UH-511-932-99

May 1999

EXOTIC EXPLANATIONS FOR NEUTRINO
ANOMALIES^{1}^{1}1Invited talk at the “8th International Symposium
on Neutrino Telescopes”, Venice, Feb. 1999.

SANDIP PAKVASA

University of Hawaii

Department of Physics and Astronomy

Honolulu, HI 96822 USA

E-mail:

I review explanations for the three neutrino anomalies (solar, atmospheric and LSND) which go beyond the “conventional” neutrino oscillations induced by mass-mixing. Several of these require non-zero neutrino masses as well.

## 1 Introduction

According to Webster’s New English Dictionary[1], amongst the meanings of the word “exotic” are: “foreign”, “strangely beautiful”, “enticing”, “having the charm or fascination of the unfamiliar”. At one time neutrino oscillations would have been considered exotic, but today they seem mundane and ordinary! The explanations to be discussed here will be definitely “strange” and “unfamiliar” but may not seem to be “charming” or “enticing”!

As is well-known, it is not possible to account for all three neutrino anomalies with just the three known neutrinos and . If one of them can be explained in some other way, then no extra sterile neutrinos need be invoked. This is one motivation for exotic scenarios. It is also important to rule out all explanations other than oscillations in order to establish neutrino mixing and oscillations as the unique explanation for the three observed neutrino anomalies.

I should mention that, in general, some (but not all) non-oscillatory explanations of the neutrino anomalies will involve non-zero neutrino masses and mixings. Therefore, they tend to be neither elegant nor economical. But the main issue here is whether we can establish oscillations unequivocally and uniquely as the cause for the observed anomalies.

I first summarize some of the exotic scenarios and then consider each anomaly in turn.

## 2 Mixing and Oscillations of massless

There are three different ways that massless neutrinos may mix and even oscillate. These are as follows.

1. If flavor states are mixtures of massless as well massive states, then when they are produced in reactions with Q-values smaller than the massive state; the flavor states are massless but not orthogonal[2]. For example, if , and for to 3 but = 50 GeV; then “” produced in -decay and “” produced in -decay are massless but not orthogonal and

(1) |

On the other hand and produced in decay will be not massless and will be more nearly orthogonal. Hence, the definition of flavor eigenstate is energy and reaction dependent and not fundamental. Current limits[3] on orthogonality of and make it impossible for this to play any role in the current neutrino anomalies.

2. When Flavor Changing Neutral Currents as well as Non-Universal Neutral Current Couplings of neutrinos exist:

Such couplings arise in R-parity violating supersymmetric theories[4]. In this case the propagation of and in matter is described by the equation:

(3) |

where and . There is a resonance at or and can convert to completely. This matter effect which effectively mixes flavors in absence of masses was first pointed out in the same Wolfenstein paper[5] where matter effects were discussed in general. The resonant conversion is just like in the conventional MSW effect, except that there is no energy dependence and and are affected the same way. This possibility has been discussed in connection with both solar and atmospheric anomalies.

3. (a) Flavor violating Gravity wherein it is proposed that gravitational couplings of neutrinos are flavor non-diagonal[6] and equivalence principle is violated. For example, and may couple to gravity with different strengths:

(4) |

where is the gravitational potential. Then if and are mixtures of and with a mixing angle , oscillations will occur with a flavor survival probability

(5) |

when is constant over the distance L and is the small deviation from universality of gravitational coupling. Equivalence principle is also violated.

(b) Another possibility is violation of Lorentz invariance[7] wherein all particles have their own maximum attainable velocities (MAV) which are all different and in general also different from speed of light: Then if and are MAV eigenstates with MAV’s and and and are mixtures of and with mixing angle , the survival probability of a given flavor is

(6) |

where .

As far as neutrino oscillations are concerned, these two cases are identical in their dependence on LE instead of L/E as in the conventional oscillations[8].

## 3 Neutrino Decay[9]:

Neutrino decay implies a non-zero mass difference between two neutrino states and thus, in general, mixing as well. We assume a component of i.e., , to be the only unstable state, with a rest-frame lifetime , and we assume two flavor mixing, for simplicity:

(7) |

with . From Eq. (2) with an unstable , the survival probability is

where and . Since we are attempting to explain neutrino data without oscillation there are two appropriate limits of interest. One is when the is so large that the cosine term averages to 0. Then the survival probability becomes

(9) |

Let this be called decay scenario A. The other possibility is when is so small that the cosine term is 1, leading to a survival probability of

(10) |

corresponding to decay scenario B. Decay models for both kinds of scenarios can be constructed; although they require fine tuning and are not particularly elegant.

## 4 Lsnd

In the LSND experiment, what is observed is the following[10]. In the decay at rest (DAR) which is which should give a pure signal, there is a flux of at a level of about of the . (There is a similar signal for accompanying in the decay in flight of . Now this could be accounted for without oscillations[11] provided that the conventional decay mode is accompanied by the rare mode at a level of branching fraction of . Assuming X to be a single particle, what can X be? It is straight forward to rule out X as being (i) (too large a rate for Muonium-Antimuonium transition rate), (ii) (too large a rate for FCNC decays of such as and (iii) (too large a rate for FCNC decays of such as .

The remaining possibilities for X are or . No simple models exist which lead to such decays. Rather Baroque models can be constructed which involve a large number of new particles[12].

Experimental tests to distinguish this rare decay possibility from the conventional oscillation explanation are easy to state. In the rare decay case, the rate is constant and shows no dependence on L or E.

One can also ask whether the events seen in LSND could have been caused by new physics at the detector; for example a small rate for the “forbidden” reaction . This is ruled out, since a fractional rate of for this reaction, leads (via crossing) to a rate for the decay mode in excess of known bounds.

## 5 Solar Neutrinos

Oscillations of massless neutrinos via Flavor Changing Neutral Currents (FCNC) and Non Universal Neutral Currents (NUNC) in matter have been considered[4, 13] as explanation for the solar neutrino observations, most recently by Babu, Grossman and Krastev[14]. Using the most recent data from Homestake, SAGE, GALLEX and Super-Kamiokande, they find good fits with and or 0.1 to 0.01 with .

Since the matter effect in this case is energy independent, the explanation for different suppression for , and pp neutrinos as inferred is interesting. The differing suppression arises from the fact the production region for each of these neutrinos differ in electron and nuclear densities. This solution resembles the large angle MSW solution with the difference that the day-night effect is energy-independent.

The massless neutrino oscillations described in Eq. (6) also offer a possible solution to solar neutrino observations. There are two solutions: one at a small angle and one at a large angle [15]. This possibility can be tested in Long Baseline experiments.

The possibility of solar neutrinos decaying to explain the discrepancy is a very old suggestion[16]. The most recent analysis of the current solar neutrino data finds that no good fit can be found: and (E=10 MeV) to 27 sec. come closest[17]. The fits become acceptable if the suppression of the solar neutrinos is energy independent as proposed by several authors[18] (which is possible if the Homestake data are excluded from the fit). The above conclusions are valid for both decay scenarios A as well as B.

## 6 Atmospheric Neutrinos

The massless FCNC scenario has been recently considered for the atmospheric neutrinos by Gonzales-Garcia et al.[19] with the matter effect supplied by the earth. Good fits were found for the partially contained and multi-GeV events with as well . The fit is poorer when higher energy events corresponding to up-coming muons are included[20]. The expectations for future LBL experiments are quite distinctive: for MINOS, one expects and The story for massless neutrinos oscillating via violation of Equivalence Principle or Lorentz Invariance is very similar. Assuming large mixing, and a good fit to the contained events can be obtained[21]; but as soon as multi-GeV and thrugoing muon events are included, the fit is quite poor[20].

In both these cases the reason that inclusion of high energy upgoing muon events makes the fits poorer is straightforward. The up-going muon events come from much higher energy and the suppression is weaker that in the lower energy events. The energy dependence expected in the above scenarios is very different: no energy dependence in the FCNC case and an averaging out of oscillations at high energy (corresponding to 50% uniform suppression) in the other scenario.

Turning to neutrino decay scenario A, it is found that it is possible to choose and to provide a good fit to the Super-Kamiokande L/E distributions of events and event ratio[9]. The best-fit values of the two parameters are and where km is the diameter of the Earth. This best-fit value corresponds to a rest-frame lifetime of

(11) |

Such a lifetime and decay length are not in conflict with current limits on nonradiative modes. Previous limits on decay lengths from accelerators are only of the order of a few km.

It is possible to construct a viable decay model for Majorana neutrinos with a massless Majoron which is predominantly singlet with an small triplet admixture[22]. The effective interaction will be given by

(12) |

With this interaction, the rest-frame lifetime of is given by

(13) |

and hence, for the above fit,

(14) |

Combining this with the bound on from decays[23], one finds

(15) |

This result justifies the above approximation of large and the scenario A.

We note in passing that with a choice of one and another and a mixing matrix with large diagonal entries and , it is possible to account for all neutrino anomalies: atmospheric, solar as well as LSND.

In this proposal, since the decays will be time dilated, at high energies, the decay probability is very small and the suppression of flux is correspondingly smaller. Indeed it turns out that it is not possible to fit the observed angular distribution of the high energy up-coming muon events[20].

If the neutrino that mixes with is different from the one that it decays into, then the in decay and the in oscillations are independent and it is possible for in oscillations to be very small. In this case (scenario B), it is possible to find an excellent fit to all the atmospheric neutrino data: contained events, multi-GeV events as well as upcoming muon events[24]. The two decay possibilities lead to different expectations for future Long Baseline experiments, e.g. for MINOS: Case A leads to whereas case B leads to .

Another proposal for explaining the atmospheric neutrinos is based on decoherence of the in the flux[25]. The idea is that are interacting and getting tagged before their arrival at the detector. The cause is unknown but could be a number of speculative possibilities such as a large neutrino background, new flavor sensitive interactions in an extra dimension, violation of quantum mechanics etc. The survival probability goes as:

(16) |

The Super-Kamiokande data can be fit by choosing and . A detailed fit to all the data over the whole energy range has not been attempted yet.

## 7 Conclusion

As I mentioned at the beginning, the main motivation for this exercise is to try to establish neutrino oscillations (due to mass-mixing) as the unique explanation of the observed anomalies. Even if neutrinos have masses and do mix, the observed neutrino anomalies may not be due to oscillations but due to other exotic new physics. These possibilities are testable and should be ruled out by experiments. I have tried to show that we are beginning to carry this program out.

## 8 Acknowledgments

I thank Milla Baldo-Ceolin for hosting this unique meeting and the outstanding hospitality. I thank Andy Acker, Vernon Barger, Anjan Joshipura, Plamen Krastev, John Learned, Paolo Lipari, Eligio Lisi and Tom Weiler for many enjoyable discussions and collaboration.

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