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Transverse spin structure of hadrons from lattice QCD QCDS/UKQCD hep-lat/0612032 (→PRL)

Transverse spin structure of hadrons from lattice QCD QCDS/UKQCD hep-lat/0612032 (→PRL). Philipp Hägler. in collaboration with D. Brömmel, M. Diehl (DESY), M. Göckeler, A. Schäfer (Regensburg U.) R. Horsley, J. Zanotti (Edinburgh U.) Y. Nakamura (DESY Zeuthen) P. Rakow (Liverpool U.)

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Transverse spin structure of hadrons from lattice QCD QCDS/UKQCD hep-lat/0612032 (→PRL)

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  1. Transverse spin structure of hadrons from lattice QCD QCDS/UKQCD hep-lat/0612032 (→PRL) Philipp Hägler in collaboration with D. Brömmel, M. Diehl (DESY), M. Göckeler, A. Schäfer (Regensburg U.) R. Horsley, J. Zanotti (Edinburgh U.) Y. Nakamura (DESY Zeuthen) P. Rakow (Liverpool U.) D. Pleiter, G. Schierholz (DESY Zeuthen) H. Stüben (ZIB) (QCDSF/UKQCD) supported by

  2. Introduction lattice quantum chromodynamics concepts non-perturbative approach „from first principles“ methods algorithms substantial progress machines fundamental question: spin structure of hadrons very difficult to directly access in experiment transverse spin structure of the nucleon enormous progress in qualitative and quantitative understanding from quark position in coordinate space experiment (perturbative) QCD effective field theory models … connection? accessible in e.g. SIDIS experiments results in this talk based on the concept of generalized parton distributions, with outlook on possible implications for intrinsic transverse momentum dependent PDFs logitudinal spin : nucleon spin sumrule, quark spin and orbital angular momentum transversity, transverse spin : transverse spin densities of quarks in the nucleon we find strong correlations between spin, OAM and coordinate space DOFs interpretation

  3. Standard processes SIDIS DVCS DIS exclusive find a process like deep ineleastic scattering (DIS) or deeply virtual compton scattering which (DVCS) experiment is sensitive to the nucleon matrix elements we are interested in factorizes contributions from higher twist complicated convolutions of numerous variables and non-perturbative observables

  4. Generalized form factors in Lattice QCD nucleon source/sink operator insertion at time t quark-path through lattice Mellin moments requires inversion of huges matrices

  5. Lowest two moments of the Soffer-bound from lattice QCD QCDSF/UKQCD PLB 2005

  6. Transversely polarized quarks in transversely polarized nucleons multipole-expansion Diehl / PhH EPJC 2005 quadrupole monopole dipole transversity basis calculate transverse spin probability density in impact parameter space

  7. Results for moments of the tensor GPDs the tensor GFFs are remarkably large

  8. Results for moments of the tensor GPDs the tensor GFF is sizeable and

  9. Lowest n=1 moments of up- and down-quark densities QCDS/UKQCD hep-lat/0612032 (→PRL) up up up down down down strong deviations from spherical symmetry

  10. n=2 moments of up- and down-quark densities up up up down down down same pattern as before for n=1 densities are strongly deformed strong correlations of coordinate and spin degrees of freedom

  11. Implications for asymmetries conjecture / hypothesis Burkardt PRD 72 (2005); Meissner, Metz&Goecke 2007 asymmetries up-quark FSI M. Burkardt 2003/2005 expect sizeable effect with opposite sign for up- and down-quarks (Sivers-effect)

  12. Sivers asymmetry measured by HERMES pion production from positrons on a transversely polarized hydrogen target Sivers asymmetry HERMES collaboration PRL 2005 cos(2Ф) in SIDIS Boer-Mulders effect unpol. DY lattice-prediction expect large negative

  13. Lattice QCD prediction for azimuthal asymmetries large(?) Boer-Mulders effect with the same sign for up and down quarks strongly distorted densities of transversely polarized quarks in an unpolarized nucleon lead to prediction of a cos(2Ф) asymmetries in SIDIS (JLab, COMPASS) could be observed in unpolarized Drell-Yan (GSI-FAIR/PANDA) Jlab proposal PR12-06-112

  14. what about the transverse spin structure of the pion? but is non-zero? First results on the spin structure of pions from lattice QCD longitudinal spin structure is trivial pion spin structure?

  15. preliminary preliminary n=2 n=1 the pion has a very suprising non-trivial transverse spin structure! First results on the spin structure of pions from lattice QCD YES

  16. Summary up- and down-quark densities strongly distorted for transversely polarized quarks in transversely polarized nucleons possible consequences for asymmetries in SDIS and Drell-Yan (following arguments by M. Burkardt) unpolarized quarks in a transversely polarized nucleon: significant SSAs (seen by e.g. HERMES, PRL 2005) transversely polarized quarks in an unpolarized nucleon: significant azimuthal asymmetries („lattice QCD prediction“, to be confirmed by e.g. Jlab, COMPASS, GSI-FAIR/PANDA measurements) the pion has a non-trivial (transverse) spin structure

  17. Interpretation of the observed deformation patterns in parts based on M. Burkardts interpretation of distortions we know from longitudinal polarized quarks/nucleons: spin of up-quarks is aligned with nucleon spin spin of down-quarks is anti-aligned with nucleon spin assume : for up- and down-quarks down-quarks in an „unpolarized“ nucleon =1/2( + )1/2 high density in the upper half plane d-quarks „unpolarized“ down-quarks in a polarized nucleon = +  high density in the lower half plane d-quarks

  18. Lattice parameters – QCDSF/UKQCD

  19. chiral extrapolation based on chPT including the -resonance in a finite volume Hemmert/Procura/Weise PRD 2003 Wollenweber, diploma thesis, TUM 2005 Gell-Mann-Oakes-Renner QCDSF/UKQCD, PRD 2006

  20. Spin density matrices and transversity answer: three transversity spin density matrix helicities lesson: we have three independent amplitudes; transversity as important as unpolarized and polarized quark distributions helicities Soffer-bound number of independent quark-nucleon helicity amplitudes = ? helicity conservation+ parity invariance

  21. Transverse spin structure of the nucleon where Diehl / PhH EPJC 2005 where let‘s add an additional degree of freedom distance of the quark to the center of momentum of the nucleon in the transverse plane

  22. Transverse spin structure of the nucleon where generalized parton distributions let‘s add an additional degree of freedom distance of the quark to the center of momentum of the nucleon in the transverse plane M. Burkardt PRD 2000

  23. How to measure the non-perturbative transversity (or tensor) form factors? very challenging – basic QCD vertices don‘t allow for a helicity-flip of a quark experiment Diehl,Gousset,Pire PRD 1999 Collins, Diehl PRD 2002 are defined by nucleon matrix elements of local quark operators! however: x-moments = operator insertion = lattice QCD

  24. Relation between GPDs and tmdPDFs GPDs tmdPDFs conjecture / hypothesis Burkardt PRD 72 (2005) asymmetries

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