Diquark breaking mechanism up to GZK cut off energies

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Diquark

Nuclear Physics B (Proc. Suppl.) 122 (2003) 396-399

breaking mechanism up to GZK cut off energies

J.-N. Capdevielle and F. Cohena* aPhysique Corpusculaire et Cosmologie, College de France, 11 Place M. Berthelot, 75231 Paris Cedex 05, France We examine the general situation of the Monte Carlo collision generators used in the simulation of GAS and based on Gribov-Regge phenomenology. The particular circumstance of the diquark breaking mechanism has been involved in cascade simulation and some consequences are pointed out for Giant Extensive Air Showers (GAS).

1. EXTRAPOLATIONS

BEYOND

LHC

The simulation of cascades at energies of 100 PeV, or more, for AUGER and EUSO experiments requires a description of the main features of multiple production at energies 1000 times larger than the energy expected for proton collisions at the LHC (equivalent to O.lEeV in the Laboratory system). The energy of the LHC is about 100 times above the energy limit of the CERN and Fermilab colliders, and the general situation of the theoretical predictions for high energy collisions is characterized by a very wide interval, comparable to the state of the art at the beginning of the 1980’s. The actual difficulty of the extrapolation is well illustrated in Fig.1 where we compare the pseudo rapidity distribution predicted for the LHC by a half-dozen of models currently employed in particle physics. The distributions shown in Fig. 1 give for the hybrid dual parton model HDPMZ [l] different extrapolations up to 1O1* GeV (histograms for HDPM2, full line for QSJET model at collider energies, full lines for 6 other models at LHC energy) following the parton distribution functions (PDF) assumed (BO and B-). The different pseudo-rapidity distributions superimposed on the collider data shown on Fig. 1 correspond to collider energies at fi = 630, 1800 GeV, LHC energies at fi = 14 TeV (full lines), HDPM2 model (histograms). In order of decreasing central rapidity densities, the 6 distributions at LHC energies (full lines) are plot*This work has been supported 1339. 0920-5632/03/$ - see front matter doi: 10.1016/S0920-5632(03)02055-3

by INTAS 0 2003 Elsevier

contract Science

99B.V.

ted for PYTHIA 6.122A, PYTHIA 6.122 model 4, PYTHIA 5.724 ATLAS, PHOJET 1.12, HERWIG 5.6, ISAJET 5.32 predicting very different behaviours [2]. We can oberve central densities of pseudo rapidity between about 3.9 (an extended plateau at the same level as the Fermi collider for ISAJET) up to 9.5, with associated average charged multiplicities rising from 70 up to 125. A comparable amplitude of the uncertainty of the predictions concerning average multiplicities and pseudo-rapidity distributions at LHC energies has been pointed out using the Dual Parton Model [8] under various assumptions on PDF [4]. For cosmic rays at 102*eV, such a situation suggests an uncertainty for the value of the average charged multiplicity for p-Air collisions ranging from 250 up to 1000 secondaries. The 3 lower histograms plotted for HDPMZ represent the situation expected for the NSD component up to LHC energies. The lines corresponding to QSJET model, as well as the histograms of HDPM2, are in good agreement with the experimental measurements at collider energies [5,6]. Both upper histograms correspond to a primary energy of 10lgeV and represents the consequences of a permutation of parton distribution functions. Extensive air showers will reach their maximum at quite higher altitudes if the highest multiplicities, like in QGSJET or PYTHIA 6.122A, are confirmed. The correlation between the central rapidity density and the average transverse momentum All rights

reserved.

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1 -Pythia6.122A 2 - Pythia 6.122 modkle 3 - Pythia 5.724 Atlas 4-PHOJET 1.13

Physics

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Figure 1. Pseudo-rapidity distributions, reproduced at collider energies, predicted for LHC and extrapolated to 10l’GeV (both upper histograms for Be and B- parton distribution functions. The central histogram and the 6 full lines starting from the top, represent the prediction for the LHC at &s) = 14 TeV.)

< pt > also plays a role in the muon and hadron radial distributions: the dependence of the average transverse momentum on energy shows a permanent increase with energy and good agreement with the HDPM2 and the experimental data [7].

2. LEPTONIC

SYNCHRONISM

IN GAS

Among our general results on the longitudinal [3] and lateral development around 100 EeV [9], we present here the time distributions of the different components. Taking advantage of the 40simulation carried out with CORSIKA, we have derived the arrival time distributions of the dif-

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ferent particles in fixed bands of distances, 550 to 650 m, 900 to 1lOOm and 1450 to 1750 m. The average arrival times r are listed in Table 1 for the different particles and axis distances. The respective r.m.s. standard deviations can be compared to the mean arrival time 7. At 600 m, they are comparable to 7 for photons, electrons and muons, about one half for hadrons and neutrons. At 1600 m from the axis, they are respectively about 70% and 40%. Electrons, photons and muons are approximately synchronous. The value of r for hadrons and neutrons is about 3 times larger. This suggests the existence of one delayed signal, with a large spread for proton and iron initiated showers. As seen from Table 1, there is no chance to distinguish proton and iron primaries by time measurements in near vertical showers. On the other hand, the delayed signal will be systematically missing in photon initated showers, as well as in showers rejuvenated after muon bremsstrahlung or initiated by a high energy neutrino interaction. The shower front delay at different distances, as well as its thickness can be established on the basis of those simulations. The delay rises approximately by 0.2 ns/m with shower axis distances up to 600 m, but this delay increases beyond 600 m up to 0.5 - 0.6 ns/m near 1500m and this information will help with axis localisation.

3. DIQUARK PRESSION EFFECT

BREAKING OF LEADING

AND SUPPARTICLE

The diquark breaking mechanism disturbs strongly the leading particle effect present in the different models used in cosmic rays. In the classical form of the dual parton model, the 3 valence quarks of the proton projectile are separated in a fast diquark and another valence quark slowed down. The diquark is recombined with one quark of the sea to produce, most commonly, an outgoing leader baryon propagating the energy deeper in the cascade. The 3 valence quarks separated will be recombined in various meson structures in pairs 1~2 >, ldii >,... or neutral mesons as l/&ddUC). The configuration with the simultaneous final state for the valence quarks of 3

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Capdevielle.

I! Cohen/Nuclear

Physics

B (Proc.

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Table 1 Average arrival times (in ns) for the different particles at 600, 1000 and 1500 m from axis.

T T T r r T

= = = = = =

600m, prim.p 600m, prim. Fe lOOOm, prim.p lOOOm, prim. Fe 1600m, prim.p 1600m, prim. Fe

7-r

T.2

483 486 1078 992 1610 1706

338 370 815 836 1484 1350

x0’s could be especially interesting with a probability of emergence that we can evaluate from the quark content and the quark additive model as l/27. Such configuration (with intermediate final states of higher probabilities, one pair of charged pions and one neutral, one pair of neutral and one charged...) will transfer a large part of energy to the electromagnetic component and this energy will be definitely missing for both hadronic and penetrating components. Remembering that for the same primary energy, the cascade theory shows that one primary photon produces at maximum, approximately two times more electrons, we can expect a large electron excess for some cascades initiated with diquark breaking. This gain is however smeared out at UHE as shown by the ratio of Nmax for photon and proton induced showers as shown in Fig. 2 (standard simulations with CORSIKA without diquark breaking). The consequences near the GZK cut off are then complex and could appear more via the larger fluctuations (LPM effect in proton showers starting with diffraction or small multiplicity). The effects could be important also in the knee region and above. For instance, the diquark breaking mechanism (with recombination in neutral channels) could explain the absence of high energy photons in EAS near 4.107 GeV pointed out by the TianShan experiment [lo]. The integral energy spectrum simulated with CORSIKA, where we have implemented the diquark breaking mechanism, reproduces the absence of particles in fragmentation altitude in Fig.3 for the neutral channel recombination following the diquark break-

TP 353 359 837 797 1278 1325

7th

772

1404 1453 2310 2231 3598 3185

2174 2174 3613 3318 4696 5215

ing (lower curve). The upper curve (spectrum obtained with standard leading particle effect in CORSIKA) represents a kind of scaling behavior for the x-distribution of very energetic y’s observed in EAS with X-ray emulsion chambers. This scaling behavior is observed and reproduced by the simulation up to lo7 GeV. We underline the lack of photons in the energy range 1 TeV to 500 TeV in the lower spectrum. For the same primary energy, because of the larger size (about 2 times larger than without diquark breaking) and the steep primary energy spectrum, the statistical weight of the lower spectrum turns out to be comparable (at fixed electron size) and is even more important than for the standard multiple production spectrum. This circumstance for the most energetic showers recorded in the Tian-Shan experiment occurs in the same energy range as predicted on the maximum depth [ll] and coincides also with the data on maximum around 0.1 EeV. 4. Conclusion The large discrepancies of the different models at LHC energies suggests wider uncertainties for the extrapolations at 100 EeV, above the GZK cut off. The estimate of the primary energy for inclined showers will be more model dependent than expected. In the case of water Cerenkov tanks, like in AUGER, there is a particular sensitivity to the muon electron abundance. This dependance has a specific behaviour with zenith angle for each model, and this difficulty will have to be taken into account.

J-N Nmax

(gammas)

Cupdeuielle, F Cahen/Nucleur

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Physics B (Proc. SuppI.) 122 (2003) 396-399 HE Y 6 in EAS at 3200111altitude

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Figure 2. Average ratio of the maximum size versus energy for showers initiated respectively by primary photon and proton, including LPM effect

The hypothesis of the valence diquark breaking above the knee has to be examined in more detail in connexion with specific features of cosmic ray data (maximum depth behaviour, coplanar emission, secondaries in fragmentation region) in parallel with the phase transition to QGP (about 30 GeV/Fm3 in 100 EeV collisions). REFERENCES 1. Capdevielle J. N., Le Gall C. Sanosyan K., tlstroparticle Physics, 13, 259 (2000) 2. Stavropoulos G. D., Proc. XXX1 Int. Symp. Multiparticle Dynamics, World Scientific, 288 (2002) 3. Capdevielle J. N. et al., Proc. XXX1 Int. Symp. Multiparticle Dynamics, World Scientific, 420 (2002) 4. P. Aurenche et al., Phys. Rev. D, 45, 92 (1992)

EylEo

Figure 3. Absence of fragmentation component at 4.107 GeV (lower energy spectrum) in case of diquark breaking in EAS at 3200m altitude.

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