Pretzelocity Pretzelocity & & Quark Angular Momentum - - PowerPoint PPT Presentation

Pretzelocity Pretzelocity & &

Quark Angular Momentum Quark Angular Momentum

Bo-Qiang Ma (马伯强

马伯强)

Bo-Qiang Ma (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

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g g

The Proton “Spin Crisis”

3 . ≈ Δ + Δ + Δ = Σ s d u 3 . Δ + Δ + Δ Σ s d u

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:

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Th t i i i Th t i i i The proton spin crisis The proton spin crisis

& 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 J Ph G 17 (1991) L53 B.-Q. Ma, J.Phys. G 17 (1991) L53 B.-Q. Ma, Q.-R. Zhang, Z.Phys.C 58 (1993) 479-482

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The Wigner Rotation The Wigner Rotation

f t ti l ( 0) (0 )

μ μ

r r for a rest particle ( ,0) (0, ) w for a moving particle L( ) ( ,0) (0, ) L( ) / m p s p p m s p w m

μ μ

= = = = r r L( ) ratationless Lorentz boost Wigner Rotation p = , , ( , )

w

s p s p s R p s p p

μ μ

′ ′ → ′ ′ = Λ = Λ u r v u r r ( , ) ( , ) L( )

w w

s p s p p R p p′ Λ = Λ

• 1

L ( ) a pure rotation p

E.Wigner, Ann.Math.40(1939)149

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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

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What is What is Δq measured in DIS q measured in DIS

• Δq is defined by

5 5

s , | | , , | | , q p s q q p s q p s q q p s

μ μ

γ γ γ γ

+

Δ = 〈 〉 Δ = 〈 〉

• Using light-cone Dirac spinors

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| | q p q q p γ γ

1d

( ) ( ) q x q x q x

↑ ↓

⎡ ⎤ Δ = − ⎣ ⎦

∫

• Using conventional Dirac spinors

0 d

( ) ( ) q x q x q x ⎡ ⎤ Δ ⎣ ⎦

∫

3

d ( ) ( ) q pM q p q p

↑ ↓

⎡ ⎤ Δ = − ⎣ ⎦

∫

u r u r u r

2 2 3

d ( ) ( ) ( )

q

q pM q p q p p p m p M

⊥

⎡ ⎤ Δ ⎣ ⎦ + + =

∫

u r －

3

2( )( )

q

M p p p m = + +

Thus ∆q is the light-cone quark spin

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• r quark spin in the infinite momentum frame,

not that in the rest frame of the proton

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

in the rest frame

q p

s S =

∑

r u r does not mean that

q

∑

in the infinite momentum frame

q p q

s S =

∑

r u r

q

Therefore it is not a surprise that the quark spin sum measured in DIS does not equal to the proton spin

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measured in DIS does not equal to the proton spin

A relativistic quark-diquark model

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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

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pQCD counting rule

h

(1 )

p

q x

± ∝

− 2 1 2 | |

z z q N

p n s s s s = Δ Δ = −

• ＋
• 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.

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Parameters in pQCD counting rule analysis

%

1 3 2 i 3

(1 )

i

q

A q x x B

− + =

−

In leading term

3 1 5 2 (1

)

i

q

B C q x x

− − =

%

2 i 5

(1 ) q x x B = −

B.-Q. Ma, I. Schmidt, J.-J. Yang, Phys.Rev.D63(2001) 037501.

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New Development: H. Avakian, S.J.Brodsky, D.Boer, F.Yuan, Phys.Rev.Lett.99:082001,2007.

Different predictions in two models

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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

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Transversity with Melosh-Wigner rotation in the quark-diquark model q q

) ( ˆ x W

V

) ( ˆ x WS

B.-Q. Ma, I. Schmidt, J. Soffer, Phys.Lett. B 441 (1998) 461-467.

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The transversity in pQCD, in similar to helicity distributions y

5 ) 2 / 1 ( 3 ) 2 / 1 (

~ ~ C A

q q 5 ) 2 / 1 ( 5 3 ) 2 / 1 ( 3

) 1 ( ) 1 ( ) ( x x B x x B x q

q q

− − − =

− −

δ

35 / 32 B 693 / 512 B 35 / 32

3 =

B 693 / 512

3 =

B

B.-Q. Ma, I. Schmidt, J.-J. Yang, Phys.Rev.D63(2001) 037501.

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Transversity in two models

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SU(6) quark- diquark model pQCD based analysis

VS VS

diquark model analysis

S

Ma, Schmidt and Yang, PRD 65, 034010 (2002)

solid curve for SU(6) and dashed curve for pQCD

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( ) pQ

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

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Three QCD spin sums for the proton spin Three QCD spin sums for the proton spin

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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

S i d bit l i li ht S i d bit l i li ht f li f li Spin and orbital sum in light Spin and orbital sum in light-cone formalism cone formalism

Ma&Schmidt, Ma&Schmidt, Phys.Rev.D 58 (1998) 096008

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The Melosh The Melosh Wigner Rotation in Wigner Rotation in The Melosh The Melosh-Wigner Rotation in Wigner Rotation in “Pretzelosity” “Pretzelosity”

J.She, J.Zhu, B.-Q.Ma, Phys.Rev.D79 (2009) 054008

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

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

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

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What is What is “Pretzelosity” ? Pretzelosity” ?

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What is What is “Pretzelosity” ? Pretzelosity” ?

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A Simple Relation A Simple Relation

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

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Pretzelosity in SIDIS Pretzelosity in SIDIS

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Quantities in Calculation Quantities in Calculation

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J.She, J.Zhu, B.-Q.Ma, Phys.Rev.D79 (2009) 054008

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J.She, J.Zhu, B.-Q.Ma, Phys.Rev.D79 (2009) 054008

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J.She, J.Zhu, B.-Q.Ma, Phys.Rev.D79 (2009) 054008

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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.

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