Transversity and dihadron fragmentation functions

Transversity and dihadron fragmentation functions

Alessandro BacchettaRegensburg University

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


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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


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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)


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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


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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.


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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


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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...


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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)

Transversity and dihadron fragmentation functions

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