Very Special Relativity

By Very Special Relativity (VSR) we mean descriptions of nature whose space-time symmetries are certain proper subgroups of the Poincar\'e group. These subgroups contain space-time translations together with at least a 2-parameter subgroup of the Lorentz group isomorphic to that generated by $K_{x}+J_{y}$ and $K_{y}-J_{x}$. We find that VSR implies special relativity (SR) in the context of local quantum field theory or of CP conservation. Absent both of these added hypotheses, VSR provides a simulacrum of SR for which most of the consequences of Lorentz invariance remain wholly or essentially intact, and for which many sensitive searches for departures from Lorentz invariance must fail. Several feasible experiments are discussed for which Lorentz-violating effects in VSR may be detectable.Comment: 3 pages, revte

Lepton Flavor Violation in B Decays?

The LHCb Collaboration's measurement of R_K = B(B+ -> K+ mu+ mu-)/B(B+ -> K+ e+e-) lies 2.6 sigma below the Standard Model prediction. Several groups suggest this deficit to result from new lepton non-universal interactions of muons. But non-universal leptonic interactions imply lepton flavor violation in B decays at rates much larger than are expected in the Standard Model. A simple model shows that these rates could lie just below current limits. An interesting consequence of our model, that B(B_s -> mu+ mu-)_{exp}/B(B_s -> mu+ mu-)_{SM} = R_K = 0.75, is compatible with recent measurements of these rates. We stress the importance of searches for lepton flavor violations, especially for B -> K mu e, K mu tau and B_s -> mu e, mu tau.Comment: 8 pages. Discussion of P'5 added; some discussion sharpened; discussion of decays with tau's modified; references adde

Zeroes of the Neutrino Mass Matrix

We assume there to be precisely three left-handed neutrino states whose Majorana masses are generated by an unspecified mechanism. Were CP conserved, the symmetric neutrino mass matrix M would be real and all six of its distinct entries could be experimentally determined. But CP is not conserved so that M is likely to be complex. As a result, not all nine of its convention-independent real parameters can be determined without an appeal to theory. Thus we examine the possibility that a restricted class of neutrino mass matrices may suffice to describe current data, namely those complex symmetric matrices several of whose entries vanish. We find that there are seven acceptable textures with two independent zeroes, and we explore their contrasting phenomenological implications. Textures with more than two independent zeroes appear to be excluded by experiment.Comment: Version to appear in PL

Can the Zee ansatz for neutrino masses be correct?

Working in the framework of three chiral neutrinos with Majorana masses, we investigate a scenario first realized in an explicit model by Zee: that the neutrino mass matrix is strictly off-diagonal in the flavor basis, with all its diagonal entries precisely zero. This CP-conserving ansatz leads to two relations among the three mixing angles $(\theta_1, \theta_2, \theta_3)$ and two squared mass differences. We impose the constraint $|m_3^2 - m_2^2| \gg |m^2_2 - m_1^2|$ to conform with experiment, which requires the $\theta_i$ to lie nearby one of four 1-parameter domains in $\theta$-space. We exhibit the implications for solar and atmospheric neutrino oscillations in each of these cases. A unique version of the Zee {\it ansatz} survives confrontation with experimental data, one which necessarily involves maximal just-so vacuum oscillations of solar neutrinos.Comment: 7 pages, harvmac, typo corrected, ref. added, text modifie

Disentangling Neutrino Oscillations

The theory underlying neutrino oscillations has been described at length in the literature. The neutrino state produced by a weak decay is usually portrayed as a linear superposition of mass eigenstates with, variously, equal energies or equal momenta. We point out that such a description is incomplete, that in fact, the neutrino is entangled with the other particle or particles emerging from the decay. We offer an analysis of oscillation phenomena involving neutrinos (applying equally well to neutral mesons) that takes entanglement into account. Thereby we present a theoretically sound proof of the universal validity of the oscillation formulae ordinarily used. In so doing, we show that the departures from exponential decay reported by the GSI experiment cannot be attributed to neutrino mixing. Furthermore, we demonstrate that the `Mossbauer' neutrino oscillation experiment proposed by Raghavan, while technically challenging, is correctly and unambiguously describable by means of the usual oscillation formalae.Comment: 16 page