Electromagnetic signals and backgrounds in heavy-ion collisions

Nuclear Physics AS66 (1994) 69c-76c North-Holland, Amsterdam

Electromagnetic Sourendu

NUCLEAR PHYSICS A

Signals and Backgrounds in Heavy-Ion Collisions

Gupta a

“HLRZ, c/o KFA Jiilich, D-5170 Jiilich, Germany Aspects of the dilepton spectrum in heavy-ion collisions are discussed, with special emphasis on using lattice computa.tions to guide the phenomenology of finite temperature hadronic matter. The background rates for continuum dileptons expected in fort~~coming experiments are summa,rised. Properly augmented by data from ongoing measurements at HERA, these rates will serve as a calibrating background for QGP searches. Recent results on the temperature dependence of the hadronic spectrum obtained in lattice computations below t,he deconfinement transition are summarised. Light vector meson masses are strongly temperature dependent. Accurate measurements of a. resolved p-peak in dimuon spectra in present experiments are thus of f~~ndamental import#ance.

1. Introduction Electromagnetic probes of t,he quark gluon plasma have been surveyed extensively in the last few years. I will not repeat the material covered by these excellent reviews [I]. Since there has not been much development in the theory of photon signals since the last Quark Matter meeting, therefore, in t,he rest of this talk I will concentrate on dilepton signals and backgrounds. Recall t,hat mass spectra for opposite sign dilept,ons form a, continuum with conspicuous resonances sitting over it, The cross sect,ion is very closely related to a theorist,‘s favourite quantity-. the spectral density of a vector correlation function. All observed resonances correspond to flavour singlet vector mesons. With sufficient mass resolution in the spectra the fate of each such meson can be seen in the dense a,nd. possibly, t.hernlalised hot matter formed as a result of heavy ion collisions. The ease with which individual resonances can be isolated and studied by well-designed experiments makes the dilepton signal a tool which is neglected only by the most foolha.rdy physicist. The continuum itself may be interesting for various reasons, many of which have been reviewed before. I shall spend most of my allotted pages on scenarios which are built for matter in, or not far from, thermal eqL~iIibri~~~~.The ma,in reason for this emphasis is t,he ease with which theorists can do these computations; but, as reported in this meeting 12, 31, t,here arc model computations now which indicat,e a fairly short thermalisation times in heavy-ion collisions. Nevertheless, it is necessary to keep in mind that t,he dense systems formed may spend a significant fraction of their lifetimes t,rying to come t,o a state of equilibrium. If they succeed, they will be doing muc.h better than most people. Uptil now very little work has been done with non-e[~~lilibriu~~ scena,rios. It should be mentioned t,hat Shuryak’s t,wo-step thermalisation model [4] is an attempt at. constructing a toy model of non-equilibrium phenomena. Other such attempts are hydrodynamical shock waves and burning walls [5], Swiss-cheese inst,ahilities [6], etc. All these dynamical

0375-9474~4/$07.~

0 1994 - Elscvier Science B.V. All rights reserved.

7oc

S. Gupta I Electromagnetic

modes

can

siblc

be married

signals

However

it is known

densities

This

feature

heavy-ion

importa.nt

The

which

To turn selected

in models

Latt,ice

‘rhese

I sha.ll divide

and

a peak

in spcc-

system

[‘il.

may not, be seen in

experiments heavy-ion

peaks

of the should

Non-equilibrium

to guide

theory.

keep

statistical

watch physics

experiments

irlto two major

talk

regions;

mass

ca.n make

part,s.

elcnlrnts

l’he

work st,a.rtcd

I shall

point

in QCD

The

t)hc second

in t,hc next, two scct,ions. phenomenolog>T.

matrix Such

any

in various

are discussed

t,ool to compute

dilept~oils n~ay Ix ilsrflil as a probe t.o date

computations

therefore,

QCD

ma.trix

will be available

I shall

speak

region.

I shall

This

is the

a year

ago [8]

for thcrIria1

ma.ttcr.

thr

t,he latt,ice

a.rc usually and

will

a few

empha.sise

is that

which

first

with

is

obtained

is being

pursued

2.1.

Low

titative

attempts

cially

Dalitz

to extend

of a ferlni. quite

recent

A first

crucially,

High

mass

can

at tempcrat lat,tice

ures

est.imatcs

is now being

clone;

the

low

mass

GcV)

(MS1

mass

region

wit,h M~lO

GcV

a.nd the intermediate

is bounded

by the p and J/c’,

as t.hr very-high

mass

region.

continuum

bremsstrahlung to heavy-ion

There

collisions

[lo].

The

on properties

time

out to be close

hadronic

on

of t,hermalised

at, such estimates

bc obtained

masses, in lattice

t,o bc understood etc.

dependent turns

seems

from pions

low-mass

hadronic [ll].

widt,hs and interact,ion computations,

and

Such

spe-

number-

a

computations

strengths I shall

quart-

dilepton

matter,

to t,his yea.r’s favollrite now exists

in terms

have been

at finit,e

summarise

a

section.

continuum t,imes arc short,

pre-equilibrium

processes.

Drell-Yan

at both

T and

the lowmass pairs,

[9] in the next

if t.hermalisa.tion pairs

GeV),

of the region

att,empt

input

These

computation

Even

(Mk5

this picture

ma.y be sbrongly

temperatures.

This

of

theory.

the Y resonances.

if the thermalisation

fraction

phenomena

non-perturbative

at high temperature.

the intermediate

collisions,

processes-

spectrum

to obtain

All computations

IIrc perturba.tion

continuum

In ha.dron-hadron of several

for non-pert,urbati\,e

elements

speaking,

beyond

mass

in lligh tempera1

in the Ilear fut.ure.

a.lso speak

region

performed

be int,ercsting

of the high mass Rougly

resonances.

have been

give clear evidence

It would,

for the relevant results

the

physics

dilept,ons

computa.tions

signal

t,o ?:.

need,

is that

levels

pas-

dileptoils.

Continuum

(lontinuuill

2.2.

pliysics.

or perturbation

the t,hermal

mass

such

yielding

continu1lm

[9].

The

close

of funtlamcntal

energy

whether with.

thereby

yield

give rise to narrow

can

to t,hc equilibrium

ca.nnot. yet deal

wit,h continuum

a norl~I’erturbative

dynamics

nlodcs

here.

t.o concrete

resonances.

ion processes,

.411 these

n1ora.l I wa.nt to draw

~1ew branch

of lattice

product

t,hat one wonders

theories

contributions

be concerned

further

110 relation

so generic

collisions.

tlilcpton

phenomena.

rrorl-equilihriu~~~

have

seems

is a growing

2.

that

!vliirh

for phenomena

utility

to sl.andard

of norl-cqulibrium

tral

signals and backgrounds in heavy-ion collisions

J/T,!), there

The the LHC

could

the high mass continuum

very high mass and RHIC

be subst,antial

region

energies.

is expected At LHC,

contribution

from

cross section to consist

in the mass open

bottom

consists

essentially range

of of

between

production.

71c

S. Gupta I Electromagnetic signals and backgrounds in heavy-ion collisions

This

has yet to be estimated.

A state-of-the-art in perturhative data

QCD

obtained

Drell-Yan

[13].

since

cross

the

section

functions data Tllc

HERA

main

illcreasing energies

this

increasing growt,ll

r 5 lop3

has been

in [la].

It, should

nf,

hand,

at I,HC

2.3.

that

mass that

there

mass

is around

the extrapolated turns

extrapolation t,he range

come

the most, poorly

uncrxtainty new results of a fa.ctor a.t RHIC

then

then

0..5 GeV)

not,

effect

once

scales

s&ion

the

involved

cutoffs.

gencrat,ors

is a roughly

in the QCD (&),

Thus fi

Wit 11

from the

predictions

schemes

a.t. each

.5 units.

of this

sect.ions,

Wit,h

At, RIIIC

comes

Detailed

MonteCa.rlo

values

following.

a plateau.

to about

cross

of cross

Carlo

arc

predictions

ctc,

and

their

[.)I, on the other

absolute

normalisa-

sepera.tely.

be compa.red

As a result

bvith a proper

of 6.

continuum

comes

understood

part

from

a complex

of the continuum

thermal

out, that

at M

this signal cross

source

of masses

dilepton

t,he thern1a.l

M Z-2.5

GeV.

may bc visible

above

when

region

for a brtter

of higher

show that

continuum.

in t,he cutoff

The

mixt,ure

of

spectrum.

signal. signal

If the

vanishes

initial

It

If the illit,ial below

temperature

a.bove the same

mass

signal

this large

hrlow

t,his region

which

sufTers

is in t,he parton to .r z

Structure

background

resummed

at small

!5 x 10-l.

New physics

measurements rrgion.

pcrt,llrbative

uncertainty t,hermal

still

yields

signal

The

an uncertainty

to t,hc intermediate a much

now

A second

corrections.

I estimate

t.urns olrt t,o have thr

two mail1

of this

cont,rol.

results

from

luminosities

function

understanding

are under

Drell-Yan

thermal

Hence

order

these

into

corresponds

of kinematics.

extrapolating

energies.

scct,ions

of uncertaint,y of interest,

is in the import,ance of three

account

are the

develops

100 GcV.

a.re fitted

it. turns

section

will be crucial

mentioned and I,HC

do

of structure

have possible

into

A consequence

for the continuum

cross

in this

at, HERA

t,han the Drell-Yan than

region

strongest

int,o play

done

Monte

of Drell-Yan

.r.

being

these

(?(a:)

continuum

1 GeV,

The

may

beelr

full

[ 171.

ambiguities. At LHC,

region

These

section

in moment,um

of the dilepton

250 MeV,

out to be about

The

are no mass

at all relevant

Drell-Yan

even for M FZ .5 GeV

[16].

pairs

Ihr fiz.50

quantjil.ies

these

region

is also the most, important tempera.turc

occurs

paramet,ers

and data

is probably

well wit,11 have

measurements

the widt,h increases

Approximate

This

the

in Ihe l>,-integrated

are predictions.

int,ermediate

sources.

energies

on &?

Intermediate

The

cross

of Drell-Yan

normalisations

estima.te

is theoretical&

and must, be taken

absolute

it is necessary

Drell-Yan

There

In the high mass

tail in the p> .-distribution.

t.ions and ot,her such dimensional of this,

GcV

computed

extremely

[14].

performed

Thus

various

One

[15].

i\gcu.

contain

640

in the Aachen

cross sections agree

is experimental-

energies;

the increase

be remembered

dependence

sections <

of t,hc Drrll-Yan

of (~2,) wit,11 S which

from

advance

distribution

of tbc perturbative

given

fi

made.

have now been

features

at fixed

cross

U(oz,)

analysed.

is 3 unitjs wide;

growth

<

were

at LHC

the ra.pidity

&?,

linear

apart

second

sections

kinematic

&,

19.J

has now been computed

in the range

from

to say, these

estimates

The

of cross

for LHC and R.HIC was presented

of energies

last

the old estimates.

on estimates

of rates

were hased on exponentiated

Needless

in t,he range

two advances affect

computation

in 1990 [12]. These

Workshop

mass

range

steeper

slope

a small

dominat,es

error over

(less t,his

12c

S. Gupta I Electromagnetic signals and backgrounds in heavy-ion collisions

It should be remembered lhat the Drell-Yan process is only one of the rna,ny ba.ckgroimds in the dilepton channel in the intermediate mass region. At the higher end of this region deca.ys of heavy-flavour quarks give rise t,o a large tliiepton rate. Such a contribution ha,cl been pointed out by Shor long ha,ck. A minijet c~rrl~~llta~ion [19] for the process A $ N --f jet.5 -+ c(b) + lep%orzs,

(1)

shows &at one should expect, a large number of single leptons per event. These combine into r? large diiepton background. This is relative/y innocuous, since the rate for unlike sign is the same a.s for like sign pairs, and thus can be subtracted. A detailed Monte Carlo study is reportedly in progress [ZO]. M ore problematic is the background from the cascade decay of hott,om into strange with unlike sign pairs. This background also needs t.o be computed. At the lower end of the intermediate mass range the situation is even more complicated. The processes which contribute in heavy-ion collisions have probably not, been completely enumerat~cd yet,. NA3G has some new data which they will discuss in t,his meeting [31]. 2.4. The deconfined phase The continuum dimuon cross section in t,he deconfinctl pha,se is the signal for which the processes discussed in the previous subsections xe the ba.ckground. It is customary to comput,e this cross section in ~ligh-t,emperaturc perturbation theory. The Ja,tticc can furnish cross checks on this procedure. In recent years several studies of lattice QCD [22, S] 1iave furnished evidence that. the high t5empernture phase really c0nsist.s of &confined quarks. Thus the primary condition for perturbation theory seems LO bc valid&xt,he degrees of beedom are correctly idcnt~ified. However, t,here a.re indicat,ions that these clua.rks, under certain circuinstances, ha.ve A study [S] has clnrihrd this situation. For ma.ss scales fairly strong self-interactions. below the Debye screening mass, one could write an effective theory for t,he quarks in t,hc form

where I’ denotes a. direct. product, of spin a,nd flavour matrices, a.nd the sum is over t,hc whole set of such products. ‘I’hc ellipsis denote ncglcctrd terms of higher mass dimcnsiou. From lattice measurements ii, has been found IS] that, a~t,llo~lgll t.hc effect,ivc rouplings 9 in the scalar and pseudo-x&r channels are large, t,hose in the vector and pseudo-v&or channels are rather small alreatly a.t temperatures close to T,. Thus, t,his observat,ion implies that perturbative computations of dilepton and photon product,ion rates may he reliable quite close to the phase transition tempera.t.ure. A similiar compntat~iori iu unquenched QCD is now in progress. For 7’ < 1 .2T,, however, perturbation theory does break down. ‘I’his is reflected in the growth of all the effective couplings as one approxlirs 7: frorrr above. It may be possible to use lattice mea.surement.s to ofhili Lhe matrix elcirtent relevant t.o pltof.on or dilcpt~on cross sections. Such studies are planned.

73c

S. Guptu J Electromagnetic signals and backgrounds in heavy-ion collisions

3. The Resonances Beavy-quark resonances have been the subject of concerted study for the last five years. The situation is slowly being clarified; there is new and exciting data this year from the NR38 collaboration [‘23]. Lighter resonances have been studied in models for many years now, There is exciting news on these from recent lattice co~~l~utations. 3.1. Charmonium Based on lattice studies of the static inter-quark potenti& heavy-qua,rkonia have been suggested as a signal for screening. Sc.reening sets in at the QCD phase t~ransition and the screening length decreases with increasing T. Consequently, different resonances are suppressed to different extent under the same physical circumstances. This year’s result from NA38 [Z] s hows a strong ET-dependence t,o the relative suppression between the $’ and the J/g. The data is compat,ible with estimates given in 1241 as well as in 1251.

0.12

0

0.5

1

1.5

2

--

5.6

2.5

5.7

5.8

5.9

6

T/L

6.1

6.2

6.3 P

Figure 1. The temperature dependence of ($$), for quenched simulations with N, = 4 (filled circles) and S (squares) and from a 4-Aavour simulation with N, = 8 (open circles).

Figure 2. The temperature dependence of fT. Data for T = 0 (open circles) and at finit,e temperatures (filled circles) 7’ = 0.757:: (a = 5.9) and T w 0.9T, (a = 5.95).

3.2. The p meson Two recent studies of quenched lattice QCD have concentrated on hadronic properties for 0 < T < T,. One of these [S] wa.s done on N, ..- ? l., ” ices on very large spatial volumes, in progress [9] extends these computations to extending to (8/T)3, at OAT,. Work il.8 T,. In both these studies the values N, = 8 on spatial volumes of (4/T)3 of the quark condensate, ($$), p ion decay constant, fX, and t,he pion and p masses have been studied. The temperature dependence of these quantities is obtained by compa.rison with T = 0 mea,surements at the same lattice spacing. It is known that the quark condensate goes to zero with a discontinuit~y at T, in both the quenched [8, 91 and 4-flavour [ZS] theories. In Figure 1 we show the measured temperature dependence of ($$)(T)/($$)(O) (the T = 0 values are taken from [27]). Two features bear comment. First, note that the discontlrui,;; :I Z/ similiar ;n the two cases. Second, (~~}

seems to be relatively temperature

independent

up to T M 0.9TC-.

S. Gupta I Electromagnetic signals and backgrounds in heavy-ion collisions

74c

A non-vanishing The

physica.

ma =

quark

pion mass

condensate is obta.ined

implies

a vanishing

pion

mass

in the

chiral

limit.

from the relation

A,m,.

(3)

Here mq is the quark the temperature compared

mass.

to the values

to these

two facts,

T = 0.9T,. of [28].

Measurements

dependence

This

on the la.ttice,

decay

is explicitly 1 and

constant,

shown 2, mass

up to 0.9T,

&,

in Figure ra.tios

thus give information

Our mea.surements

at 7’ = 0 for tempera,tures

the pion

In Figures

of A,

of the pion mass.

shows

used

-0.01

0

3a).

with

on in A,

Consequent

temperature

upto

of [9] and the T = 0 data

the data

been

no change

(see Figure

no change

2, using

have

reveal

in order

to remove

0.01

0.03

most

lattice

effects. 0.4

-

-0.1

~

-0.01

I

I

I

/

I

I

!

0

0.01

0.02

0.03

0.04

0.05

0.06

0.02

0.04

0.05

m, Figure

3.

The

dependence

The

Measurements

a temperature

where

that

Within

there

emphasise

dependence

of the quark

condensate

sector say,

of the theory. the

of this

gluon

is usually other

so strong, information

data. This

a.ssumed.

Efforts

condensa.tes then

the

on vector

different

some

of these

to extract

the

of an universal

and pseudo-vector

spectrum the

Thus of study.

neglected.

condensates

mesons

t,heory

3b.

It is

at

sector

finite-temperatures

may not be justified.

temperature

is stronger

of at lea.st

of the glue

of,

interpretation

ha.ve strong

dependence

of

to the chiral

dependence

One which

and its

temperature

The vacuum

some invisible

the temperature

If the influence

chiral

at

at a temperature

theory. objects

often

temperature

masses

is discernible.

in Figure

a.lready

role for the glue sector

are now underway.

use

of the

models, other

a dynamical

no shift

visible

on the tem-

meson

of the hadron

condensates,

quantity,

compared

effect,.

is one of t,hc primary

phenomenological

imply

shift, occurs

models

aspects

is a secondary

is that

would

dependent

of the p meson

dependent,

in the vector in fact,

sees no temperature

by many

In most

condensate

lattice

dependence. these

is characterised

st,rongly

shift

of measurement,

chiral

(circles)

(p = 5.95).

t,o be quite

is very little

phenomenological

dependence

however,

spacing

temperature

of the theory that, most

temperature QCD,

seems

there

shift, in the mass

sector

be noted

mP on mq at, 1’ M 0.9T,

lattice

the errors

is a. large

a large

the chiral

It should

hand,

show that

of 0.75T,.

at, 0.9T,

However, interesting

at t,he same

of mp, 011 the other

value

perature.

m,

of (a) ma and (b)

at T = 0 (squares)

to data

0.06

than

a few of is indeed to obtain

S. Gupta I Electromagnetic signals and backgrounds in heavy-ion collisions

ISC

The variation of the vector meson mass with the quark mass mq is shown in Figure 3b at, a temperature T M O.QT,. For comparison the corresponding data for T = 0 at the same lattice spacing, ,!j’ = 5.95 [29], is also shown. It is seen that the magnitude of the thermal shift is dependent on mg. Thus, the maximum effect is seen for the F meson, somewhat less for the w and 4, and virtually none (a.t this temperature, at least) for any heavier meson. Of course, an accurate deterI~linat.ion of the mass shift of a state heavier than the inverse lattice spacing is difficult. It is interesting to speculate what the effect of differential shifts in the masses of the p, w and 4 mesons would be on an experiment like NA38 which cannot resolve these seperate peaks. An obvious effect would be to broaden this peak. Further phenomenology might be interesting.

4

6

8

10

12

14

16 z

4

6

0

10

12

14

16 2.

Figure 4.

Local masses for the (a) pseudoscalar and (b) vector mesons at, T M 0.9T, (/3 = 5.95) for m4 = 0.05 (filled circles), 0.025 (squares) ancl 0.01 (open circles). The estimates and errors are obtained by jack-knife. The lines a,re explained in the text.

We conclude this section with some technical remarks. The masses reported here were extracted by global fits t,o vector and pseudoscalar correlation functions constructed from local sources. The well-known oscillatory behaviour in the vector channel was suppressed by the usual stratagem of defining a correlation function on even sites G(2.z)

=

;[G(Zz

- 1) + 2G(2z) $ G(2z + l)].

(3)

Local masses were extracted assuming that this correlation function can be described by one mass, i.e., by a single hyperbolic cosine. The global fits were made to a two-mass functional form by minimising a x2 functional which took into account the covariance An useful cross check is to use the fitt,ed of the measurements at different seperations. function to then extract ‘local masses’ to compare with the direct measurement. Such a comparison then checks the validity of the global fits. Example are given in Figure 4. Acknowledgements: I would like to thank Ii. Eskola, R. Ciavai, S. Gavin, ii\. Irback, F. Karsch, B. Petersson, V. Ruuskanen, H. Satz, K. Sridhar and R. Vogt for the discussions and/or colla,borations, the results of which are reflected in this t,alk.

S. Gupta I Electromagnetic

76C

signals and backgrounds in heavy-ion collisions

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