Heavy-neutrino decays at neutrino telescopes

Manuel Masip and Pere Masjuan

CAFPE and Departamento de Fısica Teorica y del Cosmos, Universidad de Granada, 18071 Granada, Spain(Received 7 March 2011; published 19 May 2011)

It has been recently proposed that a sterile neutrino �h of mass mh ¼ 40–80 MeV, mixing jU�hj2 �10�3–10�2, lifetime �h � 10�9 s, and a dominant decay mode �h ! �� could be the origin of the

experimental anomalies observed at LSND and MiniBooNE. Such a particle would be abundant inside air

showers, as it can be produced in kaon decays. We use the Z-moment method to evaluate its atmospheric

flux and the frequency of its decays inside neutrino telescopes. We show that �h would imply around 104

contained showers of energy between 0.1 and 100 TeV per year inside a 0.03 km3 telescope like

ANTARES or the DeepCore in IceCube, while the standard background is 100 times smaller.

Therefore, although it may be challenging from an experimental point of view, a search there could

confirm this heavy-neutrino possibility.

DOI: 10.1103/PhysRevD.83.091301 PACS numbers: 14.60.St, 13.35.Hb, 95.85.Ry

I. INTRODUCTION

The direct observation of neutrino interactions in differ-ent types of experiments [1] has been used to establish abasic picture of neutrino masses and mixings. From amodel building point of view, this is arguably the mostsignificant discovery in particle physics since the confir-mation of the standard model in the early 1970s, as itreveals a scale that is (most likely) not electroweak. Thepicture, however, has faced some persistent anomalies inexperiments with neutrino beams from particle accelera-tors. Basically, muon neutrinos of energy below 1 GeVseem to experience an excess of charged-current (CC)interactions with an electron in the final state. The inter-pretation of these events in terms of �� ! �e oscillations

is inconsistent with the mass parameters deduced fromsolar, atmospheric, and reactor neutrino observations.

In a recent analysis Gninenko [2] has made a verycompelling case for a massive neutrino as the origin forall these anomalies:

(i) LSND [3] observed ��e-like events ( ��ep ! eþn)with a gamma signal from neutron capture thatseem to imply an excess of ��� ! ��e oscillations.

Gninenko shows that the events could be equallyexplained through �h production (�12

� C ! �hnX)

followed by its radiative decay �h ! ��, with thefinal � converted into a eþe� pair indistinguishablefrom an electron. This explanation would work fora large enough production cross section (jU�hj2 �10�3–10�2 and m� < 80 MeV) and a short enoughdecay length (�h & 10�9 s and m� > 40 MeV).During the first years of data taking LSND alsoobserved an excess of �12

e C ! e�X events thatwere interpreted as �� ! �e oscillations but are

consistent as well with the �h hypothesis.

(ii) KARMEN [4], using a similar technique, did notconfirm the LSND anomalies. The neutrinos atLSND, however, had an average energy of100 MeV and a long high-energy tail, whereas thespectrum at KARMEN was a narrow peak around20 MeV. Gninenko shows that a 40 MeV neutrinowould be above the production threshold atKARMEN, which makes his hypothesis consistentwith the data.

(iii) MiniBooNE [5] has observed an excess of electron-like events for �e energies between 200 and475 MeV, with no significant excess at higher en-ergies. Gninenko’s fit exhibits also a good agree-ment with the data (higher-energy events aredisfavored by an increase in the decay length andare hidden by the low statistics). More recently [6],this experiment has also reported an excess in ���

data for antineutrino energies in a wider range.Gninenko’s fit is consistent as well, and could favora Dirac nature for �h.

In addition, the mass range 40 � mh � 80 MeV makes�h too heavy to be produced in pion decays and too light todistort the muon spectrum in kaon decays. The heavyneutrino is also produced when the muon itself decays,but he argues that a mixing jU�hj2 < 10�2 makes it accept-

able. Specific searches for unstable neutrinos put strongconstraints on jU�hj, but are based on decays with chargedparticles in the final state (�h ! ee�,�e�,���), never onthe decay �h ! �� induced by a magnetic momenttransition. Its large mass and short lifetime should keep�h also safe from bounds from supernovae and primordialnucleosynthesis [7]. Finally, a recent analysis [8] of muoncapture with photon emission at TRIUMF finds thatGninenko’s neutrino would imply a signal well above the30% excess (versus the standard model value) deducedfrom the data [9]. One should notice, however, that thephoton energy cut and the small size of the target volume atTRIUMF make this experiment very sensitive to the

*masip@ugr.es†masjuan@ugr.es

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neutrino lifetime. A value �h � 3� 10�9 s could imply aconsistent radiative capture rate there while explaining thedata at LSND and KARMEN (which require�h � 10�8 s) and still having an impact at MiniBooNE.1

We find the heavy-neutrino hypothesis very interestingand will study here its implications in a different type ofexperiment. Our basic observation is that �h would beabundantly produced in the atmosphere through kaon de-cays. At energies around 1 TeV its decay length becomesc�h� � 5 km, which implies that �h can reach a neutrinotelescope and then decay. The final photon would be seenthere as a pointlike event, similar to the shower from�eN ! eX or from a neutral-current (NC) interaction ofhigh inelasticity but clearly distinguishable from the muontrack in ��N ! �X.

II. NEUTRINO FLUXES AT SEA LEVEL

The atmospheric flux of any species can be easily esti-mated using the Z-moment method [10,11]. This methodprovides a set of coupled differential equations that de-scribe the evolution with the atmospheric depth t (ing=cm2) of the fluxes of parent hadrons (�H with H ¼ p,n, ��, K�, KL) and of any particles that may result fromtheir decay or their collision with an air nucleus. Thegeneric equations for �HðE; �; tÞ are

@�H

@t¼ � �H

�Hdec

��H

�Hint

þX

H0SH0H; (1)

where �Hdec (�

Hint) is the decay (interaction) length of H in

the air and SH0H describe the sources. These equations canbe solved analytically under some simplifying assump-tions, namely,

(i) the all-nucleon primary flux has a constant spectralindex �;

(ii) the energy distribution of particles from collisionsand decays scales linearly with the energy of theparent hadron;

(iii) the hadronic interaction lengths �Hint do not change

with the energy;(iv) the contributions to the nucleon flux from meson

collisions and to the pion flux from kaon collisionsare negligible.

It follows that the nucleon fluxes �N keep the same spec-tral index � at any depth, and that the source terms arereduced to

SNH ¼ �N

�Nint

ZNH; (2)

where the Z-factors

ZNH ¼Z 1

0dxx�1FNH (3)

are constants (independent of E and the zenith angle �)derived from the distribution FNHðxÞ of the fraction ofenergy taken by H after an N-air collision. The mesonfluxes �M can then be easily derived in two differentregimes. At low energies �M

dec ¼ ðE=mMÞc�M is much

smaller than �Mint and meson interactions can be ignored,

whereas at high energies the variations in �M are domi-nated by collisions with air nuclei (the air density is afunction of t and of �). A simple interpolation can be usedbetween these regimes. We take in our analysis the primaryflux, the Z-factors, and the atmospheric model in [11] (see[12] for a discussion of the fluxes at higher energies). Weobtain, for example, that the TeV charged-pion vertical fluxreaches its maximum (a 4% of the initial nucleon flux) at adepth of 200 g=cm2, and that the kaon flux there is 7 timessmaller.The lepton fluxes from meson decays can also be in-

corporated. In particular, standard neutrinos do not interactnor decay in the atmosphere and their flux equations willonly depend on source terms of type

SM�ðEÞ ¼ BðM ! �ÞZ 1

0dxx�1 �MðE=xÞ

�MdecðE=xÞ

FM�ðxÞ; (4)

where BðM ! �Þ is the branching ratio of a given decaymode, FM�ðxÞ is again the distribution of the fraction ofenergy taken by the neutrino in that decay, and the depen-dence on t and � is implicit. We obtain that, although kaonsare less abundant than pions in air showers, a lower ratio�Mdec=�

Mint makes them the main source of neutrinos at

energies above 100 GeV. The TeV flux at sea level isdominated by muon neutrinos, with � ��� � 0:42���

,

��e� 0:036���

, and � ��e� 0:023��� .

Heavy neutrinos �h will be mainly produced in charged-kaon decays. The branching ratio is

BðKþ ! �þ�hÞ � BðKþ ! �þ�Þ � jU�hj2 �h; (5)

where BðKþ ! �þ�Þ ¼ 0:64 and the kinematic factor formh ¼ 40–80 MeV is �h � ð1þm2

h=m2�Þ [13]. The frac-

tion of energy x taken by �h will have a flat distribution (aconstant FKhðxÞ) between xmin and xmax,

xminmax

¼ 1

2

�1þm2

h �m2�

m2K

��

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

4

�1þm2

h �m2�

m2K

�� m2

h

m2K

vuut :

(6)

There will be smaller contributions from Kþ ! �0�þ�h

and KL ! ���þ�h, plus the analogous K� and KL de-cays into ��h (the heavy neutrino may be a Dirac or aMajorana particle; see discussion in [2]). The equationdefining �hðE; �; tÞ is

1A global fit including TRIUMF would certainly constrainfurther the parameter space in Gninenko’s model.

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@�h

@t¼ � �h

�hdec

þX

K

SKh; (7)

where the source terms take the form in Eq. (4), �hdec ¼ðE=mhÞc�h, and the sum runs over the decay modes that

produce �h. In Fig. 1 we plot the total heavy neutrino fluxat sea level from inclinations � ¼ 0o; 60o. We have takenthe central values mh ¼ 60 MeV and jU�hj2 ¼ 0:005,

with �h ¼ 10�9 s. At 1 TeV 73% of the flux comes fromKþ decays, K� contributes a 25%, and KL just a 2%.Finally, notice that the photons produced in the air through�h decays are together with other photons and muonsinside the parent shower and are therefore nonobservable.

III. EVENTS ATA NEUTRINO TELESCOPE

As neutrinos enter the ground their sources disappearand they just experience two types of processes: heavyneutrinos �h may decay into ���, whereas �� and �e

may have neutral- or charged-current interactions withmatter. At a depth d the sea-level fluxes�iðE; �; 0Þ become

�hðE; �; dÞ ¼ �hðE; �; 0Þ exp� �d

�hdec cos�

�;

��ðE; �; dÞ ¼ ��ðE; �; 0Þ exp� �d

��int cos�

�;

(8)

where d and the decay/interaction lengths are given inmeters and we have neglected the curvature of the Earth(a good approximation for � � 85o). At 1 TeV we obtain�hdec � 5 km, whereas ��

CC � 2� 106 km and ��NC � 8�

106 km (the interaction lengths decrease with the energy as1=��N). This means that the decay of a �h crossing aneutrino telescope is 106 times more probable than theinteraction of a standard neutrino. In addition, CC ��

interactions will be clearly different from �h decays, asthe final muon will produce a track hundreds of meters

long [14]. The electromagnetic shower from a �h decaywill be pointlike (it develops in a fewmeters), similar to theone produced by a NC interaction or a �e CC process.These standard events, however, are suppressed by thelower �e fluxes (�� ! �e oscillations at L � 100 km

and E � 100 GeV are negligible) and the inelasticity dis-tribution (/ 1=y [15]) in �-N collisions.Let us be more specific. To estimate the number of

events per unit time that occurred inside a telescope oneneeds to calculate the total flux (ingoing plus outgoingneutrinos) through the surface containing the detectors.We model this region as a cylinder of section A and lengthH starting at a depth d0 (i.e., d goes from d0 to d0 þH).For a fixed angle � & 85o the neutrino flux only dependson the depth d. Therefore, the total flux through the lateralsurface of the detector will be zero (given �, the flux

through any lateral d ~S is equal to the flux leaving the

detector through an opposed lateral surface �d ~S; seeFig. 2). The number of heavy-neutrino events inside thedetector in an interval of energy and solid angle per unittime can then be calculated as the difference between thefluxes through its upper and its lower sections,

Nh ¼Z

�EdE

Z

��d�

Z

AdS cos�½�hðE; �; d0Þ

��hðE; �; d0 þHÞ�: (9)

An analogous expression can be obtained to estimate thenumber N� of interactions inside the detector produced byneutrinos from those directions. In Fig. 3 we plot in dashesthe energy distribution of the neutrinos that interact(�� and �e) or decay (�h) per year inside a detector

like ANTARES [16] (A ¼ 0:1 km2, d0 ¼ 2:2 km, H ¼0:3 km) or the DeepCore [17] in IceCube (of similar sizeand depth). The energy of the initial neutrino, however, isnot the most relevant parameter for observation; as in NCinteractions only a small fraction ymay be deposited in thedetector. In a �h decay only the photon energy is visible(we will assume an isotropic decay [2]), whereas in �e-CCinteractions all the energy carried by the neutrino goes tothe contained shower. If the inelasticity y in the event has adistribution F�shðyÞ, then the energy distribution of thecascades inside the detector will be

dNsh

dEðEÞ ¼

Z 1

0dyy�1 dN�

dEðE=yÞF�shðyÞ: (10)

100 1000 10 000 100 00010 16

10 14

10 12

10 10

10 8

10 6

E GeV

EE

cm2

ssr

1

FIG. 1 (color online). Neutrino fluxes (�i þ ��i) at sea level for� ¼ 0 (solid lines) and � ¼ 60

(dashed lines).

d

FIG. 2 (color online). The total flux through the lateral surfaceof the detection region cancels if RT d= cos� (we take� � 85

).

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Figure 3 shows in solid lines the main result of our analy-sis. The number of standard showers of energy above100 GeV from down-going neutrinos inside ANTARESis around 1300 per year (60% from �e-CC interactionsand 40% from NC interactions). For the central valuesmh ¼ 60 MeV and jU�hj2 ¼ 0:005 the heavy neutrino

would provide 26 000 extra events. If the energy thresholdis set at 500 GeV the number of standard events is reducedto 220 per year, whereas the number of events from �h

decays is just cut to 14 000.

IV. SUMMARYAND DISCUSSION

Telescopes like ANTARES or IceCube are designed toobserve upward-moving muons produced in neutrino in-teractions near the detector. These events are clean, in thesense that no particles except for neutrinos can reach thedetector after crossing the Earth. Telescopes can also ob-serve the contained showers produced in NC interactionsor in �e-CC processes. Since their development takes just afew meters, these events are pointlike, and the only signindicating whether they are caused by an upward- or adownward-going neutrino is that in the latter case they maycome together with muons.

In this paper we have shown that the decay of a long-lived neutral particle produced in the atmosphere could

change drastically (by over a factor of 100) the number ofTeV-contained showers in these experiments. In particular,we have analyzed Gninenko’s heavy neutrino, that appearsas a possibility well motivated by the results at LSND,KARMEN, and MiniBooNE. We find remarkable that itsmass, mixing, and lifetime optimize the distortion intro-duced in TeV-neutrino telescopes: below � 100 GeV �h

does not reach the telescope, and above 100 TeV its decaylength becomes too large and the signal vanishes (noticethat �h

dec grows with the energy while ��int decreases).

The heavy neutrino would be produced through kaondecays inside air showers together with a muon of similarenergy. A crucial question is then whether these decays canbe disentangled from the muon bundle associated with theparent shower. ANTARES or the DeepCore in IceCube aremore than 2 km deep, and as the zenith angle grows allmuon effects will decrease. In contrast, the zenith-angledependence of the �h events up to 85 is very mild (espe-cially at larger energies), since these neutrinos do not loseenergy in their way to the detector. Therefore, theTeV-contained showers should appear as a clear anomalythat may be accompanied by muons in vertical events butthat persists at higher zenith angles (slant depths). Thelarge number of events that we obtain could allow forspecific searches. For example, events with lower-energymuons in the upper part of the detector followed by acontained TeV shower below, or other topologies thatwould otherwise be discarded.If a heavy neutrino is the explanation of the LSND and

MiniBooNE anomalies, our results show that it will reacheffectively the core of neutrino telescopes and will decaythere at a high rate. AMonte Carlo simulation of individualshowers, including all the muon backgrounds and theresponse of the detector, should then provide the beststrategy in the search for an observable signal that confirmsor excludes this heavy-neutrino possibility.

ACKNOWLEDGMENTS

We would like to thank Juande Zornoza for discussions.This work has been partially supported by MICINN ofSpain (FPA2006-05294, FPA2010-16802, FPA2010-16696, Consolider-Ingenio Multidark CSD2009-00064,and CPAN CSD2007-00042) and by Junta de Andalucıa(FQM 101, FQM 437, and FQM 3048).

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h

NC

CCe

100 1000 10 000 100 000

0.1

1

10

100

1000

104

E GeV

dNsh

dEE

yr1

FIG. 3 (color online). Energy distribution of the containedshowers from �h ! ���, �N ! �X, and �eN ! eX at

ANTARES. We also plot (dashed lines) the energy distributionof the parent neutrino in each case.

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