Heavy neutrino decay at SHALON

The SHALON Cherenkov telescope has recorded over 2x10^6 extensive air showers during the past 17 years. The analysis of the signal at different zenith angles (\theta) has included observations from the sub-horizontal direction \theta=97^o. This inclination defines an Earth skimming trajectory with 7 km of air and around 1000 km of rock in front of the telescope. During a period of 324 hours of observation, after a cut of shower-like events that may be caused by chaotic sky flashes or reflections on the snow of vertical showers, we have detected 5 air showers of TeV energies. We argue that these events may be caused by the decay of a long-lived penetrating particle entering the atmosphere from the ground and decaying in front of the telescope. We show that this particle can not be a muon or a tau lepton. As a possible explanation, we discuss two scenarios with an unstable neutrino of mass m\approx 0.5 GeV and c\tau\approx 30 m. Remarkably, one of these models has been recently proposed to explain an excess of electron-like neutrino events at MiniBooNE.


Introduction
Cosmic rays have become a very valuable tool in astronomy, as they provide a very different picture of the sky. In particular, during the past decades gamma-ray detectors have discovered a large number of astrophysical sources (quasars, pulsars, blazars) in our Galaxy and beyond. Ground based telescopes are designed to detect the Cherenkov light of the shower produced when a 0.1-100 TeV photon enters the atmosphere. The light burst in a photon (or electron) air shower has a profile that can be distinguished from the one from primary protons or atomic nuclei, which are a diffuse background in such observations (see [1,2] for a review).
Cosmic rays may also offer an opportunity to study the properties of elementary particles. The main objective in experiments like IceCube [3] or Auger [4] is to determine a flux of neutrinos or protons as they interact with terrestrial matter. These interactions involve energies not explored so far at particle colliders, so their study should lead us to a better understanding of that physics. In addition, the size of the detector and its distance to the interaction point is much larger there than in colliders, which may leave some room for unexpected effects caused by long-lived particles. It could well be that in the near future cosmic rays play in particle physics a complementary role similar to the one played nowadays by cosmology (in aspects like dark matter, neutrino masses, etc.).
In this paper we describe what we think may be one of such effects. It occurs studying the response of the SHALON telescope [5] to air showers from different zenith angles, in a sub-horizontal configuration where the signal from cosmic rays should vanish.

The SHALON mirror telescope
SHALON is a gamma-ray telescope [6,7] located at 3338 meters a.s.l. in the Tien-Shan mountain station. It has a mirror area of 11.2 m 2 and a large field of view above 8 o , with an image matrix of 144 PMT and a < 0.1 o angular resolution. The recording of Cherenkov light is performed in 50 nsec intervals, which is enough to acquire complete information about the air shower while preventing additional light-striking. The trigger is set at bursts of 8 nsec with a signal in at least 4 PMTs, implying a 0.8 TeV energy threshold on vertical events. The telescope has been calibrated according to the observation of extensive air showers at θ = 0 o zenith angle, i.e., at an atmospheric depth of 670 g/cm 2 . Every two-dimensional image of the shower (an elliptic spot in the light receiver matrix) is characterized by 7 parameters (widely used in gamma-ray astronomy) defined from the first, second and third image moments plus the position of the maximum.

Cherenkov bursts below the horizon
The study of extensive air showers at large zenith angles [8] has included observations at the sub-horizontal direction θ = 97 o . The configuration of the telescope is depicted in Fig. 1. The mountain projects a shadow of ≈ 7 o over the horizon. The distance of the telescope to the opposite slope of the gorge is ≈ 7 km, which corresponds to 16.5 radiation lengths and a depth of 640 g/cm 2 . From that point the trajectory finds between 800 and 2000 km of rock before reappearing in the atmosphere.
In Fig. 2 we give the three most recent sub-horizontal events recorded by SHALON together with typical vertical air showers of similar image parameters. The grey scale in the plots expresses the number of ADC counts, whereas CODE is proportional to the shower energy. The five events look very much like regular extensive showers, they develop within a narrow angle and are clearly different from the smooth and chaotic distributions from reflections on the snow or lumniscences of the atmosphere. In a vertical shower the maximum is ≈ 6 km above the telescope, the Moliere radius is ≈ 150 m, and the observed angle is ≈ 1.4 o . If the sub-horizontal showers start right on the ground their maximum should be at 4 km from the telescope, defining a Moliere radius of 105 m and an angle of 1.5 o . This would make these showers almost indistinguishible from the vertical ones. Comparing the five events with vertical air showers we obtain estimated energies between 6 and 17 TeV (the values are 11, 7, 6, 8, 17 TeV). One should notice, however, that if these events had started and developed closer to the telescope their actual energy may be significantly different.

Earth-skimming neutrino interactions
The flux of sub-horizontal events is around 6 × 10 −6 times the flux of TeV cosmic rays reaching the atmosphere. Such a large flux seems to eliminate the possibility that these events are due to neutrino interactions in the air or within the last ≈ 20 cm of rock. The interaction length of a 10 TeV neutrino is ≈ 10 5 km [10]. This implies that only one out of 10 9 of them will interact to produce such an event. The expected neutrino flux from pion and kaon decays at 10 TeV is a per cent fraction of the primary proton flux, whereas the flux from the prompt decay of charmed hadrons, although uncertain, should be still smaller at these energies [11]. Therefore, the expected number of events from atmospheric neutrino interactions is 10 5 times smaller than the one observed. On the other hand, a flux of primary (non-atmospheric) neutrinos large enough would be inconsistent with observations at neutrino telescopes.
Another possibility that can be readily excluded is the decay in the air of a muon or a tau lepton produced inside the rock. A 10 TeV muon could emerge if it is produced ≈ 1 km inside the rock [10] (one out of 10 5 incident neutrinos will produce a muon there). However, the muon decay length at TeV energies is around 10 4 km, so the probability that it decays in the air in front of the telescope is again too small. The neutrino fluxes required to explain the events from µ decays or from ν interactions are then similar (and excluded). The probability for tau lepton production in the rock and decay in the air is not higher. The tau becomes long-lived at ≈ 10 8 GeV. At 10 TeV it should be produced within the last meter of rock (cτ γ ≈ 0.5 m), which reduces very much the number of events.

Heavy neutrino decay
Therefore, we have to explore possible explanations based on new physics. The ideal candidate should be a long-lived massive particle, neutral, frequently produced in air showers, and very penetrating: able to cross 1000 km of rock and decay within the 7 km of air in front of the telescope. If this particle has (possibly suppressed) couplings to the W and/or Z bosons, its mass m h should be larger than m µ (to decay in the last 7 km of air) and smaller than m τ (to cross 1000 km of rock without decaying). Notice that if its decay length at 10 TeV is cτ γ ≈ 1000 km, at GeV energies it will tend to decay far from the detectors in colliders.
An obvious possibility is a sterile neutrino. We take two Weyl spinors n and n c and add a Dirac mass term together with a Yukawa coupling to the lepton family L = (ν l l), Then the Higgs VEV v induces mixing between n and ν l : where m EW = y ν v/ √ 2, m h = m 2 n + m 2 EW , ν h = c α n + s α ν l , s α = m EW /m h , and the orthogonal combination −s α n + c α ν l remains massless. The mixing implies couplings of ν h to the W and Z gauge bosons; the first one will appear suppressed by U lh = s α , whereas the flavour-changing (heavy to light) Z coupling will be proportional to c α s α .
A first ν h model that we would like to discuss has been recently proposed by Gninenko [12] to explain an anomaly at MiniBooNE [13]. He claims that the excess of electron-like events in the interactions of the E ≈ 800 MeV ν µ beam could be caused by the decay of a heavy neutrino if m h ≈ 0.5 GeV, cτ h ≤ 30 m, and |U µh | 2 ≈ 10 −3 . This explanation requires a large transition magnetic moment [14], µ tran ≈ 10 −10 µ B , which implies a dominant decay mode The final photon would convert into a e + e − pair with a small opening angle that would be indistinguishable from an electron in MiniBooNE. At the same time, this dominant decay channel could make the required value of U µh consistent with bounds |U µh | 2 ≤ 10 −5 from BEBC [15], CHARM [16] and CHARM2 [17], as these experiments look for decays into final states with charged particles (ν h → eeν, µeν, µπ).
It is easy to see that such a particle could have an impact on the SHALON events. At 10 TeV its decay length is λ h ≈ 600 km. If ν h is produced in the atmosphere with that energy, the probability that it crosses λ ≈ 1000 km of rock and decays within the ∆λ ≈ 7 km of air in front of the telescope is (4) This implies that the atmospheric flux of heavy neutrinos should be a 1/1000 fraction of the TeV flux of primary cosmic rays. This large flux seems difficult to achieve because ν h is not produced in pion or kaon decays (as m h > m π,K ), it appears only in a |U µh | 2 ≈ 10 −3 fraction of charmed hadron decays into muons.
A slightly more frequent production rate could be expected in a second model, where ν h has a sizeable component along the tau neutrino. NOMAD [18] has set limits |U τ h | 2 ≤ 10 −2 from D s → τ ν h , and then ν h → ν τ ee, but they apply only to neutrinos lighter than m Ds − m τ ≈ 0.19 GeV. Cosmological and supernova bounds on U τ h apply to lighter values of m h as well [19]. On the other hand, LEP bounds cover just the range m h > 3 GeV [20] (decays in the detector of lighter neutrinos are too rare). Therefore, a possible candidate could have a 0.2-0.4 GeV mass, |U τ h | 2 ≈ 0.1, and negligible mixings with the other two families. The dominant decay channels would be into ν τ π 0 and into ν τ ee, ν τ µµ. If its decay length at the TeV energies of the sub-horizontal events is around 1000 km, then the probability of decay in the air in front of SHALON is ≈ 0.003. Its production in air showers would be through tau decay; one can expect |U τ h | 2 ≈ 0.1 heavy neutrinos from each tau produced in the atmosphere. These tau leptons would mainly come from the prompt decay of charmed D s mesons, and also from mesons containing a bottom quark. The flux required, a per cent of the TeV proton flux, seems still too large. Notice, however, that there are also large uncertainties in the flux and energy of the sub-horizontal events, or in the tau production rate in the atmosphere by cosmic rays [11].

Summary and discussion
When a cosmic ray enters the atmosphere it produces an extended air shower with thousands of secondary particles. Obviously, if there is any new physics it will be contained in a fraction of these events. Now, if this exotic physics includes a long-lived particle, we think that there is the potential for its discovery in cosmic ray experiments. Generically, to be detectable the particle must survive after the rest of the shower has been absorbed by the atmosphere (e.g., a long-lived gluino in horizontal air showers [21]) or the ground (a stau in neutrino telescopes [22]). In particular, a long-lived neutral particle could propagate to the center of a neutrino telescope and start there a contained shower when it decays. However, this event would look indistinguishible from a standard neutrino interaction.
In this paper we discuss several air showers obtained at SHALON in a configuration (see Fig. 1) where the expected number of events is zero. Around 1000 km of rock absorb the atmospheric flux of any standard particles but neutrinos. Neutrino interactions in the rock are frequent, but they are not observable as they disappear in just half a meter of soil. A few muons could be produced during the last km and emerge from the rock, but then the probability of muon decay within the 7 km of air in front of the telescope is too small. The crucial difference with a neutrino telescope is that here the probability of a visible ν interaction (in the air or the last centimeters of rock) is negligible.
We argue that these events may correspond to the decay of a neutral particle after it is produced in the atmosphere and has crossed 1000 km of rock. We have studied a couple of models where this particle is a heavy neutrino, and have concluded that although the required production rate seems higher than the expected one, due to a number of uncertainties on the flux and the energy of the exotic events or on the production of charmed particles in the atmosphere, none of these possibilities should be excluded.