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.