CMU-HEP95-05

DOE-ER/40682-95

The LSND Experiment and the Zee Model

Lincoln Wolfenstein

Department of Physics

Carnegie Mellon University

Pittsburgh, PA 15213 USA

A recent experiment LSND at Los Alamos has provided[1] an indication of oscillations with of order 1ev or greater and between and . Such a value of for oscillations was not expected in the standard see-saw model[2] suggested by SO(10) with a large mass hierarchy because it leads to too large a value of to fit cosmological constraints. Furthermore within that model the LSND result is inconsistent with the indications of oscillations from both atmospheric neutrinos[3] and solar neutrinos.[4]

Here we reconsider an alternative model proposed by Zee.[5] This represents the most direct way to produce Majorana neutrino masses in a theory such as SU(5) in which right-handed neutrinos are totally absent. The general features of masses and mixings in this model have been analyzed.[6] The mass matrix has the form

where is of order to . The eigenstates to a good approximation are

The state has a small mass of order whereas and have masses of order with a mass splitting

The following features follow from these equations:

1. There exist two very different values for . The large value , corresponding to short wave-length oscillations applies only to oscillations.

2. There are oscillations of to and to corresponding to a much smaller value of , , given by Eq. (1).

3. If the mixing angle for the short-wave length oscillations is , then the amplitudes of the oscillations involving are given by and , one corresponding to and the other to .

4. There exist two massive neutrinos almost degenerate in mass with masses given by .

To apply this theory to the LSND experiment we take as an example = 6ev. The theory then gives two massive neutrinos with masses each about 2.5 ev; such a scenario has been suggested as being very useful for cosmology.[7] Indeed the interpretation of the LSND experiment in terms of two almost degenerate massive neutrinos has been suggested in various papers[8]; it is required in the Zee model.

From the LSND value of it follows that either or has almost complete mixing with while the other has an amplitude of oscillation of order . For our example from Eq. (1), is of order of magnitude to ev. Thus one of the two possibilities corresponds to complete mixing with a value of appropriate to explain the atmospheric neutrino results. There is in this case no explanation of the solar neutrino results. The other possibility provides no explanation of the atmospheric neutrino results and indeed should be down to ev so as not to exacerate this problem; it does provide a prediction that the solar neutrino flux is reduced by a factor of 2.

While this does not provide a perfect explanation of the solar neutrino results, it does explain the gallium and Kamiokande results within their experimental errors. However, even taking into account the uncertainty in the flux there is at least a discrepancy with the Davis result.

In conclusion the LSND result combined with the Zee model leads to the interesting predictions there are two neutrinos almost degenerate with masses of interest for cosmology and that a large neutrino oscillation signal should be seen in either the atmospheric neutrinos or the solar neutrinos.

This research was supported by the U.S. Department of Energy Contract No. DE-FG02-91ER40682.

## References

- [1] C. Athanassopoulos et al., Phy. Rev. Lett. (to be published).
- [2] Gell-Mann, Ramond, and Slansky, unpublished (1977).
- [3] K.S. Hirata et al., Phys. Lett. B280, 146 (1992).
- [4] For an overview see Neutrino 94, Nucl. Phys. B. (Proc. Suppl.) 38, pp. 47-106 (1995).
- [5] A. Zee, Phys. Lett. 93B, 389 (1980).
- [6] L. Wolfenstein, Nuc. Phys. B175, 93 (1980).
- [7] J. Primack et al., UC Santa Cruz preprint SCIPP 94/28 (1994).
- [8] See, for example, D. Caldwell, UCSB preprint.