SIDIS Cross Sections
and Spin Asymmetries
Predictions for Ongoing and
Future Experiments
M.Elena Boglione
INFN – Sezione di Torino e Universita’ degli Studi di Torino
In Collaboration with M. Anselmino, U.D’Alesio, F. Murgia, A. Prokudin, C. Turk
QCD N06 - Monte Porzio Catone 15/06/2006
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Outline of the talk
Azimuthal and PT dependences of hadrons in unpolarized SIDIS
At small PT, (PT,<1 GeV/c) lowest order contributions + TMD distribution and fragmentation
functions describe all data
At large PT, (PT,>1 GeV/c) the usual pQCD higher order collinear contributions dominate
We can explain the full range of experimental data
New detailed predictions for azimuthal and PT dependences of hadrons produced at
HERMES, COMPASS and JLab (6 GeV).
Collins Fragmentation and Transversity Distribution Functions
New experimental data from BELLE and Hermes allow us a comprehensive fit to determine
the Collins fragmentation function and to give first indications on the Transversity
distribution function.
Analysis of AUTsin(fS+fh) at Hermes and COMPASS and of AU/AL at BELLE.
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Azimuthal and PT dependences
of hadrons in unpolarized SIDIS
Lowest order term, ds0: a virtual photon with momentum q strikes a quark with
transverse momentum k_|_. The final detected hadron,has transverse momentum
p_|_ with respect to the direction of the fragmenting quark from wich it originates,
and transverse momentum PT with respect to the photon direction.
This is the main source of hadrons with small PT.
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The first order term, ds1, includes the processes in which the quark emits a hard gluon
and those initiated by a gluon. Here the final quark can have a large transverse momentum,
even starting from a collinear configuration. This term will dominate lepto-production of
hadrons with PT larger than 1 GeV/c.
The second order term, ds2, will be taken into account through the K factor
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The <cosfh> modulation at small PT
is a higher twist effect and decreases
like1/Q for growing Q.
Therefore we expect it to be smaller
for ZEUS, where Q is huge,
than for E665 !
We ignore the Collins and Boer-Mulders
contribution: here <cos 2fh> is mainly
arising from pQCD contributions.
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Predictions for forthcoming measurements
HERMES Experiment
Hydrogen target
Ee = 27.57 GeV
Since PT and Q2 are very low,
the perturbative effects
obtained by including higher
order corrections are negligible.
<cosfh> and <cos2fh> are a
direct consequence of the intrinsic
transverse motion of partons
inside the hadrons.
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Predictions for Jlab
Predictions for COMPASS
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Spin asymmetries, Transversity and
Collins fragmentation function
Recent experimental data from BELLE, HERMES and
COMPASS shed some light on the Transversity
distribution function and on the Collins fragmentation
function.
Can we make a comprehensive analysis to extract
information on both functions ?
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HERMES and COMPASS have measured the weighted asymmetry
AUTsin(fS+fh) as a function of xB, zh and PT.
At first order in the (k /Q) expansion we have:
_|_
2e  p' 2  2 PT
 PT2 /  P'T2 
(
1

y
)
e
e 2 h q(x)ΔN Dqh(z)

2
2
2
q q 1
 p  P'T  M h
sin(φS  φh )
AUT
( x, z , PT )  
1
 PT2 /  PT2 
2
[
1

(
1

y)
]
e
e 2 f q(x)Dqh(z)

2
q q 1
 PT 
where, at first order in
 PT2  p2   z 2  k 2 
 p' 2 
M h2  p2 
M h2   p2 
 P'  p'   z  k ' 
2
T
2

2
2

k
,
Q
k 2
 2
1
k  q
f1q ( x, k  ) 
e
f1 ( x)
2
  k 
p2
 2
1
 p 
D ( z , p ) 
e
Dqh ( z )
2
  p 
h
q
1
h ( x, k  ) 
e
  k '2 
q
1

k 2
 k '2 
q
1
h ( x)
 1 / 2( g1q  f1q )
{
 g1q
p2
2e p  M h2
h
 N Dq ( z , p ) 
e
 N Dqh ( z )
Mh


 N Dqh ( z )  N q z q (1  z ) q Dqh ( z )
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Fit to the HERMES data
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Description of COMPASS data (no fit)
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Predictions for JLab
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Description of BELLE data
A 1  cos(2f1 ) f ( z1 , z2 , p1 , 2 )
 N Dqh ( z1 )  N Dqh ( z2 )
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Dqh ( z1 ) Dqh ( z2 )
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Description of BELLE data
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Description of BELLE data
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Description of BELLE data
We can describe BELLE data
Without any fit, by using the
Collins function as obtained by
fitting HERMES data and fixing
The transversity function to be
either g1 or ½(f1+g1).
BELLE data prefer h1=g1 !
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Description of BELLE data
We can describe BELLE data
without any fit, by using the
Collins function as obtained by
fitting HERMES data and fixing
the transversity function to be
either g1 or ½(f1+g1).
BELLE data prefer h1=g1 !
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Conclusions





The Collins fragmentation function has been determined by fitting HERMES
data on AUT . The transversity function was fixed to be either g1(x) or
½[g1(x)+f1(x)].
With this function we obtain an excellent description of COMPASS data
on the same asymmetry.
Predictions for JLab are given.
We then reproduce the BELLE asymmetry without fitting, and find that the
Collins function as obtained from the fit to HERMES data work really well,
showing that the Collins function is universal.
BELLE data prefer h1(x)=g1(x), giving us a first indication on the size of the
transversity function
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Future perspectives
We are eagerly awaiting new data from BELLE.
These will allow a reliable fit to fully determine the
Collins function.
Then HERMES data can be used to fix the
Transversity distribution.
For a proper analysis we have to take into account all
orders in the O(k_|_/Q) expansion.
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