SIDIS%20Cross%20Sections

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• 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.DAlesio,
F. Murgia, A. Prokudin, C. Turk
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Outline of the talk

• Azimuthal and PT dependences of hadrons in
  unpolarized SIDIS
• At small PT, (PT,lt1 GeV/c) lowest order
  contributions TMD distribution and
  fragmentation functions describe all data
• At large PT, (PT,gt1 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(fSfh) 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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EMC experimental data
ZEUS experimental data
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EMC experimental data
E665 experimental data
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ZEUS experimental data
The ltcosfhgt 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 contributio
n here ltcos 2fhgt 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. ltcosfhgt and ltcos2fhgt
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(fSfh) as a function of xB, zh and PT.
• At first order in the (k__/Q) expansion we have

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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
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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(f1g1). BELLE data
prefer h1g1 !
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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(f1g1). BELLE data
prefer h1g1 !
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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
• ½g1(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.