Physics Letters B 800 (2020) 135066
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Pion valence quark distributions from maximum entropy method
Chengdong Han
a,b
, Hanyang Xing
a,c
, Xiaopeng Wang
a,b
, Qiang Fu
a,b,d
, Rong Wang
a,e,∗
,
Xurong Chen
a,∗∗
a
Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China
b
University of Chinese Academy of Sciences, Beijing 100049, China
c
School of Physical Science and Technology, Southwest University, Chongqing 400715, China
d
Lanzhou University, Lanzhou 730000, China
e
Institut de Physique Nucléaire, CNRS-IN2P3, Univ. Paris-Sud, Université Paris-Saclay, 91406 Orsay Cedex, France
a r t i c l e i n f o a b s t r a c t
Article history:
Received
24 September 2018
Received
in revised form 16 September
2019
Accepted
18 September 2019
Available
online 31 October 2019
Editor:
W. Haxton
Keywords:
Pion
Valence
quark distributions
Maximum
entropy method
Valence quark distributions of pion at very low resolution scale Q
2
0
∼ 0.1GeV
2
are deduced from
a maximum entropy method, under the assumption that pion consists of only a valence quark and
a valence anti-quark at such a low scale. Taking the obtained initial quark distributions as the
nonperturbative input in the modified Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (with the GLR-MQ-ZRS
corrections) evolution, the generated valence quark distribution functions at high Q
2
are consistent
with the measured ones from a Drell-Yan experiment. The maximum entropy method is also applied
to estimate the valence quark distributions at relatively higher Q
2
= 0.26 GeV
2
. At this higher scale,
other components (sea quarks and gluons) should be considered in order to match the experimental
data. The first three moments of pion quark distributions at high Q
2
are calculated and compared with
the other theoretical predictions.
© 2019 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
At high energy, the scattering process with a hadron happens
on its internal constituents, namely the quarks and the gluons,
which is commonly called the partons. Parton distribution function
(PDF) is the number density information of the partons carrying
some fractions of the hadron momentum. Thanks to the factoriza-
tion
theorem based on quantum chromodynamics (QCD) theory,
the cross-section of high energy scattering on hadron is the prod-
uct
of the interaction connecting the probe and the PDFs of the
hadrons. Therefore determination of PDFs of hadrons is an impor-
tant
project continually in hadron physics study. Up to date, PDFs
of nucleons are precisely determined from the global analysis of
worldwide experimental data. However, less is know for the other
hadrons, such as the pion. Pion is the lightest hadron, acting as
the key interaction carrier between nucleons, which attracts a lot
of interests from both experimentalists and theorists.
*
Corresponding author at: Institut de Physique Nucléaire, CNRS-IN2P3, Univ.
Paris-Sud, Université Paris-Saclay, 91406 Orsay Cedex, France.
**
Corresponding author.
E-mail
addresses: rwang@impcas.ac.cn, wangrong@ipno.in2p3.fr (R. Wang),
xchen@impcas.ac.cn (X. Chen).
In experiment, the parton structure of pion is usually measured
with the muon pair production process of π − N scattering [1,2],
the leading neutron production [3–5] ep → e
nX of deep inelas-
tic
scattering assuming the pion exchange is dominant, and the
prompt photon production of π − N scattering [6]. The Drell-Yan
data of π − N scattering [1,2] accesses the valence quark distribu-
tion
of the projectile pion, while the leading neutron production at
HERA [3–5]probes the sea component of pion at small x, and the
prompt photon production mainly constraints the gluon distribu-
tion
[7]. The global fits of the pion PDFs to the experimental data
are performed by several groups, using the next-to-leading-order
QCD analysis [8], using the constituent quark model parametriza-
tion
[9,10], and using the modified DGLAP equations [11].
In
theory, it is not simple to predict the distribution of the
valence content, since the pion is not only formed as a quark-
antiquark
system but also as one of the Glodstone bosons in the
chiral symmetry breaking of SU(3) flavor. However there are lots
of progresses from the Dyson-Schwinger equations (DSE) [12–16],
the NJL model [17–19], light-front holographic QCD (LFHQCD) [20],
Lattice QCD [21], chiral quark model [22–26], constituent quark
model [27,28] and QCD sum rule [29], etc. Beyond the quark
distribution functions, the parton distribution amplitude and the
generalized parton distributions of pion are studied [30–35]. The
rainbow-ladder truncation of the DSE well incorporate the dressed
https://doi.org/10.1016/j.physletb.2019.135066
0370-2693/
© 2019 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
.