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Luciano L. Pappalardo University of Ferrara

Selected TMD results from HERMES. Luciano L. Pappalardo University of Ferrara. L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-18 2013. The phase-space distribution of partons. The full phase-space distribution of the partons encoded in the Wigner function. 2.

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Luciano L. Pappalardo University of Ferrara

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  1. Selected TMD results from HERMES Luciano L. Pappalardo University of Ferrara L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-18 2013

  2. The phase-space distribution of partons The full phase-space distribution of the partons encoded in the Wigner function 2 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  3. The phase-space distribution of partons The full phase-space distribution of the partons encoded in the Wigner function ...but  no simultaneous knowledge of momentum and position cannot be directly accessed experimentally  integrated quantities GPDs TMDs 3 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  4. worm-gears worm-gears The non-collinear structure of the nucleon The full phase-space distribution of the partons encoded in the Wigner function ...but  no simultaneous knowledge of momentum and position cannot be directly accessed experimentally  integrated quantities GPDs TMDs momentum helicity Boer-Mulders • TMDs depend on and • Describe correlations between and quark or nucleon spin (spin-orbitcorrelations) • Provide a 3-dim picture of the nucleon in momentum space (nucleon tomography) transversity pretzelosity Sivers Sivers 4 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  5. worm-gears worm-gears The non-collinear structure of the nucleon Mostly investigated in SIDIS: detection of transverse momentum of produced hadrons gives access to Collins FF chiral-odd unpol. FF chiral-even Fragmentation Functions (FF) momentum helicity Boer-Mulders FF hadron • TMDs depend on and • Describe correlations between and quark or nucleon spin (spin-orbitcorrelations) • Provide a 3-dim picture of the nucleon in momentum space (nucleon tomography) transversity pretzelosity Sivers Sivers 5 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  6. The SIDIS cross-section FF } 6 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  7. The SIDIS cross-section unpolarized beam polarization target polarization beam and target polarization } 7 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  8. The SIDIS cross-section 18 Structure Functions Leading twist Sub-leading Twist Distribution Functions } 8 L.L. Pappalardo - SPIN2012 – JINR, Dubna, Russia – September 17-22 2012 Fragmentation Functions h

  9. Selected twist-2 and twist-3 1-hadron SIDIS results 9 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  10. Sivers function Describes correlation between quark transverse momentum and nucleon transverse polarization Distribution Functions } 10 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013 Fragmentation Functions h

  11. Siversamplitudes [Airapetianet al., Phys. Rev. Lett. 103 (2009) 152002] consistent with Sivers func. of opposite sign for u and d quarks significantly positive slightly positive (isospin-symmetry) [Anselminoet al.,Eur.Phys.J.A3,2009] consistent with zero 11 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  12. Siversamplitudes [Airapetianet al., Phys. Rev. Lett. 103 (2009) 152002] significantly positive consistent with Sivers func. of opposite sign for u and d quarks significantly positive Similar kinematic dependence of slightly positive slightly positive (isospin-symmetry) [Anselminoet al.,Eur.Phys.J.A3,2009] consistent with zero 12 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  13. Sivers kaonsamplitudes: open questions +/K+ production dominated by u-quarks, but: 13 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  14. ? Sivers kaonsamplitudes: open questions +/K+ production dominated by u-quarks, but: different role of various sea quarks ? 14 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  15. ? ? Higher-twist contrib. for Kaons Sivers kaonsamplitudes: open questions +/K+ production dominated by u-quarks, but: only in low-Q2 region significant deviation different role of various sea quarks ? each x-bin divided into two Q2 bins no effect for pions, but hint of a systematic shifts for kaons 15 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  16. Pretzelosity Describes correlation between quark transverse momentum and transverse spin in a transversely pol. nucleon • Sensitive to non-spherical shapeof the nucleon Distribution Functions } 16 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013 Fragmentation Functions h

  17. The amplitudes All amplitudes consistent with zero …suppressed by two powers of Ph w.r.t. Siversamplitudes 17 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  18. Worm-gear Describes the probability to find longitudinally polarized quarks in a transversely polarized nucleon! • Can be accessed in LT DSAs Distribution Functions } } 18 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013 Fragmentation Functions h

  19. Worm-gear • The only TMD that is both chiral-even and naïve-T-even • requires interference between wave function components that differ by 1 unit of OAM  quark orbital motioninside nucleons S. Boffi et al. (2009) Phys. Rev. D 79 094012 Light-cone constituent quark model dashed line: interf. L=0, L=1 dotted line: interf L=1, L=2 19 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  20. Worm-gear • The only TMD that is both chiral-even and naïve-T-even • requires interference between wave function components that differ by 1 unit of OAM  quark orbital motioninside nucleons • Accessible in LT DSAs: S. Boffi et al. (2009) Phys. Rev. D 79 094012 Light-cone constituent quark model dashed line: interf. L=0, L=1 dotted line: interf L=1, L=2 20 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  21. Worm-gear • The only TMD that is both chiral-even and naïve-T-even • requires interference between wave function components that differ by 1 unit of OAM  quark orbital motioninside nucleons • Accessible in LT DSAs: S. Boffi et al. (2009) Phys. Rev. D 79 094012 Light-cone constituent quark model dashed line: interf. L=0, L=1 dotted line: interf L=1, L=2 Simplest way to probe 21 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  22. The amplitudes slightly positive ? consistent with zero similar observations from Hall-A and COMPASS positive!! slightly positive ? consistent with zero 22 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  23. The and amplitudes 23 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  24. Worm-gear Describes the probability to find transversely polarized quarks in a longitudinally polarized nucleon • some models support the simple relation Distribution Functions } 24 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013 Fragmentation Functions h

  25. The sin(2 amplitude Deuterium target Hydrogen target A. Airapetian et al, Phys. Rev. Lett. 84 (2000) Amplitudes consistent with zero for all mesons and for both H and D targets A. Airapetian et al, Phys. Lett. B562 (2003) 25 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  26. sin( amplitude A. Airapetian et al, Phys. Lett. B562 (2003) Positive: Hydrogen results larger than Deuteron (u-quark dominance) Positive: Hydrogen and Deuteron of same size Deuteron positive, Hydrogen  0 Positive and consistent with (u-quark dominance) 26 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  27. Subleading twist Sensitive to worm-gear , sivers, transversity + higher-twist DF and FF Distribution Functions } 27 L.L. Pappalardo – Structure of Nucleons and Nuclei – Como – June 10-14 2013 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  28. sensitive to worm-gear , Sivers function, Transversity, etc • significant non-zero signal for - and K-! Subleading-twist sin(S) Fourier component Large and negative negative 28 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  29. sensitive to worm-gear , Sivers function, Transversity, etc • significant non-zero signal for - and K-! • low-Q2amplitude larger • hint of Q2 dependence for - Subleading-twist sin(S) Fourier component Large and negative negative 29 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  30. 2-hadron SIDIS results Following formalism developed by Steve Gliske Find details in Transverse Target Moments of Dihadron Production in Semi-inclusive Deep Inelastic Scattering at HERMES S. Gliske,PhD thesis, University of Michigan, 2011 http://www-personal.umich.edu/~lorenzon/research/HERMES/PHDs/Gliske-PhD.pdf 30 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  31. A short digression on di-hadron fragmentation functions Standard definition of di-hadron FF assume no polarization of final state hadrons (pseudo-scalar mesons) or define mixtures of certain partial waves as new FFs In the new formalism there are only two di-hadron FFs. Names and symbols are entirely associated with the quark spin, whereas the partial waves of the produced hadrons are associated with partial waves of FFs. ’ ’ The cross-section is identical to the ones in literature, the only difference is the interpretation of the FFs: 31 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  32. The di-hadron SIDIS cross-section and correspond to angular momentum state of the hadron Considering all terms () there are 144 non-zero structure functions at twist-3 level. The most known is which for and reduces to the well known collinear related to transversity 32 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  33. The di-hadron SIDIS cross-section JHEP 06 (2008) 017 • independent way to access transversity • Collinear  no convolution integral • significantly positive amplitudes • evidence of non zero dihadron FF • limited statistical power (v.r.t. 1 hadron) 33 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  34. The di-hadron SIDIS cross-section JHEP 06 (2008) 017 • independent way to access transversity • Collinear  no convolution integral • significantly positive amplitudes • evidence of non zero dihadron FF • limited statistical power (v.r.t. 1 hadron) • signs are consistent for all species • statistics much more limited for • despite uncertainties may still help to constrain global fits and may assist in flavor separation • New tracking, new PID, use of rather than • Different fitting procedure and function • Acceptance correction 34 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  35. Conclusions • A rich phenomenology and surprising effects arise when parton transverse momentum is not integrated out! • Transverse effects and orbital motion of partonsare now established as key ingredients of the nucleon internal dynamics 35 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  36. Conclusions • A rich phenomenology and surprising effects arise when parton transverse momentum is not integrated out! • Transverse effects and orbital motion of partonsare now established as key ingredients of the nucleon internal dynamics • The HERMES experiment has played a pioneering role in these studies: 36 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  37. Back-up 37 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  38. Boer-Mulders function Describes correlation between quark transverse momentum and transverse spin in unpolarized nucleon Distribution Functions } 38 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013 Fragmentation Functions h

  39. The cos2 amplitudes A. Airapetian et al, Phys. Rev. D 87 (2013) 012010 - Amplitudes are significant  clear evidence of BM effect - similar results for H & D indicate - Opposite sign for consistent with opposite signs of fav/unfav Collins negative positive 39 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  40. The cos2 amplitudes A. Airapetian et al, Phys. Rev. D 87 (2013) 012010 - Amplitudes are significant  clear evidence of BM effect - similar results for H & D indicate - Opposite sign for consistent with opposite signs of fav/unfav Collins negative positive - amplitudes are larger than for pions , have different kinematic dependencies than pions and have same sign - different role of Collins FF for pions and kaons? - Significant contribution from scattering off strange quarks? Large and negative Large and negative Analysis multi-dimensional in x, y, z,and Pt Create your own projections of results through: http://www-hermes.desy.de/cosnphi/ 40 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  41. The cos amplitudes A. Airapetian et al, Phys. Rev. D 87 (2013) 012010 negative negative Large and negative Consist. with 0 Analysis multi-dimensional in x, y, z,and Pt Create your own projections of results through: http://www-hermes.desy.de/cosnphi/ 41 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  42. Transversity Describes probability to find transversely polarized quarks in a transversely polarized nucleon Distribution Functions } 42 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013 Fragmentation Functions h

  43. Collins amplitudes [Airapetianet al., Phys. Lett. B 693 (2010) 11-16] positive consistent with zero Consistent with Belle/BaBarmeasurements in e+e- (isospin-symmetry) large and negative! d u u d xh1(x) xh1(x, k ) xh1(x) xh1(x, k ) T T Soffer bound significantly positive consistent with zero Anselmino et al. Phys. Rev. D 75 (2007) 43 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  44. Sensitive to , Boer-Mulders + higher-twist DF and FF Distribution Functions } 44 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  45. A. Airapetian et al, Phys. Lett. B 648 (2007) 1996-2000 data } open circles 0.2<z<0.5 full circles 0.5<z<0.8 open squares: 0.8<z<1.0 45 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  46. H target, 2000-2007 data 0.2<z<0.7 Released yesterday!! 46 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  47. D target, 2000-2007 data 0.2<z<0.7 Released yesterday!! 47 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  48. related to <sin(2)>UL Fourier comp: • sensitive to worm-gear • suppressed by one power of Ph w.r.t. Collins and Sivers amplitudes • no significant signal observed (except maybe for K+) The sin(2+S) Fourier component • arises solely from longitudinal (w.r.t. virtual photon direction) component of the target spin 48 48 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  49. The subleading-twist sin(2-S) Fourier component • sensitive to worm-gear , Pretzelosity and Sivers function: • suppressed by one power of Ph w.r.t. Collins and Sivers amplitudes • no significant non-zero signal observed 49 49 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

  50. A short digression on the Lund/Artru string fragmentation model (a phenomenological explanation of the Collins effect) In the cross-section the Collins FF is always paired withy a distrib. function involving a transv. pol. quark. Assume u quark and proton have (transverse) spin alligned in the direction . The model assumes that the struck quark is initially connected with the remnant via a gluon-flux tube (string) When the string breaks, a pair is created with vacuum quantum numbers . The positive parity requires that the spins of and are aligned, thus an OAM has to compensate the spins This OAM generates a transverse momentum of the produced pseudo-scalar meson (e.g. ) and deflects the meson to the left side w.r.t. the struck quark direction, generating left-righ azimuthal asymmetries 50 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

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