Pretzelocity Pretzelocity & & Quark Angular Momentum - PowerPoint PPT Presentation

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

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

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

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

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

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

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

A relativistic quark-diquark model 8

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

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

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

Different predictions in two models 12

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

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

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

Transversity in two models 16

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

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

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

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

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

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

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

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

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

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

A Simple Relation A Simple Relation 27

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

Pretzelosity in SIDIS Pretzelosity in SIDIS 29

Quantities in Calculation Quantities in Calculation 30

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

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

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

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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