Intermittency in hadronic collisions

361~

Nuclear Physics A.525 (1991) 361c-364~ North-Holland, Amsterdam

INTERMITTENCY

IN HADRONIC

COLLISIONS

Ina SARCEVIC* Department

of Physics,

University

of Arizona,

Tucson,

AZ 85721,

USA

We show that the observed increase of the factorial multiplicity moments with decreasing size of the rapidit bin (the so-called “intermittency” phenomenon) is a consequence of the short range corre Kations. With the linked-pair ansatz for higher order correlations, we find all the moments to be in a very ood agreement with the NA22 and UA5 data. At very high energies, and in the large rap1.$ ity region, we find that self-similar cascade leads to a power-law behavior of the moments, in agreement with the UA5 data. We propose further tests of this particular mechanism for multiparticle production at Tevatron energies. 1. INTRODUCTION

The study of unusually space

region

tions.

The

have recently first

who proposed

large non-statistical become

theoretical

the study

of the factorial

pidity

is a number

interval

AY

(i.e.

behavior

in analogy

experimental nuclear

groups

collisionsZ,

at small

with

in small phase

was by Bialas

moments

1) >

>I

as

,

bin 6y and M is the number

of turbulence the observation

investiga-

and Peschanskii

Fi, defined

- 1). . . (n, - i +

when 6y -+ 0) is a signal

here reported

fluctuations

and experimental

of bins in the ra-

). Th e y c 1aimed . that the power-law

the onset

even though

behavior

of a dynamical

in hydrodynamics’. of intermittency

Recently, in e+e-,

some of the data show clear tendency

of these

“intermittent” several

hadronic

towards

leveling

and off

Sy.

2. INTERMITTENCY

AND SHORT-R4NGE

Here we show that ments

problem

multiplicity

in a rapidity

N (Sy)-“i,

density

theoretical

< &pm

of particles

Fi(6y)

to this

J$c n,(n,

( i.e. Sy = AY/M

moments

particle

of many

contribution

F, = < a where n,

focus

with

decreasing

correlations3, We obtain correlations

without factorial

in hadronic rapidity

and the linked-pair

For example,

the second

CORRELATIONS the observed

bin size can be expLained

invoking

moments

collisions

“new physics” Fi given by Eq.(l) ansatz

moment

increase

or a power-law

behavior

using experimental

for higher-oder

correlations.

Fz is given by SP2(Yl,Y2)dY,dY2

Fz =

* Humboldt

SPl(Yl)dYl

.rPl(Y*)dY*’

Fellow

O375-9474/91/$03.50

0

1991 - Elsevier Science Publishers B.V.

of the factorial

by the conventional

(North-Holland)

data

mo-

short-range

of the moments. on two-particle

362~

I. Sarcevic / Intermittency in hadronic collkions

where pz(yr, yz) is two-particle

correlations

where translational

is valid (i.e.

obtain

moment

Fz by integrating

* - 1). At fi 01Pl

= 22GeV -+Kll

form3 (Icz = yze expression

invariance

and pi is particle density. p(yi, yz) s

the reduced

, the experimental

In the central region,

pz( Iyz - y1 I), p1 = const),

two-particle

correlation

we can

Lz(yl, y2) ( kz E

data on !Q can be fitted with an exponential

;yz = 0.38, [ = 1.18)

. In this particular case, we find the analytic

for Fz: Fz = 1 + %(I

;

;;;““). Y

In Fig.

1 we show our parameter-free

excellent

agreement

with the NA22

reduced two-particles

correlations

present the result for F2 at fi Gaussian parametrization.

result for Fz at energy

data.

At UA5 energies,

fi

=

We find

22GeV.

the experimental

data on the

are better fitted with the Gaussian form3.

Here we only

= 200GeV

2), w h’K h is obtained

(Fig.

The results for energies

fi

= 546GeV

by integrating

and &

this

= 900GeV

can

be found in Ref. 3. With

the linked-pair

ansatz for higher

a~1czlczlcz and Its = as&!/~tzkz, we find moments data.

on Figs.

Fs with the esperimental which, by construction, on Figs.

the linked-pair two-particle

l-2 (solid lines). approximation

values for Fz.

parameters),

a.greement with the NA22

and UA5

The values for aa, u4 and us can be

by calculating

higher moments

This is possible in the linked-pair

relates higher moments to the second moment

l-2 (dashed

lines).

ansatz is supported

Excellent

agreement

by the data regardless

Fa, F4 and

approximation

Fz. The results are

with the data indicates

of the exact functional

that

form of

correlations.

3. SELF-SIMILAR

MULTIHADRON

PRODUCTION

AT VERY

At very high energies and in the large rapidity many branches

develops

simple self-similar

as a new pattern

cascade model4

heavy mass “particle”

is created,

behavior

HIGH

region the self-similar

of multiparticle

in which collision

production.

of the normalized

N .5GeV,

multiplicity

ENERGIES cascading

with

We construct

takes place in several steps.

which then decays into smaller particles

it reaches the mass of the resonance (M,, power-law

(i.e Its = aalczk2, kq =

3.

We also test our linked-pair

presented

correlations3,

F3, F4 and F5 to be in very good

This is presented

found in Ref.

order

where us, ad and a5 are energy independent

a

First,

and so on until

Syo N 1 - 2). This leads to a universal moments

Cl

:

where Cl are defined by: M

C,(Sy)

=<

& -g dJ(& C m=l

The power-law

of Eq.

n,)’ >.

77l=1

(4) implies that the plot of lnC[

versus ln(Y/Sy)

with the slope Xl E (I - l)( 1 - d,u), w h ere dF is a fractal dimension.

is a straight

line

For dct,ailed discussion

in hafkonic co~~ions

I. Sarcevic / Inte~i~en~

-1

-2

1

0

2

3

-3

-2

363~

0

-1

1

-1n dy

-1n 6y

Figure I: Theoretical results for moments Fz F3,F4 and Fs (solid lines) and the moments Fs, F4 and F5 obtained using linked-pair ansats and the experimental values for Fz (dashed lines) at energy 4 = 22, compared with the NA22 experimental data.

0.3

Figure 2: Same as Figure I, but at energy ,/Z = 200 and compared with the WA5 experimental data.

/ TT / /’ ,’

0.2

,.&

:

0

1

-ii J

I

2

3

wf/fiY)

Figure 3: Experimental data on multiplicity moments lnfi(b) (fz(b) = &(Jy)/lczfY)) as a function of In(f’/by) for energies ,,G = ZOOGeV (squares), 6 = 546GeV (diamonds) and ,,L = 900GeV (crosses) and the straight line fit to the data at large 6~.

Figure 4: Same as Figure 3, but for lnfs(liy) (May = ~3(~y)/~3(~‘)).

2

I. Sarcevic / Intermittency in hadronic collisions

364~

of the self-similar

cascade

using the theory

of fractal

and the derivation structure,

Here, we only present energies straight

&

= 200,546

UA5

line in agreement

data on the moments

values:

X4 and Xs can be found

at the point

to ln(Y/Sy) at fi UA5

= 1.2 at fi

However,

in Ref.

ln(Y/&y)

moments

(fr(6y)

4.

that

behavior.

F,(Gy)/F,(Y))

at

f

from

= 546GeV

model,

space

(it will be “longer”)

lie on the

for moments This

= 1.4

that at Tevatron

power-law

will become

line

corresponds

and ln(Y/Sy)

we predict

3-4

f4 and fs

the straight

come in (Sys N 1.8).

cascade

phase

larger value of ln(Y/Sy)

Cl

The slopes on Figs.

The results

will follow the same universal

since the available

of the moments

all the data

The deviation

= 1.3 at fi

self-similar

will have more branches

out at somewhat

and Xs II 0.344.

= 200GeV,

In our simple

the multiplicity

data.

cascade

Xz N 0.140

f,(Sy)

We note

power-law

where short range correlations

= 900GeV.

energies

3-4).

with the predicted

and the slopes

behavior

4.

and 9OOGeV (Figs.

have following starts

of the power-law

see Ref.

larger,

and the Tevatron

behavior

as the

the self-similar data will flatten

than the UA5 data.

4. CONCLUSION We have shown that in the small 6y region, Fi with decreasing correlations.

In the 6y +

agreement

with

have found agreement pattern

size of the rapidity

that

the present

0 limit, data.

the self-similar

at Tevatron

moments

slowly

increase

implies

Finally,

of factorial

with conventional

saturate

At very high energy

cascade

with the UA5 data.

the observed

bin can be explained

moments

short range

to the predicted

values,

and in the large 6y region,

power-law

we have proposed

behavior further

of the moments,

in we in

tests of the self-similar

energies.

ACKNOWLEDGEMENTS Part of the work presented

with P. Carruthers.

I also thank

discussions.

H. Eggers

and Q. Gao

supported

in part by the United

and Nuclear

Physics,

whom

here was done in collaboration

NATO

States

for many

Department

Collaboration

Research

useful

of Energy,

This

Division

Grant and Humboldt

H. Satz, work was

of High Energy Fellowship.

REFERENCES 1) A. Bialas and R. Peschanski, Phys. Lett. 207B, 59 (1988). 2) For a review,

Phys.

see A. Bialas, talk presented

3) P. Carruthers and I. Sarcevic, H. Eggers, Q. Gao and I. Sarcevic, 4) I. Sarcevic

Nucl.

and H. Satz, Phys.

B2’73,

703 (1986);ibid.

at Quark Matter

B308,

‘90 Conference,

857 (1988);

this volume.

Lett. 63, 1562 (1989); P. Carruthers, Phys. Rev. University of Arizona preprint AZPH-TH/SO-9. Lett.

233B,

251 (1989).