Experimental Studies of Spin Duality P. Bosted (JLab) Jlab Users Meeting, June 2005  Bloom-Gilman duality in inclusive g 1  Factorization in polarized SIDIS  Single-spin asymmetries in SIDIS

P. Bosted, JLab Users Meeting, June Bloom-Gilman Duality in g 1  g 1 more sensitive resonance structure  Expect duality “working” at higher Q 2 than F 1 UNPOLARIZED F 1 = 4/9 u(x) + 1/9 d(x) Sum  1/2 +  3/2 POLARIZED g 1 = 4/9  u(x) + 1/9  d(x) Difference  1/2 -  3/2

P. Bosted, JLab Users Meeting, June Hall B Experiment Eg1b Scattering of 1.6 and 5.7 GeV longitudinally polarized electrons off longitudinally polarized NH 3, ND 3 g 1 determined from: a)Raw asymmetry b)Polarizations c)Dilution from N d)Model for R=  L /  T e)Model for A 2 f)Model for F 1

P. Bosted, JLab Users Meeting, June CLASS PRELIMINARY CLAS Eg1b Results for g1  Arrows (L to R) show W=1.7, 1.5, 1.2 GeV  Every 4 th Q 2 bin shown  Resonant structure clearly visible low Q 2  Gradually disappears at high Q 2  Data Q 2 >1 GeV 2 oscillate around fit to high Q 2 data protondeuteron Q 2 =0.2 Q 2 =0.4 Q 2 =0.8 Q 2 =1.7 Q 2 =2.5

P. Bosted, JLab Users Meeting, June PROTON: CLAS PRELIMINARY Integrals of g 1 in Different W regions  Integrate g 1 for models, data in various W regions  Global duality for Q 2 >2 GeV 2  Local duality does not work as well (  (1234) low, S  (1535) high all Q 2 ) GRSV TM, AAC TM DIS fit Q 2 =10  (1234) M<W<2 1.38<W< <W<1.78

P. Bosted, JLab Users Meeting, June DEUTERON: CLAS PRELIMINARY Integrals of g 1 in Different W regions  Global duality for Q 2 >1.5 GeV 2  Adding elastic peak (open circles) helps   (1234) still low all Q 2  2 nd and 3 rd resonance region work amazingly well (isospin averaging) GRSV TM, AAC TM DIS fit Q 2 =10  (1234) M<W<2 1.38<W< <W<1.78

P. Bosted, JLab Users Meeting, June  Similar to Eg1, but fixed Q 2 =1.1 GeV 2, W<1.9 GeV  Also measured g 2 : less model dependence for g 1  Both proton and deuteron (still under analsysis)  Good statistical accuracy RSS Experiment in Hall C

P. Bosted, JLab Users Meeting, June RSS Experiment in Hall C Q 2 =1.1 GeV 2 proton  On average, see agreement with PDF/TM models.   (1234) low  2 nd and 3 rd resonance regions high See next talk for Hall A results on 3 He

P. Bosted, JLab Users Meeting, June Semi-Inclusive Deep Inelastic Scattering (SIDIS): Probes orbital motion of quarks through quark transverse momentum distribution Access to new PDFs not accessible in inclusive DIS. k T -dependent parton distributions Sivers transversity Mulders, This talk Off-diagonal PDFs vanish if quarks only in s-state! In addition T-odd PDFs require FSI (Brodsky et al., Collins, Ji et al. 2002) This talk

P. Bosted, JLab Users Meeting, June SIDIS kinematic plane and relevant variables

P. Bosted, JLab Users Meeting, June Missing mass of pions in ep->e’  X Duality question: is a cut on M x (equivalent to z at low p t ) needed for SIDIS factorization to work? Note absence of Delta in  0 ! -- 00 ++ n 00  ++

P. Bosted, JLab Users Meeting, June Target polarization P T about 0.7 (0.3) for NH 3 (ND 3 ) Beam polarization P B about 0.7 Dilution factor f varies from 0.1 to 0.3: used Lund model for n/p ratio (agrees with Hall C data) and preliminary Hall B data for A-dependence Depolarization factor D LL (y) evaluated assuming R=  L /  T same as for inclusive. Assumed A perp =0 (not measured) No radiative corrections applied “  + ” and “  - ” include some K +, K - for P>1.5 GeV  0 events cleanly identified with two photons Determination of SIDIS g 1 /F 1 (approximately A 1 )

P. Bosted, JLab Users Meeting, June x-dependence of SIDIS proton g 1 /F 1 Good agreement with HERMES  + data at higher W. x-dependence follows PEPSI (Lund) Monte Carlo using GRSV polarized PDFs (LO) Magnitude also in good agreement with simulation W>2 GeV, Q 2 >1.1 GeV 2, 0.4<z<0.7

P. Bosted, JLab Users Meeting, June Simple picture in valence region:  p (  + ) = 4u(x)D + (z) + d(x)D - (z)  p (  - ) = 4u(x)D - (z) + d(x)D + (z)  p (  + ) = 4  u(x)D + (z) +  d(x)D - (z)  p (  - ) = 4  u(x)D - (z) +  d(x)D + (z) (g 1 /F 1 ) +- =[  p (  + )+  p (  - )]/[  p (  + )+  p (  - )] = [4  u(x) +  d(x)] / [4u(x) + d(x)] = (g 1 /F 1 ) inclusive Similarly for  0 (g 1 /F 1 ) 0 = (g 1 /F 1 ) inclusive Polarized SIDIS: factorization tests (g 1 /F 1 ) +- and (g 1 /F 1 ) 0 should be independent of z and p t, and equal to inclusive (g 1 /F 1 )

P. Bosted, JLab Users Meeting, June SIDIS: factorization studies g 1 /F 1 for inclusive, for the sum of     , and for   are fairly consistent with each other in the range 0.4<z<0.7, as expected in LO if factorization works. Cuts used: Mx>1.4 GeV, Q 2 >1.1 GeV 2, W>2 GeV GRVS Significant ?

P. Bosted, JLab Users Meeting, June z-dependence of SIDIS proton g 1 /F 1 CLAS 5.7 GeV PRELIMINARY No significant z-dependence seen for  0 and  + +  - for 0.3<z<0.7, as expected if factorization holds Good agreement with PEPSI predictions including dropoff at high z for  -, due to increasing importance of  d(x)]

P. Bosted, JLab Users Meeting, June p t -dependence of SIDIS proton g 1 /F 1 No p t dependence for  0 (green), as expected if factorization works  + (red) and  - (blue) individually show p t dependence, but the sum of the two (not shown) is almost independent of p t, as expected if factorization works Reasonable agreement with PEPSI predictions. PRELIMINARY CLAS 5.7 GeV

P. Bosted, JLab Users Meeting, June Q 2 -dependence of SIDIS proton g 1 /F 1 PRELIMINARY CLAS 5.7 GeV No Q 2 dependence for Q 2 >1.1 GeV 2. Evidence of HT for Q 2 <1.1 GeV 2 W>2 GeV 0.4<z<0.7

P. Bosted, JLab Users Meeting, June SIDIS g 1 /F 1 for Deuteron Results don’t agree as well with PEPSI using GRSV, more sensitive to un-favored fragmentation function and NLO corrections than proton (although errors are about a factor of two larger) NLO QCD fits including new SIDIS CLAS data can help constrain polarized PDFs in valence region PRELIMINARY CLAS 5.7 GeV

P. Bosted, JLab Users Meeting, June Longitudinally Polarized Target SSA  Clear   dependence seen for proton target and  +,  0  Fit A*sin(  ) + B*sin(2  ) for Twist-3 and Twist-2 respectively

P. Bosted, JLab Users Meeting, June SSA: x-dependence Twist-2 Higher Twist T The h L functions depend on both x and p t, so no simple factorization tests aren’t possible. However, can check if (x,p t,z) dependence follows model expectations

P. Bosted, JLab Users Meeting, June SSA: x-dependence PRELIMINARY 5.7 GeV Twist-2 Higher Twist Data in rough agreement with Efremov et al. predictions, except for  0 sin(  ) term (evidence for terms not involving Collins fragmentation?)

P. Bosted, JLab Users Meeting, June SSA: P T -dependence of sin  moment  sin  LU(UL) ~F LU(UL) ~ 1/Q (Twist-3) GeV Beam and target SSA for  + are consistent with increase with P T GeV

24 Global duality seems to work for inclusive g 1 for Q 2 >2 GeV 2 for proton and Q 2 >1.5 for deuteron Local duality does not seem to work for proton for any resonance region, but does seem to work for the deuteron for 2 nd and 3 rd resonance region Factorization tests on polarized SIDIS data work surprisingly well for W>2 GeV, Q 2 >1.1 GeV 2, 0.3<z<0.7, p t <1 GeV, even for Mx<2 GeV (another evidence of quark-hadron duality) Breakdown of factorization at high z: may be due to Delta excitation or diffraction vector meson production (ongoing analysis) Data may be used even with 6 GeV to study TMD PDFs, at least in limited kinematic region Summary

P. Bosted, JLab Users Meeting, June QUESTIONS Factorization W<2 GeV? Factorization for kaons at low energy? NLO treatment TM corrections Electroweak current? … we’re just in the beginning!

P. Bosted, JLab Users Meeting, June Future: more  0 data in SIDIS 1)SIDIS  0 production is not contaminated by diffractive  2)HT effects and exclusive  0 suppressed 3)Simple PID by  0 -mass (no kaon contamination) 4)Provides complementary to  +/- information on PDFs disadvantages: reconstruction efficiency (requires detection of 2  ) advantages:

P. Bosted, JLab Users Meeting, June CLAS+Inner Calorimeter (IC) IC at CLAS opens new avenue for studies of spin and azimuthal asymmetries of exclusive and semi-inclusive     CLAS CLAS+IC CLAS IC 424 PbWO4 ……..crystals Reconstruction efficiency of high energy  0 with IC increases ~ 4 times due to small angle coverage IC  E /E=0.0034/E+0.038/√E+0.022

P. Bosted, JLab Users Meeting, June  UL ~ KM Longitudinally polarized target SSA using CLAS+IC 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 H unf =-1.2H fav H unf =-5H fav H unf =0 50 days of CLAS+IC curves,  QSM from Efremov et al