Structure of the QCD vacuum and excited hadronic matter

377c

Nuclear Physics A522 (1991) 377c-396~ North-Holland, Amsterdam

STRUCTURE

E.V.

OF THE

QCD

VACUUM

AND EXCITED

MATTER

Shuryak

Physics

Department,

Brookhaven

National

Laboratory,

This talk describes the latest development as in theoretical and experimental efforts quark-gluon

1.

HADRONIC

plasma

phase

by means

Upton,

New York

11973

in the theory of the QCD vacuum, as well to study its “melting” into the so-called

of high energy

collisions

of hadrons

and nuclei.

INTRODUCTION This

excited

talk includes hadronic

concerning

matter.

the topic

what we meant the coming moment

two large subjects: Before

one.

Strong

If one is interested journal

with

Planck

scale,

is assumed

this

decades

in the definition

of nuclear

i t includes

Although

physics,

papers

1 GeV. This definition

misleading:

interactions,

In the latter,

the period

toward

QCD

with

is that

changed

during

community

is at the

was observed, at these

the

keV

to

physics

lo-20

years

but now this dividing which

are becoming

splitting

between

line now

of people. one observes

typical

TeV

scale,

in hard

physics,

that

clear

and physics

and now the interests

physics.

from

and high energy

energies

works

nuclear

energies

consult

was indeed meaningful

QCD”

well,

with

nuclear

of “testing

the non-perturbative

here we find overlap

groups

community

with their

really

remarks

main point

he would probably

between

activity

it is exactly

different

in high energy

of electroweak

Perturbative

boundary

at this scale not so great

precisely,

Their

physics

dealing

about

for many

of highly

in this field.

to be somewhere

point

in 1990’s.

with a part of high energy

that

the focusing

and physics

is to be significantly

there,

completely

vacuum

let me make some general

Physics

it is explained

ago, when indeed

More

trends

Nuclear

in previous

convergence

name.

is becoming

shifted

physics

one of the main

of the QCD

we begin their discussion,

of this conference,

by nuclear

theory

processes

cases

seems

to come

of people

is, to 0.1-l

In some

of strong

GeV

are more

energy

it is so strong,

scale. that

physics

interaction. to the end. and more Certainly it becomes

This manuscript has been authored under contract number DE-AC02-76CH00016 with the U.S. Department of Energy. Accordingly, the U.S. Government retains a non-exclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others

to do so, for U.S.

Government

purposes.

03759474/91/$03.50 @ 1991 - Elsevier Science Publishers B.V. (North-Holland)

378~

E. K Shwyak / QCD vacuum and ercited hadmnic matter

completely

impossible

distributed

between

a completely

to say where Nuclear

illogical

works

Physics

should

be published.

As a result,

A and B ( as well as between

way, representing

author

background

Phys.

papers

Rev.

and position

are

C and D) in

rather

than

paper

cant ent . Scientific

communities

of different

problems.

Let me enumerate

specialised

conferences

1. traditional nuclei,

nuclear

working

excited

easy task,

heavy

systems,

common

interaction

between

so vast Starting

as QED

understand

physics

(section

breaking

the last

vacuum, few years

systems

both

spiration

of this

activity

high energy imental additional

density,

remarks

Then

come

plasma

reasons,

is logically

interaction

own

much

in the 1990’s,

making

lattice

I describe phase

to recent

the so-called

attention

quark-gluon

in the previous

of &CD”.

It is not an

speaking,

complete

(even

strong).

QCD

is the

celebrated

QED

I hope that

strong

and finally

QCD

the content

of this talk.

to concentrate

current

status

transition. progress

will play the same

ideas leading

I briefly

discuss

plasma

talk by Prof.

attempts

to

the latest

of new phase

lattice

symmetry

(section

of high

at high energies’.

(QGP)2.

of

chiral

at high temperature

manifestation

to studies

of the theoretical

in understanding

collisions

Considering

on a few new points.

was paid to production

to possible

large

one.

and have

and nuclear

was related

on them.

in

etc.

strictly

becomes

as well as its restoration

in hadronic

side are discussed

modification

for macroscopically

side, I first have tried to summarize

and then

hadronic

those

as “understanding

I would like to outline

of the corresponding

in the QCD

During

with their

in 1 GeV region.

looking

from other

where

be systematic

systems.

2),

nucleon

in particular

plays in the atomic

the introduction,

excited

forces,

into quark-gluon

which

will be fruitful

from the theoretical

macroscopic

results

field theories

I cannot

&CD,

community,

Apart

distances,

them

physics

subjects,

of people,

related

etc.;

can be formulated

be done.

at very small

on nuclear

and reactions

transition

aim, in short,

is deficient

Completing

hundreds

on very closely

experimentdists”);

ion collision

of quantum

role in nuclear

spectroscopy

phase

but it should

only example

matter

on nonperturbative

(“numerical

energy

(all include

working

of dense nuclear

calculations

Their

physicists,

doing hadronic

3. theorists

4. high

some of them

are now focused

etc.):

theory

2. people

backgrounds

3).

multiplicity

The

main

in-

of matter

at

Most news from the exper-

S. Nagamiya

so I make only short

379c

E. V. Shuryak / QCD vacuum and excited hadronic matter

Ironically attention

enough, hot hadronic

matter

(consisting

mainly

of pions) has attracted

little

in the past, and it was in most cases assumed to be just an ideal pion gas. Only

recently

it was realised, that it is more like some liquid, in which strong (momentum

dent) interaction

plays an important

is the existence surface.

of attractive

interaction

between its constituents,

This, in turn, makes it more difficult

present theoretical

and experimental

under consideration. soft puzzles”,

2. MELTING The

motto

which creates a kind of a

for the constituents

indications

to leave the system.

observed

OF THE

QCD

can explain

“three

in various reactions.

VACUUM

of this conference

does not contribute

We

that this is also true for the “pion liquid”

In section 5 we show, that these ideas presumably

recently

depen-

role. The main difference between any liquid and a gas

is “beauty

much to it. However,

even more in the spirit of Japan): above,

that the ultimate

Where

then have we to start from?

of the nucleus”,

but unfortunately

let me suggest a similar motto

“beauty

of the vacuum”.

aim of all strong interaction Certainly,

Indeed,

my talk

(which

I hope is

we have emphasised

physics is “understanding

of &CD”.

with the ground state, as we do for any other

quantum system. Even the ground state of QCD is a complicated quark fields. collective

Pions,

nucleons and all other low mass hadrons

excitations,

similar,

understanding

theory of their interaction

matter

spectroscopy

and scatterings.

them to temperatures

of the order of 200 MeV vacuum themself

else but their Certainly,

etc., but we cannot understand

solids from the very beginning,

comparable

we would hardly

The simpler way is, say, try to heat the

and see what other phases can be created.

nuclei exciting

gluonic and

of what solids (or nuclei) are made of.

Going further, if we want to understand start with phonon

are nothing

say, to phonons in solids (or nuclear vibrations).

we may make successful effective them without

matter, made of fluctuating

Analogously,

one may try to destroy

to nuclear binding energy.

Moreover,

(or, more precisely, energy densities few GeV/fm3)

which starts to be melted.

This phenomenon

at 2’

it is the QCD

is the central topic of the

present talk. Now I come to discussion of the latest lattice results concerning phase transitions temperature.

Certainly

are their technical comment

I am not able to discuss here how lattice calculations

limitations

that these “numerical

etc., or show many particular experiments”

at high

are made, what

results obtained.

Let me only

are rapidly reaching the level of ordinary

high

E.V. Shutyak j QCD vacuum and excited hadrtmic matter

38Oc energy experiments,

in terms of big and well organ&d

collaborations,

cost of the projects,

etc. Let me concentrate less answered recently.

on the following physical questions, which, I hope, are more or In the QCD vacuum we have two non-perturbative

confinement and cbiral symmetry breaking.

phenomena,

Are they related or not? Or, in more definite

way, are there two independent phase transitions on the phase diagram with different physics, or just one? T


tot4slo>

massive

0

states

Cl.1 % Figure 1: (a) Schematic phase diagram of hadronic matter for Nf > 2 on the plot quark mass m versus temperature. (b) Quark condensate versus temperature according to’.

Impressive amount of numerical studies done during the Iast few years has shown that the former alternative seems to be case. The resulting picture can be described as follows. Let all our Nf quarks have the same mass m, so we may plot simple phase diagram on the temperature-mass

plane, see Fig. l(a).

Roughly speaking, there are three different worlds,

with completely different features of the phase transition.

“Gluonic world” at the right has

only heavy quarks (m above 1 GeV, as if all quarks are charmed). strong first order deconflnement

transition.

It was shown to have

This means that the jump in energy density

Se = ep1asma- Eh&ronieis very large, actually several times more than eh&ronic by itself. Another extreme is the world of light quarks at the left. At zero mass we have chiral symmetry, which is to be discussed below in more details. Here there appears to be another strong first order transition

connected with chiral symmetry restoration3.

It is seen till

E.?! Shwyak f QCD vacuum and exited hadronic mutter mass is approximately

381~

100 MeV for Nf = 3,4..., while for NJC= 2 the transition is not

that strong and may be second order. If two masses are light and that of strange quark is changed, the last first order signal also disappears somewhere at m, = 100 MeV. (Is there deconfinement in this transition or not, one unfortunately cannot even ask in the rne~il~~~ way.) In the middle of Fig. l(a) there is the “intermediate mass world”, which attracted most attention and computer power during the last year, including e.g. “homemade” 16 Gigaflop 256 processor complex* at Columbia University. The resulting conclusion is actually the main news: no strong first order transition is seen here.

Thus, it is demonstrated that

deeonfinement and third restoration transitions do not even cross each other at our phase diagram.

~spectively,

the old idea that they are indeed two different phenomena has

obtained new support. The real world certainly corresponds to the light quark world, for u, d quarks have very small masses, of the order of few MeV only.

Also m, = 150 MeV is somewhere at the

threshold of the light quark region, so in QCD &Jf = 2.5 in some sense.

(Remarkably

enough, it seems to be close to the end of the transition line.) Now, at high energy collisions we are therefore iooking for chiral symmetry restoration. Unfortunately, it turns out to be very difficult to get some deep understanding based on lattice data concerning the underlying mechanism of these phase transitions (we discuss why it is so below) . Therefore, in the next section I switch to another approach, the theory of instantons.

3. RECENT PROGRESS IN WNDERSTA~DING BREAKING

OF CHIRAL SYMMETRY

AND RESTORATION

The classical papers from the early 60’s on the so--called sigma models, have considered pion and sigma fields and have explained how the latter obtains non-zero expectation value and the former becomes massless. Later Weinberg6 derived his famous Lagrangian, describing low energy pion interactions. This approach was used for hadronic matter, and in order to show that it is indeed fruitful let me present e.g. Fig. l(b) from recent paper7, where effect of the pion gas on the quark condensate was calculated using this interaction. in chiral perturbation theory. These results are very general and hold for small T/F= ratio, where F, = 93 MeV is the pion decay constant. However, the real understanding of physics of chiral symmetry restoration can only be reached if we consider the problem at the more fundamental level, starting from quarks Bnd

gluons. But in order to explain ah that, I have to come for a while into some discussion of the formalism involved. For example, s~ont~eous

magnetization

of iron is usu~ly discussed by the fo~iowing

sequence of steps. Due to rotational invariance, all states should be classified to total spin J.

Bowever, large systems may have such close levels with different J, that even infinitely

small magnetic field H can mix them up and create a (rotationally non-invariant)

state with

fixed orientation. Chiral symmetry is a consequence of the fact that in massless theory with vector interaction,

right and ieft-h~ded

quark fields are completely independent, so that di~ere~t

rotations can be made for them in flavor space, The quark mass m plays, in this problem, the same role as small magnetic field in the example above: it breaks the chiral symmetry and relates otherwise independent right and Ieft-handed

quarks. The question is again

whether it can produce the asymmetric vacuum, even for i&nitely

smd1 m.

The formalism used naw is somewhat different, so we have to explain at least the terminology. space-time,

Suppose we take the given ~o~gurat~on

usuahy in the so-called Euclidean (imaginary)

to average over all its possible indurations tion.)

of the gauge field Am,

where z is

time formalism. (Later we have

of the gauge field with the proper weight func-

Trying to understand quark behaviour in this case we may try to diagonal&e the

so-called Dirac operator ~~~(~)

= X$x(r)

where 6 = ~~fi8, +gA~(~)~a)

(Note that in Eu-

clidean time formalism there is no distinction between space and time coordinates.) call the states $x(s)

“the states with fixed virtuality” A. Using them one can easily compute

the quark propagator S = (B + QCD statistics

Let me

sum proportions

im)-r , or the weight of this gauge field configuration in the to detffi + in~)~f which comes from the integration over

all quark fields. Now, the nontrivial m -+ 5 limit (indicating third symmetry breaking) can exist only if there exist quark states with arbitrary small virtuality. In particular, one can see it from the following expression for the quark condensate:

(d$> = CA m/(X2 i- m2) which just fohows

from its definition as trace of the propagators taken at zero distance and averaged over all points. In the Iimit~m -+ 0 we get in the r.h.s. the density of eigenvaIues at zero. (Unfortunately,

it is exactly these small ~ge~v~ues

which are very di~cuit

to get 0x1

the lattice, due to finite size effects and other technical problems. Due to that, most lattice works are done for rather large quark masses, say 50 IvIeV or so. It is physically import~t~ say, the pion mass is in this ease about 500 MeV!)

383~

E. K Shuryak j QCD vacuum and excited hadrmic matter

_._ ..--.+

’ INSTANTON G$v=O &=O A;=0 A$#0 _-_--____ __““-----

(b)

0)

__“______

____-____

(cl

--_rx~~-L~-~~_--ErO ~ -

~ -

Figure 2: Schematic picture of the gluon field energy versus topological coordinate, Instanton is tunneling from one zero energy state to another, which is connected with rearrangements of occupations of light fermion states near the surface of the “Dirac sea”. Thus instanton can be considered as vertex emitting pairs of light quarksg.

Figure 3: Three possible phases of the instanton ensemble in the QCD vacuum: crystal, liquid and gas.

Now, what is the physical nature of these ““quark states -with zero virtuality”?

Do they

really correspond to some real process ? Can we understand their physics in the simpler way, without real evaluation of all eigenvalues for many gauge field configurations, as lattice people try to do? I hope the answer is “yes” and the reason for that is that we know specific types of gauge field configurations, instantons8.

which provide such small eigenvdues:

these are instantons

and anti-

Certainly I cannot now go into discussion of what they are, but only mention

that they describe tunneling from, say, naive classical vacuum A:(z)

= 0 to another one,

in which the field strength Gj&, is also zero, but the potential is non-zero and cannot be obtained from it by continuous gauge transformation.

Schematic picture is shown in Fig. 2.

If there are massbss fermions in the theory, instantons drive the axial anomaly. Physically it means, that tunneling does not change fermion states, but change their occupations, as shown in the lower part of Fig. 2. Thercfore, each instanton can be considered9 as the vertex with 2Nf fermionic lines. Chirality of quarks and anti-quarks cannot close them in loops in the massless theory.

are opposite, so one

Quarks and anti-quarks

the tunneling event shouId be absorbed elsewhere, for example by anti-instanton tunneling event).

produced by (backwaxd

384c

E. V. Shuryak / QCD vacuum and excited hadronic matter

Using this language made of instantons, a kind of a “crystal” symmetries.

one may say, that the QCD

connected

clusters (e.g.,

very small “virtualities”

breaking

of translational

(see Fig. 3b) in which all instantons are effectively

breaking of the chiral symmetry.

instanton-

is some complicated

anti-instanton

pairs, or molecules)

are there and therefore

from phenomenological

“instanton

we passed to developed

of the corresponding

statistical

correspondence

quantitative

sum12113. Results

remains unbroken.

to be in the liquid phase, breaking of the needed magnitude.

Further,

shown to break into separate molecules

theory based on computer

of

studies

are in remarkable

vacuum was indeed shown

and producing

T > T, (above

quark condensate

200 MeV)

(see Ref. 14) and chiral symmetry

Figure 4: Ratio of the correlation

was really

and simple approximations

The QCD

the chiral symmetry at temperatures

instantons

of these calculations

to what we observe in the reai world.

connected,

(see Fig. 3c), no states with

chiral symmetry

liquid model”‘e

the mean field type”

If it is

and color

Finally, if it is a “gas” made of finite

During the last few years the progress in the theory of interacting decisive:

matter

by quark lines. The question is what is its structure.

(see Fig. 3a), we get spontaneous

If it is a “liquid”

we have spontaneous

vacuum

this liquid is

becomes restored.

functions of currents with quantum num-

bers of corresponding mesons to those, corresponding to free quark propagation, versus the distance x between the currents. The points are from the instanton liquid calculation’“.

38%

E. K Shuyak / QCD vacuum and excited hmhnic matter

Moreover, mesonic correlation functions with different quantum numbers were recently calculatedr5.

They show different behaviour depending on quantum numbers (see Fig. 4 ).

The curve going up for pion means that it is light, while that for scalar channel going down means scalars are all heavy. Certainly here I cannot discuss details here, so I can only say that these curves agree with experiment,

sometimes with surprising accuracy . In many

respects, this theory works better than available lattice calculations (for which in principle all configurations

not only superpositions

of instantons)

are included, and it is orders of

magnitude simpler.

4. LOOKING

FOR QUA~I~-GLUON

PLASMA

The idea “to melt the &CD vacuum” is of course very attractive,

but many practical

questions can be asked, say, whether one csn really produce macroscopically in laboratory

large system

conditions, whether it may indeed become well thermalized, etc.

Addressing the former issue, let us say that now in CERN nuclear collision experiments with 0’6 and S3” beams up to several hundreds of pions are produced, and this number will be at least one order of magnitude larger for Pb beam to appear soon. This large “fireball” comes through diRerent stages of its evolution, with energy densities varying from l-3 GeV/fm3 at the beginning to those one order of magnitude smaller, at which final break-up into noninteracting

secondaries takes place. Pion interferometry

the breakup is about 7-10

tells us that the radius at

fm, so it is already larger than radii of the heaviest nuclei.

Let me also emphasize, that data for nuclear collisions are now s~~~plemented by those from Tevatron specialised experimentr6, (CM) energy proton-antiproton

triggering for high multiplicity events in 1.8 TeV

collisions. The corresponding energy density is of the order

of 10 GeV/fm3, but the system is of course not large (although they still has up to about 20 particles per unit rapidity). Transverse hydrodynamical collective phenomena. phase transition

flow was for a long time considered as the most obvious

However, it was emphasized long agoI

that as one approaches the

region, the equation of state becomes very “soft”, which means that by

increasing the energy density we do not increase pressure much.

This statement

is most

obvious for the so-called mixed phase, for which pressure is unchanged at all, but softness is more general prediction independent on the details of the phase tra,nsition. Only when the initial energy density becomes significantly larger than the critical one (above few GeV/fm3) some collective flow of quark-gluon plasma was predicted.

1.0

0

LN A

dy

x PIONS o KAONS q ANTIPROTONS

5

15

10

20

B! dv

Figure 5: Mean transverse momenta of various secondaries versus ~AT/~~ (e&ctive energy density). (a) Hydrodynamics with phase tra.nsition’*; (b) FNAL data16. Detailed calculations in the hydra framework l8 have indeed suggested existence of some plateau in the < pt > versus dlVJdy plot (see Fig+ 5a). Such “plateau” was indeed observed by CERN experiments: the mean it is about the same, whatever number of secondaries is produced. But new Tevatron data are different (see Fig. 5b). As predicted, the rise is most pronounced in heavy secondaries, which is consistent with transverse Aow interpretation Let me now show the shape of mt = (m2 + pt2) r/z distributions for different secondaries, measured at CERN”g, Fig, 6a. Note that all of them have the same slope, which is 200 MeV. Nothing like that is seen neither at lower energies (AGS) nor at larger ones (Tevatron), wbere different secondaries have different slopes (see e.g. Fig. 5e again). I think here we see the m~ifestatio~

first

of the “‘mixed” phase, and the slope is nothing else but the critical temperature

T,, although many more studies are needed to make this statement really convincing+

150

225

300

T (MeV)

Figure 6: {a) Transverse mass spectra for various types of secondaries for SS collisions, NA35 ~OIlaboration. (b) Temperature profile function F(T) versus temperature (for comparison, each spectrum is normalized to one). The open and closed points correspond to WA80 and KELIOS data for reactions indicated, while stars represent pp data from ISR. Note now the concave shape of the pion md distribution at small ps: naively speaking this may lead to slopes as small as 50 MeV. Does it mean that so cold pion gas is indeed created? This point of view is not acceptable because of the following reasons: (if Breakup temperatures lower or about 100 MeV contradict our knowledge of the pion gas kinetics (see below): in this case practically no collisions between pions may take place. {ii) Even if some unknown mechanism can cool the pion system to lower temperatures, we then should observe the size of the emitting system to be essentially larger than 7-8 fm, measured by i~te~eromet~.

Thus, we have the so-called “soft pion puzzle” (to which we return later).

Let me now come to other topics, which are believed to be much better signals for quarkgluon plasma formation. The first idea’ was to use photons and lepton pairs because they are the “penetrating probes” without secondary interactions. Also their production rate in plasma phase is believed to be relatively easy to estimate. Unfort,unately, so far there is no data on direct photons in the kinematical region of interest, and the existing dilepton data from the NA38 collabora.tion at CERN are not yet completely analyzed.

388c

E. K SMyak

/ QCD VUCUU~and excited ha&&c

However, the NA38 experiment

matter

looking for dileptons have produced other surprising

data21, concerning production of vector mesons, especially 4, J/$.

The former is found

to be enhanced by the factor 3 in central nuclear collisions compared to f?p or peripheral collisions, while the latter is by the factor 2 suppressed. In first approximation this different behaviour can be understood from the fact that strange quarks are copiously produced in the plasma, while charmed ones are too heavy for this to be the case, and they a,re produced only in the initial hard collisions of gluons. Now there are strong debates on the exact origin of relative suppression of J/$ compared to dileptons with similar masses.

It may be due to charmed quark deconfinement in the

plasma (as suggested originally in Ref. 22)1 or due to J/$J splitting in hot hadronic matter23, or initial stage interaction

of colliding gluons in nuclei 24. The last idea got support from

recent FNAL experiment, where similar suppression in pA relative to np data wrasobserved. One may, in principle, use more information to understand all that. In particular, Karsch and Petronzio25 have suggested that J/$ can jump out of the “hot spot” if its pt is large enough. And indeed, at pt > 2 GeV this suppression disappears, and they concluded from it that the size of the spot is only1-Z fm, while if we assume strong suppression at the hadronic stage as well, we expect much larger size (remember, by interferometry beams.

size at breakup measured

is about 8 fm). Certainly, much will be clarified by experiments with Pb

In this case we certainly have much larger size of the system, even at the hottest

stage. If the Karsch-Petronzio

idea is right, suppression should be seen up to much higher

pb in this case. If the reason for more J/$ at larger pt is “initial stage res~attering” of the gluons, we will see no change while coming from #I6 to Pb beams.

5. NEWS ABOUT

NOT HADRONIC MATTER

The topic of this section is the closest one to nuclear physics of this talk: we consider a pion gas, with density of the order of that in nuclear matter. and with different (and quite specific) interaction. systems.

Of course, pions are bosons,

Also we do not of course have stable

On the other hand, high energy nuclear collisions produce hundreds (and soon

thousands) of pions, so these pionic systems can be much larger than even the heaviest nuclei. Our discussion below develops into two different directions. review of the theory, and here we introduce qu~iparti~les

The first one is a brief

with pion quantum number, the

“qnasipions”, following t,he experience of low temperature physics, especially that of liquid He*. Another part of this section is an attempt to explain few unexpected phenomena observed recently in various high energy reactions.

Their list includes in reticular:

‘I. enhanced production of pions at small pi found in nuclear collisions”“; 2. enhanced prod~lction of soft photons and low-mass dileptons in various hadronic reactions27; 3. an unexpectedly sharp two-pion annihilation threshold seen in the dilepton spectra at Berkeley28; 4. strong clustering of pions, produced in various hadronic reactions. Let us start with some general remarks about pions. are the lightest hadrons, so that if temperature

They are special because they

T is small enough, only pions are excited.

This fact is not occasional, but related to the specific nature of pions. In the chiral world they are massless, exactly for the same reason as e.g. acoustical phonons in solids: they are Goldstone modes, a remnant of the spontaneously

broken symmetry.

(Translational

symmetry for solids, chiral one for the QCD vacuum.) At small T the mean interparticle ideal gas approach is justified.

distances are large, l/T, so interaction is small and

Also discussion of massless pions makes the problem simpler,

so we start with this case. At small temperatures we get then simple formula for the energy density e(T) = (~z/~~)~4 Interaction

of pions is also quite specific and related to their Goldstone nature.

In the

chira1 world, pions with momenta Ic + 0 cannot interact with anything including themselves. (Exactly

because of this feature acoustical phonons propagate distances much larger than

molecule free paths, therefore we can hear each other.)

This feature makes this gas even

more ideal at small 2’. Accounting for momentums-dependent bation theory, considering T/F,

pion-pion interaction, one can use chiral pertur-

as a small parameter, while at so~s~~hat larger T one has

to include resonances. We summarized results on energy density in Fig. 7a, where e(T)/T4 is plotted versus T. For the ideal gas this ra.tin is close to one, until ~nteractior~ of pions makes some modifications

(see the dotted line). Much more dramatic things happen if one takes

into account nonzero pion mass and, even more important, becomes much more temperature-dependent

hadronic resonances.

The ratio

(see the solid line in Fig. ‘?a). We also show

simple paramete~zat~on

for the ~‘pion+reson~ces”

ago2*: e(T) = T”/T;,To

= 1~~~~~ wh’ICh is shown by the dashed line. One can see that

suggested by the author many years

E. JX Shutyak / QCD vacuum and excited hadronic matter

390~

: 1.5 -

j/+----

-e ‘,

1.0

I._Ix__.. -_/: .i’ / I : :

0.5 -

A

;/’

: ,,*’

~i .‘,’

,J

, 50

1W

150

m

T(MdY)

K/m,

Figure 7’: (a) Ratio of the energy density of excited hadronic matter e(T) to T4, versus temperature 2’. The dotted, dash-dotted and solid line are from3’ for interacting massless pions, massive pions and pions together with resonances, respectively. The dashed curve corresponds to par~etrisation~‘. (b) Qualitative picture of the modification of the pion dispersion curve in hot “pion liquid”. The “quasipion” with internal momentum corresponding to point A moves to point B as it goes out of the system. it approximately describes the energy density dependence on temperature over the whole interval. Summarising, above T around 100 MeV or so, corrections to the ideal pion gas energy become large. Now we come to kinetics in the pion matter. Again Goldstone nature of the pion plays an important role: apart from small effects related with scattering lengths, the r?r cross section is essentially proportional to pion momenta. Therefore mean time between collisions depend on T as follows2Q: rCOll= constF:/T”.

Goity and Leutwyler have recently made extensive

calculations3o supporting this expression and getting more accurate const=12. Note, that at ‘I’ = 200 MeV rC-,ais smali, .7 fm/c, b ut at our other extreme T = 100 MeV it is already about 25 fm/c, comparable to the lifetime of even the largest fireballs considered. Another useful way to look at rc-,nis to compare its inverse, the imaginary part of the pion energy Im E, = l/rc,ll, with its real part. The corresponding ratio can be estimated as follows Im E,f Re E, = .03(TfF,)4

It is still only about .1 at T = 140 MeV, but it is of

391c

E. K Shuyak / QCD vacuum and excited hudronic matter

the order I at Tc = 200 MeV.

Therefore,

in the former case the pions are still propagating

rather well, while in the latter case they are strongly

absorbed.

Now we come to the central point of this section: matter,

but they interact

The main pion-pion potential modes.

interaction

is proportional

should grow with momentum Let us mention

strongly

with many particles

modified

directly

to pion momenta

examples

curve of elementary

by neutron scattering by Landau

respectively,

minimum

excitations

experiments.

curve is

is developed. in liquid He*, measured

Note the secondary minimum

and called the “roton”

minimum.

for phonon non-linear

interactions,

this curve, with accounting

our collective

of cases in which the dispersion

at larger L, so that even secondary

was suggested

in hot

and change their properties.

as well. Such a situation is common for all Goldstone

two well-known

1, The famous dispersion

pions are not only scattered

simultaneously

Modern

which

theory

of

can be found e.g.

in Ref. 31. 2. In Fig. 3 we show the pion dispersion ated theoretically (With

increasing

energy

Migdal

evalu-

(see e.g. Ref. 32 and references therein).

nuclear density,

modification

may reach zero at some critical

rearrangement

curve in cold dense nuclear matter,

and spontaneous

pion condensation.

of pions may become

momentum

production

&.

so strong

that their

If so, it should lead to vacuum

of the pion field. This phenomenon

We are not going to discuss here whether

is known as

these calculations

are

reliable or not at such high densities.) The

expected

qualitative

behaviour

“pseudopotential”

is slightly

repulsive

of the dispersion

curve is shown in Fig.

at small momenta

but becomes

attractive

7b:

the

at larger

ones. We do not want to have many free parameters,

so we do not speculate

secondary

for the modified pion dispersion curve

w(k)

minima and assume simple parametrisation

= (m;

+ u(T)%~)‘/~

m t ro d ucing the temperature-dependent

It is close to one till about T = 150A4eV, Now we return to “soft pion puzzle”, nuclear collisions Goldstone

theorem,

Therefore,

pion interactions

spectra

compared

slope parameter

u(T).

and then rapidly decreases. or enhancement

to pp, or peripheral

in any type of kinetic

the experimental opposite

compared

about possible

of soft pion production

collisions.

It is puzzling

in central

because,

due to

should be small for soft pions for all types of processes.

calculations

one might

to the thermal

expect

at low momenta

ones, while experiments

a dip in

show quite the

trend!

However, quantitative

pion modification explanation

phenomenon

discussed above can provide

of the soft pion component

at least a semi-

at small pt (see Fig. 8a).

Climbing

392c

2.6 i

2.4 2.2 2.0 1.8 1.6 R 1.4

t

1.2

t

1.0 0.8 0.6 0.4 0.2 0

1.6 0.8 Pt (GeVlc)

2.4

"0

200

400

600

Pt (MeV)

Figure 8: (a) The ratio of the pt spectra of X-Oin central and peripheral OW collisions (WA80) (points), while the shaded area is the ratio of x- HELIOS spectra for SS collisions to pp ones. (b) The ratio of the spectra calculated in the quasipion model with and without modification of the dispersion curve. out of the attractive potential well, the outgoing pion reduce its momenta (see Fig. 7b). If the dispersion curve is flat at low momenta, rather large phase space in terms of internal momenta corresponds to soft outgoing pions. It leads to very effective production of nearly stopping pions33(see Fig. 8b), which seems to explain the data. Another consequence of the pion modification is that some of them are reflected from the boundary which presumably makes the system lifetime longer. The second striking phenomenon observed in high energy collisions during the last years is observation27 of an excess of the produced soft photons over the theoretical expectations (see Fig, 9). The reason this is disturbing is that emission of the soft photons is described by the classicai electrodynamics,

which demands the simple bremsstrahlung

to be the main

effect, provided photon energies w are small compared to inverse lifetime of the radiating system. Attempts to describe these data in conventional models of the collisions has failed, (see e.g. Ref. 34) in which the Lund version of the string model was used. The results obtained

E. K Shutyak / QCD vacuum and excited hadronic matter

I N,

393c

= 400

I N, = 400 I N,=

10

I

1000

100

10

Pt( MeV1 Figure 9:

The ratio of the observed

photon

yield

to bremsstrahhmg

pre-

dictions, versus p\t. The dashed area shows predictions of the Lund mode134, while solid and dashed curves are for the quasipion model with and without pion modificat ion33.

with such space-time momenta,

picture more or less reproduce

production

was evaluated

in the “quasipion”

shown in Fig. 9 show indeed much stronger in the Lund model.

cancellation

final scattering Comparing

observe

that at intermediate

of scattering

describe

observed

experimental

contribution,

than, say,

several times

photon momenta

there

and at low w all but the

between

the coherent

seems that we can naturally

data shown in Fig.

excess for low pt < 30 MeV

effects of the pion modification

region

Recently,

from the b~msstrahlun~

becomes irrelevant.

cannot

transition

Interesting,

in the amplitude

these results with

strong

deviations

model in Ref. 33. The results

The main reason for that is that pions are rescattered

before they come out of the system.

definitely

in wide range of

up to those of the order of few hundreds MeV (see the shaded region in Fig. 9).

Soft photon

partial

low energy theorem

on the photon

and incoherent

regimes

9, one notes that we

or so.

However,

we do

radiation,

especially

in the

of radiation.

Moreover,

it

explain the data shown by solid points in Fig. 9).

first dilepton experiments

at Berkeley2* have studied the lepton pair production

at energies as low as 4.9 GeV for proton-nucleus

and about 1 GeV/N

in Ca Ca collisions.

The data are well described by known sources except for the peak above two pion mass. One may think about n+rr-

annihilation,

and in fact s-dependence

of this peak is consistent with

E. K Shutyak / QCD vacuum and excited hudrmic matter

394c

that for pion pair production.

However, attempts

to ascribe it to pion annihilation meet

certain problems. First of $11, production of two soft pions is suppressed by smallness of the phase space.

Second, the annihilation of soft pions into a virtual photon is suppressed at

threshold because it takes place in the P wave. Let us emphasize that conditions of this experiment

are quite different from nuclear

collisions at CERN. There are no hundreds of pions in a fireball, but just one pair of them. However, kinematics are now such that pions are produced snd ~nj~lated

in nuclear matter,

Gale and Kapusta 32 have used this fact, suggesting that pion dispersion curve is modified so strongly in the compressed nuclear matter, that secondary ~nimum

in w(k) is developed. If

so, annihilation of two “quasipions” leads to a peak in the dilepton spectrum, corresponding to the diiepton mass equal to twice the minimum value of w(k). with the double-pion

It may well be mixed

threshold, and now there is no suppression mentioned above because

momentum is now far from zero value. It may we11be that the peak seen in these experiments is indeed of this nature.

6. SUMMARY 1. Latest results of numerical experiments with lattice gauge theory have shown that deconfinement

transition

is strong first order, but it exists only in the

“Lgluonic worid” , or for quark masses roughly above 1 GeV. For small masses (and for real &CD) chiral symmetry restoration is the main phenomenon, strong f&t-order

Again

transition seems to take place between hadronic gas and quark-

gluon plasma. However, in the inte~ediate

mass region (roughly 0.1-1 GeV) no

first order phase transition is seen, which means that deconfinement and chiral restoration are in fact two different phenomena. 2. Much progress was made in understanding of chiral symmetry breaking in the QCD vacuum and its restoration interacting instantons. gas transition,

at high temperatures

based on the theory of

The phase transition is understood as liquid - molecular

with some details in striking correlation to what people see OR

the lattice. In particular, it explains why at such small quark masses as 50-100 MeV one finds strong changes of the chiral symmetry physics. Also the theory of inst~tons

proved to be very effective in predicting properties of mesonic

correlation functions.

E. V; Shwyak / QCD vacutun ad

excited hadronk matter

395c

3. Various high energy collisions are now used fur search of the superdense hadronic matter. There is evidence that for energy density of the order of 1-3

GeV/fm3

the equation of state is soft, which is expected near the phase transition.

At

larger energy density some collective flow may be observed at Tevatron. Maybe we have some first evidence for appearance of the “mixed phase’* from CERN experiments.

Suppression of J/d

and enhancement of Q; found by NA38 ex-

periment in GERN are discussed at various angles. Let me finish this section, reminding you once more of the long-standing statement: looking for dileptons with pt (or invariant masses M) about 14

GeV we probabiy have a chance

to see dileptons produced in the plasma phase, above hadronic production and Drell-Yan contribution. 4. Hadronic matter at ‘I’ = 100 - 200 MeV is not an ideal pion gas, but rather a liquid in which strong attractive interaction between pions is important.

In

particular, it modifies the pion dispersion curve. Also, it makes it difficult for the pion to leave the system, and presumably explains the excess of soft pions observed in CERN nuclear collisions. Other “soft puzzles” also can be related to these phenomena. REFERENCES 1.

Proceedings of Quark mattez-88, Nordkirhen, 2. Phys. C. 38 (1988); Proceedings of Quark ~a~~er-~9, Lenox, Nucl. Phys. A498 (1989); Proceedings of Quark matter-96, , Nucl. Phys. (in press)..

2.

E.V. Shuryak, Phys. Lett. 78B (1978) 150, Yad. Fis. 28 (1978) 796. The &CD Vacuum, Hadrons and the Superdeme Matter, World Scientific 1988; D.J. Gross, R.D. Pisarsky and L.G. Yaffe, Rev. Mod. Phys. 53 (1981) 43; B. Muller, Lecture Notes in Physics 225, {Sprjnger-Verla~ 1985); J. Cleymans, R.V. Gavai and E, Suchonen. Phys. Rep. Cl30 (1986) 217.

3.

J.B. Kogut et at, Phys. Rev. D39 (1989) 636 S. Gottlieb et oL, Phys. Rev. D40 (1989) 2389 M.P. Grady et al., Nucl. Phys. IX00 (1988) 149.

4.

N.H. Crist, Columbia preprint CU-TP-447 S. Qhta, Columbia preprint CU-tp-446.

5.

M. Gell-Mann and M. Levy, Nuovo Cimento 16 (1960) 705..

6.

S. Weinberg, Phys. Rev. Dll (1975) 3583.

7.

J. Gasser and H. Leutwyler, Phys. Rep. 87 (1982) 79..

8.

A.A. Belavin, A.M. Polyakov, A.A. Schwartz and Yu. S. Tyupkin. (1975) 35.

9.

G. ‘t Hooft, Phys. Rev. D14 (1976) 3432.

10.

Phys. Lett. B59

E.V. Shuryak, Nucl. Phys. I3203 (1982) 93, 116,I4~.H243 (1983) 231.

11,

D.I. Dyakonov and V. Yu. Petrov, Nucl. Phys. B245 (1984) 259, I3272 (1986) 457.

12.

E.V. Shuryak, Nucl, Phys. B302 (1988) 559,574,599,621.

396~

E. K Slwyak

/ @XI vacuum and excited hadronic matter

13.

E.V. Shuryak and J.J.M. Verbaarschot, CERN-TH-5492/89,

14.

E.M. Ilgenfritz and E.V. Shuryak, Nucl. Phys. B319 (1989) 511.

Nucl. Phys. in press,

15.

E.V. Shuryak, Nucl. Phys. B319 (1989) 521,541; B328 (1989) 85,102.

16.

T. Alexopoulos et al., Phys. Rev. Lett. 64 (1990) 991; F. Turkot, Talk at Quark Matter-Q& Menton, 1990.

17.

E.V. Shuryak and O.V. Zhirov, Phys. Lett. 89B (1980) 253.

18.

M. Kataja, P.V. Ruuskanen, L.D. McLerran and H. van Gersdorff, Phys. Rev. D34 (1986) 2755.

19.

G. Odyniec (NA35), Talk at Workshop on Relativistic aspects of Nuclear Physics, Rio de Janeiro, 1989 (WSPC, Singapore, in press).

20.

E.V. Shuryak, Jad. Fis. (Sov. J. of Nucl. Phys.) 16 (1972) 395.

21.

C. Baglin et al., (NA38 ~011.) Phys. Lett. 220B (1989) 471; 3. Varela, Talk at Quark hatter-Q~, Menton.

22.

T. Matsui and H. S&z, Phys. Lett. 178b (1986) 416.

23.

J. Ftacnik, P. Liehard and J. Pisut, Phys. Lett. B207 (1988) 194; S. Gavin, M. Gyulassy and A. Jackson, Phys. Lett. 207B (1988) 257,

24.

S. Gavin and M. Gyulassy, Phys. Lett. 214B (1988) 241; J. Hufner, Y. Kurihara and H.J. Pirner, Phys. Lett. 215B (1988) 218; J.P. Blaizot and J.Y. Ollitrault, Phys. Lett. 217B (1989) 392.

25.

F. Karsch and R. Petronzio, Z. Phys. C37 (1988) 627.

26.

R. Albrecht et a&, (WA80 ~011.) Phys. Lett. Bf19 (1987) 297.; A. Bamberger et al., (NA35 ~011.) Phys. Lett. B184 (1987) 271.; A. Sandoval et ak., (HELIOS ~011)Nud. Phys. A 4655 (1987).

27.

P.V. Chliapnikov et al., Phys. Lett. 141B (1984) 276; U. Gurlach, (HELIOS ~011.) Proc. of 24-th Int. Conf. High. Energy Phys., Munich 1988; W.J. Willis, Nucl. Phys. A478 (1988) 151C; J. Schukraft, (HELIOS ~011.) Talk at 7th Int. Conf. Quark ,vatter-88, Lenox, Massachusetts 1988.

28.

G. Roche et at., (DSL ~011.) First observation of dielectron production at the Bevalac. LBL preprint, Berkeley 1988; L.S. Schroeder. Talk at HIPAGS Workshop, BNL, March 1990.

29.

E.V. Shuryak, Phys. Lett. 207B (1988) 345.

30.

J.L. Goity and H. Leutwyler, Bern University Preprint 1990.

31.

D. Pines, Can. J. Phys. 65 (1987) 1357.

32.

C. Gale and J. Kapusta, Phys. Rev. C35 (1987) 2107; L.H. Xia et tsl, Nucl. Phys. A485 (1988) 721; 3. Kapusta, Talk at HIPAGS Workshop, BNL, March 1990.

33.

E.V. Shuryak, Pion modi~~ation in hot hadronic matter and %sltrasoft” phenomena in high energy collisions. CERN-TH-5386189 and “L. Van Hove Festschrift”, World Scientific, (1990). Physics of the pion liquid. BNL-44522, 1990..

34.

B. Andersson et al., Preprint LUTP 88-1, Lund 1988.