17. Fragmentation functions in
e
+
e

,
ep
and
pp
collisions
1
17. FRAGMENTATION FUNCTIONS
IN
e
+
e

,
ep
AND
pp
COLLISIONS
Revised October 2009 by O. Biebel (LudwigMaximiliansUniversit¨at, Munich, Germany),
D. de Florian (Dep. de F´
ısica, FCEyNUBA, Buenos Aires, Argentina), D. Milstead
(Fysikum, Stockholms Universitet, Sweden), and A. Vogt (Dep. of Mathematical Sciences,
University of Liverpool, UK).
17.1. Introduction to fragmentation
The term ‘fragmentation functions’ is widely used for two related if conceptually
di±erent sets of functions describing ²nalstate single particle energy distributions in
hard scattering processes (see Refs. [1,2] for introductory reviews, and Refs. [3,4] for
summaries of recent experimental and theoretical research in this ²eld).
The ²rst are crosssection observables such as the functions
F
T,L,A
(
x, s
)ins
em
i

inclusive
e
+
e
−
annihilation at centerofmass (CM) energy
√
s
via an intermediate photon
or
Z
boson,
e
+
e
−
→
γ/Z
→
h
+
X
,g
ivenby
1
σ
0
d
2
σ
h
dx d
cos
θ
=
3
8
(1 + cos
2
θ
)
F
h
T
+
3
4
sin
2
θF
h
L
+
3
4
cos
h
A
.
(17
.
1)
Here
x
=2
E
h
/
√
s
≤
1 is the scaled energy of the hadron
h
(in practice the approximation
x
±
x
p
p
h
/
√
s
is often used), and
θ
is its angle relative to the electron beam in the
CM frame. Eq. (17
.
1) is the most general form for unpolarized inclusive singleparticle
production via vector bosons [5]. The transverse and longitudinal fragmentation functions
F
T
and
F
L
represent the contributions from
polarizations transverse or longitudinal
with respect to the direction of motion of the hadron. The parityviolating term with the
asymmetric fragmentation function
F
A
arises from the interference between vector and
axialvector contributions. Normalization factors
σ
0
used in the literature range from the
total cross section
σ
tot
for
e
+
e
−
→
hadrons, including all weak and QCD contributions,
to
σ
0
=4
πα
2
N
c
/
3
s
with
N
c
= 3, the lowestorder QED cross section for
e
+
e
−
→
μ
+
μ
−
times the number of colors
N
c
. LEP1 measurements of all three fragmentation functions
are shown in Fig. 17.1.
K. Nakamura
et al.
,JPG
37
, 075021 (2010) (http://pdg.lbl.gov)
July 30, 2010
14:36