QUARK STRUCTURE FUNCTIONS OF MESONS AND THE DRELL ...

SLAC-PUB-2247 January 1979 (T/E)

QUARKSTRUCTUREFUNCTIONSOF MESONSAND THE DRELL-YAN PROCESS* **

Edmond L. Berger and Stanley J. Brodsky Stanford Linear Accelerator Center Stanford University, Stanford, California 94305

ABSTRACT The polarization of massive lepton depend in detail meson-induced

pairs

reactions,

rest

and longitudinal

produced in hadronic

on the internal

at small transverse in the pair

properties

theory

change from predominantly momentum fraction

two angular

are associated

components of the valence

hadrons.

For

to predict

that

the decay angular

momentum of the pair,

distributions

are shown to

dynamics of the incident

2 sin 8 as the longitudinal

Q-2(1-x)'

collisions

we use QCD perturbation

frame will

momentum distribution

l+cos2e

of the pair respectively

quark structure

distribution to

x F + +1. with

(l-~)~

The and

function

of the

of Energy under contract

number

meson.

(Submitted

to Physical

*

Work supported by the Department EY-76-C-03-0515.

**

Permanent address:

Review Letters)

High Energy Physics Division, Laboratory.

Argonne National

-2The Drell-Yan

process'

hadrons to reconfigure massive lepton

pair

is approached

(i.e.,

their with

aspects

in deep inelastic

stituents

at short

In this pair

effects

with

dictions3'4 large with

for

an analysis

QCD radiative

important

of meson-induced of perturbative

treatments

is controlled

con-

in Fig.

1.

massive lepton quantum chromo-

by including

explicit

2 We assume that

in the

describes

a qi

the momentum dependence

by the Bethe-Salpeter

gluon exchange in the asymptotic The same model3 yields

Q2, and for baryon valence

description

can thus

of the hadronic

at large momentum transfer,

the power behavior

experiment.

dynamics

process

and to measure other

the meson bound state.

of the meson wave function

idea is sketched

internal

of hadrons not normally

domain, the meson wave function

and that

and thus by single

distance

spin properties)

we report

low momentum transfer bound state,

functions

We go beyond the usual

associated

* 1)) an annihilating

The Drell-Yan

MB + !2+R-X in the context

dynamics (QCD).

of a

distance.

letter,

production

short

scattering

of the dynamics (e.g.,

production

iq + y* + Ea' is taken far off-

is probed.

the structure

of colliding

As the edge of phase space

the far off-shell

wave function

be used to determine accessible

the local

four-momentum Q'.

< in the subprocess

and consequently

of the hadronic

momentum into

'I = Q2/s + 1 or x = 9,/Q? F

quark q or anti-quark shell,

A+B + EEX measures the ability

kernel

This

freedom limit. the standard

pre-

of meson and baryon form factors structure

functions,

all

--

at

-consistent

Our focus here is on the consequences of the QCD

of internal processes

hadron dynamics; can be treated

logarithmic

corrections

in the conventional

due to

manner.

-3The most striking MB + I1+R-X are its

Q-2(1-x)o with

for

the valence

the polarization

function

angular

QCD picture

specified

distribution

function

photon y* -f Q+Q-.

(1-x)2

relative

for

quark structure

of the virtual

has both a scaling5

component, with

a different

consequences of this

predictions

of the meson and for The structure

testable

and a non-scaling

Each is associated

magnitude.

in the lepton

6

pair

rest

frame,

For

+Mq + Q Q X, we obtain da

=

(1-x)2

+ $ - kt sin82 Q2

(1+cos20)

Here x is the momentum fraction

(light-cone

variable)

G from the meson, kt is the average of its and case cation

= i; Q bn is defined l

of the non-scaling

different

ways:

the angular

.

(1)

of the annihilating

squared transverse

in the lepton

pair

rest

momentum,

frame.

Identifi-

piece in the data can be made in several

the x dependence of the cross section

(0) dependence at fixed

at fixed

Q2,s;

and s dependence at fixed

x,QL,s;

Q2/s. The dominant

contribution to IT-N + U+JJ-X at large Q2 arises from the * +&J + y + u u , where the antiquark G comes from the IT- and

annihilation

u from the nucleon.

We concentrate

the 5 is far off-shell quark as nearly is not indicated

xF + 1).

in the lowest

in a physical

is sufficent

1 are required

gauge, the scaling

Q2 + 0~ can be identified

solely

meson momentum p equally

between the constituent

approximation

can be discarded

region

where only

to treat nucleon

order diagrams shown in Fig;

in Fig.

(axial)

It

Thus, the incident

free and on-shell.

Both diagrams

Tr-q + y*q. although

(i.e.,

on the kinematic

with

as it

Fig.

l(a)

l

the u structure

1 for

by gauge invariance, contributions We partition q and i;

does not affect

as the incident

this

simplifying

our conclusions.

-4The kinematics light-cone

of the annihilating

variables

where m denotes servation

antiquark

xa = (p~+p~)/(p"+p3),

are specified Setting

and kTa.

p: = m2,

the bare quark mass, we use energy and momentum con-

to derive +2 k + xam2 - x,(1 - xa> mz Ta Cl- Xa>

As xa + 1, pi becomes large carried

with

and far

as x

a

+ 1.

freedom,

the single

gluon exchange approximation

Salpeter

we suppose that

of the asymptotic

kernel

for

The invariant

amplitude

shown in Fig.

1 will

large momentum behavior

to us,

yield

a good

of the Bethe-

7

corresponding

U(P+) YV v(P-)

c

arguments based on

in the range of xa of interest

the q< bound state.

c/42=

The squared four momentum

invoking

Therefore,

asymptotic

representation

(2)

2 1, k2 = (PI - %P) 2 = +(pf: -I- m2) - +rn 71,

by the gluon in Fig.

also becomes large

space-like.

.

to Fig.

1 is

+ Q

S(P1) Y, Uh(P/2) G_,(PD)

A

1

Ya u(pb)

where c uxiex x pseudoscalar. over the soft expression binding

for

= ($$+m>y5 The factor

specl 'fies $,