Physics Letters B 748 (2015) 323–327
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Physics Letters B
www.elsevier.com/locate/physletb
The exclusive limit of the pion-induced Drell–Yan process
S.V. Goloskokov
a
, P. Kroll
b,c,∗
a
Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Moscow region, Russia
b
Fachbereich Physik, Universität Wuppertal, D-42097 Wuppertal, Germany
c
Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
a r t i c l e i n f o a b s t r a c t
Article history:
Received
23 June 2015
Received
in revised form 10 July 2015
Accepted
10 July 2015
Available
online 14 July 2015
Editor:
A. Ringwald
Based on previous studies of hard exclusive leptoproduction of pions in which the essential role of the
pion pole and the transversity generalized parton distributions (GPDs) has been pointed out, we present
predictions for the four partial cross sections of the exclusive Drell–Yan process, π
−
p →l
−
l
+
n.
© 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
In recent years hard exclusive leptoproduction of mesons and
photons has been studied intensively by both experimentalists and
theoreticians. It became evident in the course of time that within
the handbag approach which is based on QCD factorization in the
generalized Bjorken regime of large photon virtuality and large
photon–proton center-of-mass energy but fixed x-Bjorken, it is
possible to interpret these processes in terms of generalized par-
ton
distributions and hard perturbatively calculable subprocesses
with, however, occasionally strong power corrections for meson
production (for a recent review see [1]). Exploiting the universal-
ity
property of the GPDs, one may use the set of GPDs extracted
from meson leptoproduction, in the calculation of other hard ex-
clusive
processes. Of particular interest are processes with time-
like
virtual photons. Thus in [2] predictions for time-like DVCS
(γ p →l
−
l
+
p) have been given, their experimental examination is
still pending. The high-energy pion beam at J-PARC put into opera-
tion
in the near future, offers the possibility of measuring another
exclusive process with time-like virtual photons, namely the exclu-
sive
limit of the Drell–Yan process, π
−
p →l
−
l
+
n. The purpose of
this letter is to present predictions for the cross sections of this
process taking into account what has been learned in the anal-
yses
of pion leptoproduction [3,4]. The data on the cross section
for π
+
leptoproduction [5,6] demonstrate the prominent role of
the contribution from the pion pole at small invariant momentum
transfer, t, and it became evident that it is to be calculated as a
*
Corresponding author at: Fachbereich Physik, Universität Wuppertal, D-42097
Wuppertal, Germany.
E-mail
addresses: goloskkv@theor.jinr.ru (S.V. Goloskokov),
kroll@physik.uni-wuppertal.de (P. Kroll).
one-particle-exchange (OPE) term rather than from the GPD
E [7].
In the latter case the pion-pole contribution to the π
+
cross sec-
tion
is underestimated by order of magnitude. A second impor-
tant
observation has been made in [3,4]: The interpretation of the
transverse target spin asymmetries in π
+
leptoproduction mea-
sured
by the HERMES Collaboration [8] necessitates contributions
from transversely polarized photons which are to be modeled by
transversity GPDs within the handbag approach. This observation
is supported by a recent CLAS measurement of π
0
leptoproduc-
tion [9].
Since
for the process π
−
p → l
−
l
+
n the same GPDs contribute
as for pion leptoproduction and the corresponding subprocesses
are just
ˆ
s ↔
ˆ
u crossed ones
1
H
π
−
→γ
∗
(
ˆ
s,
ˆ
u) =−H
γ
∗
→π
+
(
ˆ
u,
ˆ
s) (1)
where
ˆ
s and
ˆ
u denote the subprocess Mandelstam variables, one
can exploit the knowledge acquired there. One thus gains pre-
dictive
power, there is no free parameter or soft hadronic matrix
element left for the Drell–Yan process. Our analysis markedly dif-
fers
from a previous study performed by Berger et al. [11] where
only predictions for the longitudinal cross section at leading-twist
accuracy have been given. It should be stressed that their and our
predictions for that cross section differ by about a factor of 40
due to the different treatment of the pion pole contribution. Our
findings may be of help in the preparation of a Drell–Yan exper-
iment
[12]. Future data on the exclusive pion-induced Drell–Yan
process may reveal whether or not our present understanding of
hard exclusive processes in terms of convolutions of GPDs and hard
subprocesses also holds for time-like photons. This is a non-trivial
1
Adetailed discussion of the space- and time-like connection of the leading-twist
amplitudes can be found in [10].
http://dx.doi.org/10.1016/j.physletb.2015.07.016
0370-2693/
© 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.