Transversity and dihadron fragmentation functions

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Transversity and dihadron fragmentation functions

• Alessandro Bacchetta
• Regensburg University

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• Work funded by
• http//www.avh.de/
• In collaboration with M. Radici, Università di
  Pavia

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Outline

• Introduction
• Dihadron FF to probe transversity
• Dihadron FF in DIS
• Dihadron FF in ee- annihilation
• Dihadron FF in pp scattering

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Why is fragmentation into two hadron interesting?

• They can be used for TRANSVERSITY MEASUREMENT
  (the relative transverse momentum of the two
  hadrons can replace in single-pion
  production)

• They reveal SPIN TRANSFER EFFECTS IN
  HADRONIZATION (the angular distribution of two
  hadrons can be sensitive to the spin of the quark)

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Collinear single-hadron fragmentation
The only relevant variable is the fraction of
longitudinal momentum (z)
p
quark
For unpolarized hadrons, the only fragmentation
function at leading twist is
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Noncollinear single-hadron fragmentation
p
The relevant variables are the fraction of
longitudinal momentum (z) AND the transverse
momentum
quark
For unpolarized hadrons at leading twist there
are two fragmentation functions
and
Collins FF relation between quark spin and kT
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Collinear dihadron fragmentation
No transverse momentum of the pair center of mass.
h1
fraction of longitudinal momentum carried by the
pair invariant mass of the pair polar angle of
the hadrons in their center of mass frame azimuth
angle of the pair plane
quark
h2
There are two fragmentation functions at leading
twist and
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Collinear dihadron fragmentation
No transverse momentum of the pair center of mass.
h1
quark
h2
Interference fragmentation function relation
between quark spin and RT
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The dihadron interference fragmentation function
is a chiral odd object that can be used
to probe transversity

• Collins, Heppelmann, Ladinsky, NPB420, 565
• Collins, Ladinsky, hep-ph/9411444
• Ji, PRD49, 114
• Jaffe, Jin, Tang, PRL 80, 1166, hep-ph/9709322
• Radici, Jakob, Bianconi, PRD 65, 074031,
  hep-ph/0110252

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Interpretation of function
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Interpretation of function
Cut-diagram representation
Orbital angular mom.
Quark helicity
The orbital angular momentum projection has to
change one unit, e.g.
s-p wave interference
p-p wave interference
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Dependence on
Considering only s and p waves (at low invariant
mass)
A. Bacchetta, M. Radici, PRD67, 094002
Each one of these functions contains different
and interesting physics...
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Dependence on
Breit-Wigner shape
See next talk by P. van der Nat
R. Jaffe,X. Jin, J. Tang, PRL 80 (1997)
Radici, Jakob, Bianconi, PRD 65, 074031
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Dihadron FF in semi-inclusive DIS
l
two-hadron plane
l'
y
scattering plane
z
x
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AUT asymmetry
A. Bacchetta, M. Radici, PRD69, 074026
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Comparison with single-hadron
l
hadron plane
l'
y
z
scattering plane
x
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AUT in single-hadron production

• Drawbacks
• Several terms
• Convolutions
• Evolution
• Universality

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Dihadron FF in ee- annihilation
Boer, Jakob, Radici, PRD 67, 094003
e-
RCT
PD
P1D
P1C
RDT
PC
e
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Dihadron FF in pp? scattering
PA
F
RCT
RC
SB
P1C
F
PC
SB
PB
Bacchetta, Radici, hep-ph/0409174
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Dihadron FF in unpolarized pp scattering
Bacchetta, Radici, hep-ph/0409174
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Conclusions

• Dihadron interference fragmentation functions are
  good candidates to probe h1(x)
• They are easy to deal with from the theoretical
  and maybe also from the experimental point of
  view
• They can be measured in SIDIS (HERMES, CLAS,
  COMPASS), in ee- annihilation (BELLE, BABAR), in
  pp collisions (PHENIX, STAR, GSI, LHC, TEVATRON)