Deep inelastic scattering and the EMC effect

lil

DEEP INELASTIC SCATTERING AND THE ^{EMC EFFECT}

by

Gerald

Vincent

Dunne

,

B.Sc. (na),Hons

Thesis ^presented for

in

the Department of

the degree

of

Master

of

^Science

Phys i cs

at

The ^{Un i} vers i

ty of

^{Ade I a i de.}

February ¹ 986

Âwnauri,

^?,t'

/llrt'¡

^i98tr

Statement:

This thesis contains no material which has been accepted

for

the award

of

any other degree

or

^diploma

in

^any University and

that, to

the best of

my knowledge and bel

ief,

the thesis contains no material previously published

or written

^by another person, except where due reference is made i n the

text of

the thes i s.

I

consent

to

the thesis being made available

for

photocopying and

loan

if

appl icable, provided due acknowledgement

is

^given.

Gerald

V.

^Dunne

C¡ntents

Abstract

Introductlon

I

IntroducÈion

to

^Deep

Inelastic

Scatt,erlnE

page

(i)

(rf ₎

L2

l5 t7

20 2L 25 2B

I I Kinematlcs

Structure Functlons

The Deep

Inelastlc

^Reglon

Introduction

ShorE dlstance ^OPE Light-cone ^OPE

Appllcation of the ltght-cone OPE to DIS

I I

5

r.2

1.3

2.1 2.2 2.3 2.4 2.5

2 The Quark-Parton ^Model IntroductLon

Infinite

^momentum frame and BJorken scallng Free _Quark Model

Sum Rules

in

the Quark Parton ^Model Beyond the Quark-Parton ^Model

3.

Operator Product Expanslons

7

7

3.1 3.2 3.3 3.4

4 The Renormallzat,lon Group and DIS Anomalous dlmensions

Asymptotl-c freedom

Renormalfzatton Group applied

to

DIS moments Sum Rules

in

QCD

35 37 39 48

4.r

4.2 4.3 4.4

page

5

lte

EllC Effect Introduction

Target dependence

fn

QCD

Change

ln

confl-nement scale

Space-tirne picture

of

DIS; Correlatlon functions An Inconslstency

6.

The Off-Shell Model 5.1

5.2 5.3 5.4 5.5

54 57 58 64 6B

6.1 6.2 6.3 6.4 6.5

Introductlon Ferml averaging The

off-shell

^model

Results The Deuteron

Conclusl-on

AcknowledgemenÈs

Appendix A: nucleon structure funct,lon parameÈrlzatLon

Appendlx B: program

for

calcLum

References

70 7L 75 78 90

95

96

97

100

r03

(¡)

Abs t ract :

This thesis contains

a

^review

of

theoretical and experimental aspects

of

^deep

inelastic

scattering. The main predictions of

quantum chromodynamics are presented folìowing the introduction

of

the quark-parton model, operator product expansions and the

renormaì ization ^group.The recently discovered EMC

effect

suggests

the need

for

a

significant

change

in

the usual QCD treatment of deep

inelastic

scattering from nuclear targets. The currentìy popular modeì involving changes

in

the quark confinement scale from target

to target is

discussed, and an inconsistency with the space-time picture

of

^deep

inelastic

scattering

is

^pointed

out.

A new explanation, the

off-shell

model,

is

proposed and the

results

for

various nuclei are compared with experimental data.

I I I I

I

I

i

(¡¡)

Introductlon:

Deep lnelastic scatterlng provides a unique opportunlty ln the ^study of the st,rong lnteracÈlons because iÈ ls both experlmentally ^and theoretlcally accessible. The agreement between experLment and the predlctlons of perturbaÈtve _QCD ls qul-te remarkable. Thfs thesls ^provldes an exÈenslve revLe¡v of the theoretlcal predlctlons of QCD concernlng the deep inelastlc region. A slgnlflcanÈ ^problem with the usual treatmenÈ of deep inelastic scatterlng fron nuclear targets has come to llght recently. Thls thesis ^proposes a ^nerü explanatlon for thls ^problem, the ^so- called ^rEMC effect,r.

Chapter I contains a revlew of the basic kfnemaÈLcs of deep lnelastic scaÈtering, defining the lmportant ^kLnenatLc variables, and the rstructure functlons ^| . The second chapter discusses the quark-parton nodel which was

the flrst serlous ÈheoretLcal treatment of deep lnelastic scattering. ^The main predict.ion of the quark-parton nodel 1s rBjorken scallngr, ^a

phenomenon observed (approxl-naÈely) ln experlments. ^The operator ^product expanslon, one of Èhe najor mathematical tools Ln the QCD dlscusslon of deep inelastlc scatterfng, ls introduced 1n chapter 3. Then, in Chapter 4, Èhe field theory ^quanÈum chromodynamics ls used fn conJunctl-on wlth the operator product expanslon and the renormalizatlon group to predict ^the behaviour of the structure functions as functions of the ^kinematlc varlables. ChapÈ.er 5 contains a dlscusslon of the recently dl-scovered (1983) EMC eff.ect. The essence,of Èhe EMC dlscovery ls ^{ÈhaL deep Lnelastlc} scattering of lepÈons from nucleons has a significant dependence on ^t,he t.arget nucleus. An lnconslsÈency 1n Èhe currently most popular

rexplanatlonr of the ^EMC effect is polnted out in thls chapter. In ^Ëhe

(iii¡

flnal

chapter,

a

new pârameter-free ¡node1

Ís

proposed whLch conslstently lncorporaEes

target

dependenee

lnto the

QCD

theory of

deep lnelastlc

scatterfng. Thts involves

accountLng

for the

roff-shelL-nesst

of

the

nucleons

ln a glven

nucleus

due to nuclear btnding effects.

^Thls necessltates

a

nodlfLcatlon

of the usual

Fermf averaglng procedures and

also

Lntroduces

a

^tqz

- rescallng'effect.

^The new.meÈhod

ls

applfed ^Ëo

many

different target nuclef,

and good agreement

wlth

experimental data ls

obtal-ned.