5 December 19%

ELSEVIER

PHYSICS LEll-ERS B

Physics Letters B 389 (19%) 78-82

Fusion of strings and cosmic rays at ultrahigh energies

N. Armesto, M.A. Braun ‘, E.G. Ferreiro, C. Pajares, Yu.M. Shabelski 2 Departamento de Fisica de Particulas, Universidade de Santiago de Compostela, 157064antiago de Compostela, Spain

Received 21 June 1996; revised manuscript received 6 August 1996

Editor: R. Gatto

Abstract

It is shown that the fusion of strings is a source of particle production in nucleus-nucleus collisions outside the kinematical limits of nucleon-nucleon collisions. Together with another effect of string fusion, reduction of multiplicities, this sheds some light on two of the main problems of ultrahigh energy cosmic rays, the chemical composition and the energy of the most energetic detected cosmic rays.

PAC.9 13.85.Ni; 13.85.T~; 12.38.Mh; 96.40.Dl

In the standard models of hadronic interactions [ l- 41, strings, chains or pomerons are exchanged between the projectile and target. The number of strings grows

with the energy and with the number of nucleons of

the participant nuclei. In the first approximation strings

fragment into particles and resonances in an indepen- dent way. However, the interaction between strings

becomes important with their number growing. This interaction has been introduced into some of the mod-

els [ 5-101. In particular, fusion of strings has been incorporated into the Dual Parton Model (DPM) [ 81

and the Quark Gluon String Model (QGSM) [ 11 I. Some of the effects of string fusion like strangeness and antibaryon enhancement [ 121, reduction of long

range correlations [ 131 and multiplicity suppression have been studied comparing the results with the exist- ing experimental data. Also predictions for the Rela- tivistic Heavy Ion Collider (RHIC) and Large Hadron

’ Permanent address: Department of High Energy Physics, Uni-

versity of St. Petersburg, 198904 St. Petersburg, Russia.

2 Permanent address: Petersburg Nuclear Physics Institute,

Gatchina, 188350 St. Petersburg, Russia.

Collider (LHC) are avalaible. In this paper we ex-

plore another effect of string fusion, namely particle production in nucleus-nucleus collisions outside the kinematical limits of nucleon-nucleon collisions (the

so-called cumulative effect). It is shown that this effect is important already at

present avalaible energies. A nonnegligible number of baryons and mesons are produced with momenta greater than the ones of the colliding nucleons. This ef- fect, together with the reduction of multiplicities, pro- vides a natural explanation of some features of cosmic

ray data like the rise of the average shower depth of

maximum X,, (the amount of air penetrated by the

cascade when it reaches maximum size) [ 14,151 with

increasing energy from 10” eV to lOI eV, and the ex- istence of events with energy above 10zo eV [ 14,161, higher than the expected cut-off [ 171 due to the scat- tering of cosmic rays with the microwave radiation background. Usually the first feature is explained by an enrichment of protons in the composition of pri- mary cosmic rays [ 151 as energy increases. However, as we show, if the composition of the primary cosmic

0370-2693/%/$12.00 Copyright 0 1996 Elsevier Science B.V. All rights reserved. PII SO370-2693(96>01248-8

N. Armesto et al./ Physics Letters B 389 (19%) 78-82 79

rays is kept fixed in the energy range between 1017 eV and lOi eV, string fusion leads to a suppression of the multiplicity similar to the one produced by changing heavy nuclei (Fe) by protons in the composition of the primary. On the other hand, since the momentum of a fused string comes from summing the momenta of its ancestor strings, it is possible to obtain particles with more energy than the initial nucleon-nucleon en- ergy. Therefore, if several strings fuse, the observed cosmic ray events with energy above 102’ eV may actually correspond to three or four times less initial energy than that apparently measured. String fusion could make these events compatible with the existence of the above mentioned cut-off.

To study these effects we use a Monte Carlo code based on the QGSM, in which the fusion of strings has been incorporated [ 111. A detailed description of the Monte Carlo String Fusion Model (SFMC) and com- parison with experimental data can be found in Refs. [ 1 l-131. A hadron or nucleus collision is assumed to be an interaction between two clouds of partons formed long before the collision. Hadrons and nuclei are considered on the same footing. The nuclear wave function is taken as a convolution of the parton distri- bution in a nucleon with the distribution of nucleons in the nucleus (given by the Wood-Saxon shape) 3. Each parton-parton interaction leads to the creation of two colour strings. Since both the projectile and the target must remain colourless, strings have to be formed in pairs.

A probabilistic picture of string fusion is assumed, in which two strings fuse when they overlap in trans- verse space. In this manner the interaction between strings is taken into account, irrespective of whether it is attractive or repulsive. The quantum numbers of the fused string are determined by those of the interacting partons and its energy-momentum is the sum of the energy-momenta of the ancestor strings. In particu- lar, the colour charges at the ends of the fusing strings sum into the colour charge of the ends of the resulting string according to the SU( 3) composition laws. E.g., two triplet strings fuse into an antitriplet and a sextet string, with probabilities l/3 and 2/3 respectively. In the present calculations only fusion of two strings is taken into account.

3 Fermi motion of the nucleons is taken into account.

Taole 1 Comparison of experimental data [ 221 on the invariant differential cross section (+ = Eg (GeV mb/(GeV/c)3 sr nucleon) for rr+

and K+ vs p (GeV/c) , laboratory angle 118’, PIas = 400 GeV/c, for p-Li and p-Ta collisions with the String Fusion Model code results, with and without string fusion.

Reaction p Data Without fusion With fusion

p-Li, (T for 7r+ 0.200 5.75f0.79 0.293 1.89ztO.26 0.381 0.672f0.046 0.474 0.217f0.016 0.580 (0.509kO.044) 10-l 0.681 (0.128f0.012)10-’

p-Ta,, u for ?r+ 0.200 8.57f1.14 0.293 2.20f0.3 1 0.394 0.78f0.068 0.489 0.309f0.032 0.583 0.135f0.017 0.680 (0.386f0.076) 10-l

u for K+ 0.539 (0.241f0.100)10-’ 0.584 (0.372f0.763) lo-*

3.53 4.77 0.314 1.41 0.07 0.38

0 0.34 0 0.094 0 0.009

5.65 6.60 0.19 1.57 0.038 0.38 0.032 0.173

0 0.072 0 0.038

0 0.037 0 0

Particle production outside the nucleon-nucleon kinematical limits (cumulative effect) has been stud- ied both theoretically and experimentally [ 18-221. In the string fusion approach it is naturally explained by the increased longitudinal momentum of fused strings. In the laboratory system it originates from the relativistic motion of partons inside the nucleons. String fusion picks up several quarks which move in the backward direction. Generating p-A events in our code and comparing the cumulative particle spectrum with the only existing high-energy data of [22] we observe a reasonable agreement, as can be seen in Tables 1 and 2 where the invariant differential cross sections for production of p, IT+ and K+ are shown4 .

Passing to nucleus-nucleus collisions, 10 000 S-S central collisions and 1000 Pb-Pb central collisions at fi = 19.4 AGeV have been generated. Also 1000 Pb-Pb central collisions at RHIC energies ( 4 = 200 AGeV) have been simulated. Central collisions are de-

4 The VaheS of XF = Pz /P,“” (c.m.s.) in the experimental data of [22] would lie (in p-p collisions), for example, in the range - 1.27 + - 1.47 for proton production at 11 go.

80 N, Armesto et ai./Physics Letters B 389 (1996) 78-82

Table 2 Comparison of experimental data 1221 on the invariant differential cross section u = E% (GeV mb/(GeV/c)’ sr nucleon) for

protons vs p (GeV/c), laboratory angle 11 So, PtXh = 400 GeV/c, for p-Li and p-Ta collisions with the String Fusion Model code results, with and without string fusion.

Reaction p Data Without fusion With fusion

p-Li, D for protons 0.385 4.17f0.23 1.24 2.82 0.476 I .76&O. 11 0 1.01 0.581 0.61ztO.04 0 0.47

p-Ta, u for protons 0.395 29.9f1.5 IS.1 22.3 0.490 13.2f0.7 0 12.57 0.585 5.2&0.3 0 2.5

Fig. I. x,c distributions for _rp > 1 in S-S collisions ( 10000 events) at fi = 19.4 AGeV of mesons (a) and baryons (b) with (continuous line) and without (dashed line) string fusion. No mesons are found in the no fusion case.

fined as those with impact parameter b = 0. Distribu- tions of baryons and mesons in S-S and Pb-Pb central collisions at SPS energies with XF larger than 1 are shown in Figs. 1 and 2. In Table 3 the average number of negative particles and of particles with 1~~1 > I per event are given for S-S and Pb-Pb central collisions at fi = 19.4 AGeV, for Pb-Pb central collisions at fi = 200 AGeV and for Fe-air central collisions at

(b

Fig. 2. XF distributions for XF > 1 in Pb-Pb collisions (1000 events) at 4 = 19.4 AGeV of mesons (a) and baryons (b) with (continuous line) and without (dashed line) string fusion. No mesons are found in the no fusion case.

Table 3 Average number of negative particles (neg) and of particles with (XF/ > I (cum) per event for different reactions in the string fusion model with fusion.

Reaction (une,) (k”,)

central S-S, fi = 19.4 AGeV 90 0.27 central Pb-Pb, fi = 19.4 AGeV 805 1.78 central Pb-Pb, fi = 200 AGeV 2292 2.02 central Fe-air 3 Et B h = IO” eV 446 0.4

1017 eV (in this latter case 1000 events have been gen- erated). The results on the cumulative production for

Pb-Pb collisions at fi = 200 AGeV are very similar to the ones at ,/% = 19.4 AGeV. This small change is

due to a moderate increase of the number of strings with energy.

To study the case relevant for cosmic rays we con- sider (Table 3) Fe-air central collisions at lOI eV.

The average number of strings per event was found to be 225, from which 62 double strings are formed. As mentioned, our code only includes fusion of two strings. Assuming that the probability for triple fusion is roughly the square of that for double fusion, one would expect that 18 strings join to form triple strings and 4 strings join to form a quadruple string. There-

N. Armesto et al. /Physics Letters B 389 (19%) 78-82

fore the probability of obtaining particles with 1~~1 > 2 or even ]XF 1 > 3 does not seem to be negligible. The energy around 3 . 10” eV measured in several cos-

mic ray experiments could then be lowered by a factor

2 to 4 if there are particles in the shower with 1~~1

> 2 or 1~~1 > 3. This lower energy for the primary may lie below the energy cut-off due to the scattering of cosmic rays on the microwave background. Notice

that two rare phenomena are compared, namely events

with enegy larger than 102’ eV and Fe-air events con- taning particles with IXF I > 1. The comparison would

be quite conclusive with more statistics on Fe-air col- lisions and information on their centrality. For this the

Auger project [ 231 will be welcomed.

Recently it has been pointed out [24] that above

some threshold in the density of strings (in tranverse

space), their fusion will give rise to a percolation phe- nomenon. In this case many strings could be grouped

forming a new string which, after its decay, could orig- inate particles with ]xFl much larger than 1. If so,

the energy of the primary could be lowered by more

than one order of magnitude. The critical threshold is around 9 strings/fm2, which is quite close to the den-

sity of strings obtained in Fe-air central collisions at lOI eV. At higher energies the density grows above

the percolation threshold. On the other hand, string fusion produces a suppres-

sion of multiplicities, which can explain the rise of the average shower depth of maximum in cosmic rays as

the energy increases, without requiring any change in

the chemical composition. It is usually accepted that there is a change in the cosmic ray chemical composi-

tion between lOI eV and lOI eV, from a heavy com- position at 10 l6 eV to a light one at energies higher than lOI eV. In a simple model of two components

[ 151 the change in the composition of the primary

goes from approximatly 75% of iron component and a 25% of proton component at lOI eV to 50% of iron and a 50% of proton at lOI eV. To study this point,

we have computed the multiplicities of minimum bias p-air and Fe-air interactions with and without string fusion in the range of energies from 1016 to lOI eV.

As it can be seen in Fig. 3, with string fusion the mul- tiplicity for a constant composition of 10% of proton and 90% of iron in the whole range of energy es- sentially reproduces the multiplicity obtained without string fusion for a uniform change in the composition from 75% Fe and 25% proton at lOI eV to 50% Fe

log,, E (e’C

Fig. 3. Total multiplicity dependence on the primary energy for

a fixed composition (n,) = 0.1 (n,_ar) + 0.9 (qe-dr) in the

fusion case (solid line) and a uniform change in the composition

from (Q) = 0.25 (“p--air) + 0.75 (“Fe-air) at lOI eV t0 (nf)

= 0.5 (np-air) + 0.5 (nFe-_air) at 10” eV in the no fusion case

(dashed line).

and 50% proton at 1019 eV. This can be understood as follows: The multiplicity for both cases, fusion and

nonfusion, is given by the effective number of strings

times the mean multiplicity of each string. The effec- tive number of strings is less for the fusion case than

for the nonfusion one, and the difference between both

increases with the energy and with the atomic num-

ber A - string fusion will be stronger for Fe-air than

for p-air collisions - due to the increasing number of

fused strings. Thus the string fusion does the same job as the composition change.

Therefore, the change in the energy behaviour of

the average shower depth of maximum X,,,,, can be

due to a change in the interaction mechanism with the existence of collective effects like string fusion, and

not to a change in the chemical composition of the pri-

mary cosmic rays. Further studies of this point would require combining the code used in this paper with the

standard codes which describe the full cascade. Work in this direction is in progress.

These predictions of string fusion can be detected

in future experiments at RHIC, LHC and cosmic ray experiments (concretely the Auger proyect [ 231) .

Finally we would like to thank N.S. Amelin, A. Capella, J.W. Cronin, G. Parente, J. Ranft and E. Zas for useful comments and discussions and the Comision

82 N. Armesto et al./Physics Letters B 389 (1996) 78-82

Interministerial de Ciencia y Tecnologfa (CICYT) of Spain for financial support. M.A. Braun thanks IBER- DROLA, E.G. Ferreiro thanks the Xunta de Galicia and Yu.M. Shabelski the Direcci6n General de Politica Cientifica of Spain for finantial support. This work was partially supported by the INTAS grant 93-0079.

References

Ill

[21

L31 141

ISI

161 r71

[81

9. Andersson, G. Gustafson and 9. Nilsson-Almqvist, Nucl. Phys. B 281 (1987) 289; M. Gyulassy, CERN preprint CERN-TH 4794 ( 1987). A. Capella, UP. Sukhatme, C.-I. Tan and J. Tran Thanh Van, Phys. Rep. 236 (1994) 225. K. Werner, Phys. Rep. 232 (1993) 87. H. Serge, H. Stocker and W. Greiner, Nucl. Phys. A 498 (1989) 567~. C. Pajares, Proceedings of the International Workshop on Quark Gluon Signatures, Strasbourg, France, October l-4, 1990; M.A. Braun and C. Pajares, Phys. Lett. B 287 (1992) 154; Nucl. Phys. B 390 (1993) 542, 559. 9. Andersson and P Henning, Nucl. Phys. B 355 ( 1991) 82. H. Sorge, M. Berenguer, H. Stocker and W. Greiner, Phys. L&t. B 289 ( 1992) 6. H.-J. Mohring, J. Ranft, C. Merino and C. Pajares, Phys. Rev. D 47 (1993) 4142; C. Merino, C. Pajares and J. Ranft, Phys. L&t. B 276 (1992) 168.

[91 K. Werner and J. Aichelin, Phys. Lett. B 308 (1993) 372.

[ 151 T.K. Gaisser et al., Phys. Rev. D 47 (1993) 1919. [ 161 N.N. Efimov et al., Proceedings of the International

Workshop on Astrophysical Aspects of the Energetic Cosmic Rays, Kofi 1990; N. Hayshida et al., Phys. Rev. Lett. 73 (1994) 3491; S. Yoshida et al., Astropart. Phys. 3 (1995) 105.

117 1 K. Greisen, Phys. Rev. Lett. 16 (1966) 748; G.T. Zatsepin and V.A. Kuzmin, JETP Len. 4 ( 1966) 78: EW. Stecker, Phys. Rev. Len 21 (1968) 1016.

[ 181 A.M. Baldin et al., Yad. Fiz. 20 (1974) 1210; Sov. J. Nucl. Phys. 20 ( 1975) 629.

[IO] J. Ranft, A. Capella and J. Tran Thanh Van, Phys. Len B 320 ( 1994) 346.

[ 11 I N.S. Amelin, M.A. Braun and C. Pajares, Phys. Lett. B 306 (1993) 312; Z. Phys. C 63 (1994) 507.

[ 121 N. Armesto, M.A. Braun, E.G. Ferreiro and C. Pajams, Phys. Lett. B 344 (1994) 301.

[13] N.S. Amelin, N. Armesto, M.A. Braun, E.G. Ferreiro and C. Pajares, Phys. Rev. I&t. 73 (1994) 2013.

[ 141 D.J. Bird et al., Phys. Rev. Lett. 71 (1993) 3401; Astrophys. J. 424 (1994) 491.

[ 191 M.I. Strikman and L.L. Frankfurt, Phys. Rep. 76 ( 1981) 215.

[20] A.V. Efremov, A.B. Kaidalov, V.T. Kim, G.I. Lykasov and N.V. Slavin, Sov. J. Nucl. Phys. 47 (1988) 868.

[21] M.A. Braun and V. Vechermin, Nucl. Phys. B 427 ( 1994) 614.

[22] Y.D. Bayukov et al., Phys. Rev. C 20 (1979) 764; Phys. Rev. C 22 ( 1980) 700.

[23] The Pierre Auger Project, Design Report, October 1995. [24] N. Armesto, M.A. Braun, E.G. Ferreiro and C. Pajares,

Santiago, preprint US-FT/33-96 (hep-ph/9607239) (1996).