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TMDs and Azimuthal Asymmetries in a Light-Cone Quark Model

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

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  1. 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)

  2. 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

  3. 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]

  4. 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

  5. P S P S P  D P  D S P S P P  D P  D P  P D  S

  6. 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

  7. 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

  8. 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.

  9. 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!

  10. 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

  11. 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

  12. 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.

  13. 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

  14. 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

  15. 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

  16. 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

  17. 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

  18. BACKUP SLIDES

  19. 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

  20. 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

  21. 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)

  22. 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

  23. Angular Momentum Decomposition of h1Tu 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]

  24. 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

  25. Angular Momentum Decomposition of h1Td Lz=0 and Lz=2 Lz=+1 and Lz=-1 SUM partial cancellation ofPP and DS terms weak deformation

  26. Pretzelosity: predictions

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