We review the data obtained with the emulsion chambers boarded on Concorde for the events collected above 106 GeV and their specific properties (large multiplicities, multiclusters, coplanar emission): the main features are compared to the expectation of our HDPM2 Monte Carlo collision generator. This multiproduction event generator has been adjusted and tuned, according to the 

pseudo-rapidity distributions recently observed at √s = 630 GeV, as well as to previous Fermi-lab results at √s = 1800 GeV: an increase of the total inelasticity (0.72 for NSD component) near the knee region and a more important violation than usually expected for Feynman’s scaling in forward region are observed. In such cirumstance, we have

simulated large and giant air showers taking into account, in addition, new processes, such as diquark breaking, up to energies exceeding 1020 eV for P.AUGER and EUSO experiments

Capdevielle, J.N.

Cohen, F.

Kurp, I.

Le Gall, C.

Szabelska, B.

Szabelski, J.

English

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IL NUOVO CIMENTO Vol. 24 C, N. 4-5 Luglio-Ottobre 2001High energy cosmic rays in the low stratosphereand extrapolation above LHC energies(∗)J. N. Capdevielle(1), F. Cohen(1), I. Kurp(2), C. Le Gall(1)B. Szabelska(2) and J. Szabelski(2)(1) PCC, Colle`ge de France - 11 Pl. M. Berthelot, 75231 Paris Cedex 05, France(2) The Andrzej So#ltan Institute for Nuclear Studies - 90-950 #Lo´dz´ 1, Box 447, Poland(ricevuto l’8 Novembre 2000; approvato il 12 Febbraio 2001)Summary.—We review the data obtained with the emulsion chambers boarded onConcorde for the events collected above 106 GeV and their specific properties (largemultiplicities, multiclusters, coplanar emission): the main features are compared tothe expectation of our HDPM2 Monte Carlo collision generator. This multiproduc-tion event generator has been adjusted and tuned, according to the pseudo-rapiditydistributions recently observed at√s = 630 GeV, as well as to previous Fermi-labresults at√s = 1800 GeV: an increase of the total inelasticity (0.72 for NSD com-ponent) near the knee region and a more important violation than usually expectedfor Feynman’s scaling in forward region are observed. In such cirumstance, we havesimulated large and giant air showers taking into account, in addition, new pro-cesses, such as diquark breaking, up to energies exceeding 1020 eV for P.AUGERand EUSO experiments.PACS 13.85.Tp – Cosmic-ray interactions.PACS 96.40.De – Composition, energy spectra, and interactions.PACS 96.40.Pq – Extensive air showers.PACS 01.30.Cc – Conference proceedings.1. – The French-Japanese emulsion chamber exposures on the ConcordeRegular supersonic atlantic flights provide one “plateau exposure” of more than 2hours. The same X-ray emulsion chamber carried one hundred times above the At-lantic is then exposed during 200 hours at least at an average altitude of 17 km. Thiscorresponds, as indicated by the Concorde flight curve to an atmospheric depth of 100–105 g cm−2. During the last 20 years, 8 emulsion chambers have been flown on theConcorde for different measurements, very high energy jets, stratospheric γ-ray families,(∗) Paper presented at the Chacaltaya Meeting on Cosmic Ray Physics, La Paz, Bolivia,July 23-27, 2000.c© Societa` Italiana di Fisica 531532 J. N. CAPDEVIELLE, F. COHEN, I. KURP, ETC.Table I. – Some remarkable events recorded during Concorde flights.Event ΣEγ(TeV) nγ nch VertexJFa1 18 4 26 producerJF1af1 260 150 - cabin wallJF2af1 1586 211 - 100 m aboveJF3.1 55 - 24 producerJF3.2 51 - 54 producerJF5.1 138 18 - 5 kmγ-ray flux [7, 1-3], gamma-ray energy spectrum in the interval 1–50 TeV, hyperstrangebaryonic matter [4] and more recently emulsions for dosimetry (neutrons between 1 and10 MeV). All the detectors, but the last one, were enough thick to measure, at least, theenergy of secondary γ-rays up to 1000 TeV, allowing to initiate the collection of infor-mation on multiproduction in the energy range between the limit of the present collidersand the LHC. Those events (3 of them are above 106 GeV) are listed in table I.The event JF1af1 resulted from a collision generated in cabin wall, about 3 m abovethe chamber and this circumstance was providential to build the rapidity distributionof the 150 γ’s of energy exceeding 200 GeV. The characteristics of this event, high mul-tiplicity, large transverse momentum suggest a classification in the nonsingle diffractivecomponent with high z as expected from the negative binomial distribution. However,the multicluster structure and a pair of sharp spikes in the rapidity distribution requiremore simulations in 3 directions (fluctuations for individual events and random accumu-lation of secondaries by pure chance, Alpha primary and QGP). At larger energy, around107 GeV, one impressive stratospheric family was collected; the probability to observesuch energy with a so small time of exposure (area 40 cm × 50 cm for each chamber) isreduced and can be only compensated by a wide solid angle. This event was effectivelyvery inclined with a zenith angle of 52◦.2. – The coplanar event of 107 GeVThe 211 γ’s (above 200 GeV) of this event were identified with their respective coor-dinates and energies; the analysis was then focused on the typical multicluster structureand the planarity, ascertained by naked eye on the X-ray film, was confirmed, suggestinga multijet structure [3]. It is interesting to compare the event seen by naked eye from thepicture of the X-ray film (fig. 1) and an event simulated at the same energy showing alsoan alignement obtained by pure chance from coincidence of favourable geometric andnuclear conditions. The similarity of the clusters (gammas above 10 TeV are plotted)with those of fig. 1 is especially interesting. Tracing back the genetics of this event, itbelongs to the normal NSD multiple production with high multiplicity. The first collisionoccurred at an altitude of 24 km and the regression coefficient of the 32 gammas (above10 TeV) is 0.968 with a total energy deposited of 815 TeV. The main features generatingthe alignement are here:– high multiplicity,– important zenith angle.HIGH ENERGY COSMIC RAYS IN THE LOW STRATOSPHERE ETC. 533Fig. 1. – Coplanar emission visible in the event JF2af2 from the X-ray film. Several points withminor separations (bremsstrahlung or pair creation near the chamber) are superposed.Both circumstances combine as follows: the probability to get a large transversemomentum is enhanced in high-multiplicity events and this large pt can be devoted to ahigh energy gamma. This emission can be close, as here, to the vertical plane. The restof the cluster is displaced in the opposite direction (pt conservation and the maximalseparation between gamma’s appear in the horizontal plane (the emulsion or X sheets)with a characteristic gap visible in fig. 1 and in some events of Pamir). On our sampleof 100 events, we have counted 2% of events with r ≥ 0.95, 6% events with r ≥ 0.9, 10%and 18% with r exceeding respectively 0.8 and 0.7. The combination of a large transversemomentum generated in the vertical plane (or in the neighbourhood) for an energeticsecondary at 1st collision can be at the origin of the alignments observed in emulsionchambers. In that case the coplanar emission appears near 107 GeV where the ratioprimary energy-energy threshold of the chamber is the most favourable. More simulationswill be needed to confirm the increase of the probability of alignment observation at largezenith angle with a characterictic gap. The zenith angle distribution of coplanar events,associated to the frequency versus observed energy are probably the best criteria tounderstand if we have here a pure geometrical high-multiplicity fluctuation in the NSDcomponent artefact or if this is a footprint of new physics.3. – Extrapolation at ultrahigh energiesA special set of simulations has been carried out with the same zenith angle as forJF2af2 of 52◦ for 100 events. This was done with the model HDPM2 taking into accountrecent features of collider physics such as pt versus central rapidity density (UA1-MIMIexp.) and recent results of Fermi-lab for pseudorapidity up to 5.5 [5]. The pseudo-rapiditydistributions obtained with HDPM2 for 2000 collisions NSD are shown in fig. 2 [6].As it was not possible to scan each individual event simulated, it was requested tocalculate the linear regression line from the coordinates of the gammas and to plot onlythe events with a regression coefficient larger than 0.9. The event no. 47 of this serialselected by this method shows a nice alignment of 32 gamma’s. As it can be ascertained,there are not very large differences between the HDPM2 and the QGS-jet model atcollider energy. The extrapolations at higher energy can be different according to theparton distribution function assumed and there are several sets of parameters available.Another difficulty in the extrapolation can come from modifications generating wideramplitudes such as the mechanism of diquark breaking. Such effect can suppress the534 J. N. CAPDEVIELLE, F. COHEN, I. KURP, ETC.Fig. 2. – Pseudo-rapidity distributions with HDPM2.leading-particle effect, classical for hadronic cascades if we consider that the valencediquark of the projectile is broken: the recombination of the diquark with one valencequark is impossible and a leading proton cannot emerge. We estimate that in suchcircumstance the maximum depth of EAS will be shifted systematically at higher altitudeby 50 g cm−2 and this mechanism could help the understanding of a more realistic masscomposition above the knee.4. – Topological problems in giant EASOther difficulties may occur independently of the interaction model in the topologicalapproach of the observables used to estimate the primary energy, for instance the profileof the lateral distribution assumed and the core localization. We propose instead ofNKG and other Euler beta-functions, the employment of the Gaussian hypergeometricformalism giving also normalization and better skewness, under the formf(x) = g(s)xs−a(x+ 1)s−b(1 + dx)−c ,(1)which has the advantage (for values of parameters respecting the conditions of conver-gence s−a+2 > 0 and c−2s+ b−2 > 0) to be exactly normalized in terms of Gaussianhypergeometric function FHG = F (c, s− a+ 2, c+ b− s; 1− d) byg(s) =Γ(c+ b− s)2πΓ(s− a+ 2)Γ(c− 2s+ b+ a− 2)FHG .(2)HIGH ENERGY COSMIC RAYS IN THE LOW STRATOSPHERE ETC. 535Table II. – Best parameters to simulated e+e−+ muons (all charged) lateral distribution fitusing JNC01 formula.p10 p20 Fe10 Fe20log10Ne 10.75 10.72 10.70 10.65rM 21.26 21.26 19.18 19.18r0 8785. 8785. 9536. 9536.a 1.91 1.91 1.82 1.82s 1.03 1.04 1.03 1.04b 3.32 3.32 3.31 3.31β 10.0 10.0 10.0 10.0χ2(50) 12.1·106 19.5·106 6.87·106 10.4·106χ2P (50) 12.2·106 20.2·106 6.94·106 10.6·106Ξ 2.61 1.77 5.20 1.95Table III. – Columns a present total number of charged particles Ne in 1010, columns b theratios E0/Ne in GeV (E0 = 1011 GeV) and columns c the ratios (600)/Ne in 10−8 particles/m2.m(600) =d(log )d(log r)at 600 m.proton 10◦ proton 20◦ iron 10◦ iron 20◦(600) 290 m−2 318 m−2 369 m−2 356 m−2E0/(600) 3.4 · 108 3.1 · 108 2.7 · 108 2.8 · 108(GeV m2)m(600) –3.9 –3.6 –3.6 –4.0fit 1a 1b 1c 2a 2b 2c 3a 3b 3c 4a 4b 4cYakutsk 1.8 5.6 1.6 1.7 5.9 1.9 2.3 4.3 1.6 1.9 5.3 1.8Linsley’s 8.2 1.2 0.3 8.0 1.3 0.3 10.5 0.9 0.3 8.9 1.1 0.4AGASA #1 2.4 4.2 1.2 2.6 3.8 1.2 3.1 3.2 1.1 2.9 3.4 1.2AGASA #2 3.3 3.0 0.8 3.6 2.8 0.8 4.2 2.4 0.8 4.0 2.5 0.8this work 5.6 1.8 0.5 5.6 1.9 0.6 5.1 2.0 0.7 4.5 2.2 0.7The empirical distributions, such as AGASA function [8], as underlined by Vishwanath [9]enters in the category of hypergeometric Gaussian functions [10].The value used in AGASA function for the coefficient Ce is just an approximation;the exact value isCe =Γ(β + η − α)2πΓ(2− α)Γ(β + η − 2)1FHG.The hypergeometric Gaussian function can be easily calculated from the hypergeometricseries. This equation is equivalent to our version (3) containing the age parameter s withthe relations between respective coefficients: x = rrM , d =rMr0 , s = 1.03, α = a − s,η = b−s+α. (The value of s is taken from the longitudinal development simulated.) We536 J. N. CAPDEVIELLE, F. COHEN, I. KURP, ETC.Fig. 3. – Fits to all charged particles lateral distribution from simulations (average from 10EAS). Primary particle energy 1011 GeV. Lines are normalized to (600 m).have adjusted with MINUIT the parameters of our hypergeometric function (table II)to the average lateral distributions (set JNC01 for charged, JNC02 for electrons) of 10showers at 1020 eV simulated with CORSIKA (QGSJET model), as shown in fig. 3.In each case, the adjustment has been performed with 50 points from the simulationdistributed from 0.1 m up to 10 km from the axis position for charged particles (muonsand electrons) as shown in fig. 3. The advantages of JNC01 formula can be seen in fig. 3and in table III. The major part of the particles is contained inside 200 m from the axisand only the skewness of the hypergeometric function allows a reliable relation betweenHIGH ENERGY COSMIC RAYS IN THE LOW STRATOSPHERE ETC. 537size and density at 600 m. This method has been applied to the showers contained inthe catalogues of Volcano Ranch and Yakutsk. The core position has been obtainedby minimization with Minuit program between different formulas available for lateraldensities written versus the coordinates X, Y as(r) = (√(X −Xc)2 + (Y − Yc)2) ,(3)where the core coordinates Xc and Yc are taken as two additive parameters in the mini-mization. The adjustments are generally improved when compared to the original treat-ments, turning to lower sizes (in the case of Yakutsk formula) and better approximationof the density at 600 m.5. – ConclusionAs pointed out in sect. 2 the coplanar emission might not be a new characteristicof multiproduction near 107 GeV. More calculations at mountain altitude are requestedto check if similar circumstances can be extended to the events observed in the PamirX-ray chamber experiment. The large multiplicities of secondaries in those events remainhowever a common feature which could explain the tolerable agreement of models likeQGSJET with EAS data. The hypergeometric approach gives a better accuracy in theinterpolation of densities at 600–1000 m, a more reliable estimation of the shower size(when the axis is in the array), a better axis localization and finally a more correctconstraint of the primary energy.∗ ∗ ∗JNC is indebted to the colleagues of the emulsion division in Tokyo ICR/INS whohave performed the complete scanning of this work. This work has been partly supported(JNC and CLG) by INTAS contract 1339.REFERENCES[1] Capdevielle J. N. et al., Proceedings of the 16th ICRC (Kyoto), vol. 6 (1979), p. 324.[2] Capdevielle J. N. et al., Proceedings of the 20th ICRC (Moscow), vol. 5 (1987), p. 182.[3] Capdevielle J. N. et al., J. Phys. G, 14 (1988) 503.[4] Capdevielle J. N. et al., Proceedings of the 24th ICRC (Rome), vol. 1 (1995), p. 910.[5] Capdevielle J. N. et al., Proceedings of the 26th ICRC (Salt Lake City), vol. 1 (1999),p. 111.[6] Capdevielle J. N., Le Gall C. and Sanosyan K., Astropart. Phys., 13 (2000) 259.[7] Iwai J. et al., Nuovo Cimento A, 69 (1982) 295.[8] Nagano M. et al., J. Phys. G., 18 (1992) 423.[9] Vishwanath P. R., Proceedings of the 23rd ICRC (Calgary), Rapporteur Papers, vol. 6(1993), p. 384.[10] Capdevielle J. N. and Procureur J., Proceedings of the 18th ICRC (Bangalore), vol.11 (1983), p. 307.

High energy cosmic rays in the low stratosphere and extrapolation above LHC energies

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High energy cosmic rays in the low stratosphere and extrapolation above LHC energies

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