transversity and dihadron fragmentation functions
DESCRIPTION
Transversity and dihadron fragmentation functions. Alessandro Bacchetta Regensburg University. Work funded by http://www.avh.de/ In collaboration with M. Radici, Università di Pavia. Outline. Introduction Dihadron FF to probe transversity Dihadron FF in DIS - PowerPoint PPT PresentationTRANSCRIPT
14.10.2004 A. Bacchetta - Dihadron fragmentation functions
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• Work funded by
http://www.avh.de/
• In collaboration with M. Radici, Università di Pavia
14.10.2004 A. Bacchetta - Dihadron fragmentation functions
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Outline
• Introduction• Dihadron FF to probe transversity• Dihadron FF in DIS• Dihadron FF in e+e- annihilation• Dihadron FF in pp scattering
14.10.2004 A. Bacchetta - Dihadron fragmentation functions
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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)
hP
• They reveal SPIN TRANSFER EFFECTS IN HADRONIZATION (the angular distribution of two hadrons can be sensitive to the spin of the quark)
14.10.2004 A. Bacchetta - Dihadron fragmentation functions
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Collinear single-hadron fragmentation
quark
The only relevant variable is the fraction of longitudinal momentum (z)
1( )D z
For unpolarized hadrons, the only
fragmentation function at leading twist is
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Noncollinear single-hadron fragmentation
The relevant variables are the fraction of longitudinal momentum (z) AND the transverse momentum
For unpolarized hadrons at leading twist there are two
fragmentation functions and
quark
21 ( , )TH z k2
1( , )TD z k
Tk
Collins FF: relation between quark spin and kT
14.10.2004 A. Bacchetta - Dihadron fragmentation functions
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“Collinear” dihadron fragmentation
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
There are two fragmentation functions at
leading twist: and
h1
h2
quark
21( ,cos , )RD z M 1 ( ,cos , )RH z M
R
R
z
MTR
No transverse momentum of the pair center of mass.
14.10.2004 A. Bacchetta - Dihadron fragmentation functions
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“Collinear” dihadron fragmentation
Interference fragmentation function: relation between quark spin and RT
h1
h2
quark
1 ( ,cos , )RH z M
TR
No transverse momentum of the pair center of mass.
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The dihadron interference fragmentation function is a chiral odd object that can be used to probe transversity
1H
•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
14.10.2004 A. Bacchetta - Dihadron fragmentation functions
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Interpretation of function
h1
h1
h2
quark
h2
quark
_
1H
h
quark
h
quark
_
Collins function 1H
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Interpretation of function 1H
+ _
Lz Lz-1Cut-diagram representation
The orbital angular momentum projection has to change one unit, e.g.
( ,1) ( ,0)
( ,1) ( ,0)
p s
p p
Orbital angular mom.
Quark helicity
s-p wave interference
p-p wave interference
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Dependence on R
1 1 1cos , co( s) sp ppR RH H H
A. Bacchetta, M. Radici, PRD67, 094002
Considering only s and p waves (at low invariant mass)
Each one of these functions contains different and interesting physics...
14.10.2004 A. Bacchetta - Dihadron fragmentation functions
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Dependence on M
1 1 1( ,cos , ) ( , ) cos ( , )sp ppR Rz zM MH H z MH
R. Jaffe,X. Jin, J. Tang, PRL 80 (1997)
Breit-Wigner shape
Radici, Jakob, Bianconi, PRD 65, 074031
See next talk by
P. van der Nat
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Dihadron FF in semi-inclusive DIS
two-hadron plane
scattering plane
x
zy
hP
1P
2P
TR
TS
S
R
1 2( )ep e h h X
l
l'
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AUT asymmetry
1 1( )sin( )sin
( )sin sin ( )
UT R S R
S R
A h H
M
Q
B y
V y
A. Bacchetta, M. Radici, PRD69, 074026
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Comparison with single-hadron
y
x
z
hadron plane
scattering plane
hP
TS
S
h
l
l'
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AUT in single-hadron production
1 1
1 1
1 1
( )sin( )
( )sin( )
( )sin(3 )
( )sin
( )
[ ]
[ ]
[ ]
sin(
[
]2 )
]
[
UT h S
h S
h S
S
T
T
h S
I h H
I f D
I h
A
H
MI
Q
B y
A y
B y
V y
VM
IyQ
Drawbacks:
•Several terms
•Convolutions
•Evolution
•Universality
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Dihadron FF in e+e-
annihilation1 2 1 2( )( )C C D De e h h h h X
1 1 11( ) ( )cos( )C D
c cUU R
c cR H Hd A y D D B y
PC
e-
e+
RCT
P1C
PD CR
RDT
DR
P1D
Boer, Jakob, Radici, PRD 67, 094003
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Dihadron FF in pp scattering
PC
SB
SB
RC
PA
PB
RCT
P1C
1 11sin( )sin [ ]B C T T
aN S R C
bab c
cdA I f Hdh
Bacchetta, Radici, hep-ph/0409174
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Dihadron FF in unpolarized pp scattering
cos( ) cos(2 2 )C D C DUU R R R Rd A B C
Bacchetta, Radici, hep-ph/0409174
1 1
1 1
1
1
1 1
1
1
[ ]
[ ]
[ ]
T T
a b c dab cd
aab c d
a
ab g
c d
c
b
b
g
d
H H
G G
A I f f d D D
B I f f d
C I f f d
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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 e+e- annihilation (BELLE, BABAR), in pp collisions (PHENIX, STAR, GSI, LHC, TEVATRON)