Duality in Semi-Inclusive DIS P. Bosted (JLab) First Workshop on Quark-Hadron Duality and the Transition to pQCD June 6, 2005 Semi-inclusive processes Factorization as a test of quark-hadron duality Factorization tests in unpolarized SIDIS Kinematic dependences of g1/f1 PT dependence of spin and azimuthal asymmetries Summary & Outlook Note mes

P. Bosted, Duality Workshop, June 2005 Semi-inclusive DIS Main focus of SIDIS studies: orbital angular momentum of quarks parton distributions at large x X.Ji Where region I/II boundary? Can useful information come from Region II? P. Bosted, Duality Workshop, June 2005

P. Bosted, Duality Workshop, June 2005 kT-dependent parton distributions 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. 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) Mulders, This talk Note mes transversity Sivers This talk P. Bosted, Duality Workshop, June 2005

SIDIS kinematic plane and relevant variables P. Bosted, Duality Workshop, June 2005

Missing mass of pions in ep->e’pX D++ p- D0 Duality question: is MX>1.4 GeV (approximately z<0.7 for Q2-2.5 GeV2, W=2.5 GeV) needed for SIDIS factorization to work? Note absence of Delta in p0! P. Bosted, Duality Workshop, June 2005

Factorization Test from Unpolarized Multiplicites Multiplicity (proportional to D+(z)) is approximately independent of x for W>3 GeV, Q2=2.5 GeV2, x<0.5, and 0.25<z<0.6 P. Bosted, Duality Workshop, June 2005

Factorization Test from Unpolarized Multiplicites Dup+ KKP (LO) Multiplicity (proportional to D+(z)) is also approximately independent of x for W>2 GeV, Q2=2 GeV2, 0.1<x<0.6, and 0.45<z<0.7 at E=5.5 GeV from CLAS at JLab P. Bosted, Duality Workshop, June 2005

Rpd should be independent of x-dependence of Rpd should be same as Unpolarized SIDIS: new test Simple picture in valence region: sp(p+) = 4u(x)D+(z) + d(x)D-(z) sp(p-) = 4u(x)D-(z) + d(x)D+(z) sd(p+) = [u(x)+d(x)] [4D+(z) + D-(z)] sd(p-) = [u(x)+d(x)] [4D-(z) + D+(z)] Rpd= [sp(p+) + sp(p-)] / [sd(p+) + sd(p-)] = [4u(x) + d(x)] / 5[u(x)+d(x)] = sp(x)/sd(x) Rpd should be independent of z and pt x-dependence of Rpd should be same as inclusve sp(x)/sd(x) in valence region P. Bosted, Duality Workshop, June 2005

Unpolarized SIDIS: new test Rpd is independent of z for 0.4<z<0.7 for W=2.5 GeV, Q2=2.5 GeV2, x=0.3, low pt Good agreement GRV (using PEPSI MC, solid histogram) 10% level deviations for z>0.7 (Mx>1.4 GeV) Influence of Delta? P. Bosted, Duality Workshop, June 2005

Unpolarized SIDIS: new test Rpd is independent of pt for z=0.55 W=2.5 GeV, Q2=2.5 GeV2, x=0.3 Good agreement GRV (using PEPSI MC, solid histogram) P. Bosted, Duality Workshop, June 2005

Pretty good agreement with GRV (using PEPSI MC, solid histogram) Unpolarized SIDIS: new test Rpd follows expected x-dependence for z=0.55 W=2.5 GeV, Q2=2.5 GeV2, low pt Pretty good agreement with GRV (using PEPSI MC, solid histogram) P. Bosted, Duality Workshop, June 2005

CLAS Experiment Setup and Kinematics Scattering of 5.7 GeV polarized electrons off polarized NH3, ND3 ~8M p+ in SIDIS kinematics x x

Determination of g1/F1 (approximately A1) Target polarization PT about 0.7 (0.3) for NH3 (ND3) Beam polarization PB 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 DLL(y) evaluated assuming R=sL/sT same as for inclusive. Assumed Aperp=0 (not measured) No radiative corrections applied “p+” and “p-” include some K+, K- for P>1.5 GeV p0 events cleanly identified with two photons

x-depenence of SIDIS proton g1/F1 W>2 GeV, Q2>1.1 GeV2, 0.4<z<0.7 Good agreement with HERMES p+ data at higher W. x-dependence follows PEPSI (Lund) Monte Carlo using GRSV polarized PDFs (LO) Magnitude also in good agreement with simulation P. Bosted, Duality Workshop, June 2005

(g1/F1)+- and (g1/F1)0 should be independent of Polarized SIDIS: factorization tests Simple picture in valence region: sp(p+) = 4u(x)D+(z) + d(x)D-(z) sp(p-) = 4u(x)D-(z) + d(x)D+(z) dsp(p+) = 4du(x)D+(z) + dd(x)D-(z) dsp(p-) = 4du(x)D-(z) + dd(x)D+(z) (g1/F1)+-=[dsp(p+)+dsp(p-)]/[sp(p+)+sp(p-)] = [4du(x) + dd(x)] / [4u(x) + d(x)] = (g1/F1)inclusive Similarly for p0 (g1/F1)0= (g1/F1)inclusive (g1/F1)+- and (g1/F1)0 should be independent of z and pt, and equal to inclusive (g1/F1) P. Bosted, Duality Workshop, June 2005

SIDIS: factorization studies Significant ? GRVS g1/F1 for inclusive, for the sum of p+ ,p- , and for p0 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, Q2>1.1 GeV2, W>2 GeV P. Bosted, Duality Workshop, June 2005

z-depenence of SIDIS proton g1/F1 No significant z-dependence seen for p0 and p++ p- for 0.3<z<0.7, as expected if factorization holds Good agreement with PEPSI predictions including dropoff at high z for p-, due to increasing importance of dd(x)] CLAS 5.7 GeV PRELIMINARY P. Bosted, Duality Workshop, June 2005

pt-depenence of SIDIS proton g1/F1 No pt dependence for p0 (green), as expected if factorization works p+ (red) and p- (blue) individually show pt dependence, but the sum of the two (not shown) is almost independent of pt, as expected if Reasonable agreement with PEPSI predictions. CLAS 5.7 GeV PRELIMINARY P. Bosted, Duality Workshop, June 2005

Q2-depenence of SIDIS proton g1/F1 PRELIMINARY CLAS 5.7 GeV No Q2 dependence for Q2>1.1 GeV2. Evidence of HT for Q2<1.1 GeV2 W>2 GeV 0.4<z<0.7 P. Bosted, Duality Workshop, June 2005

SIDIS g1/F1 for Deuteron CLAS 5.7 GeV PRELIMINARY 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

Longitudinally Polarized Target SSA Clear f dependence seen for proton target and p+, p0 Fit A*sin(f) + B*sin(2f) for Twist-3 and Twist-2 respectively P. Bosted, Duality Workshop, June 2005

P. Bosted, Duality Workshop, June 2005 SSA: x-dependence Twist-2 Higher Twist The hL functions depend on both x and pt, so no simple factorization tests aren’t possible. However, can check if (x,pt,z) dependence follows model expectations T P. Bosted, Duality Workshop, June 2005

P. Bosted, Duality Workshop, June 2005 SSA: x-dependence Twist-2 Higher Twist Data in rough agreement with Efremov et al. predictions, except for p0 sin(f) term (evidence for terms not involving Collins fragmentation?) 5.7 GeV PRELIMINARY P. Bosted, Duality Workshop, June 2005

SSA: PT-dependence of sinf moment ssinfLU(UL) ~FLU(UL)~ 1/Q (Twist-3) CLAS @4.3 GeV CLAS @5.7 GeV Beam and target SSA for p+ (not sensitive to MX-cut) are consistent with increase with PT P. Bosted, Duality Workshop, June 2005

P. Bosted, Duality Workshop, June 2005 Summary Factorization tests with both unpolarized and polarized data work surprisingly well for W>2 GeV, Q2>1.1 GeV2, 0.3<z<0.7, pt<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) Target fragmentation may come into play at lower z than naively expected (ongoing analysis) Data may be used even with 6 GeV electrons to study PDFs, at least in limited kinematic region More data planned all final states at 6 GeV and with 11 GeV at Jlab. High statistical accuracy tests will better quantify the useful kinematic range of SIDIS P. Bosted, Duality Workshop, June 2005

P. Bosted, Duality Workshop, June 2005 QUESTIONS Factorization W<2 GeV? Factorization for kaons at low energy? NLO tretment TM corrections Electroweak current? … we’re just in the beginning! P. Bosted, Duality Workshop, June 2005

P. Bosted, Duality Workshop, June 2005 support slides….. P. Bosted, Duality Workshop, June 2005

First glimpse of Twist-2 TMD h1L┴ For Collins fragmentation function use HERMES data Distribution functions from cQSM from Efremov et al PRELIMINARY CLAS-5.7GeV Systematic error only from unknown ratio of favored and unfavored Collins functions (R= H1d→p+/H1u→p+), band correspond to -2.5<R<0 More data required with p- & p0 Exclusive 2 pion background may be important

SIDIS (g*p->pX) x-section at leading twist: TMD PDFs f1 h┴1 g1 T-odd h┴1L f┴1T g1T h1 h┴1T kT-even kT-odd The structure functions depend on Q2, xB, z, PhT 1) Unpolarized target 2) Longitudinally pol. target 3) Transversely pol. target Studies of PDFs require three experiments P. Bosted, Duality Workshop, June 2005

Future: more p0 data in SIDIS advantages: SIDIS p0 production is not contaminated by diffractive r HT effects and exclusive p0 suppressed Simple PID by p0-mass (no kaon contamination) Provides complementary to p+/- information on PDFs disadvantages: reconstruction efficiency (requires detection of 2g) P. Bosted, Duality Workshop, June 2005

CLAS+Inner Calorimeter (IC) 424 PbWO4 ……..crystals CLAS+Inner Calorimeter (IC) IC IC sE/E=0.0034/E+0.038/√E+0.022 CLAS+IC CLAS Reconstruction efficiency of high energy p0 with IC increases ~ 4 times due to small angle coverage CLAS IC at CLAS opens new avenue for studies of spin and azimuthal asymmetries of exclusive and semi-inclusive g, p0,h,r+ P. Bosted, Duality Workshop, June 2005

Longitudinally polarized target SSA using CLAS+IC sUL ~ KM 50 days of CLAS+IC curves, cQSM from Efremov et al Hunf=-5Hfav Hunf=-1.2Hfav 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

P. Bosted, Duality Workshop, June 2005 SIDIS factorization Structure functions FUU,FLL… factorize into TMD distribution and fragmentation: Naïve Factorization (Mulders and col.) QCD Factorization (Ji and col.) TMD FF hard scattering soft factor TMD PDF SIDIS Factorization proved for low PT !!! P┴ has contributions from distribution, fragmentation and soft gluon radiation P. Bosted, Duality Workshop, June 2005

ALU x-dependence: CLAS @ 4.3 and 5.7 GeV Photon Sivers Effect Afanasev & Carlson, Metz & Schlegel Beam SSA analyzed in terms of the Sivers effect by F.Yuan using h1┴ from MIT bag model 0.5<z<0.8 Beam SSA analyzed in terms of the Collins effect by Schweitzer et al. using e(x) from cQSM Separation of different HT contribution will require independent measurements of separate contributions P. Bosted, Duality Workshop, June 2005

double spin asymmetry A1p P. Bosted, Duality Workshop, June 2005

P. Bosted, Duality Workshop, June 2005 NH3 dilution Dilution function extracted from PEPSI-MC is consistent with data P. Bosted, Duality Workshop, June 2005