Lorentz andCPTviolation in the neutrino sector

Abstract

We consider neutrino oscillations in the minimal Standard-Model Extension describing general Lorentz and CPT violation. Among the models without neutrino mass differences is one with two degrees of freedom that reproduces most major observed features of neutrino behavior. DOI: 10.1103/PhysRevD.70.031902 PACS number͑s͒: 11.30.Cp, 11.30.Er, 14.60.Pq Quantum physics and gravity are believed to combine at the Planck scale, m P Ӎ10 19 GeV. Experimentation at this high energy is impractical, but existing technology could detect suppressed effects from the Planck scale, such as violations of relativity through Lorentz or CPT breaking ͓1͔. At experimentally accessible energies, signals for Lorentz and CPT violation are described by the Standard-Model Extension ͑SME͒ ͓2͔, an effective quantum field theory based on the Standard Model of particle physics. The SME incorporates general coordinate-independent Lorentz violation.The character of the many experiments designed to study neutrino oscillations ͓3͔ makes them well suited for tests of Lorentz and CPT symmetry. The effects of Lorentz violation on propagation in the vacuum can become more pronounced for light particles, and so small effects may become observable for large baselines. Applying this idea to photons has led to the best current sensitivity on any type of relativity violation ͓4͔.In this work, we study the general neutrino theory given by the minimal renormalizable SME ͓2͔. In this setup, as in the usual minimal Standard Model, SU(3)ϫSU(2)ϫU(1) symmetry is preserved, the right-handed neutrino fields decouple and so are unobservable, and there are no neutrino mass differences. The neutrino behavior is contained in the termswhere the first term is the usual Standard-Model kinetic term for the left-handed doublets L a , with index a ranging over the three generations e, , . The coefficients for Lorentz violation are (a L ) ab , which has mass dimension one and controls the CPT violation, and (c L ) ab , which is dimensionless. It is attractive to view these coefficients as arising from spontaneous violation in a more fundamental theory ͓5͔, but other origins are possible ͓1͔. The Lorentz-violating terms in Eq. ͑1͒ modify both interactions and propagation of neutrinos. Any interaction effects are expected to be tiny and well beyond existing sensitivities. In contrast, propagation effects can be substantial if the neutrinos travel large distances. The time evolution of neutrino states is controlled as usual by the effective Hamiltonian (h eff ) ab extracted from Eq. ͑1͒. The construction of (h eff ) ab is complicated by the unconventional time-derivative term but can be performed following the procedure in Ref. ͓6͔. We findTo leading order, the 4-momentum p is p ϭ(͉p͉;Ϫp). The analysis of neutrino mixing proceeds along the usual lines. We diagonalize (h eff ) ab with a 3ϫ3 unitary matrix U eff , h eff ϭU eff † E eff U eff , where E eff is a 3ϫ3 diagonal matrix. There are therefore two energy-dependent eigenvalue differences and hence two independent oscillatio...

Global three-parameter model for neutrino oscillations using Lorentz violation

“…This feature is also present in the bicycle model, and it matches the atmospheric-neutrino data [36,40]. At high energies, the limiting behavior of both 32 and 31 21 32 is also linear, but with logL / ÿ logE.…”

“…The c and a coefficients combine to produce a Lorentz-violating seesaw mechanism [18], in which the model effectively reduces to a two-flavor limit with a pseudomass term [36]. The only significant probabilities are for the transitions $ and $ , which involve 21 and are large only at energies above about 100 MeV.…”

“…Note, however, that mass terms proportional to the unit matrix may play a role in ensuring stability and causality of the underlying theory [46]. To maintain the possibility of satisfying criteria (iii) and (vii) while keeping the number of degrees of freedom small, we further restrict attention to effective Hamiltonians of the form (5) adapted from the simple scheme of the bicycle model [36]. In that model, the high-energy pseudomass is created from a Lorentz-violating seesaw mechanism involving a (c L )-type coefficient in the ondiagonal h eff ee component together with off-diagonal (a L )-type coefficients.…”

“…The LSND collaboration recently analyzed the siderealtime dependence of their reported e appearance signal [21], using the short-baseline approximation [22]. Since this signal cannot be incorporated within the standard three-neutrino massive model, a possible explanation is Lorentz violation.…”

“…However, it has been shown that some special combinations of coefficients for Lorentz violation can mimic a masslike energy dependence through a Lorentz-violating seesaw mechanism, even if the Hamiltonian contains no mass terms. The so-called ''bicycle'' model [36] offers a simple example with only two coefficients for Lorentz violation. Despite having no neutrino mass in the Hamiltonian, the model reproduces many features of the neutrino-oscillation data through a pseudomass term generated by a seesaw.…”