a simple model of large transverse-energy events in proton-nucleus interactions

Volume 172, number 3,4 PHYSICS LETTERS B 22 May 1986

A SIMPLE MODEL OF LARGE TRANSVERSE-ENERGY EVENTS IN P R O T O N - N U C L E U S INTERACTIONS

N. P I S O T O V A

Department of Nuclear Physics, Comenius University, CS-842 15 Bratislava, Czechoslovakia

P. L I C H A R D and J. PIS(JT

Department of Theoretical Physics, Comenius University, CS-842 15 Bratislava, Czechoslovakia

Received 8 February 1986

Qualitative features of the preliminary data on large transverse-energy proton-Pb collisions at 200 GeV/c obtained by the HELIOS collaboration at CERN are reproduced by a simple model in which the large transverse energy is built up by a large amount of soft final-state hadrons.

Recently the HELIOS collaboration at the CERN- SPS collider obtained preliminary data [1 ] on the distribution in transverse energy, ET, in p - P b collisions at 200 GeV/c incident proton momentum. E T is a sum of transverse energies of all particles produced within the laboratory pseudorapidity interval 0.6 < 77 < 2.4. A surprising feature o f the data is that it contains, although with a probability o f about 10 -6 , also events with E T >1 50 GeV, what is by a factor of 2.5 larger than the kinematic limit (2ELabmp)l l2 for a proton--proton interaction. In a collision of a proton with a cluster consisting of n nucleons the kinematic limit is (2ELa b nmp) 1/2 and the data seem to require collisions with clusters o f n ~ 9. This line of thinking is, however, most likely misleading. In a few experi- ments [2], the large-E T events are built up by contributions of many final-state particles, each o f them contributing about 0.4 GeV to the total transverse energy E T .

The motivation o f the present work has been an attempt to understand at least in a crude way the qualitative features o f the preliminary data [ 1 ] on E T distributions and to learn whether these features can have a simple, standard, explanation or whether it is necessary to invoke some basically new mecha- nisms, like scattering on large clusters within nuclei or plasma formation. Since we are not interested at

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the present stage in a detailed theory o f the process, we tried the simplest model possible.

The purpose o f this note is to point out that the qualitative features o f the E T distributions obtained in ref. [1] can be reproduced by a simple model in which a large E T is built as a sum v i a large amount o f contributions due to soft final-state hadrons, each with a transverse energy of about 0.4 GeV.

The model does not pretend to be a theory of this complicated process, it just indicates a way of looking at large-E T events in hadron-nucleus collisions.

The model is based on the following assumptions: (i) In hadron-nucleus collisions each of the

"wounded" nucleons in the nucleus gives rise to a "string" which then decays into soft final-state hadrons. This idea has been built in several ways into numerous models [3,4] of multiparticle production in hadron-nucleus collisions. As an example we show in fig. 1 the picture o f the hadron-nucleus collision in the model o f Bial'as, Czy~ and Lesniak [3]. When passing through the nucleus the proton interacts with some of the nucleons and a string is attached to "wounded" nucleons. These strings extend over the target fragmentation region (in rapidity) and join be- fore the central rapidity region (fig. 1). The average number of strings kp in the target fragmentation

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Fig. 1. The formation of strings in a ha&on-nucleus collision according to the model [3].

region is thus roughly the same as the number of "wounded" nucleons,

Xp ---- (V) =AOpn/OpA , (1)

where tTpn is the non-diffractive pro ton-nucleon and ariA the proton--nucleus cross section. Taking

inel " Opn ~ 30 mb,A = 207 and ~TpPb(exp) = 1747 mb we obtain ~tp ~ 3.8. The average number o f strings in the target fragmentation region should be in fact somewhat larger than the estimated 3.8 since also secondary particles can occasionally produce a short string and contributions of spectator nucleons could also be included into these short strings. Phenome- nologically the average number of strings should be determined by the ratio

Xp -~ ( dn/dy)pA/ ( d/'//dy)pp [target fragm, region •

(ii) The distribution o f the number of strings N can be approximated by a Poisson distribution with the average value Xp. This is certainly a simplifica- tion. This distribution should be estimated more realistically from Glauber model considerations. Since, however, we are interested at present only in the qualitative features of the data, we shall stay with this approximation.

0ii) Each of the final-state hadrons originated by a fragmentation o f a string has transverse energy typ- ical for soft processes, e.g. e T ~ 0.4 GeV. The data [2] indicate that at the SPS and CERN-ISR the transverse energy distribution of softly produced particles is to a large extent independent of the energy of the incident hadron and of the final-state multiplicity. Since the large-E T events contain many particles, in the estimates performed below we shall take all secondary hadrons as having e T = 0.4 GeV. The inclusion of an experimental e T distribution into the model would make it more realistic but less transparent. At this stage we stay with the simplified assumption

with e T = 0.4 GeV for any final-state hadron * 1 (iv) The average rapidity density of hadrons origi-

nated from the fragmentation of a string is the same as in the e+e - or hadron-hadron collisions, that means about 3 hadrons per rapidity unit. Within the laboratory pseudorapidity interval 0.6 < r / < 2.4 we thus expect the average number o f final-state hadrons to be 5.4.

(v) Particle multiplicities at lower energy h a d r o n - hadron and e+e - collisions can be qualitatively described by Poisson distributions in the number of pairs ofhadrons. We shall therefore assume that the number of hadron pairs from a particular string, within the interval 0.6 < r / < 2.4 is a Poisson distrib- uted quantity with the average value/a = 2.7. Each pair carries the transverse energy 0.8 GeV. This assumption about the transverse energy fluctuations in a given rapidity interval can be directly verified on pp data, preferably at 200 GeV/c.

The distribution P(n) ofhadron pairs within the pseudorapidity interval 0.6 < r / < 2.4 is then given by the compound Poisson distribution

P(n) = ~ PS(N)Ph(nl) ... P h ( n N ) g , n l , n2 , . . . , n N

N X ~ ( n - ~ n i ) (2)

Here PS (N) = (xN/N!) exp(-X,,) is the Poisson distri- • 1 J ~ "

butlon in the number of strings created in the p - P b collision and Ph(ni) = (Idni/ni [) exp(-/a) is the Poisson distribution of hadron pairs within 0.6 < ~7 < 2.4 from the ith string, # = 2.7. In the simplified model considered in this note the transverse energy E T associated with a particular n is 0.8 n GeV.

The compound Poisson distribution (2) is described in sufficient detail, including an algorithm for calculatingP(n) in ref. [5].

In fig. 2 we compare the E T distributions obtained in p - P b collisions at 200 GeV/c [1] with a few cases of the compound Poisson distributions• We made no attempts at optimization and plot just a few selected cases with values of Xp and/a close to the expected values. Distributions with/a = 2.7, Xp = 5.5 or with

,1 The inclusion of a realistic e T distribution would make the total E T distributions somewhat broader.

452


I dN

N dE T

10 -t ~- ,...-,. / ~.7:-'~ ." x

10-31-/ -;

10-/'; ;

10 -5

10 -6

1°-7

:.'.,

oa-.\

",po'A • o'.,, X o -.~,

\ "%

5b 6'o ET[ jC-~V]

70

Fig. 2. The comparison of data on the E T distribution in p-Pb collisions at 200 GeV/c with compound Poisson distributions (data circles). Compound Poisson with/~ = 2.7 and kp = 4.5 (dash-dotted line). With/~ = 2.7 and kp = 5.5 (dotted line). With # = 3 and kp = 5 (dashed line). Simple Poisson with (n) = 15 (double dash-double dotted line).

# = 3, Xp = 5 describe reasonably the qualitative features of the data. These values of Xp are about 20% higher then the simple estimate Xp ~ 3.8 following from eq. (1). Taking into account the dynamical complexity of the target fragmentation region, the model dependence of the estimates and the possibil- ity of additional strings due to secondary particles, this increase in Xp is not very surprising.

For comparison we show in fig. 2 also the simple Poisson distribution with (n) = Xp/a = 15. The latter one is obviously far too narrow. This, in our opinion, indicates clearly that the E T distribution is due to a compound (and not single) stochastic distribution. Some elements of stochasticity must certainly be present when the total E T at, say ,E T = 40 GeV is built up by contributions of about 100 hadrons * 2

• 2 Compound stochastic distributions describe well also the multiplicity distributions in hadron-hadron collisions at high energies [6,7]. Also here it is a consequence of the internal structure of colliding particles.

The model described above can be extended natu- rally to E T distributions in p ion-nuc leus collisions. We assume that strings formed in a p ion-nuc leus collision behave in the same way as in a pro ton-nucleus collision. The parameter in the compound Poisson distribution should have therefore the same value in both cases. The parameter X (the average value of the number of strings created) should be different. Using the formula (1) we have

X~r = A 0"Irp/qlr A .

Taking r °i~nnel ~ 20 mb and putting (/~rA ~ OpA we obtain as a rough estimate

2 hTr ~ $ ~ 'p •

The compound Poisson distributions for E T in p i o n - Pb collisions are presented in fig. 3.

To conclude : The compound Poisson distribution following from a model in which large-E T events are due to soft hadrons produced from strings formed by "wounded" nucleons describes the qualitative fea-

~ l d N

10 -1

- ? .

10 -2 %

10-3

10 -4

10-5

10 -6

'\.'~3 \,,,,

+.',

10-7f ET[GeV] 0 1~3 2'0 5'0 610 70 - -

"\ . \

\

i

3'0 40

Fig. 3. E T distributions in pion-Pb collisions following from the model of strings attached to "wounded" nucleons:

= 3 and hrr = 3.33 (dashed line). ~ = 2.7 and hlr = 3.67 (dotted line). ~ = 2.7 and hlr = 3 (dash-dotted line).

453


tures o f the E T distributions in p - P b collisions [1 ]. The model, roughly speaking, is based on the assump. tion that large4~ T events are due to numerous soft collisions o f the incoming proton with nucleons in the Pb-nucleus. The collision w i t h e T ~ 50 GeV i s thus due to 1 5 - 2 0 soft collisions, each of them re- leasing about 3 GeV transverse energy. The values o f the parameters kp and/a of those distributions which describe reasonably the data are not far from values expected in some models of hadron-nucleon interactions. The target fragmentation region is, however, so complicated from a dynamical point of view that all model estimates o f ~,p and/a can be considered only as orientation values.

We believe that this model can be thought of as a sort o f a "standard background" to more interest- ing processes. Less mundane events, like plasma for- marion, should be seen as a signal above this background.

A useful test o f the model would be provided by the A-dependence o f E T distributions. The A-dependence o f these distributions is governed by the A- dependence o f the parameter kp.

The model leads also to simple predictions con- ceming the lepton/pion ratio in large-E T events. The model treats individual "strings" as independent, even at large values o f E T. If this is correct than the lepton/pion ratio at low values of PT should be roughly the same as in the p ro ton-pro ton interac-

t.ion. Predictions for E T distributions in heavy-ion collisions following from this model will be presented elsewhere.

v

The authors are indebted to V. Cem~, and C. Fabjan for discussions which stimulated the present work and to M. Seman, J. Dolej]i, J. Form~nek and V. Sim~k for valuable comments.

References

[ 1] A. Franz, The transverse energy distribution in proton- lead collisions, Talk Second Intern. Conf. on Nucleus- nucleus collisions (Visby, Sweden, June 1985).

[2] C. De Matzo et al., Phys. Rev. D29 (1984) 363; A. Faessler, Phys. Rep. 115 (1984) 1.

[3] A. Bia/as, W. Czy~ and L. Lesniak, Phys. Rev. D25 (1982) 2328.

[4] A. Capella and J. T~an Thanh Van, Phys. Lett. B 93 (1980) 46; S. Ban-Hao and C.Y. Wong, Phys. Rev. D32 (i985) 1706; I. Otterlund et al., Z. Phys. C21Y(1983) 281.

[5 ] W.T. Eadie, D. Drijatd, F.E. James, M. Roos and B. Sadoulet, Statistical methods in experimental physics (North-Holland, Amsterdam, 1973), in particular section 2.5 and p. 34.

[6] T. Sj6strand, Multiple patton-patton interactions in hadronic events, preprint Fermilab-Pub/85/119-'1" (August 1985).

[7] T.T. Chou and C.N. Yang, Phys. Rev. D32 (1982) 1692; Phys. Rev. Lett. 54 (1985) 510;55 (1985) 1359.

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a simple model of large transverse-energy events in proton-nucleus interactions

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