Fisica dello Spin

XVIII SEMINARIO NAZIONALE di FISICA NUCLEARE E SUBNUCLEARE

Mauro Anselmino Torino University

and INFN

Fisica dello Spin

Why spin ….?

Spin is one of the most fundamental concepts in physics, deeply rooted in Poincaré invariance and

hence in the structure of space-time itself. All elementary particles we know today carry spin, among them the particles that are subject to the

strong interactions, the spin-1/2 quarks and the spin-1 gluons. Spin, therefore, plays a central role

also in our theory of the strong interactions, Quantum Chromodynamics (QCD), and to

understand spin phenomena in QCD will help to understand QCD itself.

Research Plan for Spin Physics at RHIC, 2005

Polarized Deep Inelastic Scattering: exploring the proton longitudinal spin structure

 Helicity distributions - Δq, Δg - and their QCD evolution

 Polarized structure functions: g

₁

, g

₂

 Data and “spin crisis” (not a real crisis)

 The spin carried by the gluons

 Flavour separation

 Weak interactions

 Missing information

Surprises: Transverse Single Spin Asymmetries (unintegrated polarized parton distributions)

 Single Spin Asymmetries (SSA) in elastic processes

 Single Spin Asymmetries in pQCD and in data

 Parton intrinsic motion and spin

 Spin - Transverse Momentum Dependent distribution and fragmentation functions

 Phenomenology of SSA in inclusive processes

 Mysteries: spin asymmetries in pp → pp processes

The last missing piece of the proton structure: transversity

 The parton transverse spin distribution, h

₁

 A partner for h

₁

 Transversity in Drell-Yan processes

 Transversity in SIDIS processes

 Collins function from e

⁺

e

^-

data

 Hunting strategies for h

₁

What do we know, and how, about the proton structure?

θ

X

l’, E’

l, ^{E,s p, S}

 



 L W

E E Mq E

' 2

' d d

d

4



2



Main source of information is DIS

l, s l’

q

p,S

X

L



W



Polarized Deep Inelastic Scattering

parity conserving case (one photon exchange)

 0



^ _



W



q W q q

p x Q

  2

2



    



 ^{ }



( l , l ,' s ) 2 l l ' l ' l g l l ' 2 im  s ( l l ' )

L      

2

2

q

Q  

_{ }

q

_

q q p p

p ˆ   

₂

sin 2 '

4

²

2



EE

Q  p  q  M ( E  E ' )  M 

y _  E

 

 











 

 

 

 



 



  



) ,

) ( (

) ) ,

(

) ,

ˆ ( ) ˆ

, ( )

, , (

2 2 2

2 1

2 2

2 2 1

Q x q g

p

p q S S

q Q p

x q g

p q S

i

Q x q F

p p Q p

x q F

q g q

S q p W





 

















current conservation

 

  

  cos 2

sin 2 ' 2

4 '

d d

d

_{1 2 2 2}

4 2

2









 F

M F q

E E

unp

measuring dσ one extracts information on the structure functions F

₁

, F

₂

, g

₁

and g

₂

F

_1,2

related to q(x,Q

²

), g(x,Q

²

) quark, gluon distributions

g

₁

related to ∆q(x,Q

²

), ∆g(x,Q

²

) quark, gluon helicity distributions

  _ ^

   



 

 







 







_{1 2}

2 2

2 cos

' ' 4

' d d

d '

d d

d g

M x E g

E E E Q

E E







 q q

q  q  q

_

 q

_

g  g

_

 g

_

 g  g

_

 g

_

q

l l’

L



W





q

p,S

X

QCD parton model





...

) 2 (

) ) (

( )

,

(

⁽¹⁾

0



2

 





 Q C x

x C x

C

_{i s i} ^s _i



 

 



 





 

         

  ^{e C q q} _N ^{C g}

Q x

g

_g

f q

q q

1 2

) 1 ,

(

^{2 2}

1

) ,

(

d ,

₂

1

q y Q

y C x y q y

C ^{ } 

x

^ _ ^{ }

s

^ _ ^

coefficient functions

) ,

( )

, ( )

,

( x Q

²

q x Q

²

q x Q

²

q 

_^



_^



) ,

( )

, ( )

,

( x Q

²

g x Q

²

g x Q

²

g 

_^



_^



0 )

(

)

1 ( )

(

⁰

0

   

 C

_q

x  x C

_g

x

 ^{q q} 

e Q

x g

q

q

  

 

²

2

1

2

) 1 ,

at LO (

helicity distributions

scheme dependent

...

) 2 (

) ) (

( )

,

(

⁽¹⁾

2

0

 

 Q P x

x P x

P

_{ij s ij} ^s _ij



 

 

 







 

 

 



 

 

 









P g P

P Q P

Q g

_{gq gg}

qg s qq



 2

) (

dln

d

²

2

 

 ^{  }





q

q q

splitting functions

QCD evolution

NS NS

qq s

NS

Q P q

Q x

Q  q   



 2

) ) (

, dln (

d

₂ ²

2

) 2 (

) 1 2 (

) 1

( u u d d s s

q

_NS

           



de Florian, Navarro, Sassot

Dirk Ryckbosh, DIS 2005

1 . 0 d

) ,

2 ( 1

¹

0

2









 ^S

^q

 ^{x Q x}

Research Plan for Spin Physics at RHIC February 11, 2005

Figure 11: Left: results for Δg(x,Q

²

= 5GeV

²

) from recent NLO analyses [1, 2, 36] of polarized DIS. The various bands indicate ranges in Δg that were deemed consistent with the scaling violations in polarized DIS in these analyses. The rather large differences among these bands partly result from differing theoretical assumptions in the extraction, for example, regarding the shape of Δg(x) at the initial scale. Note that we show xΔg as a function of log(x), in order

to display the contributions from various x-regions to the integral of Δg. Right: the “net gluon

Direct measure of Δg needed

6 . 0 d

) ,

( )

(

1 . 0 d

) ,

2 (

1

¹

0

2 1 2

0

2

 



 



  ^S

^q

    ^{x Q x}   ^S

^g

 ^Q    ^{g x Q x}























 S

_q

S

_g

L

_q

L

_g

2

1

 large p

_T

di-hadron production in SIDIS,

 high p

_T

pions and jets at RHIC,

 direct photon production at RHIC,

 charm production at RHIC,

 role of orbital angular momentum

q q g 





, qg qg gg

gg  

 q qg 

c c gg 

Spin (J

_z

) sum rule

de Florian, Navarro, Sassot

large p

_T

di-hadron production in SIDIS

h

1

h

2

c cd

ab p

b g

q q d c b a

p

a

f D

f

_{/ /}

, , , , ,

/

d ˆ

d     

^



_





PDF FF

pQCD elementary interactions a

b c

 0

D

X

X

 ^ˆ

f

f

(collinear configurations)

X pp   ⁰

factorization theorem

p

p

X p

p  

⁰

RHIC

GeV

 200

s

c cd

ab b

a g

q q c b a

D f

f

_/

, , , ,

d ˆ

d         

^



_





Δq, Δg

pQCD elementary FF asymmetries a

b c

 0

D

X

X

 ^ˆ

f

f

polarized case: measure

S p,

S p,













d d )

( d ) (

d

) (

d ) (

d  











 

A

LL

 ^{d ˆ ( ) d ˆ ( )} 

2

d    1     

RHIC proposal

2005

prompt photon production at RHIC

X

pp  

Flavour separation - W production at RHIC

a

b X

X

 ^ˆ

f

f



p

 , p

l 

) ( ) ( )

( )

( x

₁

d x

₂

d x

₁

u x

₂

A

^W

  u   for W

^

change u  d

) ( d ) ( d

) ( d ) ( d











 







 A

L

parity violating longitudinal single spin asymmetry













 

 cd u d W l ab :













u  W  l

d













u  W  l

d













d  W  l

u

GeV

 500

s

  ^





q

2 2

2 2

1 2 1

1

( , )

) ,

) ( ,

( e q x Q

Q x q e

F Q g

x A

q q q

  ^



q

2 2

2

2 2

2 2

1

( , ) ( , )

) ,

( )

, ) (

, ,

( e q x Q D z Q

Q z D Q

x q Q e

z x

A

_h

q q

q

h q h q

Flavour decomposition in SIDIS, lN  lhX

DIS

SIDIS

) (  q   q

h

D

q

 q

,...

, , ,

, ,

,

, u u d d d s s

u

_V



_s

 

_V



_s

  



Unknowns:

...

?

?

? s s u d

q

q

_s

       



large x behaviour

) 1 (

) ,

(

) ,

(

q

2 2

2 2

1 1 1

 



 



 

u x u

Q x q e

Q x q e

F A g

q q q

 

 

 



  

 



  

 



 

 

 







 

 



 

 











 

 

 

 

 

 



  



) , ( )

, ˆ (

ˆ

) , ˆ (

ˆ ˆ

ˆ ˆ

2 ˆ 1 1

) , ) (

( ) )

, (

) , 2 (

) ,

ˆ ( ) ˆ

, ( )

, , (

2 2 5

2 4

2 3

2 2 2

2 1

2 3

2 2

2 2 1

Q x q g

q g q

Q x q g

p p p q p

q s

Q x g p q p

p q p s

s s

q p p

Q x q g

p

p q S S

q Q p

x q g

p q S

i

Q x q F

p p i q

Q x q F

p p Q p

x q F

q g q

S q p W



























 

























Charged–Current Deep-Inelastic Scattering (neutrino factory)

p,S

X

 ^l







q

q q s s

s ˆ 

₂





S. Forte, M. Mangano, G. Ridolfi

W

5 4

3 2

2 2

2 2

2 5

2 2

2 2

2 5

2 2

2 2

2 1

2 2

2 2

2 1

2xg g

0

) ,

( )

, ( )

, ( )

, ( )

, (

) ,

( )

, ( )

, ( )

, ( )

, (

) ,

( )

, ( )

, ( )

, ( )

, (

) ,

( )

, ( )

, ( )

, ( )

, (

















































































g g

Q x s Q

x c Q

x d Q

x u Q

x g

Q x s Q

x c Q

x d Q

x u Q

x g

Q x s Q

x c Q

x d Q

x u Q

x g

Q x s Q

x c Q

x d Q

x u Q

x g

W W W W

LO QCD parton model results

Some combinations of the polarized structure functions are of particular interest. For example:









































u u d d s s c c

g

₁^{W W}