We consider the process of muon pair production by 

high-energy muons and its consequences for the characteristics of muon flux underground. It is shown that

the accounting of this process in the muon propagation through the rock results in an additional flux of narrow double- and triple-muon events which is comparable to the

conventional flux of narrow muon bundles with low multiplicity

Kudryavtsev, V. A.

Ryazhskaya, O. G.

Kudryavtsev, V A

Ryazhskaya, O G

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Muon pair production by muons and narrow muon bundles underground

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IL NUOVO CIMENTO VOL. 21 C, N. 2 Marzo-Aprile 1998Muon pair production by muonsand narrow muon bundles undergroundV. A. KUDRYAVTSEV and O. G. RYAZHSKAYAState Scientific Center of the Russian FederationInstitute for Nuclear Research of the Russian Academy of Science, Moscow, Russia(ricevuto il 14 Marzo 1997; approvato il 10 Aprile 1997)Summary. —We consider the process of muon pair production by high-energy muonsand its consequences for the characteristics of muon flux underground. It is shown thatthe accounting of this process in the muon propagation through the rock results in anadditional flux of narrow double- and triple-muon events which is comparable to theconventional flux of narrow muon bundles with low multiplicity.PACS 96.40.Tv – Neutrinos and muons.Muon bundles, discovered independently by G. Wataghin in 1941 [1] and E. Amaldi andC. Castagnoli in 1952 [2], are produced in Extensive Air Showers (EAS) initiated by pri-maries with energies more than 100 TeV. The study of muons in EAS provides informationabout the energy spectrum, composition and cross-section of cosmic-ray particles at veryhigh energies. Multiplicity and pair separation distribution of muons in the bundles arestudied usually in the underground experiments. The former distribution is connectedwith the primary isotopic composition and the latter one is connected with the cross-section of primary cosmic-ray particles. The new methods of muon bundle analysis aredeveloping now. These methods include the measurement of the dependence of the anglebetween muons in the bundle on their lateral separation (“decorrelation function”) [3] andsearch for muon clusters in the high-multiplicity events [4, 5]. For the analysis of muonbundles, it is very important to be sure that all detected muons were produced in EAS.The process of muon pair production by muons is usually neglected in the propaga-tion of muons because of its small cross-section which is 4 orders of magnitude less thanthe cross-section of electron pair production. However, for muon interactions with high-energy transfer (v = E=E 10 2, where Eis the muon energy and E is the energytransferred to the secondary particle(s)), the cross-section of muon pair production isabout 100 times less than the bremsstrahlung cross-section which is the most importantstochastic process for the propagation of high-energy muons through large thickness ofmatter. If the energy transferred to the muon pair is high enough, the muons producedin such interaction (or at least one muon) can reach the level of observation together withthe initial muon. This can result in the observation of double- (or triple-) muon events.G SocietÁa Italiana di Fisica 171172 V. A. KUDRYAVTSEV and O. G. RYAZHSKAYAFig. 1. – Energy distribution of muons in double- and triple-muon events at the depth of 3 km w.e.In this paper we estimate this effect and discuss its applications for underground muonphysics.The new three-dimensional Monte Carlo code MUSIC [6] has been used to propa-gate muons from the sea level to the level of observation. The code takes into accountthe stochasticity of all processes (bremsstrahlung, inelastic scattering, electron pair pro-duction, knock-on electron production) with the energy transfer v > 10 3. It calculatesthe angular deviation and lateral displacement of muons due to multiple scattering andstochastic processes. The process of muon pair production is not included originally inthis code. We have added this process with the differential cross-section from [7, 8]. Wehave taken into account the energy transfers v > 10 3. The cross-section given in [8] iscalculated in the case of full screening with the logarithmic accuracy. In the muon prop-agation through the standard rock we consider only one (if this takes place) interactionwith muon pair production. Actually, the mean muon path to the interaction with muonpair production (v > 10 3) is about 60 km w.e. (for E> 1 TeV). It is obvious that theprobability of two interactions up to the relevant depth is an order of magnitude less thanthat of one interaction. However, this fact together with the uncertainty of the cross-section, mentioned above, increases the uncertainty of the result up to about 10%. Whenthe interaction with muon pair production occurred during the muon transport throughthe rock, all three muons have been propagated up to the observation depth using theoriginal code. We did not take into account the scattering of muons due to the process ofMUON PAIR PRODUCTION BY MUONS ETC. 173Fig. 2. – Distribution of lateral separations of muons in double- and triple-muon events at the depthof 3 km w.e.muon pair production. As is shown in [6], the scattering of muons due to stochastic pro-cesses can be neglected, because the resulting angular deviation and lateral displacementare much less than those due to multiple-scattering process.Ten millions of muons were sampled according to the initial sea-level muon energyspectrum in power law form with power index  3:7 and were propagated up to the depthsof 3 and 10 km w.e. The low-energy edge of the muon spectrum at sea level was equal to900 GeV for 3 km w.e. and 9 TeV for 10 km w.e. These energies correspond to the muonsurvival probabilities  0:003. 3404569 and 399421 muons were survived at the depthx = 3 and 10 km w.e., respectively. The muon survival probabilites averaged over the sealevel muon spectrum are lower by (0:2 0:2)% and (0:1 0:2)% for x = 3 and 10 km w.e.than those obtained using the original code without muon pair production process (theerror is determined by the statistics used in the original code). This result proves thatthe muon pair production process gives a small contribution to the muon intensity under-ground and can be neglected for this purpose. Among the survived muons we have found1958 double- and 631 triple-muon events at the depth of 3 km w.e. and 382 double- and53 triple-muon events at the depth of 10 km w.e. Since most of the existing detectors areplaced at small or median depths (x  5 km w.e.), we will discuss below the characteristicsof these events at the depth of 3 km w.e.The energy distribution of muons in double- and triple-muon events at the depth of 3km.w.e. is shown in fig. 1. The distribution of the lateral separations of muons in suchevents is shown in fig. 2.174 V. A. KUDRYAVTSEV and O. G. RYAZHSKAYAThe mean energy of muons is equal to 342 GeV. This energy is higher than that of con-ventional single muons with the same initial spectrum (247 GeV ). The mean initial energyof muons at sea level is equal to 3810 GeV which is also higher than the value obtained forconventional single muons (1923 GeV ). This fact can be explained in the following way. Toproduce a muon pair with an energy sufficient to reach the level of observation (for at leasttwo muons), the initial muon should have an energy higher than the mean initial muon en-ergy for survived muons. Of course, the higher the mean initial muon energy is, the higherthe mean energy should be at the observation depth. The fact that muon energy is dividedbetween three muons and these muons lose the energy during the propagation throughthe rock is less important at this depth.The distribution of pair separations (r) presented in fig. 2 differs from that for conven-tional multiple-muon events (muon bundles). The distribution shown in fig. 2 is narrowwith a peak at r  0. This is due to the fact that muon pairs are produced along all path ofmuons down to the observation level. The main contribution to the distribution at small ris given by triple-muon events when the muon pair is produced near the observation level.The distribution of pair separations in conventional muon bundles is determined by twoeffects: i) the spread of muons in EAS due to the transverse momentum transferred to pi-ons and kaons; ii) the spread of muons due to the multiple scattering along the muon pathin the rock. The mean separation (hri) is equal to 0.43 m for the events presented in fig. 2(0.63 m for double-muon events), while it is of the order of several meters for conventionalmuon bundles.The ratio of multiple-muon events obtained with the code (hereafter we will call them“narrow muon bundles”) to the conventional single muons is 7:6  10 4. This ratio is muchless than the ratio of conventional muon bundles to the single muons which is of the or-der of several percent. However, the ratio of narrow muon bundles to the conventionalmuon bundles is increased with the decrease of r. We have calculated this ratio using theexperimental data of LVD [9]. The ratio of multiple-muon events measured by the firstLVD tower to single muons is about 0.027 [9]. For simplicity, we have considered onlydouble-muon events and found the ratio of muon pairs with r < 0:5 m to the single muonsto be 7:6  10 4. Among 1958 double-muon events (narrow muon budles) we have found1171 events with r < 0:5 m. Some fraction of these muon pairs cannot be resolved withtracking detectors due to their finite spatial resolution. The geometrical resolution of ex-isting tracking detectors is of the order of 1-2 cm. The “physical” resolution is limited bythe muon interactions inside the detector volume and the properties of the tracking de-tectors (streamer tubes, for example). We estimate the real resolution to be of the orderof 5 cm. Thus, we assume that the narrow muon bundles (muon pairs) can be resolved ifr > 0:05 m. The number of muon pairs with 0:05 < r < 0:5 m is equal to 978, and the ratioof such events to the single muons is equal to 2:9  10 4. This ratio has to be comparedwith 7:6  10 4, which is the ratio of muons pairs with r < 0:5 m in detected muon bundlesto the single muons. We can conclude that one third of the narrow muon pairs (r < 0:5 m)observed by an underground detector should be due to the events initiated in the muonpair production process.The number of double-muon events with r < 0:5 m detected by one LVD tower during7154 hours of operation can be estimated as 470 [9]. According to our calculations, duringthe same time one LVD tower should detect about 180 double-muon events (narrow muonbundles) initiated by the muon pair production process, while the remainder of 290 eventsare due to the conventional muons bundles. The excess of 180 events over the predictednumber of 290 conventional muon bundles can be easily seen by a high-resolution trackingdetector. A narrow pair separation distribution of the events can be a signature of thisMUON PAIR PRODUCTION BY MUONS ETC. 175excess.The relative contribution of narrow muon bundles will increase with a decrease of theupper limit of r. Our estimates based on LVD [9] and Frejus [10] data show that thechange of an upper limit of r from 0.5 m down to 0.25 m results in the increase of thefraction of narrow muon bundles in the total sample of muon bundles up to about 60% oreven higher. This decreases, however, the predicted number of events.The unresolved muon tracks can be seen as a single-muon track with the energy losswhich is about two or three times more than the most probable energy loss of singlemuons. Such events are clearly seen in the detector “BARS” [11]. The possibility toselect such events statistically from the background of single muons with a high-energyloss depends on the detector structure and characteristics (thickness of matter crossed bymuon in the detector volume, energy resolution of the detector etc.). Our estimates basedon the calculations [12] for one LVD tower with reasonable selection criteria for muon en-ergy loss and number of “hitted” scintillation counters show that unresolved double-muonevents can contribute up to (20-30)% to the tail of the distribution of single-muon energyloss. However, the number of such events after the selection criteria applied will be aboutone order of magnitude less than the number of resolved muon tracks.The same estimations can be done for triple-muon events. The ratio of narrow-to-conventional triple-muon boundles is higher than for double muons. The analysis of triple-muon events is more complicated, however, because they can be seen as triple-, double- orsingle-muon events depending on the spatial resolution of the detector.After the simulation of muon transport through the standard rock taking into accountthe process of muon pair production by muons, and the estimation of the effects causedby multiple muons in the underground detectors, we can conclude that: i) the processof muon pair production by muons, being negligible for the calculation of muon survivalprobabilities and single-muon intensities underground, is quite important for the study ofmuon bundles in the range of pair separation r < 0:5 m; ii) the distribution of pair separa-tions in events initiated by muon pair production process is very narrow and differs fromthat in conventional muons bundles; iii) such narrow muon bundles can be selected statis-tically from the background of conventional muon bundles using underground detectorswith high spatial resolution; iv) the cross-section of muon pair production by muons canbe evaluated from these measurements.  We are grateful to Prof. G. T. ZATSEPIN for useful discussions. This work has beendone under the financial support of the Russian Fund of Fundamental Researches (grant96-02-19007).REFERENCES[1] DAMY DE SOUZA SANTES M., POMPEIA P. A. and WATAGHIN G., Phys. Rev., 59 (1941) 902.[2] AMALDI E., CASTAGNOLI C., GIGLI A. and SCINTI S., Nuovo Cimento, IX (1952) 969.[3] GRILLO A. F. and PARLATI S., Astroparticle Phys., 2 (1994) 335.[4] BATTISTONI G. et al., Proc. XXIV ICRC, Rome, 1 (1995) 508.[5] MACRO COLLABORATION, Proc. XXIV ICRC., Rome, 1 (1995) 528.[6] ANTONIOLI P., GHETTI C., SARTORELLI G., KOROLKOVA E. V. and KUDRYAVTSEV V. A.,to be published in Astroparticle Phys.[7] KELNER S. R., Sov. J. Nucl. Phys., 5 (1967) 1092.176 V. A. KUDRYAVTSEV and O. G. RYAZHSKAYA[8] BUGAEV E. V., KOTOV YU. D. and ROZENTAL I. L., Cosmic Muons and Neutrinos (Moscow,Atomizdat) 1970.[9] LVD COLLABORATION (AGLIETTA M. et al.), Nucl. Phys. B (Proc. Suppl.), 35 (1994) 243.[10] RHODE W., PhD Thesis, University of Wuppertal, 1993 (in German).[11] BELKOV S. V., DENISOV A. G. et al., Proc. XXV ICRC, Durban, 6 (1997) 329.[12] KUDRYAVTSEV V. A. and RYAZHSKAYA O. G., Preprint LNGS-92/26, 1992.

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Muon pair production by muons and narrow muon bundles underground

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