aa r X i v : . [ a s t r o - ph ] A ug TH I NTERNATIONAL C OSMIC R AY C ONFERENCE
Prompt muons in extended air showers
J. R
IDKY , D. N OSEK , P. T RAVNICEK , P. N ECESAL Institute of Physics of the Academy of Sciences of the Czech Republic, Prague, Czech Republic Institute of Particle and Nuclear Physics, Charles University, Prague, Czech Republic [email protected], [email protected]
Abstract:
We present results of simulations of a muon content in the air showers induced by very highenergy cosmic rays. Muon energy distributions and muon densities at ground level are given. We dis-cuss a prompt muon component generated by decays of charm mesons. The method combines stan-dard Monte Carlo generators incorporated in the CORSIKA code and phenomenological estimates of thecharm hadroproduction.
Introduction
Extended air showers (EAS) are initiated by veryenergetic primary cosmic ray (CR) particles in-teracting with air by producing many secondaryhadrons that may produce other hadrons in sub-sequent interactions. In the EAS development aspecial role is played by neutral pions that rapidlydecay into gammas. These gammas start an elec-tromagnetic shower carrying typically 90% of theinitial energy. The rest of the energy showed upas muons from hadronic decays. Whereas theelectromagnetic part of the shower is well under-stood, the muon component depends strongly onthe mechanism of the hadronic interactions, prop-erties of which are not well known at incident en-ergies above a few hundred of GeV in c.m.s.Available data in the GeV– TeV energy rangeobtained with surface and underground detectorsare still too discrepant to draw definite conclu-sions on the muon spectra induced in EAS. It isknown that direct measurements of low energymuons [1, 2] as well as experimental data on highenergy muons [3, 4, 5] are not described satisfac-torily by simulations using the currently employedhadronic interactions model [6, 7, 8, 9]. Some in-teresting features about the EAS muon productionhave been recently obtained using the high energyhadronic interaction model EPOS [10]. A prelim-inary analysis of EPOS results showed that dueto the enhanced (anti)baryon production the num- ber of muons in the EAS increases more rapidlywith energy than in the currently used high energyhadroproduction models. Nonetheless, one cannotexclude the possibility that something important ismissing in interaction models, especially, concern-ing the very high energy region.In this work, we briefly discuss the relationshipbetween the hadronic multiparticle production andEAS observables. A special attention is paid tocharm secondaries that are accessible in hadronicinteractions during the EAS development initiatedby very high energy CR primaries, typically at en-ergies greater than 1 PeV [11]. The main goal is todiscuss the impact of the production of charm par-ticles and their prompt decays on the EAS muoncontent that is relatively easily measured with greataccuracy.
Model of prompt muon production
The number of muons registered by a ground arrayis one of the most important observables in EASphysics. It depends on the primary energy and thedetails of consecutive collisions of shower hadronswith air nuclei.At GeV energies the EAS muon component isdominated by conventional sources, i.e. the weakdecays of relatively long–lived mesons, pions andkaons. At very high energy pion or kaon decaysbecome very rare. For energies of the order of
ROMPT MUONS σ cc ≈ mb at energiesof 200 GeV in c.m.s. We assume that the charmcross section in p-Air collisions grows up logarith-mically [12], σ cc ≈ . σ inel at the incident en-ergy of 100 TeV reaching a value σ cc ≈ . σ inel slightly above the incident energy of 10 EeV, seealso [15].In the present approximation, mesons and nucle-ons are generated in nucleon–air collisions and inconsecutive hadron–air collisions. Part of the ini-tial energy of the interaction is carried by the in-volved conventional hadrons ( p, n, π, K, η ). Thenumber of these hadrons remains unchanged dur-ing the collision, their energies are degraded anda modest fraction of their total energy, typicallyless than 20%, is transformed into the energy offinal charm degrees of freedom. Energy spectraof produced charm particles are mimicked usingspectra of ordinary secondaries. Because at the en-ergy of interest their secondary interactions seldomoccur, it is assumed that charm particles ( D, Λ c ) p, E=1 EeV L og d N µ / d E µ E µ [ TeV ] Q Figure 1: Ground level energy spectra of muonsoriginated in EAS with (open circles) and without(full circles) charm production are shown in upperpanel. The incident proton energy is set to 1 EeV.Corresponding excess of muons born in EAS withcharm production is shown in lower panel as afunction of muon energy.decay very rapidly ( cτ ≈ − µ m). Eventhough there are many semi–leptonic decay chan-nels for charm particles and most of them havemore than three particles in the final state we do notinvestigate these processes in detail. We assumethat charm particles decay mostly into muons withtypical branching ratios for semi–leptonic decays BR(D , Λ c → e , µ ) ≈ − ; also hadronicdecay modes producing secondary mesons are in-cluded in the model. EAS simulations
Being formed during a multistep hadronic cascade,the EAS muon content is closely connected to themechanism of hadron–air collisions. These colli-sions are investigated in the standard treatment. Toobtain the energy spectra of conventional particlesthe QGSJET01 model [6] of hadronic interactionsis employed. The GHEISHA procedure is used totreat hadronic collisions of secondary particles atsmall energies. To describe the propagation of the TH I NTERNATIONAL C OSMIC R AY C ONFERENCE -0.2-0.100.1 p Q N p Log E [ GeV ] Q E Figure 2: Ground level excesses of the total num-ber (upper panel) and energy (lower panel) ofmuons in EAS with charm production are depictedas functions of the primary proton energy. Muonenergies are constrained as E µ ≥ . , , , and GeV.particles in EAS down through the atmosphere theEAS simulation code CORSIKA [16] is adapted.Charm particles are produced at the expense of theenergy of secondary baryons and mesons producedin subsequent hadron–air collisions in which theinteraction energy exceeds 150 GeV in c.m.s.; noaccount of their energy spectra is taken. Electron–photon cascades due to the decays of neutral pionsare treated by common standards.The CR primary protons are assumed to interactwith the air nuclei at various incident energies of100 TeV–10 EeV. The primary zenith angle isfixed at zero degrees; the altitude of the initial in-teraction is left free. In all simulations, a standardU.S. atmosphere is used.The kinetic energy cutoffs for EAS hadronsand muons are chosen to 0.3 GeV; for elec-trons/positrons and photons we use cutoffs of20 MeV and 2 MeV, respectively. In all calcu-lations a thinning level of − and a maximumweight factor of are adopted for both electro-magnetic as well as hadronic particles. In orderto minimise influence of shower to shower fluctu-ations we average over 100 air showers; statisticaluncertainties are shown in figures. -0.2-0.100.1 p, E = 10 PeV Q N p, E = 10 EeV p, E = 10 PeV r [ m ] Q E p, E = 10 EeV r [ m ] Figure 3: Ground level lateral excesses of the num-ber (upper panels) and energy (lower panels) ofmuons in EAS with charm production initiated bythe proton primary with the incident energy of10 PeV and 10 EeV are depicted. Results for muonenergies E µ ≥ . , and GeV are shown.To visualise effects associated with the EAS charmproduction we use the asymmetry–like quantity Q = N ′ µ − N µ N ′ µ + N µ , where N ′ µ and N µ are the number orenergy densities of muons originating respectivelyin EAS with or without charm production and reg-istered by the ground detector. This quantity mea-sures an excess of muons originated in EAS withcharm production over muons in showers gener-ated in conventional models. Numerical results
Depending on the primary energy, a fraction ofcharm particles with respect to hadrons producedin all consecutive collisions during the EAS devel-opment is − − − in our calculations. Anenergy fraction carried by these charm particles in-creases more rapidly with the increasing primaryenergy from a value of − at the PeV regionreaching − at the energy of 10 EeV.The energy spectra of muons initiated by the pro-tons of the primary energy of 1 EeV and detectedat the ground as obtained in our simulations withthe QGSJET01 high–energy interaction model are ROMPT MUONS depicted in Fig.1. Depending on the initial energy,the energy spectra of muons fall off by about 4–6orders of magnitude in the 10 GeV–10 TeV range.These spectra have typical profiles with a visibleexcess of hard muons due to charm production.At the primary energies of interest, secondary pi-ons and kaons are mostly above the critical en-ergy ( E cr < TeV) and so predominantly gen-erate conventional muons in interactions, whilecharm particles being below their critical energy( E cr > PeV) give prompt muons of high en-ergies. This effect is remarkably large reaching afactor of two for highest muon energies studied.Some general features of our simulations that canbe observed by the ground level detector or under-ground are summarised in Fig.2. Here excesses ofthe total number and energy of muons originated inEAS with charm production are shown as functionsof the incident energy of the CR proton. The totalnumber of muons and their energy are depicted formuons with energies E µ ≥ . , , , and GeV that in our calculations imitate the rockoverburden for underground experiments.It is well visible that muons in EAS with charmproduction deposit remarkably more energy in thedetector than muons in conventional showers. Thiseffect is pronounced with the increasing lower en-ergy cut for muons. Our simulations show thatcharm particles carrying away a non–negligiblefraction of the incident energy can be responsiblefor the delay of the energy absorption along theEAS axis. On the other hand, the number of muonsborn in EAS with charm production and registeredat the ground or underground remains relativelystable with the increasing primary energy and, al-though mostly smaller, it does not differ consider-ably from the number of muons in showers gener-ated in conventional models.Examples of the lateral number and energy densi-ties of muons initiated by the protons of the pri-mary energies of 10 PeV and 10 EeV are depictedin Fig.3. We have found a small but visible deficitof muons in very high energy EAS with charmproduction with respect to conventional showers.On contrary, due to charm production an excessof muon energy that should be deposited near theshower axis in the ground detector or undergroundis observed.
Conclusions
The calculation of the EAS muon content suffersin principle a significant uncertainty due to thelack of knowledge of the properties of the charmproduction in the hadron–nucleus collisions. Weshowed that a simple phenomenological treatmentof prompt muons can reveal interesting observablefeatures. More precise analysis will be carried outin the future.
Acknowledgements
This work is supported by the Ministry of Educa-tion, Youth and Sports of the Czech Republic underContracts Nos. LC 527 and MSM 0021620859.