Nuclear collisions in the dual parton model

Nuclear physics A461 (1987) 501~. 512~ North-Holland, Amsterdam

NUCLEAR COLLISIONS

5Olc

IN THE DUAL PARTON MODEL

A. CAPELLA and J. TRAN THANH VAN (presented by A. Capella) Laboratoire de Physique Theorique et Particules ElEmentaires, Universite de Paris XI, Bltiment 211, 91405 Orsay, France After a brief description of the Dual parton model and of the main results obtained in hadron-hadron, hadron-nucleus and nucleus-nucleus collisions, we present some recent results on the leading baryon and charged particle spectra in nuclear collisions. 1. THE PHYSICAL BASIS OF THE MODEL The Dual

parton

model

Although

teractions.

(DPM) is a non-perturbative

being

a phenomenological

approach to strong in-

model,

it is based on a very

namely the l/N expansion, which is valid for any gauge field

general framework,

theory with N degrees of freedom. It was introduced by t'tlooft' and later on it in order to satisfy unitarity-Veneziano

was modified by Veneziano' shown

that

modified

there

is a one-to-one

l/N expansion

Reggeon calculus3. order

terms, both

The

basic

in the

have more complicated

correspondence

reason

for this

l/N expansion

topologies

yields

However the underlying former,

energetic

the nucleus

the graphs model

correspondence

is that

formulae

particles

higher model,

than lower order ones. Reggeon calculus

(elastic rescatte-

identical to those in the Glauber model.

physical picture is quite different since,

and therefore

in this

: Gribov's

and in the multiple-scattering

The simplest version of the perturbative ring approximation)

between

and those in a multiple-scattering

has also

(including

the

can not cascade.

leading

in the

one) are formed

outside

This is at the origin of the well

known phenomenon of nuclear transparency. 2. THE MECHANISM The mechanism the following.

OF PARTICLE PRODUCTION of particle

production

In a single nucleon-nucleon

resulting

from the l/N expansion

collision,

is

each nucleon splits into

a valence quark and a diquark and two chains or strings of type qq-q, are formed. When a given nucleon undergoes a multiple collision,

its sea consti-

tuents are also excited. In general if a nucleon suffers m inelastic collisions, 2.m chains (valence

or and

strings

are formed,

sea) constituents

as shown

in figure

on the nucleon

1. Notice that the 2m

side are dressed ones, in the

sense that they carry together the whole momentum of the nucleon. 0375%9474/87/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)

B.V.

A. Capella, J. Tran Thanh Van / The Dual parton model

502c

11)

vk-

.

.

.

.

c

9s c

c c c

,'(11 c c

:I21 c c

= (3) c c

9”

c

.

c c c 5 (2ml

Is c c

c c

c c c c

~(2m_21C,(2m_ll c c

c c

FIGURE 1 DPM mechanism for a baryon projectile suffering m inelastic collisions with a nuclear target. The 2m chains are attached to the valence quarks and diquarks of the m wounded nucleons of the target

In the DPM the longitudinal nucleon

taken by the various

are determined intercepts

within

fraction valence

the model

of the dominant

Cm

are

1

of the incoming

and sea constituents

from very general

Regge trajectories.One

om (x1, x2'...X2m l:Cm& where the constants

xi of the momentum

2m-1 .n 1=1

determined

1 xi

from

(structure

functions)

arguments, in terms of the 4 obtains :

xi,"

6(1- 2,

normalization

xi)

to

(1)

unity.

One can

see from eq. (1) that, due to the l/Jx factor, the valence quark will be slow -1 in average, the sea constituents (x factors in eq. (1)) will be even slower, and,

due

provides

to the

b-function,

the diquark

a natural explanation

will

be fast

of the leading particle

In order to obtain the spectra of the hadrons has

to

perform

corresponding calculable

a convolution

between

quark and diquark

within the model.

One then proceed

a) If one aims at a very detailed of the produced Lund Monte Monte

Carlo

hadrons.one

Carlo)

in order

versions

b)

is only

particle,

to describe

can

jet universality.

Triple

the fragmentation

functions

(eq.

(i)) and the

The latter are not

:

event by event) description (for instance

the hadronization

has been presented

the 2-jets

of each chain. Some are already available5.

by G. London

(see

this Proceedings).

interested

one

fit to the nucleon-nucleon

the nuclear

as follows

(eventually

This

in each chain one

functions

functions.

has to use a Monte Carlo

at Saclay,

by 3. Pansart,

If one

produced

produced

of the DPM for nuclear collisions

One of them, developed contribution

structure

fragmentation

in the average. effect.

use data,

in the average the fragmentation

of a given

functions

or from hard scattering

Regge arguments

6

spectra

obtained

type of from

a

data if one assumes

can also be used in order to constrain

. Once the latter are determined,

spectra with no extra free parameter.

the DPM predicts

503c

A. Capella, J. Tran Thanh Van / The Dual parton model

As a last

step one has to sum

(i.e. configurations the Glauber-Gribov Before the

with different

number of chains)

remark

looses

at low pT, multiple

does

scattering

as a result

in describing

hadron-hadron energies.

described.

with

the nucleus.

Thus

billiard

nucleons

1,

ball

of different of the target.

COLLISIONS

collisions

met with considerable

and in particular

The rapid increase

inclusive

of its collision

through

i.e. collision

collisions7,

predicted

rapidity

distributions

The model

also provides

success

cp collision

of the central

ISR to collider energies was quantitatively are also well

given by

from figure

is not the result of successive

in this way, has already

CERN collider

lo

with weights7

nucleon with the various

FOR HADRON-HADRON

The model defined

and double

configurations

it is evident

not propagate

but of "parallel"

of the incoming

as

that,

its identity

and therefore

type of collisions,

3. RESULTS

let me

nucleon

nucleon

constituents

scatering

model.

continuing,

incoming

a target

over all multiple

plateau

Single'

by the mode18.

and

charge

up to

from

correlations

a quantitative

11

description

of the multiplicity distributions at various energies and for different rapi13 12 . dity regions as well as of the long-range forward-backward correlation Here the only new assumptions 1) Particles

(resonances)

:

a chain are produced

(Poisson).

produced

in different

It is worth

noticing

that the DPM is one of the rare models which

understanding

multiplicity

rapidity

region

is at variance

are uncorrelated.

of the KNO scaling violations

ISR and the CERN collider the

chains

randomly

2) Particles a dynamical

of

are the following within

energies.

distribution

Moreover

increase

it predicts

with

energy

IyI < y. than in the whole rapidity with those of most other models

The DPM has been recently

extended

fully applied to a description

observed

provide

between

the

that the moments

faster

interval.

in a central This prediction

and will be tested quite soon. 14 production and sucess-

to diffractive

of the UA 4 data15

on

diffractive

production

of high mass systems. Finally, so-called quark meson - the

let me stress

held-back

in a proton

configuration

been

'*

striking

.

in which

of the incoming

indeed, realized meson

is slowed

down

splits into a slow valence

the momentum have

that one of the main features of the model is the 16 valence quark effect : namely the fact that a valence

(antiquark)

the valence

quark

meson being strongly

experimental

in nature

by the interaction.

quark

confirmation

for an incoming

Likewise,

an incoming

and a fast antiquark

(quark)

and antiquark

share equally

suppressed.

Recently, there

that the held-back effect is, 17 , as well as for an incoming proton

A. Capella, J. Tran Thanh Van / The Dual parton model

504c

4. RESULTS FOR NUCLEAR COLLISIONS The DPM for hadron-nucleus and extended

collisions

to nucleus-nucleus

hadron-nucleus literature.

and

was introduced

collisions

nucleus-nucleus

They include rapidity

in ref.20.

collisions

are

distributions

in ref.4 Many

already

of charged

(see also 191,

results

for

both

available in the particles 4,5,19,20

X-d~stributio~for different types of produced particles 495 , multipli21 city distributions and forward-backward correlations2'. In the following forward

I will concentrate distributions

on some recent results

and the leading

concerning

both the charged

baryon spectra for collision

particle

of 160 on various

nuclei at 200 GeV per nucleon. The study of the leading interesting

problem,

nuclear matter. densities

momentum

spectrum

two

basic

hadrons.

needed

provide

power of

us with the baryon

related

to

to the former via energyto compute

Baryon density

determine

whither

the energy densi-

and energy density

a quark-gluon

are

plasma

can

in a heavy-ion

collision. 23 spectrum

al Leading baryon

in Sect.

collisions,

2, in order

one

needs

In ref. 24 the fragmentation

to compute

the

function

that the DPM prediction and antiproton-nucleus this fragmentation

corresponding

for the leading

fragmentation

function.

baryon has been obtained

in proton-nucleus

baryon spectrum

with the experimental

and the formalism

the baryon spectrum

leading baryon spectrum

It has been shown in this same reference

are in agreement

function

the

for the leading

from a fit to the pp and pp spectrum.

computed

is a very

regions of phase space. On the other hand the char-

by the colliding

As mentioned in nuclear

collisions

to the stopping

of this spectrum would

is a fu~ldamental ingredient

parameters

be produced

in nuclear

it is related

(which is, of course,

conservation)

ty deposited

spectrum

because

The knowledge

in the different

ged particle

baryon

mainly

as a function

described

data.

in Section

Using 2, we have

of the number of collisions

(figure 21. We observe collisions.

a softening The average

in the literature coefficient

of the baryon spectrum with the increasing properties

by various

defined

parameters.

as follows

baryon after m collisions.

after

as i~hy>~ = y,,, - m

tributions

collisions.

number of

have been characterized

One of them is the inelasticity

: let eE>m be the mean energy of the lea;;ng

The inelasticity

, = (l-I,,1 m_l. Another defined

of this pheno~non

coefficient I, is given by 26 useful parameter is the average rapidity

shift

, where , is the average baryon density m

These two parameters

in figure 2. The results

for

have been computed

m>l are plotted

from the dis-

in figure 3. For

A. Capella, J. Ttan Thanh Van / The Dual parton model

50%

P,,,=ZOOGeV/c

_3

_2

0

Y-Ymax FIGURE 2 The rapidity distribution of the leading baryon produced in the hadronization of a diquark-quark string, as a function of the number, m, of inelastic collisions suffered by the baryon to which the diquark belongs.

m=f

we obtain

from

a

I,-0.5

and l

phenomenological

mentioned

there,

single

inelastic

quark,

whereas

tituents of vatence

whose

it

= 1. Such a difference

analysis

of

the

is a straightforward

collision

in all extra momentum

energy

experimental result

is removed

collisions

distribution

was found in ref. 25

from

the energy function

data

in the

and,

DPM.

the diquark

as

it was

Indeed,

in a

by a valence

is also taken by sea cons-

is very

different

from

that

quarks.

In order to check the predictions data are available,

we compare

of the models

in a case where experimental

in figure 4 the results

of the model with the

A. Capella, J. Tran Thanh Van / The Dual parton model

0.2

0.15

I

0.1

0.05

0' 2

4

6

8

10

m FIGURE 3 Average rapidity of the baryon spectrum of fig. 2 as function of the number m of collisions. The inelasticity coefficient 1, is also given. experimental

data of ref. 28 on the leading proton

at the ISR (Js = 31 GeV/Nucleon). edges of the rapidity

spectrum

in a-o collisions

We see a very good agreement

space where spectator

protons

ding (which have not been taken into account

except

and intra-nuclear

in our calculation)

at the casca-

give important

contributions. Let us turn next to heavy ion collisions. leading baryon rapidity at laboratory

momentum

we mean a collision

densities

of 200 GeV/c/Nucleon.

in which all the nucleons

see that in going from total to central of the baryon density rapidity

in the central

shift) is obtained.

ponding one for all charged contamination

In figure

for total and central

rapidity

particles

is about 10 % at y*-0

In this case by central collision of the oxygen participate.

collisions

By comparing

5 we have plotted the 160 + 207 Pb collisions

a significative

region

We

increase

(and of the mean baryon

this baryon density with the corres-

(see Sect. 4b) we see that the baryon and becomes

In order to study more in detail this effect,

100 % at y*w - 1.5. let us consider

events where

-all the baryonic fragments of the lightest nucleus have a longitudinal momenturn fraction x lower than certain fixed value xc(xc < 1). Obviously by decreasing xc we are selecting

events

in which baryons

(i.e. events more and more inelastic).

However,

are more and more "stopped" by doing SO, the cross section

507c

A. Capella, J. Tran Thanh Van / The Dual parton model

1 a_&

~/S,31GeV/nucleon

_

DPM

0.8

t

i

0.E dN dy 0.4

0.;

I Y FIGURE 4 DPM prediction for the leading baryon spectrum produced in o-o collisions at Js = 31 GeV/nucleon compared with the date of ref. 28. corresponding

to these

resting

is to study

a

point

negligible

let

us consider

ratio

of central selected

ratio

for

cases

collisions).

of

great difference

these between

sing R one obtains for 0-Pb collisions

the

p-Pb

corresponding and

0-Pb

by the inelastic

6 we have plotted

two

cases.

We

see

increase

in order

shift one has to consider

cross

with

the intehaving

definiteness us define

the

section

of

(the cross section

the relative rapidity

this figure

rate of the shift versus

that there

is a

In the first case by decreashift. On the contrary

a significative very

Let

section

the average from

For

R is the cross

of the rapidity

to obtain

events

events.

collisions.

p-Pb and 0-Pb collisions.

a regular

Therefore

can be stopped without

In both cases R measures

In figure

R for

and smaller.

: in the case of p-Pb(O-Pb),

events divided

events.

gets smaller

how much the baryons

section

the

R as follows

the selected

the

cross

events

low values

increase

of rapidity

of R. This quantifies

the penalty

(i.e. low values of Rl one has to pay when one tries to increase

the

density

baryon

nucleon)

in the

as a projectile.

central

region

by using a nucleus

instead of a

508c

A. Capella, .I. Tran Thanh Van / The Dual parton model

---_---

total

dN dv 20

10 -

.3

-2

-1

0

1

2

3

V

FIGURE 5 DPM prediction for the leading baryon spectrum produced in 0-Pb collisions at 200 GeV/c/Nucleon. The full line corresponds to the total collision and the dashed one to a central collision. b) Spectra of charged The fragmentation well

known.

proton

data,

particles

function

In any case,

corresponding

once

the corresponding

27

they

to all charged

are obtained

from

particle

are rather

a fit to the proton-

date for o-o are well reproduced

in the model

(fig. 7). The

corresponding

fig. 8. We obtain

results

for

0-Pb

at 200 GeV

a rather large density

region in the case of a central collision. can be computed

from this density

dN E=

of charged

x&E>

particles

The energy deposited

using the standard

dy y=O

per nucleon

t

formula

are given

in

in the central by unit volume

509c

A. Capella, J. Tran Thank Va?l / The Dual parton model

per nucteon

PLab =200‘X/C

0.2

0

0.6

0.4

1

0.8

R FIGURE 6 The average rapidity shift of the leading baryon spectrum in p-Pb and 0-Pb collisions at 200 GeV/c/Nucleon, computed in the DPM, as a function of the degre of centrality of the collision, characterized by the ratio R. collisions, the ratio R is defined as asP-Pb/oi~~~b where o is the cross-section of the selected events cross-s&tion ucO-Pb = 794 mb.

with -0.4 obtain

and the longitudinal

1.5 GeV/(fermi13.

extension

of the system, L-l

In the case of a Ca projectile

fermi, we

on a lead target we

get 2 GeV/(fermi13. c) Multiplicity For nuclear the

same

Extensive (of

a few

values

of

distributions

reactions,

assumptions

are in progress

of GeV)

A, with

quantities

can be computed

we

a tendency

to become

narrower

Iy*l 'YD

is considered.

find

for

discussion

of the DPM can be found

collisions.

(see also ref. 21). At fixed energies approximate

the

KNO

KNO

curves

scaling

of Et distributions

in the talk by G. London

for

corresponding

than those for smaller A when a central

A rather detailed

in the DPM with

1 and 2 (sect. 3) used for hadron-hadron

calculations hundreds

and Et distributions

these

different

to

rapidity

large A

interval

in a Monte Carlo version

(J. Pansart,

this proceedings).

5. CONCLUSIONS The DPM is a non-perturbative general

principles

approach

to strong

such as the l/N expansion

interactions

and unitarity.

based on

The model

leads

A. Capella, J. Tran Thanh Van / The Dual parton model

51oc

1.4

-

1.2

-

1,

-

0.8

-

0.6

-

0.4

-

0.2

-

0.

Ia

6

FIGURE 7 Rapidity distributions of charged particles for pp and a-a collisions in the DPM. Data from ref. 29

to a unified

particle

and nucleus-nucleus prediction using

as

power, sole

production

collisions allowing

input

the

mechanism

for hadron-hadron,

in terms of "elementary"

to

compute

fragmentation

hadron

In this way we have been able to make detailed and

a-a

also

collisions,

made

predictions

collisions Thus,

for

compare the

forthcoming

in nuclear

determined

calculations

quite well with

It has great

pp data.

for hadron-nucleus

available

experiments

reactions

from

on

data.

We have

nucleus-nucleus

at CERN. the

a reliable new

which

spectra

functions

hadron-nucleus

strings.

physics

DPM

(and especially

tool to test whether or,

on the

standard framework.

contrary,

its Monte any new piece

Carlo

implementations)

of experimental

is consistent

with

what

provides

data contains

is expected

in a

511c

A. Capella, J. Tran Thanh Van / The Dual parton model

‘so+207Pb

. . . . . . . . . . . total _________

central

,_

semicentral

yai200 Gevk/N

Y Rapidity

distributions

FIGURE 8

of negative

particles

in the DPM

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A. Capella, J. Tran Thanh Van / The Dual parton model

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