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1 Probes of Orbital Angular Momentum at HERMES - a drama with prologe, some slides, and a (not yet so) happy end - G Schnell Universiteit Gent gunarschnell@desyde For the hermes Collaboration Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 1/34

2 Prologue proton spin and orbital angular momentum Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 2/34

3 Orbital Angular Momentum S N = 1 2 ( ) = 1 2 Σ + G + Lq z + L G z OAM Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 3/34

4 Orbital Angular Momentum S N = 1 2 ( ) = 1 2 Σ + G + Lq z + L G z OAM Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 3/34

5 Orbital Angular Momentum S N = 1 2 ( ) = 1 2 Σ + G + Lq z + L G z OAM Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 3/34

6 Orbital Angular Momentum S N = 1 2 ( ) = 1 2 Σ + G + Lq z + L G z OAM Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 3/34

7 Orbital Angular Momentum S N = 1 2 ( ) = 1 2 Σ + G + Lq z + L G z OAM S N = 1 2 Σ + Lq z +JG }{{} J q Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 3/34

8 Orbital Angular Momentum S N = 1 2 ( ) = 1 2 Σ + G + Lq z + L G z OAM S N = 1 2 q (δq + δ q) + Lq,G T S N = 1 2 Σ + Lq z +JG }{{} J q Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 3/34

9 Characters Theory & Experiment Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 4/34

10 Theory measure Σ & G Jaffe s OAM Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 5/34

11 Theory measure Σ & G Jaffe s OAM measure Σ & J q Ji s OAM Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 5/34

12 Theory measure Σ & G Jaffe s OAM measure Σ & J q Ji s OAM Ji s golden recipe : J q = 1 2 lim t x dx [H q (x, ξ, t) + E q (x, ξ, t)] Deeply Virtual Compton Scattering (DVCS) excellent probe for GPDs E, H further information from other exclusive processes, eg, exclusive π or ρ production Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 5/34

13 Theory measure Σ & G Jaffe s OAM measure Σ & J q Ji s OAM Ji s golden recipe : J q = 1 2 lim t x dx [H q (x, ξ, t) + E q (x, ξ, t)] Deeply Virtual Compton Scattering (DVCS) excellent probe for GPDs E, H further information from other exclusive processes, eg, exclusive π or ρ production measure transversity (δq) Leader s OAM Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 5/34

14 Theory measure Σ & G Jaffe s OAM measure Σ & J q Ji s OAM Ji s golden recipe : J q = 1 2 lim t x dx [H q (x, ξ, t) + E q (x, ξ, t)] Deeply Virtual Compton Scattering (DVCS) excellent probe for GPDs E, H further information from other exclusive processes, eg, exclusive π or ρ production measure transversity (δq) Leader s OAM What about Sivers? Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 5/34

15 Theory measure Σ & G Jaffe s OAM measure Σ & J q Ji s OAM Ji s golden recipe : J q = 1 2 lim t x dx [H q (x, ξ, t) + E q (x, ξ, t)] Deeply Virtual Compton Scattering (DVCS) excellent probe for GPDs E, H further information from other exclusive processes, eg, exclusive π or ρ production measure transversity (δq) Leader s OAM What about Sivers? and other TMD s learn sth about transverse momentum of partons inside proton Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 5/34

16 HERMES at DESY Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 6/34

17 HERMES at DESY Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 6/34

18 Act One Bethe & Heitler meet Compton Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 7/34

19 Ji s recipe provides clean way to measure J q,g involves new class of parton distributions: Off-Forward or Generalized Parton Distributions (GPDs) at leading twist there are 8 (E, H, Ẽ, H, E T, H T, ẼT, H T ) but only 2 of them needed for Ji s sum-rule recipe: E, H accessible in exclusive reactions, eg, Deeply-Virtual Compton Scattering (DVCS) E, H, Exclusive Vector-Meson Production E, H Ẽ, H Exclusive Pseudoscalar-Meson Production Ẽ, H Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 8/34

20 Deeply Virtual Compton Scattering e + p e + p + γ clean & simple exclusive process: t q q x+ ξ x- ξ GPDs (x, ξ, t, Q ) P P 2 x: long momentum fraction 2 x x : skewedness parameter ξ = t = (q q ) 2 : momentum transfer γ γ Q 2 = q 2 Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 9/34

21 Deeply Virtual Compton Scattering e + p e + p + γ clean & simple exclusive process: DVCS and Bethe-Heitler (BH) indistinguishable BH cross section much larger at HERMES access DVCS amplitudes through DVCS-BH interference e e γ γ p p p e γ e γ p interference leads to characteristic azimuthal asymmetries Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 9/34

22 Azimuthal Asymmetries in DVCS Interference DVCS & BH cause azimuthal asymmetries in cross-section: Beam-charge asymmetry A C (φ) : dσ(e +, φ) dσ(e, φ) Re[F 1 H] cos φ Beam-spin asymmetry A LU (φ) : dσ( e, φ) dσ( e, φ) Im[F 1 H] sin φ Long target-spin asymmetry A UL (φ) : dσ( P, φ) dσ( P, φ) Im[F 1 H] sin φ Transverse target-spin asymmetry A UT (φ, φ s ) [TTSA]: dσ(φ, φ S ) dσ(φ, φ S + π) Im[F 2 H F 1 E] sin (φ φ S ) cos φ + Im[F 2 H F1 ξẽ] cos (φ φ S) sin φ (F 1, F 2 are the Dirac and Pauli form factors, calculable in QED) ( e H, e E, Compton form factors involving GPDs H, E, ) Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 1/34

23 Azimuthal Asymmetries in DVCS Interference DVCS & BH cause azimuthal asymmetries in cross-section: Beam-charge asymmetry A C (φ) : dσ(e +, φ) dσ(e, φ) Re[F 1 H] cos φ Beam-spin asymmetry A LU (φ) : dσ( e, φ) dσ( e, φ) Im[F 1 H] sin φ Long target-spin asymmetry A UL (φ) : dσ( P, φ) dσ( P, φ) Im[F 1 H] sin φ Transverse target-spin asymmetry A UT (φ, φ s ) [TTSA]: dσ(φ, φ S ) dσ(φ, φ S + π) Im[F 2 H F 1 E] sin (φ φ S ) cos φ Only TTSA sensitive to E! (F 1, F 2 are the Dirac and Pauli form factors, calculable in QED) ( H, e E, e Compton form factors involving GPDs H, E, ) + Im[F 2 H F1 ξẽ] cos (φ φ S) sin φ Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 1/34

24 Exclusivity at HERMES HERMES cannot reconstruct full event use missing-mass technique to select exclusive events: background estimated using Monte Carlo exclusive missing-mass bin ( 15 GeV < M x < 17 GeV ): roughly 15% contribution from SIDIS (ep e p π X) and associated BH (ep e + γ) Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 11/34

25 Constraining H Part I BSA Im[F 1 H] sin φ Beam Spin Asymmetry: 1 P B N + (φ) N (φ) N + (φ)+n (φ) (± beam helicity) A LU e + p e + γ X (M x < 17 GeV) HERMES PREL 2 (refined) P1 + P2 sin φ + P3 sin 2φ φ sin A LU e + p e + γ X HERMES PRELIMINARY 2 (refined analysis) P1 = -4 ± 2 (stat) P2 = -18 ± 3 (stat) P3 = ± 3 (stat) <-t > = 18 GeV 2, <x B > = 12, <Q 2 > = 25 GeV φ (rad) sin φ A LU M x< 17 GeV = -18 ± 3 (stat) ± 3 (sys) <-t > = 18 GeV 2, <x B > = 12, <Q 2 > = 25 GeV significant sin φ modulation in exclusive region M x (GeV) Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 12/34

26 Constraining H Part II BCA Re[F 1 H] cos φ Beam Charge Asymmetry: N + (φ) N (φ) N + (φ)+n (φ) (± beam charge) A C 6 4 HERMES PRELIMINARY (<-t c > = 12 GeV 2 ) e ± p e ± γ X (M x < 17 GeV) c + c1 cos φ + s1 sin φ A C cos φ 25 2 HERMES PRELIMINARY (refined analysis, <-t c > = 12 GeV 2 ) e ± p e ± γ X χ 2 / ndf : 1147/ 8 c = 9 ± 2 (stat) c1 = 59 ± 28 (stat) s1 = 94 ± 28 (stat) φ (rad) significant cos φ modulation in exclusive region M x (GeV) Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 13/34

27 Constraining E Transverse TSA Target Spin Asymmetry: 1 S T N (φ) N (φ) N (φ)+n (φ) ( target polarization) extract sin(φ φ S ) cos φ and cos(φ φ S ) sin φ amplitudes A sin (φ φ S) cos φ UT A cos(φ φ S) sin φ UT 4M t f(x B,y,Q 2 ) Im [F 2 2 H F 1 E] c BH,unp sensitive to GPD E 4M t f(x B,y,Q 2 ) Im 2 c BH,unp insensitive to GPD E [ ] F 2 H F1 ξẽ Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 14/34

28 hermes Constraining E Transverse TSA Target Spin Asymmetry: 1 S T N (φ) N (φ) N (φ)+n (φ) ( target polarization) extract sin(φ φ S ) cos φ and cos(φ φ S ) sin φ amplitudes sin(φ-φ A s )cos(φ) UT HERMES PRELIMINARY (in HERMES acceptance) e + p e + γ X (M x < 17 GeV) cos(φ-φ A s )sin(φ) UT t (GeV 2 ) x B Q 2 (GeV 2 ) Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 14/34

29 hermes Constraining E Transverse TSA Target Spin Asymmetry: 1 S T N (φ) N (φ) N (φ)+n (φ) ( target polarization) extract sin(φ φ S ) cos φ and cos(φ φ S ) sin φ amplitudes sin(φ-φ A s )cos(φ) UT HERMES PRELIMINARY (in HERMES acceptance) e + p e + γ X (M x < 17 GeV) cos(φ-φ A s )sin(φ) UT t (GeV 2 ) Q 2 (GeV 2 ) model calculation [hep-ph/56264] Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 14/34 x B J u = J u =2 J u =4 (hep-ph/56264)

30 hermes Constraining E Transverse TSA Target Spin Asymmetry: 1 S T N (φ) N (φ) N (φ)+n (φ) ( target polarization) extract sin(φ φ S ) cos φ and cos(φ φ S ) sin φ amplitudes sin(φ-φ A s )cos(φ) UT cos(φ-φ A s )sin(φ) UT HERMES PRELIMINARY (in HERMES acceptance) t (GeV 2 ) model calculation [hep-ph/56264] e + p e + γ X (M x < 17 GeV) Data Model J u = O(3%) x B J u = J u =2 J u =4 (hep-ph/56264) Q 2 (GeV 2 ) Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 14/34

Give the Real Photon some Mass Exclusive Vector-Meson

extract sin(φ φ S ) amplitude of TTSA sensitiv to H E

E also sensitive to gluon GPDs Gunar Schnell, DESY

31 Give the Real Photon some Mass Exclusive Vector-Meson Production ep e p ρ the other promising probe of E extract sin(φ φ S ) amplitude of TTSA sensitiv to H E complimentary information to DVCS TTSA for constraining E also sensitive to gluon GPDs Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 15/34

32 Exclusive ρ Production TTSA [E H] sin(φ φ S ) Target Spin Asymmetry: 1 S T N (φ) N (φ) N (φ)+n (φ) ( target polarization) A UT (φ,φ s ) HERMES PRELIMINARY e p e ρ p sin (φ-φ A s ) UT 4 2 HERMES PRELIMINARY e p e ρ p -1-2 sin (φ-φ A s ) =46 ± 37 UT -2 < Q 2 > = 2 GeV 2 < -t > = 13 GeV 2-3 < x > = 9 < Q 2 > = 2 GeV 2 < -t > = 13 GeV φ-φ s (rad) x no σ L /σ T separation yet! Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 16/34

33 Exclusive ρ Production TTSA [E H] sin(φ φ S ) Target Spin Asymmetry: 1 S T N (φ) N (φ) N (φ)+n (φ) ( target polarization) qualitative agreement with model prediction [hep-ph/56264] model HERMES data slight preference for J u > Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 16/34

34 Act Two Collins helps Transversity Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 17/34

35 Measurement of Chiral-Odd Transversity Distribution How can one measure transversity? Need another chiral-odd object! }{{} CHIRAL EVEN Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 18/34

36 Measurement of Chiral-Odd Transversity Distribution How can one measure transversity? Need another chiral-odd object! Semi-Inclusive DIS σ ep ehx = q δq σ eq eq F F q h chiral-odd DF }{{} CHIRAL EVEN chiral-odd FF Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 18/34

37 Measurement of Chiral-Odd Transversity Distribution How can one measure transversity? Need another chiral-odd object! Semi-Inclusive DIS σ ep ehx = q δq σ eq eq F F q h chiral-odd DF }{{} chiral-odd FF CHIRAL EVEN use T-even transverse polarization transfer FF Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 18/34

38 Measurement of Chiral-Odd Transversity Distribution How can one measure transversity? Need another chiral-odd object! Semi-Inclusive DIS σ ep ehx = q δq σ eq eq F F q h chiral-odd DF }{{} chiral-odd FF CHIRAL EVEN use T-even transverse polarization transfer FF use T-odd Collins FF 1-hadron SSA Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 18/34

39 Measurement of Chiral-Odd Transversity Distribution How can one measure transversity? Need another chiral-odd object! Semi-Inclusive DIS σ ep ehx = q δq σ eq eq F F q h chiral-odd DF }{{} chiral-odd FF CHIRAL EVEN use T-even transverse polarization transfer FF use T-odd Collins FF 1-hadron SSA use T-odd Interference FF 2-hadron SSA Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 18/34

40 Collins Fragmentation Function π y x P h z P h Collins function H1 describes left-right asymmetry in the direction of outgoing hadron Originally proposed by Collins (& Heppelman) T-odd need interference of amplitudes basically unknown, but first fits to available data become available first data from Belle supports non-zero H 1 π Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 19/34

41 Azimuthal Single-Spin Asymmetries z y A UT (φ, φ S ) = k q k S p had φ S x φ uli 1 S N + h (φ, φ S) N h (φ, φ S) N + h (φ, φ S) + N h (φ, φ S) sin(φ + φ S ) q + [ ] e 2 kt ˆP h q I h q M 1T (x, p2 T )H,q 1 (z, kt 2 ) h I[ ]: convolution integral over initial (p T ) and final (k T ) quark transverse momenta 2D-fit of A UT to get Collins (and other) asymmetries: A UT (φ, φ S ) = 2 sin(φ+φ S ) l UT sin(φ + φ s) + Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 2/34

42 Collins Asymmetries (Lepton-Beam Asymmetries) 2 sin(φ+φ S ) π UT π + III HERMES PRELIMINARY lepton beam asymmetry amplitudes not corrected for acceptance and smearing published results confirmed with much higher statistical precission lepton-beam asymmetries 2 sin(φ+φ S ) π UT π - 66% scale uncertainty (vs virtual-photon SSA in publication) kin prefactors ( depolarization factors ) still included overall scale uncertainty of 66% VM fraction π - π + x z P h [GeV] x z PYTHIA6 modified by HERMES P h [GeV] positive for π + and negative for π as maybe expected (δu > maybe expected (δd < ) unexpected large π asymmetry role of disfavored Collins FF most likely: H,disf 1 H,fav 1 no (new) constraint on transversity yet Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 21/34

43 Collins Asymmetries (Lepton-Beam Asymmetries) 2 sin(φ+φ S ) π UT 2 sin(φ+φ S ) π UT VM fraction π + π π - π + x 66% scale uncertainty III HERMES PRELIMINARY lepton beam asymmetry amplitudes not corrected for acceptance and smearing z P h [GeV] x z PYTHIA6 modified by HERMES P h [GeV] published results confirmed with much higher statistical precission lepton-beam asymmetries (vs virtual-photon SSA in publication) kin prefactors ( depolarization factors ) still included overall scale uncertainty of 66% BELLE s Collins FF HERMES positive for π =?! + and negative transversity for π as maybe expected (δu > maybe expected (δd < ) unexpected large π asymmetry role of disfavored Collins FF most likely: H,disf 1 H,fav 1 no (new) constraint on transversity yet Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 21/34

44 Act Three Death and Resurrection of Sivers Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 22/34

45 Naive T-oddness for Distribution Functions T-oddness requires interference of amplitudes with different imaginary parts (also requires L z in wave function) Distribution functions in terms of handbag diagrams: no interference no T-odd DF possible (Collins: T-symmetry of QCD requires T-odd DF to vanish ) SIVERS FCT VANISHES!! Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 23/34

46 Naive T-oddness for Distribution Functions T-oddness requires interference of amplitudes with different imaginary parts (also requires L z in wave function) Distribution functions in terms of handbag diagrams: Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 23/34

47 Some words about Sivers Effect Thanks to Brodsky, Hwang, Schmidt: quark rescattering via soft gluon exchange correlates transverse spin with direction of outgoing hadron requires L z Thanks to Collins, Ji, Yuan, Belitzky : Soft gluon is model for gauge link needed for gauge invariance Gauge links provide necessary complex phase for interference T-Symmetry of QCD requires opposite sign of Sivers function in DIS and DY slightly different approach by Burkardt using impact parameter dependent PDF s ( chromodynamic lensing ) Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 24/34

48 Some words about Sivers Effect Thanks to Collins, Ji, Yuan, Belitzky : Thanks to Brodsky, Hwang, Schmidt: quark rescattering via soft gluon exchange correlates transverse spin with direction of outgoing hadron requires L z in proton LFWF Soft gluon is model for gauge link needed for gauge invariance Gauge links provide necessary complex phase for interference T-Symmetry of QCD requires opposite sign of Sivers function in DIS and DY slightly different approach by Burkardt using impact parameter dependent PDF s ( chromodynamic lensing ) Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 24/34

49 2 sin(φ-φ 2 sin(φ-φ S ) UT π S ) UT π π + π - 2 sin(φ φ S ) q UT q e2 q I 66% scale uncertainty III HERMES PRELIMINARY not corrected for acceptance and smearing Results on Sivers Moments from [ pt ˆP h M data f,q 1T (x, p2 T ) Dq 1 (z, K2 T ) ] π + : positive; π : consistent with zero first evidence for non-zero Sivers fct: f,u 1T < (u-quark dominance) Exclusive ρ asymmetry (25 prel): A UT (φ,φ s ) HERMES PRELIMINARY e p e ρ p x z P h [GeV] -1 VM fraction π - π Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 25/34 x z PYTHIA6 modified by HERMES P h [GeV] -2 sin (φ-φ A s ) =46 ± 37 UT < x > = 9 < Q 2 > = 2 GeV 2 < -t > = 13 GeV φ-φ s (rad) small syst error from vector mesons

50 Chromodynamic Lensing Understanding the Sivers Moments approach by M Burkardt: spatial distortion of q-distribution u(x, b ) d(x, u X b(x, ) b ) d X (x, b ) (obtained using anom magn moments & impact parameter dependent b y PDFs) b y b y b y x = x = x 1 = 1-4 x = b x b x b x b x b y b y b y b y -2-4 x = x = x 3 = x = b x b x b x b x Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 26/34

51 Chromodynamic Lensing Understanding the Sivers Moments approach by M Burkardt: spatial distortion of q-distribution u(x, b ) d(x, u X b(x, ) b ) d X (x, b ) (obtained using anom magn moments & impact parameter dependent b y PDFs) b y b y b y -2 + attractive QCD potential x = 1-4 (gluon exchange) b x transverse asymmetries x = x 1 = b x b x x = b x } φ S = π/2 φ = π 2 b y sin(φ φ -2 S ) > x = b x 2 2 b y b y x = x 3 = b x b x 2 b y -2-4 x = b x Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 26/34

52 Chromodynamic Lensing Understanding the Sivers Moments approach by M Burkardt: spatial distortion of q-distribution (obtained using anom magn moments & impact parameter dependent b y PDFs) model data suggests b y b y L u b y > z -2 + attractive QCD potential x = 1 x = x 1 = 1 x = (gluon exchange) b x transverse asymmetries } φ S = π/2 φ = π b y sin(φ φ -2 S ) > u(x, b ) d(x, u X b(x, ) b ) d X (x, b ) x = b x b y b y b x b x x = x 3 = b x b x b y b x x = b x Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 26/34

53 Act Four The long wait for Mr Cahn & The Amsterdam Conspirancy Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 27/34

54 SSA & Unintegrated Distribution and Fragmentation Functions Leading-Twist Distribution Functions Fragmentation Functions }{{} T-odd {}}{ SSA require one and only one T-odd function Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 28/34

55 SSA & Unintegrated Distribution and Fragmentation Functions Leading-Twist Distribution Functions Fragmentation Functions SSA require one and only one T-odd function SSA through Sivers function or Collins function Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 28/34

56 SSA & Unintegrated Distribution and Fragmentation Functions Leading-Twist Distribution Functions Fragmentation Functions SSA require one and only one T-odd function SSA through Sivers function or Collins function Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 28/34

57 SIDIS Cross Section (up to subleading order in 1/Q) σ XY Beam Target Polarization y z k x dσ = dσuu + cos 2φ dσuu Q cos φ 1 dσ2 UU + λ e Q sin φ dσ3 LU { +S L sin 2φ dσul Q sin φ dσ5 UL + λ e [dσll ]} Q cos φ dσ7 LL +S T { sin(φ φ S ) dσ 8 UT + sin(φ + φ S ) dσ 9 UT + sin(3φ φ S ) dσ 1 UT k q p had + 1 Q ( ) sin(2φ φs ) dσut 11 + sin φ S dσut 12 +λ e [ cos(φ φ S ) dσ 13 LT + 1 Q S φ S φ uli 1 Q ( cos φs dσlt 14 + cos(2φ φ S ) dσlt 15 ) ]} Mulders and Tangermann, Nucl Phys B 461 (1996) 197 Boer and Mulders, Phys Rev D 57 (1998) 578 Bacchetta et al, Phys Lett B 595 (24) 39 Trento Conventions, Phys Rev D 7 (24) Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 29/34

58 Unpolarized Data Set large data sample with unpolarized nucleons on tape study cos φ (Cahn) and cos 2φ (Boer-Mulders) moments ongoing large Cahn effect observed in muon scattering probe of intrinsic transverse momentum [see talk by M Anselmino] Boer-Mulders effect probes quark spin-orbit correlations all very promising, BUT much harder to study (in SSA many of the systematics cancel here not!) Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 3/34

59 The (not yet so) happy end Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 31/34

60 So much data but what is L z? have some indication that L u z & J u > however, no model-independent extraction possible: DVCS gives access to GPDs (needed for Ji s recipe), but can only constrain GPD models, no direct measurement of GPDs possible Sivers function related to OAM, but how? transversity extraction requires knowledge of Collins FF how is Leader s OAM related to Ji s OAM? unpolarized-target data still under investigation Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 32/34

61 But there is hope! Outlook have gone a long way to understand Sivers effect full trust in theorists to find relation L q z f,q 1T Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 33/34

62 But there is hope! Outlook have gone a long way to understand Sivers effect full trust in theorists to find relation L q z f,q 1T similarily to extraction of q from A 1 (purity mechanism), extract Sivers function directly from Sivers moments Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 33/34

63 But there is hope! Outlook have gone a long way to understand Sivers effect full trust in theorists to find relation L q z f,q 1T similarily to extraction of q from A 1 (purity mechanism), extract Sivers function directly from Sivers moments model-independent interpretation of transverse SSA needs P h -weighted asymmetries Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 33/34

64 But there is hope! Outlook have gone a long way to understand Sivers effect full trust in theorists to find relation L q z f,q 1T similarily to extraction of q from A 1 (purity mechanism), extract Sivers function directly from Sivers moments model-independent interpretation of transverse SSA needs P h -weighted asymmetries Collins effect measured at BELLE use it to extract transversity Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 33/34

65 But there is hope! Outlook have gone a long way to understand Sivers effect full trust in theorists to find relation L q z f,q 1T similarily to extraction of q from A 1 (purity mechanism), extract Sivers function directly from Sivers moments model-independent interpretation of transverse SSA needs P h -weighted asymmetries Collins effect measured at BELLE use it to extract transversity 25 data set adds substantially to current analysis Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 33/34

66 But there is hope! Outlook have gone a long way to understand Sivers effect full trust in theorists to find relation L q z f,q 1T similarily to extraction of q from A 1 (purity mechanism), extract Sivers function directly from Sivers moments model-independent interpretation of transverse SSA needs P h -weighted asymmetries Collins effect measured at BELLE use it to extract transversity 25 data set adds substantially to current analysis HERMES will take more data with recoil detector more data to constrain GPD H Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 33/34

67 But there is hope! Outlook have gone a long way to understand Sivers effect full trust in theorists to find relation L q z f,q 1T similarily to extraction of q from A 1 (purity mechanism), extract Sivers function directly from Sivers moments model-independent interpretation of transverse SSA needs P h -weighted asymmetries Collins effect measured at BELLE use it to extract transversity 25 data set adds substantially to current analysis HERMES will take more data with recoil detector more data to constrain GPD H even after HERMES spectrometer retired COMPASS, JLAB & RHIC experiments will continue unravel L z Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 33/34

68 Epilogue Thanks to the Organizers! Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 34/34

69 Epilogue Thanks to the Organizers! Gunar Schnell, DESY Workshop on Orbital Angular Momentum Albuquerque, Feb 24 th, 26 p 34/34

Subleading-twist effects in single-spin asymmetries in semi-inclusive DIS on a longitudinally polarized hydrogen target

Subleading-twist effects in single-spin asymmetries in semi-inclusive DIS on a longitudinally polarized hydrogen target G Schnell, H Ohsuga, H Tanaka, T Hasegawa, T Kobayashi, Y Miyachi, T-A Shibata Tokyo