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TMDs and Azimuthal Asymmetries in a Light-Cone Quark Model Barbara Pasquini (Uni Pavia & INFN Pavia, Italy) in collaboration with S. Boffi, S. Cazzaniga P.Schweitzer A.V. Efremov
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TMDs and Azimuthal Asymmetries in a Light-Cone Quark Model Barbara Pasquini (Uni Pavia & INFN Pavia, Italy) in collaboration with S. Boffi, S. Cazzaniga P.Schweitzer A.V. Efremov (Uni Pavia & INFN Pavia) (Uni Connecticut) (JINR, Dubna)
Outline • Three-Quark Light-Cone Amplitudes of the Nucleon • Spin-Spin and Spin-Orbit Correlations in T-even TMDs • Single Spin Azimuthal Asymmetries in SIDIS • Conclusions • overlap representation in terms of three-quark light-cone amplitudes • results in a light-cone quark model • relations of the TMDs in different relativistic valence quark models
Three-Quark Light Cone Amplitudes Lz = 2 Lz =-1 • classification of LCWFs in angular momentum components [Ji, J.P. Ma, Yuan, 03; Burkardt, Ji, Yuan, 02] total quark helicity Jq Lz =0 Jz = Jzq + Lz parity time reversal isospin symmetry 6 independent wave function amplitudes: Lz = 1 LCWF: invariant under boost, independent of P internal variables: [Brodsky, Pauli, Pinsky, ’98]
Light-cone Gauge A+=0 and advanced boundary condition for A S S P P no gauge link complex light-cone amplitudes P P D D S S P P D D P P P P S S Light Cone Amplitudes Overlap Representation of TMDs
P S P S P D P D S P S P P D P D P P D S
Light-Cone Constituent Quark Model • Instant Form (canonical) eigenvalue equation • Light-front eigenvalue equation generalized Melosh rotations Instant form:x0 time;x1, x2, x3 space Light-front form:x+ time;x-, x space free mass operator : interaction operator
Light Cone Spin Lzq =1 Lzq =2 Lzq = -1 Lzq =0 • Instant-form wave function: • momentum-space component: S wave • spin and isospin component: SU(6) symmetric Lzq=0 Jz=Jzq Melosh Rotations • Light-cone wavefunction Jz = Jzq +Lzq • non-zero quark orbital angular momentum: Six independent wave function amplitudes The six independent wave function amplitudes obtained from the Melosh rotations satisfy the model independent classification scheme in four orbital angular momentum components
TMDs in a Light-Cone CQM • SU(6) symmetry Nu =2 Nd =1 Pu =4/ 3 Pd = -1/3 momentum dependent wf factorized from spin-dependent effects 3 relations between the TMDs B.P., Cazzaniga, Boffi, PRD78, 2008.
Relations of TMDs in Valence Quark Models • (1), (2), and (3) hold inLight-Cone CQM ModelsBP, Pincetti, Boffi, PRD72, 2005; BP, Cazzaniga, Boffi, PRD78, 2008 • (1) and (2) hold inBag ModelAvakian, Efremov, Yuan, Schweitzer, hep-ph: 0805.3355 • (3) holds in spectator model, (1) and (2) are recovered only if mass of axial-vector-diquark = mass of scalar-diquark Jakob, Mulders, Rodrigues, NPA626, 1997 • (2) holds in covariant quark-parton model see talk by P. Zavada, Monday, Nucleon-Spin Joint Sessions • SU(6) symmetry • no gluon dof valid at low hadronic scale • not restricted to S and P wave contributions (1) (2) (3) All 8 leading twist TMDs contain independent information on the nucleon structure and there are NO EXACT relations between TMDs in QCD BUT having well-motivated approximations is valuable!
Transversity x h1q • Dashed area: extraction of transversity from BELLE, COMPASS, and HERMES data Anselmino et al., PRD75, 2007 (courtesy of A. Prokudin) • Predictions from Light-Cone CQM evolved from the hadronic scale 20 to Q2= 2.5 GeV2using two different momentum-dependent wf solution of relativistic potential model • no free parameters • fair description of nucleon form factors • phenomenological wf • three fit parameters • , and mq fitted to the anomalous magnetic moments of the nucleon and to gA up down Schlumpf, Ph.D. Thesis, hep-ph/9211255 Faccioli, et al., NPA656, 1999Ferraris et al., PLB324, 1995 BP, Pincetti, Boffi, PRD72, 2005
Collins SSA • Preliminary HERMES data HERMES data: Diefenthaler, hep-ex/0507013 from Light-Cone CQM evolved at Q2=2.5 GeV2 from HERMES & BELLE data Efremov, Goeke, Schweitzer, PRD73 (2006); Anselmino et al., PRD75 (2007); Vogelsang, Yuan, PRD72 (2005) More recent HERMES, COMPASS and BELLE data not yet included in the fit of Collins function Schweitzer, Boffi, Efremov, BP, in preparation
h1L • opposite sign of h1 with with • chiral odd, no gluons • h1L:SP and PD interference termsh1: SS and PP diagonal terms h1L h1 • Wandzura-Wilczek-type approximationAvakian, et al., PRD77, 2008 h1L (1) WW approx. Light-Cone CQM WW approx.
sin(2) A UL from Light-Cone CQM from HERMES & BELLE • HERMES data Efremov, Goeke, Schweitzer, PRD73 (2006); Anselmino et al., PRD75 (2007); Vogelsang, Yuan, PRD72 (2005) Airapetian, PRL84, 2000; Avakian, Nucl. Phys. Proc. Suppl. 79 (1999) (no evolution) Schweitzer, Boffi, Efremov, BP, in preparation
Pretzelosity down up Spectator ModelJakob, et al., NPA626 (1997) • large, not constrained by positivity • sign opposite to transversity • light-cone quark model and bag model peaked at smaller x • related to chiral-odd GPD Light-Cone CQMBP, et al.: PRD78, 2008 [Meissner, et al., PRD76, 2007] Bag Model Avakian, et al., hep-ph:0805.3355 down • positivity satisfied • helicity – transversity = pretzelosity Soffer inequality up
Pretzelosity in SIDIS: first insights from HERMES & BELLE Efremov, Goeke, Schweitzer, PRD73 (2006); Anselmino et al., PRD75 (2007); Vogelsang, Yuan, PRD72 (2005) • Preliminary COMPASS deuteron data on Kotzinian [on behalf of COMPASS Coll.]: hep-ex:0705.2402 from Light-Cone CQM • at x > 0.1 the statistic is not sufficient to be sensitive to pretzelosity • suppression at small x does not exclude sizeable effects at larger x Schweitzer, Boffi, Efremov, BP, in preparation
Pretzelosity in SIDIS: perspectives • At small x: • There will be data from COMPASS proton target • There will be data from HERMES • More favorable conditions at intermediate x (0.2-0.6) • experiment planned at CLAS with 12 GeV(H. Avakian at al., LOI 12-06-108) Light-Cone CQM Error projections for 2000 hours run time at CLAS12 Schweitzer, Boffi, Efremov, BP, in preparation
Summary relativistic effects due to Melosh rotations in LCWF introduce a non-trivial spin structure and correlations between quark spin and quark orbital angular momentum three non-trivial relations among T-even TMDs valid at low scale in a large class of relativistic quark models Light-Cone CQM able to describe the x dependence of transverse and longitudinal SSAs promising predictions to extract “pretzelosity” in at x (0.2 - 0.6) • General classification of TMDs in terms of three-quark Light-Cone amplitudes withdifferent orbital angular momentum • Model calculation in a Light-Cone CQM • Single Spin Asymmetries in SIDIS
Collins SSA 2002-2004 HERMES data: Diefenthaler, hep-ex/05070132002-2005 HERMES data: Diefenthaler, hep-ex/0706.2242; hep-ex/0612010; COMPASS data: Alekseev, hep-ex/0802.2160
Spin-Orbit Correlations and the Shape of the Nucleon spin-dependent charge density operator in non relativistic quantum mechanics spin-dependent charge density operator in quantum field theory nucleon state transversely polarized Probability for a quark to have a momentum k and spin direction n in a nucleon polarized in the S direction G.A. Miller, PRC76 (2007) TMD parton distributions integrated over x
Spin-dependent densities • Fix the directions of S and n the spin-orbit correlations measured with is responsible for a non-spherical distribution with respect to the spin direction • Diquark spectator model: wave function with angular momentum components Lz = 0, +1, -1 deformation due only to Lz=1 and Lz=-1 components Jakob, et al., (1997) s S x x S x : chirally-odd tensor correlations matrix element from angular momentum components with |Lz-L’z|=2 up quark K =0 K =0.5 GeV K =0.25 GeV G.A. Miller, PRC76 (2007)
Light Cone Constituent Quark Model s S x x S x adding the contribution from Lz=0 and Lz=2 components B.P., Cazzaniga, Boffi, arXiv:0806.2298 [hep-ph] up quark deformation induced from the Lz=+1 and Lz=-1 components
Angular Momentum Decomposition of h1Tu Lz=0 and Lz=2 Lz=+1 and Lz=-1 SUM PP and DS termsadd with the same sign strong deformation from spherical shape B.P., Cazzaniga, Boffi, arXiv:0806.2298 [hep-ph]
Spin dependent densities for down quark • Light-cone CQM: contribution of Lz=+1 and Lz=-1 components plus contribution of Lz=0 and Lz=2 components s s S S x x x x S S x x • Diquark spectator model: contribution of Lz=+1 and Lz=-1 components
Angular Momentum Decomposition of h1Td Lz=0 and Lz=2 Lz=+1 and Lz=-1 SUM partial cancellation ofPP and DS terms weak deformation