) 1) ep 0 photons (~2M events) tight cuts on PID,missing mass MX 2) epγ 1 photon in Calorimeter (~ events) cut on the direction θ γx <0.015, 3) epγγ 2 photon(π 0 ) in Calorimeter (~70000 events) cut on the direction θ πx <0.02, epγ(dvcs) epγ(π 0 ) Kinematic coverage of 5.75 GeV(red) and 5.48(blue) CLAS data sets Angular cut most efficient in separating π 0

14 π 0 MC vs Data Exclusive pi0 production simulated using a realistic MC Kinematic distributions in x,q 2,t tuned to describe the CLAS data

15 π 0 beam SSA cross section Main unknown in corrections of photon SSA are the π 0 contamination and its beam SSA. 1.6<Q 2 <2.6, 0.22<x<0.32 Use epγγ to estimate the contribution of π0 in the ep and epγ samples CLAS 5.7 GeV PRELIMINARY Contamination from π 0 photons increasing at large t and x and also at large f. Significant SSA measured for exclusive π0s also should be accounted

16 BH cosφ moment A LU c BH 0 λ (1+ c s I I I BH BH s2 sinφ λ 2 sinφ λ 2( 1 /2 0 )sin2 BH BH BH 1 / c0 cosφ ) c0 BH cosφ moment can generate ~3% sin2φ in the A LU s c c φ

17 DVCS SSA kinematic dependences at 5.7 GeV PRELIMINARY Fine binning allows to observe the x and Q 2 dependence A LU for ep->ep[γ] sample with -t<0.5 GeV 2 Preliminary data for fully exclusive epγ is consistent with the ep data and consistent with GPD base predictions

18 Dedicated DVCS experiments Dedicated detection of 3 particles e, p and γ in final state Firmly establish scaling laws (up to Q 2 ~ 5 GeV 2 ), if observed, or deviations thereof understood, first significant measurement of GPDs. Large kinematical coverage in x B and t e p γ e JLab/Hall A HRS JLab/CLAS Calorimeter and superconducting magnet within CLAS torus 424 PbWO4 crystals e Beam LH2 target p γ e Electromagnetic calorimeter Plastic scintillator array HRS + PbF 2 + Plastic scintillator H(e,e γp) D(e,e γn)n dedicated calorimeters

19 Extraction of GPD H from A LU moment c LU epγ 2<Q 2 <2.4 GeV A LU /c LU ξ(f 1 +F 2 )H +kf 2 E ~20% ~ Red[blue] points correspond to projected A LU [un]corrected for π0 (bin by bin) H stands for the ratio of the A LU and prefactor calculated for all events in a bin (averaged over φ) Curves are for a simple model for CFF H (blue) and H+ (red)

20 Target Spin Asymmetry: t- Dependence Unpolarized beam, longitudinal target: ~ Δσ UL ~ sinφim{f 1 H+ξ(F 1 +F 2 )(H +.. } Δσ LL ~ cosφre{f 1 H+ξ(F ~ 1 +F 2 )(H +.. } Kinematically suppressed First data available(5 CLAS days), more(60 days) to come at 6 GeV Measurements with polarized target will constrain the polarized GPD and combined with beam SSA measurements would allow precision measurement of unpolarized GPDs.

21 C. Hadjidakis et al., PLB 605 Exclusive ρ meson production: ep epρ 0 CLAS (4.2 GeV) Regge (JML) GPD (MG-MVdh) CLAS (5.75 GeV) GPD formalism (beyond leading order) describes approximately data for x B <0.4, Q 2 >1.5 GeV 2 Analysis in progress Two-pion invariant mass spectra Decent description in pqcd framework already at moderate Q 2

22 e p Exclusive π + π and π + π 0 e p ρ π + π - e - p e - nρ+ π + π 0 ρ 0 ρ+ n Provide access to different combinations of orbital momentum contributions J u,j d ρ 0 -> 2J u + J d, ρ + -> J u -J d

23 Exclusive ρ 0 production on transverse target 2Δ (Im(AB*))/π Α UT = Α 2 (1 ξ 2 ) Β 2 (ξ 2 +t/4m 2 ) - Re(ΑΒ )2ξ 2 ρ 0 A~ 2H u + H d B ~ 2E u + E d ρ 0 ρ + A ~ H u -H d B ~ E u -E d E u, E d 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

24 TMD measurements in SIDIS (γ*p πx) TMD PDFs related to interference between L=0 and L=1 light-cone wave functions. TMD Process FF Moment f 1T ep eπx D 1 sin(φh φs) h 1 ep eπx H 1 sin(φh φs ) h 1L ep eπx H 1 sin(φh φs ) S T (q P T ) φs =π/2-φ h φs =π-φ h f L ep eπx D 1 sinφh Survive in jet limit g ep eπx D 1 sinφh h L ep eπx H 1 sinφh Significant beam and target SSA were observed in all listed channels, more data under way

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

26 Sivers SSA at Expected precision of the A UT with transversely polarized target Measurement of π 0 A UT at CLAS would allow model independent extraction of the Sivers function π+ Sivers A UT ~ Simultaneous measurement of SIDIS, exclusive ρ,ρ+,ω and DVCS asymmetries with a transversely polarized target.

27 Polarized target SSA using CLAS at 6 GeV q q h1 L ( x ) H 1 ( z ) sin 2 φ q AUL = D 60 days of CLAS+IC UL q q f ( x ) D ( z ) (L= cm -2 s -1 ) q 1 1 curves, χqsm from Efremov et al H unf =-5H fav H unf =-1.2H fav H unf =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

28 Target SSA measurements at CLAS σ sin φ UL S L M Q y 2 q 1 y eq xf L ( x) D1 Σ q, q q ( z) p 1 sinφ+p 2 sin2φ ep e πx CLAS PRELIMINARY W 2 >4 GeV 2 Q 2 >1.1 GeV 2 y< <z<0.7 M X >1.4 GeV 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 P T <1 GeV 0.12<x<0.48 Significant SSA measured for pions with longitudinally polarized target Complete azimuthal coverage crucial for separation of sinφ, sin2φ moments

29 A LU x-dependence: 5.7 GeV π+,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 π 0 may provide a FF independent access to g

30 Measuring the Q 2 dependence of SSA σ sinφ LU(UL) ~F LU(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

31 CLAS12 High luminosity polarized (~80%) CW beam Wide physics acceptance (exclusive, semi-inclusive current and target fragmentation) Wide geometric acceptance 12GeV significantly increase the kinematic acceptance and accessible luminosity Provides new insight into - quark orbital angular momentum contributions - to the nucleon spin - 3D structure of the nucleon s interior and correlations - quark flavor polarization

32 Summary Current JLab data are consistent with a partonic picture, and can be described by a variety of theoretical models. High luminosity, polarized CW beam, wide kinematic and geometric acceptance allow studies of exclusive and semi-inclusive processes, providing data needed to constrain relevant 3D distribution functions (TMDs,GPDs) Experimental investigation of properties of 3D 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. CLAS12 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.