, , ,, AAA AA  llpp



 l l

p p

Transversity via Drell-Yan processes

Physics with polarized antiprotons at GSI-PAX

A

Transverse Single Spin Asymmetries

QCD “theorem”: (Sivers)_D-Y = – (Sivers)_DIS

Time-like e.l.m. form factors

SSA in

F

Elastic processes

SL SS

LL NN

N

A A A A

A , , , ,

A

F

form factors and vs.

spin misteries like in pp ?

Polarization data has often been the graveyard of fashionable theories.

If theorists had their way, they might

just ban such measurements altogether out of self-protection.

St. Croix, 1987

Parton distributions

are fundamental leading-twist quark distributions

quark distribution – well known quark helicity distribution – known

transversity distribution – unknown

all equally important

related to

positivity bound

q

q , 

h

 q , q 

)







 q q q









 q q q











q q q

 q q 



q

T

q



q 



q

q q

T

q   

 |

| 2









 g g g

+ –

– –

+

+ +

+ +

+ =  ^q _q ⁽ ₍ ^x _x ^{, Q} _{, Q}

⁾ ₎

+ – =  ^q

⁽ _q ^x ₍ ^, _x ^Q _{, Q}

⁾

₎

 ^{  } 

 | |

2

1 i

in helicity basis

+ –

+ –

 ) ,

(

1

x Q

h

h1 must couple to another chiral-odd function. For example:

D-Y, pp → μ⁺μ^- X, and SIDIS, l p → l π X, processes

+

+ –

+

+ –

+ –

– – +

–

+ –

h

x h

h

x Collins function

J. Ralston and D.Soper, 1979 J. Cortes, B. Pire, J. Ralston, 1992

J. Collins, 1993

Elementary LO interaction:

3 planes: plane ┴ polarization vectors, p-γ* plane, μ⁺μ^- γ* plane





1 9

4

2 1

2 1

2 2

1 2

2 2

2

x q x q x

q x q x e

x s M dx

dM d

a a

a a

a a F

 



^ 



/

2

/

2

1

x x x M s x Q s

x

x

    







  *   q

q

plenty of spin effects

 

 

 



 







q q

q q q q q q

TT

TT

e q x q x q x q x

x h

x h

x h

x h

a e

A ( ) ( ) ( ) ( )

) (

) ( )

( )

ˆ ( d

d

d d

2 1

2 1

2

2 1

1 1

2 1

1 1

2









h₁ from

) cos(2 cos

1 sin d ˆ

d ˆ

d ˆ d ˆ

ˆ ² ₂















 



 _^  _^

aTT

RHIC energies:

small x₁ and/or x₂

h_1q (x, Q²) evolution much slower than Δq(x, Q²) and q(x, Q²) at small x A_TT at RHIC is very small

smaller s would help Martin, Schäfer, Stratmann, Vogelsang Barone, Calarco, Drago

2 2

100 GeV

GeV

200 

 M

s

10

2 

 

X l l p

p



h₁ from

 

 ^{( ) ( ) ( ) ( )}  ^{ˆ ( ( ) ) ( ( ) )}

) ( )

( )

( )

ˆ (

2 1

2 1

1 1

2 1

2 1

2

2 1

1 1

2 1

1 1

2

x u x u

x h

x a h

x q x q x

q x q e

x h

x h

x h

x h

a e

A

q q

q q q q q q

TT

TT





 

 

2 2

2 GeV GeV

210

30  

 M

s

GSI energies: ^{large x1,x2}

one measures h₁ in the quark valence region: A_TT is estimated to be large, between 0.2 and 0.4

at GSI

X l l p

p



Energy for Drell-Yan processes

"safe region":

M  M

s M





QCD corrections might be very large at smaller values of M:

yes, for cross-sections, not for A_TT K-factor almost spin-independent

Fermilab E866 800 GeV/c

H. Shimizu, G. Sterman, W. Vogelsang and H. Yokoya, hep-ph/0503270 V. Barone et al., in preparation

s=30 GeV² s=45 GeV²

s=210 GeV² s=900 GeV²

s=30 GeV² s=45 GeV²

s=210 GeV² s=900 GeV²

data from CERN WA39, π N processes, s = 80 GeV²

J/ψ

q q

q

l⁺

l^–

l⁺

l^–

all vector couplings, same spinor structure and, at large x₁, x₂

measure A_TT also in J/ψ resonance region







 J X l l

p

p /





 



2

) )(

(

J J

V l V

q

M i

M M

v u

g u

v

g 



2

) )(

(

M

v u

e u v

e





q

 *

*

/

ˆ

ˆ

a

a



) ( ) (

) ( )

( )

( ) ( ) (

) ( )

( )

ˆ (

2 1

2 1

1 1

2 1

2

2 1

1 1

2

x u x u

x h

x h

x q x q g

x h

x h

a g

A

q

V q

q q q

V q TT

TT

 

 

Single Spin Asymmetries (and their partonic origin)

p_q

P_q π

k_┴ Collins effect = fragmentation of polarized quark depends on P_q· (p_q x k_┴)

P

p k_┴ Sivers effect = number of partons in polarized

proton depends on P· (p x k_┴)

q

p k_┴ Boer-Mulders effect = polarization of partons in

unpolarized proton depends on P_q · (p x k_┴)

P_q q

Collins: chiral-odd Sivers: chiral-even

Boer-Mulders: chiral-odd

These effects may generate SSA











 









d d

d d

AN

BNL-AGS √s = 6.6 GeV 0.6 < p_T < 1.2 p^↑p

E704 √s = 20 GeV 0.7 < p_T < 2.0 p^↑p

STAR-RHIC √s = 200 GeV 1.1 < p_T < 2.5 p^↑p

E704 √s = 20 GeV 0.7 < p_T < 2.0 p^↑p

SSA, SIDIS

Transversity and SSA in Drell-Yan processes

) cos(2 sin

cos 1

d 

 

  

 

) ,

( )

,

(

1  







 h x k h x k



Boer-Mulders functions

) sin(

sin

A

     

) ,

( )

,

(

1  





 h x k h x k



extract these unknown chiral-odd functions from unpolarized cross-section

combine above measurement with measurement of A_N to obtain information on h₁

This A_N expected of the order of a few percents

A. Bianconi, M. Radici

D. Boer, 1999

GSI at

processes in

SSA

Other p p

) ( )

,

(

1 Y

-

D

f x k f x

A





Sivers function usual parton distribution

Direct access to Sivers function

test QCD basic result:

( f

)

  ( f

)

q q

T DX

p p

N

f D

A

 (

) 

usual fragmentation function

process dominated by

no Collins contribution

q q  c c

same process at RHIC is dominated by

gg  c c

Electromagnetic form factors J^μ_em

p p'

) ( )

' (

|

|' J p u p u p

p

  



 





 F

( Q

)    / 2 m

F

( Q

)  q



2

1

F

F

G

    G

 F

  F

Κ = 1.79

2 2

/ 4 m

 Q



In pQCD

4 1

 Q

F

6 2

 Q

F

JLAB: F₂/F₁ ~ 1.25 GeV/Q difficult to separate F₁,F₂ or G ,G

p p¯

In time-like region G_E and G_M may have relative phases

P l⁺

l^-

θ

L N S

there may be a SSA: σ^N - σ ^–N σ^N + σ ^–N

= A_y = P_y

 





 1

/

|

| sin

|

| ) cos

1 (

) Im(

) 2 sin(

2 2

2 2

*

E M

M y E

G G

G A G







 

P_y can be very large: predictions depend strongly on model assumptions for F₂/F₁

Unexpected spin effects in pp elastic scattering

larger t region can be explored in

p p

pp p

p

pp p

p













Unexpected large polarization in

p

p  p p

What about

p

p  p p

Conclusions

A_TT in D-Y processes at GSI energies:

highway to transversity

A_N and SSA: many effects expected and test of QCD theorem:

(Sivers)_D-Y = – (Sivers)_DIS

…the transverse-spin asymmetries whose measurement is suggested for these

experiments, are remarkably insensitive to shifts in the overall normalization. In summary, perturbative corrections appear to make the cross sections larger independently of spin.

They would therefore make easier the study of spin asymmetries, and ultimately transversity distributions. (G. Sterman et al.)

Exploration and separation of proton form factors, spin results from new time-like region

Spin asymmetries in proton-antiproton elastic processes: as mysterious as in proton-proton?