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A Revisit of
the Nuclear EMC Effect
Bo-Qiang Ma （马伯强）
Peking University (北京大学)
July 30, 2013, SDU, Weihai
Talk at《2013 EIC物理学术会议》
In collaboration with Yunhua Zhang, Lijing Shao, Baogui Lu
Outline
Introduction and motivation
Parton distribution functions (PDFs) in a
statistical modelZhang, Shao, and Ma, Phys. Lett. B 671, 30 (2009)
Nuclear EMC effect in a statistical modelZhang, Shao, and Ma, Nucl. Phys. A 828, 390 (2009)
Summary
Outline
Introduction and motivation
Parton distribution functions (PDFs) in a
statistical modelZhang, Shao, and Ma, Phys. Lett. B 671, 30 (2009)
Nuclear EMC effect in a statistical modelZhang, Shao, and Ma, Nucl. Phys. A 828, 390 (2009)
Summary
Parton Model and Deep Inelastic Scattering
DIS
Parton distribution functions (PDFs)
A PDF is defined as the probability density for finding a particle with a certain longitudinal momentum fraction x at momentum transfer Q^2.
Due to the complicated non-
perturbative effect, we still
have difficulty to calculate
PDFs absolutely from the first
principal theory of QCD at
present!
• The CTEQ6 parton distribution functions
in the MS renormalization scheme and Q
= 2 GeV. [wikipedia]
Structure functions：
Nuclear EMC effect – the theoretical expectation
0 10.5x
0.25 0.75
1.0
nucleon Fermi motion
The expected structure functions of nucleons inside nucleus are only slightly different from those of free ones.
P.R. Norton, Rep. Prog. Phys. 66, 1253 (2003)
Nuclear EMC effect – the experimental data
Observation that structure functions are altered in nuclei stunned
much of the HEP community 30 years ago
~1000 papers on the topic; BUT more data are needed to uniquely
identify the origin: What alters the quark momentum in the nucleus?
Quark Structure of Nuclei:
Origin of the EMC Effect
x
D
A
F
F
2
2
Nuclear EMC effect (European Muon Collaboration)
shadowing
anti-shadowing
EMC effect
Fermi motion
Nucleons inside a nucleus have a remarkably different
momentum configuration as expected!
Many models on EMC effect
pion excess model [Smith’83, PLB; Ericson & Thomas’83, PLB]
cluster model [Jaffe’83, PRL; Carlson & Havens’83, PRL]
Q^2-rescaling model [Close et al.’83, PLB; Jaffe et al.’84, PLB]
nucleon swelling model [Deus’84, ZPC]
deconfinement model [Jaffe’83, PRL]
x-rescaling model [Staszel et al.’84, PRD; Akulinichev et al.’85, PRL]
……
“All models of the EMC effect are wrong, including mine.”
——N. N. Nikolaev (1990)
Statistical models on PDFs and EMC
As can be speculated, with partons bound in the wee
volume of the nucleon, not only the dynamic, but also
the statistical properties, for example, the Pauli
exclusion principle, should have important effect on the
PDFs.
Various models according to the spirit of QCD have
been brought forward, therein statistical ones, providing
intuitive appeal and physical simplicity, have made
amazing success.
PDFs： Bhalerao，Bourrely and Soffer，Zhang and Ma，Cleymans，Mac and Ugaz，Devanathan and Ganesamurthy，Bickerstaff and Londergan，Alberg and Henley， et al.
EMC：Angelini and Pazzi，Rozynek and Wilk，et al.
Our motivation
1、to illustrate whether
the statistical effect is
important and to which
aspects of the nucleon
structure it is important,
2、to indicate that the
statistical effect may be
an important source to
the EMC phenomenon,
not how well it matches
the experimental
results
So,
we do not make any effort to fit
the experimental data
intentionally,
for PDFs, there is no arbitrary
parameter put by hand in our
model, and all parameters are
basic statistical quantities,
and, for the EMC effect, we
only introduce temperature T
versus atomic number A as a
free parameter to mimic the
nuclear effect.
Outline
Introduction and motivation
Parton distribution functions (PDFs) in a
statistical modelZhang, Shao, and Ma, Phys. Lett. B 671, 30 (2009)
Nuclear EMC effect in a statistical modelZhang, Shao, and Ma, Nucl. Phys. A 828, 390 (2009)
Summary
Derivation of the PDFs
Worthy to mention that, including the s flavor will not introduce
any extra parameter, due to
Analysis of our PDFs
Determination of unknown parameters
Constraints in
the proton：conservation laws
Gottfried sum：SG=0.235
NMC, Phys. Rev. Lett. 66 (1991) 2712
Statistical PDFs ：results
From Zhang, Shao, and Ma, Phys. Lett. B 671, 30 (2009)
• the flavor asymmetry of the
nucleon sea is naturally
generated.
• d/u(x=1) = 0.55 is close to
the prediction of the naive
SU(6) quark model.
p-n isospin symmetry
Calculation indicates that s quark contributes less than 7% both
to the total light-front momentum fraction x and to the total
invariant mass square of the system
the contribution of heavier flavors is negligible.
Outline
Introduction and motivation
Parton distribution functions (PDFs) in a
statistical modelZhang, Shao, and Ma, Phys. Lett. B 671, 30 (2009)
Nuclear EMC effect in a statistical modelZhang, Shao, and Ma, Nucl. Phys. A 828, 390 (2009)
Summary
The idea on the nuclear EMC effect
The main idea: We introduce the temperature T as a
parameter versus the atomic number A and fit the above
analytic expression to the experimental data in the EMC region.
just considering the u, d flavors and the gluon,
including the s flavor and taking the mass of s quark ms = 130 MeV
including the s flavor and taking ms = 70 MeV
Statistical EMC：results
Zhang, Shao, and Ma, Nucl. Phys. A 828, 390 (2009)
the larger A, the
smaller T and thus
the bigger V;
consequently, the
smaller chemical
potentials
consistent with
other models, e.g.,
the nucleon swelling
model and Q^2-
rescaling model
Parameters
remarks
We preform a new statistical approach and
obtain analytic expressions of the parton
distribution functions in terms of light-front
kinematic variables in the whole x region [0, 1].
And we utilize the concise statistical model to
mimic the nuclear EMC effect. Here, we treat
the nucleon temperature T as a parameter of
the atomic number A and find that the nuclear
effect can be explained as a shift of T; the larger
A, the more significant influence.
The predicted ratios of the PDFs of iron to deuterium. The colored curves are our results, The dashed, dotted, and dash-dotted curves correspond to the predictions of the cluster model, the Q^2-rescaling model, and the pion excess model, respectively.
Sukhatme’92, ZPC
Carlson & Havens’83, PRL
Smith’83, PLB
Ericson & Thomas’83, PLB
Berger et al.’84, PRD
Close et al.’83, PLB
Jaffe et al.’84, PLB
Close et al.’85, PRD
The cluster model
uuuddd
udd
uud
udd
uud
udd
uud
udd
uuduuuuudddd
udd
9-quark cluster
6-quark cluster
udd
udd
The pion-excess model
udd
uud
udd
uud
udd
uud
udd
uud
udd
udd
uddπ
π
π
π
π
π
π π
ππ
udd
uud
The predicted PDFs differ significantly from model to
model, and to distinguish various models and look into
the immanent cause of the EMC effect, we suggest
more experiments to identify the PDFs in nuclei,
especially for antiquarks, the strange quark, and the
gluon.
The dimuon yield in Drell-Yan [Alde et al.’90, PRL] process
can detect the sea content in nuclei as a useful probe.
Lu and Ma [PRC, 06] also advised that the semi-inclusive
hadron productions in DIS are sensitive to the sea quark
content.
The process of charmed quarks production in DIS can probe
the gluon constituent via the photon-gluon fusion mechanism,
and the strange quark content can be detected in Λ–K
process.
Anti-Lambda production as a probe of the
nuclear sea structure?
有三类原子核模型可以解释EMC效应: 团簇模型,Pi盈余模型, 重新标度模型.
通过考察原子核与核子荷电轻子半单举过程中末态强子anti-Lambda的产率比对x的依赖性，我们发现 anti-Lambda能够区分定性描述原子核EMC效应的三类不同原子核结构模型.
B.Lu and B.-Q. Ma, Phys. Rev. C 74 (2006) 055202
Different sea behaviors in nuclei
Different predictions of anti-lambda production
Anti-Lambda Productionfor Nuclear Physics
Anti-Lambda production charged lepton
semi-inclusive deep inelastic scattering
off nuclear target is ideal to figure out
the nuclear sea content, which is
differently predicted by different models
accounting for the nuclear EMC effect.
B.Lu and B.-Q. Ma, Phys. Rev. C 74 (2006) 055202
Outline
Introduction and motivation
Parton distribution functions (PDFs) in a
statistical modelZhang, Shao, and Ma, Phys. Lett. B 671, 30 (2009)
Nuclear EMC effect in a statistical modelZhang, Shao, and Ma, Nucl. Phys. A 828, 390 (2009)
Summary
Summary
We illustrate that the statistical effect may
be important to the nucleon structure
and indicate that the statistical effect may
also be explained as an important source to
the EMC phenomenon.
further experimental searches on the sea
and gluon content of the nucleus can push
forward the progress in this direction.
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