Structure of two-body correlations in high energy hadron production

Volume 48B, number 2

PHYSICS LETTERS

STRUCTURE

21 January 1974

OF TWO-BODY CORRELATIONS

IN HIGH ENERGY

HADRON

PRODUCTION

M. Le BELLAC

Laboratotre de Physique Theortque, Umversttd de Nice, France H.I. MIETTINEN* and R G. ROBERTS

Rutherford High Energy Laboratory, Chtlton, DMcot, Berkshire, UK Recewed 15 October 1973 Revised manuscript recleved 30 November 1973 Experimental reformation on diffractmn is used to estimate long range effects m multiparticle production Diffractively produced secondaries are found to produce a plateau in the central region Diffraction accounts for 30% of the observed correlations and the remainder, consistent wxth being short range, corresponds to a cluster size of 2 4 charged particles. Recent measurements o f rapidity correlations between two charged particles and charged and neutral particles at the N A L [1] and the CERN (ISR) [2, 3] laboratories show that i) the correlations are dominantly o f shortrange nature, n) their size is very large; (pure short-range effects resulting from cluster production would demand the size of the produced clusters to be around four charged particles per cluster) and ill) the charged-charged and charged-neutral correlations are roughly of the same size These new results provide poweful constraints for theoretical models o f multi-particle production. Although correlation data alone could be explained by simple cluster production models, any realistic analysis must be consistent with other known features of multxbody production The N A L [4] and ISR [5] experiments have clearly demonstrated, in addition to non-&ffractive production, the presence of a diffractive component accounting for roughly 20% o f the inelastic cross-section. Furthermore, diffractive production is well known to cause long-range correlations. Whde the long and short range correlations are expected to separate naturally asymptotically, it is still a difficult task to make this separatxon at NAL and ISR energies. In this letter we use experimental Information on diffractive scattering, 1.e. size o f ODIFF,M2 and t dependence, associated multiplicity distributions, to analyze the structure of the observed two-body correlations We find i) that diffractively produced secondaries populate the central as well as fragmentation region, n) the diffractive component is responsible for ~ 30% of the observed correlations and lil) the remaining 70% are consistent with short range and correspond to a cluster size of 2.4 +- 0 4 charged particles This is in rough agreement with the results o f Pirila and Pokorskl [6], Hayot and Morel [7], Berger and Fox [8] and Schmldt~Parzefall [9] The observation [4, 5] o f high-mass diffraction Implies that pions from the diffractive fireball can leak into the central region even to y = 0 This situation, unlike that of older versions of the two-component model, arises because the heavy fireball travels slowly in the c.o.m system and its decay then populates the central region. To obtain a rough estimate of the yield o f diffractive plons we describe the diffractive spectrum in terms o f only the scahng term.

do/ dt d(M2 /s) = G( t) (M2 /s) ap(O)- 2aP(t)

(1)

with the conventional notations. Integrating eq. (1) over t and assuming as a first approximation that ap, = 0 we have * Herman Rosenberg Foundation Fellow On leave of absence from the Research Institute for Theoretical Physxcs, Unwerslty of Helsinkl, Finland Present address Theory Dwlslon, CERN 1211 Geneva 23 115

Volume 48B, number 2

PHYSICS LETTERS

21 January 1974

do/d(lnM 2) = constant ; M o2 <,M 2 <~rs.

(2)

with r ~- 0.1 A fireball with mass M travels in the centre-of-mass system wxth a rapidity 0 = ~-ln(s/M 2) so that: do/d0 = constant ,

- ½ 1 n r ~ 1 ~ [41 ~<½ ln(s/M2o).

(3)

The rapidity of the pions inside the fireball smears out the distribution (3), and we expect only a slight dip in (1/OD) (doD/dY) at y = 0, especially if the fireball decays longitudinally. Using the result of Frazer et al. [10] that the average diffractive multiplicity is given by (nD(s)) = ½a lns + b , where a is the coefficient of lns in the total multlphcity distribution, we expect that 1 dqD

o D dy ~½a~½ odylda in the central region. To carry out an accurate estimation we have parametnsed the diffractive spectrum using our recent trIple-Regge analysis [ 11 ]. The cut-off parameter r is unnecessary since the tram-limit effectively gives an M 2 cut-off proportional to s

The diffractive plon spectrum is given by

2 -dM~ do dy - 2fdM n 2 nP(n, (n(M2))) {Dn(Y-~M2))+Dn(Y+C)(M2))}

daD

(4)

where P(n, (n(M2))) is the multiplicity distribution and D n ( Y - 0 ) the rapidity distribution for emitted particles in the fireball rest frame. Using data at NAL [4] we have chosen a Polsson distribution for P and the parametrisation for the average associated multiplicity of Roberts and Roy [12]. Our choice for D n lies somewhat in between an lsotropic and a longitudinal decay. The shape is Gausslan whose width is

On [21n(M/nml)] 1/2

(5)

where rn±, mean transverse mass ~ 0.4 GeV. We have plotted in fig. 1 the spectrum of negative pions obtained with the following parametrization. Gppp(t) = 5.6 e 5t mb/GeV 2

ap(t) = 1 + 0.25 t

GppM(t ) = 2.0 e 2t mb/GeV 2

aM(t ) = 0.5 + t

(n (M2)) =

0.28M

for

M 2>/20

0.91 ln.M 2 - 1.5

for

M 2 )" ~0.

Our calculation gives the value 0.29 for the plateau height. One can also compare with total spectrum (1/o) (do/dy). Using the NAL [1] and ISR [13] data we estimate 1 dToI a aYly=0

0 . 8 5 -+ 0.05

for negative particles at Plab = 1500 GeV/c. The plon yield associated with fast protons has recently beem measured at ISR [14]. Their results, which indicate considerable particle yield in the central region, agree well with the prediction of our model calculation When more than one production mechanism is present, the nett correlation is given, only by the correlations from the individual mechanisms, but also from terms due to the simultaneous existence of these mechanisms. 116

Volume 48B, number 2

PItYSICS LETTERS

I

I

I

I

I

I

I

I

T

1 d<7 o" dy

Full spectrum

__-

1 dff 0

Diffractive spectrum

~-o

~ d-fib Backward exc~tahon only o'o d~

v ~ ' = 53 GeV 2 00

21 January 1974

100

05C 1

do-

02[

0113

00E -5 U

Fig 1 Normalized rapidity distributions for negative particles at ~ = 53 GeV Full hne complete spectrum (see text) Dashed line diffractwe spectrum. Dashed-dotted line dlffractwe spectrum correpsondmg to backward excitation only Nohce that the expermlental data ofref [1] have been mulUphed by a factor 1 15 to account for K- and ~-productlon Denoting C~, C D the correlations from non-diffractive and diffractive components, respectively, and C.D the long-range correlation mentioned above we have

On OD C(vl'Y2) =~- C~r(Yl'Y2)+ o- CD(Yl'Y2) +0Do C D ( Y l ' Y 2 )

(6)

Tr

where

(1 do

l dOD (!do l dOD (7) CnD(Yl'Y2)= \OdYl aD dYlJ \ady 2 OD dY2,] C(Yl,Y2) can be taken &rectly from experimental data. CD(Yl,X2) is calculated from our model using the expresrion for d2OD/dYl dy 2 analogous to eq. (4) and C~rD is got through eq (7) using the experimental doD/dY. Eq. (6) can then be used to estimate C~ which we interpret as orlganating from the production of clusters. In the same spirit as previous studies of correlations [ 6 - 9 ] we attempt to relate the size of C, with the size of the cluster. In the cluster model, the average number of charged pamcles per cluster is essentially given by p~ where

PTr-

(n(n-1))c (1 (n)c = a

d°~yl/dY2C(Yl,Y2)

(8)

dYl,]

Figs. 2a and 2b show a comparison of our estimates of the contributions of C D and CTrD to the frachonal correlation with the results of the CERN-Hamburg-Vienna collaboration [2]. From fig. 2b we see that diffractive effects account for roughly 30% o f the expertmental correlations. Using eqs. (6) and (8) we obtain P~r = 1.51 - 0.36OD/OTr

1.34

aD/Or

(9)

Choosing o D = 9 mb this gives p~ = 2.4, 1.e. there are, on average, 2.4 charged parhcles per cluster. Taking into account errors from the data on C(Yl, Y2) and on on the uncertainty o f OD1FF, we estimate the accuracy ofp~ r 117

Volume 48B, number 2 0B

PHYSICS LETTERS

i

i

, 'V~

9ch=0

~ 2 ~

i

R (gc~a)

~ ,IT=t.5 6eV

i

,

i

~ch=-25

06

~

,

]; V-~ = 53 ~ ~={S

i

GeV 6eV

t

0~ a

R (~ch~b)

b) A

02

02

0

-02

i

= 53 GcV

/ , %

01.

08

21 January 1974

-5

-t.

-3

-2

-I

YB

0

I

2

3

t,

5

°1

-02

-; -i

-~ -~ -I

d

~

~

~

Z

~

Fig 2 a) Fractional charged-neutral correlation R ( y 1 = 0, Y2) = ain(d°/dYl)(d°/dY2)/(d°/dYl)(do/dY2)- 1 measured by the CHV Collaboration [2] The lower line shows the result of the model calculation for the long range term plus the diffractive correlations. with choice o D = 9 mb The errorbars of the model calculation correspond to a variation of -+2 mb m the diffractwe cross-section Expermaental data from ref [ 1 ] b) Fractional correlation R ( y 1 = - 2 5, Y2) The data and the model calculations as m fig a). not worse t h a n 20%. Our estimate o f P,r = 2.4 -+ 0.4 Is shghtly higher than the value PTr = 2 o b t a i n e d by Pirila and Pokorskl [61 and Schmld-Parzefall [9] b u t agrees w i t h that o f H a y o t and Morel [7]. Berger and F o x [8] estimated PTr = 2.8 w h i c h w o u l d be obtained m our calculation ff ODil~F was 7 mb However we w o u l d still attrib u t e a large part o f the observed correlation to diffractive effects. Finally, f r o m our analysis we w o u l d predict the fractional 7r-7r- correlation to be 0.4 at y l = Y2 = 0 at 1500 GeV/e We are grateful to Drs. E. Berger and P.D. R o y for useful discussions. T w o o f us (M.L.B. and H I.M.) thank Dr. R.J.N. Phflhps for his hospitality in the T h e o r y Division of the R u t h e r f o r d Laboratory. H.I.M. thanks the H e r m a n Rosenberg f o u n d a t i o n for financial support.

[ 1] ANL-NAL Collaboranon, S. Bansh et al, results presented at the Vanderbildt Conference, March 1973, NAL-Conf.-73/25 EXP, ANL-NAL Collaboration, Y Cho et al, Phys Rev. Lett. 31 (1973) 413 [2] CERN-Hamburg-Vlenna Collaboration, H Dlbon et al, Phys Lett. 44B (1973) 313 [3] Plsa-Stony Brook CoUaboratlon, prehmmary results quoted m M Jacob, lectures presented at 1973 CERN]JINR School of Physics, Ebeltoft, Denmark, CERN-TH-1683, June 1973. [4[ NAL-UCLA Collaboration, F.T Dao et al, Phys Lett 45B (1973) 399, 45B (1973) 402, ANL-NAL Collaboration, S.J Barish et al, ANL/HEP 7338 (1973). 15} CERN-Holland-Lancaster-Manchester Collaboration, M.G Albrow et al., Nucl Phys B54 (1973) 6; See also J C Sens, invited paper presented at the Conf on Recent advances m pamcle physics, The New York Academy of Sciences, New York (March 1973). [6] P Plrda and S Pokorskl, Phys Lett. B43 (1973) 502,CERN-TH-1686 (June 1973) [7] F Hayot and A Morel, Saclay preprmts DPh-T/73/58 [8] E L. Berger and G C Fox, Phys Lett. 47B (1973) 162 [9} W Schmldt-Parzefall, Phys Lett 46B (1973) 399. [10] W R Frazer, D R Smder and Chung-l-Tan, University of Califorma, San Diego preprmt, UCSD-10p10-127 (1973). [ 11 ] H 1 Mlettlnen and R G. Roberts, unpubhshed analys]s Some detads are given m ref. [ 101 [12] R G Roberts and D P Roy, Phys. Lett. 46B (1973) 201. [ 13] Bntlsh-Scandmavtan ISR Collaboration, data quoted m E. Ldlethun Lectures presented at the XIII Cracow School of Theoretical Physics, Zakopane, June 1973 [14] CERN-lqolland-Lancaster-Manchester Collaboration, data quoted m J C Sens, lectures presented at the 14th Scottish Unwersmes Summer School m Physics, Middleton Hail, July-August 1973

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