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Pretzelocity Pretzelocity & & Quark Angular Momentum Quark Angular Momentum Bo-Qiang Ma ( Bo-Qiang Ma ( ) ) PKU PKU ( ) ? 2nd Workshop on Hadron Physics in China and

  1. Pretzelocity Pretzelocity & & Quark Angular Momentum Quark Angular Momentum Bo-Qiang Ma ( 马伯强 Bo-Qiang Ma ( 马伯强 马伯强 ) 马伯强 ) PKU PKU ( 北京大学 北京大学 ) ? 2nd Workshop on Hadron Physics in China and Opportunities with 12 GeV JLab July 28 2010 July 28 2010 July 28, 2010 July 28, 2010 Collaborators: Enzo Barone, Stan Brodsky, Jacques Soffer, Andreas Schafer, Ivan Schmidt, Jian-Jun Yang, Qi-Ren Zhang, and students g g 1

  2. The Proton “Spin Crisis” Σ Σ = Δ Δ + + Δ Δ + + Δ Δ ≈ 0 0 . . 3 3 u u d d s s In contradiction with the naïve quark In contradiction with the naïve quark In contradiction with the naïve quark In contradiction with the naïve quark model expectation: model expectation: 2

  3. Th The proton spin crisis The proton spin crisis Th t t i i i i i i & the Melosh the Melosh- -Wigner rotation Wigner rotation g It is shown that the proton “spin crisis” or “spin puzzle” can • be understood by the relativistic effect of quark transversal y q motions due to the Melosh-Wigner rotation. The quark helicity ∆ q measured in polarized deep inelastic The quark helicity ∆ q measured in polarized deep inelastic • scattering is actually the quark spin in the infinite momentum frame or in the light-cone formalism and it is different from the frame or in the light-cone formalism, and it is different from the quark spin in the nucleon rest frame or in the quark model. B Q M B.-Q. Ma, J.Phys. G 17 (1991) L53 J Ph G 17 (1991) L53 B.-Q. Ma, Q.-R. Zhang, Z.Phys.C 58 (1993) 479-482 3

  4. The Wigner Rotation The Wigner Rotation r r μ μ μ μ = = f for a rest particle ( ,0) t ti l ( 0) (0, ) (0 ) w m p s r r = = for a moving particle L( ) ( ,0) (0, ) L( ) / p p m s p w m p = L( ) ratationless Lorentz boost Wigner Rotation u r v ′ ′ → , , s p s p μ μ u r r ′ ′ = Λ = Λ ( , ) ( , ) s s R p s p s p p p p w w p ′ Λ = Λ -1 ( , ) L( ) L ( ) a pure rotation R p p w E.Wigner, Ann.Math.40(1939)149 4

  5. Melosh Rotation for Spin Melosh Rotation for Spin- -1/2 Particle 1/2 Particle The connection between spin states in the rest frame and infinite momentum frame Or between spin states in the conventional equal time dynamics and the light-front dynamics 5

  6. What is What is Δ q measured in DIS q measured in DIS Δ = 〈 γ γ 〉 • Δ q is defined by s , | | , q p s q q p s μ μ 5 + Δ = 〈 γ γ γ γ 〉 , | | | | , q q p p s q q q p q p s 5 5 • Using light-cone Dirac spinors 1 d ∫ ∫ ⎡ ⎡ ⎤ ⎤ ↑ ↓ Δ = Δ − 0 d ( ) ( ) ( ) ( ) q q x q x q x x q q x x ⎣ ⎣ ⎦ ⎦ • Using conventional Dirac spinors u r u r u r ∫ ∫ ⎡ ⎡ ⎤ ⎤ Δ Δ = ↑ − ↓ 3 d d ( ) ( ) ( ) ( ) q q pM pM q q p p q q p p ⎣ ⎣ ⎦ ⎦ q u r 2 + + 2 ( ) － p p m p = = ⊥ 0 3 M M + + q 2( )( ) p p p m 0 3 0 Thus ∆ q is the light-cone quark spin or quark spin in the infinite momentum frame, not that in the rest frame of the proton 6

  7. Quark spin sum is not a Lorentz invariant quantity Quark spin sum is not a Lorentz invariant quantity Thus the quark spin sum equals to the proton in the rest frame does not mean that it equals to the proton spin in the infinite moment m frame the infinite momentum frame r u r ∑ ∑ = in the rest frame s S q p q does not mean that r u r ∑ = in the infinite momentum frame s S q p q q Therefore it is not a surprise that the quark spin sum measured in DIS does not equal to the proton spin measured in DIS does not equal to the proton spin 7

  8. A relativistic quark-diquark model 8

  9. B.-Q. Ma, Phys.Lett. B 375 (1996) 320-326. B.-Q. Ma, I. Schmidt, J. Soffer, Phys.Lett. B 441 (1998) 461-467. A relativistic quark-diquark model 9

  10. pQCD counting rule ± ∝ − (1 ) p q x h = Δ Δ = − 2 1 2 | | - ＋ p n s s s s z z q N • Based on the minimum connected tree graph of hard gluon exchanges gluon exchanges. • “Helicity retention” is predicted -- The helicity of a valence quark will match that of the parent nucleon valence quark will match that of the parent nucleon. 10

  11. Parameters in pQCD counting rule analysis % 1 A + = − − 3 q (1 ) 2 q i x x In leading term i B B 3 3 % 1 − = C − 2 (1 = − 5 q (1 ) ) 2 q q i x x x x i B 5 B.-Q. Ma, I. Schmidt, J.-J. Yang, Phys.Rev.D63(2001) 037501. New Development: H. Avakian, S.J.Brodsky, D.Boer, F.Yuan, Phys.Rev.Lett.99:082001,2007. 11

  12. Different predictions in two models 12

  13. The Melosh The Melosh- -Wigner Rotation in Wigner Rotation in g Transversity Transversity I.Schmidt&J.Soffer, I.Schmidt&J.Soffer, Phys.Lett.B 407 (1997) 331 13

  14. Transversity with Melosh-Wigner rotation in the quark-diquark model q q ˆ x ˆ ( ) ( ) W S x W V B.-Q. Ma, I. Schmidt, J. Soffer, Phys.Lett. B 441 (1998) 461-467. 14

  15. The transversity in pQCD, in similar to helicity distributions y ~ ~ A C − − δ = − − − ( ( 1 1 / / 2 2 ) ) 3 3 ( ( 1 1 / / 2 2 ) ) 5 5 ( ) q q ( 1 ) q q ( 1 ) q x x x x x B B 3 5 3 = 3 = 32 32 / / 35 35 512 512 / / 693 693 B B B B B.-Q. Ma, I. Schmidt, J.-J. Yang, Phys.Rev.D63(2001) 037501. 15

  16. Transversity in two models 16

  17. SU(6) quark- pQCD based VS VS S diquark model diquark model analysis analysis Ma, Schmidt and Yang, PRD 65, 034010 (2002) solid curve for SU(6) and dashed curve for pQCD ( ) pQ 17

  18. The Melosh The Melosh- -Wigner Rotation in Wigner Rotation in g Quark Orbital Angular Moment Quark Orbital Angular Moment Ma&Schmidt, Ma&Schmidt, Phys.Rev.D 58 (1998) 096008 18

  19. Three QCD spin sums for the proton spin Three QCD spin sums for the proton spin X. X.- -S.Chen, X. S.Chen, X.- -F.Lu, W. F.Lu, W.- -M.Sun, F.Wang, T.Goldman, M.Sun, F.Wang, T.Goldman, PRL100(2008)232002 PRL100(2008)232002 19

  20. S i Spin and orbital sum in light S i Spin and orbital sum in light-cone formalism d d bit l bit l i i li ht li ht cone formalism f f li li Ma&Schmidt, Ma&Schmidt, Phys.Rev.D 58 (1998) 096008 20

  21. The Melosh The Melosh Wigner Rotation in The Melosh The Melosh-Wigner Rotation in Wigner Rotation in Wigner Rotation in “Pretzelosity” “Pretzelosity” J.She, J.Zhu, B.-Q.Ma, Phys.Rev.D79 (2009) 054008 21

  22. “Pretrel” or “Brezel” “Pretrel” or “Brezel” 22

  23. “Pretrel” or “Brezel” “Pretrel” or “Brezel” 23

  24. “Mahua( “Mahua( 麻花 麻花 )”: the Chinese Preztel )”: the Chinese Preztel 24

  25. What is What is “ Pretzelosity” ? Pretzelosity” ? 25

  26. What is What is “ Pretzelosity” ? Pretzelosity” ? 26

  27. A Simple Relation A Simple Relation 27

  28. Connection with Quark Orbital Angular Momentum Connection with Quark Orbital Angular Momentum 28

  29. Pretzelosity in SIDIS Pretzelosity in SIDIS 29

  30. Quantities in Calculation Quantities in Calculation 30

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  32. J.She, J.Zhu, B.-Q.Ma, Phys.Rev.D 79 (2009) 054008 32

  33. J.She, J.Zhu, B.-Q.Ma, Phys.Rev.D 79 (2009) 054008 33

  34. J.She, J.Zhu, B.-Q.Ma, Phys.Rev.D 79 (2009) 054008 34

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  45. Conclusions Conclusions Conclusions Conclusions • Relativistic effect of Melosh-Winger rotation is important in hadron spin physics is important in hadron spin physics. • The pretzelosity is an important quantity for e p et e os ty s a po ta t qua t ty o the spin-orbital correlation. • New way to access quark orbital angular momentum is suggested momentum is suggested. 45

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