Target Fragmentation
and
Fracture Functions
an introduction
• tools to handle target fragmentation in semiinclusive
•
deep
inelastic
scattering
L. Trentadue Semi-Inclusive Reactions (SIR) Workshop 2005 Session: Target Fragmentation
Friday, May 20, 2005
presented by
Misha Osipenko
Semi-inclusive process
e(k )  H ( P)  e(k )  h( ph )  X
Q  (k  k )
2
2
Q
x
2 Pq
Pph
z
Pq
pT

transverse
momentum
2
Semi Inclusive Deep Inelastic Scattering
Current Fragmentation
Hadron is emitted from
the struck quark
after absorption of
the virtual photon
Hadrons may also come from elsewhere !
Semi Inclusive Deep Inelastic Scattering
Target Fragmentation
pT>>QCD>0
Fracture Function
Fracture Functions = Fragmentation + structure
The combination of the Fracture Function with the target-Fragmentation
evolution
gives the evolution equation:
Homogeneus ( usual Altarelli Parisi type) term + Inhomogeneus term
+
Several properties:
1) Fracture Functions satisfy unitarity
2) Fracture Functions
factorize
2
3) Extended M(x,z,t,Q )-Fracture Functions satisfy
Gribov-Lipatov-Altarelli-Parisi type evolution
equations
Applications:
Diffraction:
s
t
Diffractive structure
functions represent
asymptotic limit of the
fracture functions
Observed diffractive cross
section demonstrates Q2
behavior similar to that
expected from pQCD.
Next-to-leading Fracture Functions
LO
NLO
Q2=4.2 GeV2
x=0.495
Other interesting applications and
developments:
LEPTO event generator
exhibits target fragmentation
contribution amplified in case
of polarization asymmetries.
 q( x) H ( x, z ) 
q e q( x) H ( x, z )  q( x)  H ( x, z ) 


h
A1 
 q( x)H ( x, z ) 
2
q eq q( x) H ( x, z ) 1  q( x) H ( x, z) 


2
q
Additional term can
reach 10%
Fracture Functions : spin dependent
•Real scale in the target-current fragmentation separation is t, which
can be small also at large Q2 or invariant mass s (HERMES, NOMAD).
•Fracture functions naturally generates T-odd SSA.
Fracture Functions Future:
As Misha (Osipenko) will show to you
later in this session Jlab experiments
may give some further insights hopefully
in target fragmentation in SIDIS
and
further assess the combined
current + target
final state description
Fracture
Functions
an introduction
• tools to handle target fragmentation
L. Trentadue Semi-Inclusive Reactions (SIR) Workshop 2005 Session: Target Fragmentation
Friday, May 20, 2005
presented by
Misha Osipenko
•DGLAP evolution equation with standard splitting functions
2

(
Q
)

du i
2
h
2
h x
2
S
Q
M
(
x
,
z
,
t
,
Q
)

P
(
u
)
M
(
,
z
,
t
,
Q
)

q
q
i
2

Q
2 x /(1 z ) u
u
i
1
•Momentum sum rule
tmax

h
1
dt  dzzM qh ( x, z, t , Q 2 )  (1  x) F2q ( x, Q 2 )
0
0
•Process independent definition
1 z
 tr   
ij
0
dxi
xi
1 z

0
dx j
xj


ij
M ih ( N1 ) ( xi , z, t , Q2 ) F2j ( N2 ) ( x j , Q 2 )  M ih( N2 ) ( xi , z, t , Q 2 ) F2j ( N1 ) ( x j , Q 2 )  hard
(i  j  h)
Hadron-hadron
collisions
N1+N2hX
In assumption of the factorization
+