Interpreting the LSND anomaly : sterile neutrinos or CPT - violation or . . . ? ∗

We first study how sterile neutrinos can fit the 5σ ν̄μ → ν̄e LSND anomaly: 3+1 solutions give a poor fit, but better than than 2+2 solutions (the best fit regions are somewhat different, so that MiniBooNE could discriminate). If instead MiniBooNE will find no νμ → νe signal, we will have a hint for CPT violation. Already now, unlike sterile neutrinos, CPTviolating neutrino masses can nicely accomodate all safe and unsafe data. We study how much CPT must be conserved according to atmospheric and K2K data and list which CPTviolating signals could be discovered by forthcoming solar and long-baseline experiments. Oscillations between the three Standard Model neutrinos are described by two independent squared neutrino mass differences, allowing to explain only two of the three neutrino anomalies (atmospheric [1], solar [2] and LSND [3]) as oscillations. A joint fit is not possible even if one trusts only the safest data from atmospheric, solar and reactor [4] neutrino experiments: the the up/down atmospheric asymmetries and a ∼ 1/2 disappearance of solar νe. Most global fits of neutrino data drop the LSND anomaly because the other ones are considered as more solid. In quantitative terms, we have a 7σ solar anomaly (although it can be reduced to 4σ by dropping solar model predictions), a 14σ atmospheric anomaly and a 5σ LSND anomaly. The ‘number of standard deviations’ is here näıvely computed as (∆χ) = (χSM − χ 2 best) , where χbest is the χ 2 value corresponding to the best-fit oscillation, and χSM corresponds to massless SM neutrinos. In section 1 we discuss how and how well oscillations with extra sterile neutrinos can fit the LSND anomaly [5]. In particular we study which one of the two different kind of four-neutrino spectra (1+3 or 2+2) is favoured by the †On leave from dipartimento di Fisica dell’Università di Pisa and INFN. ∗ The ν̄μ → ν̄e LSND anomaly is presented as an evidence for a μ → e oscillation probability of (0.264 ± 0.081)% [3], that differs from zero only by slightly more than 3σ. However, from a table of the likelihood L, obtained from the LSND collaboration and computed on an event-by-event basis, we read χ SM − χ best = −2 ln Lbest LSM = 29 rather than ∼ 10. Apparently, some mark of oscillations that cannot be summarized by the number of ν̄e events is hidden in the full LSND data, maybe in the energy distribution. However a large range of different ∆m values fits almost equally well the LSND data. present data, and by an eventual future confirmation of the LSND data. An extra sterile neutrino can improve the situation, but some contradiction between different sets of data remains, expecially in the 2+2 scheme. This situation suggests to look for alternative interpretations of the LSND anomaly. One possibility is that either the atmospheric or the solar anomaly is not due to oscillations. We will not consider this possibility, although various mechanisms (even unplausible ones) can fit the data as well as oscillations [6, 7]. In view of this situation, it is interesting that all data can be consistently fitted by the CPT-violating neutrino spectrum illustrated in fig. 1. This solution was proposed in [8] when the initial 2.6σ LSND hint for νμ → νe [9] decreased down to 0.6σ, leaving an anomaly only in ν̄μ → ν̄e [3]. Unlike sterile neutrinos, this solution also satisfies (unsafe?) bounds from nucleosynthesis and SN1987A. Despite the lack of theoretical grounds, this bold speculation is interesting because can be tested soon. If CPT violation were the right answer, MiniBooNE [10] (the experiment designed to test LSND, looking for νμ → νe) will not see the LSND oscillations; a ν̄μ → ν̄e experiment is also needed to directly test this possibility. If CPT is badly violated as in fig. 1, one generically expects detectable CPT-violating signals in atmospheric and solar oscillations. In any case it remains interesting to constrain CPT-violation in neutrino masses. In section 2 we compute the present bounds and list the possible CPT-violating signals and surprises that could appear in forthcoming solar and long-baseline experiments.