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Register a new userSearching for the CP-Violation Associated with Majorana Neutrinos
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The effective Majorana mass which determines the rate of the neutrinoless double beta decay, |<m>|, is considered in the case of three-neutrino mixing and massive Majorana neutrinos. Assuming a rather precise determination of the parameters characterizing the neutrino oscillation solutions of the solar and atmospheric neutrino problems has been made, we discuss the information a measurement of |<m>| > (0.005 - 0.010) eV can provide on the value of the lightest neutrino mass and on the CP-violation in the lepton sector. The implications of combining a measurement of |<m>| with future measurement of the neutrino mass in tritium beta-decay experiments for the possible determination of leptonic CP-violation are emphasized.
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If the present or upcoming searches for neutrinoless double beta decay give a positive result, the Majorana nature of massive neutrinos will be established. From the determination of the value of the effective Majorana mass parameter |<m>|, it would be possible to obtain information on the type of neutrino mass spectrum. Assuming 3-neutrino mixing and massive Majorana neutrinos, we discuss the information a measurement of, or an upper bound on, |<m>| can provide on the value of the lightest neutrino mass m1. With additional data on the neutrino masses obtained in tritium beta decay experiments, it might be possible to establish whether the CP-symmetry is violated in the lepton sector. This would require very high precision measurements. If CP-invariance holds, the allowed patterns of the relative CP-parities of the massive Majorana neutrinos would be determined.
The parity transformation law of the fermion field $psi(x)$ is usually defined by the $gamma^{0}$-parity $psi^{p}(t,-vec{x}) = gamma^{0}psi(t,-vec{x})$ with eigenvalues $pm 1$, while the $igamma^{0}$-parity $psi^{p}(t,-vec{x})=igamma^{0}psi(t,-vec{x})$ is required for the Majorana fermion. The compatibility issues of these two parity laws arise in generic fermion number violating theories where a general class of Majorana fermions appear. In the case of Majorana neutrinos constructed from chiral neutrinos in an extension of the Standard Model, the Majorana neutrinos can be characterized by CP symmetry although C and P are separately broken. It is then shown that either choice of the parity operation, $gamma^{0}$ or $igamma^{0}$, in the level of the starting fermions gives rise to the consistent and physically equivalent descriptions of emergent Majorana neutrinos both for Weinbergs model of neutrinos and for a general class of seesaw models. The mechanism of this equivalence is that the Majorana neutrino constructed from a chiral neutrino, which satisfies the classical Majorana condition $psi(x)=Coverline{psi(x)}^{T}$, allows the phase freedom $psi(x)=e^{ialpha} u_{L}(x) + e^{-ialpha}Coverline{ u_{L}(x)}^{T}$ with $alpha=0 {rm or} pi/4$ that accounts for the phase coming from the different definitions of parity for $ u_{L}(x)$ and ensures the consistent definitions of CP symmetry $({cal CP})psi(x)({cal CP})^{dagger}= pm igamma^{0}psi(t,-vec{x})$.
From the data release of OPERA - CNGS experiment, and publicly announced on 23 September 2011, we cast a phenomenological model based on a Majorana neutrino state carrying a fictitious imaginary mass term, already discussed by Majorana in 1932. This mass term can be induced by the interaction with the matter of the Earths crust during the 735 Km travel. Within the experimental errors, we prove that the model fits with OPERA, MINOS and supernova SN1987a data. Possible violations to Lorentz invariance due to quantum gravity effects have been considered.
In this talk, we present a recent investigation of the sufficient and necessary conditions for CP conservation in the leptonic sector with massive Majorana neutrinos in terms of CP-odd weak-basis invariants. The number of weak-basis invariants to guarantee CP conservation in the leptonic sector is clarified and a new set of invariants are advocated for the description of CP conservation, given the physical parameters in their experimentally allowed regions.
It is well known that one can use B -> pi pi decays to probe the CP-violating phase alpha. In this paper we show that these same decays can be used to search for new physics. This is done by comparing two weak phases which are equal in the standard model: the phase of the t-quark contribution to the b -> d penguin amplitude, and the phase of Bd-Bd(bar) mixing. In order to make such a comparison, we require one piece of theoretical input, which we take to be a prediction for |P/T|, the relative size of the penguin and tree contributions to Bd -> pi^+ pi^-. If independent knowledge of alpha is available, the decay Bd(t) -> pi^+ pi^- alone can be used to search for new physics. If a full isospin analysis can be done, then new physics can be found solely through measurements of B -> pi pi decays. The most promising scenario occurs when the isospin analysis can be combined with independent knowledge of alpha. In all cases, the prospects for detecting new physics in B -> pi pi decays can be greatly improved with the help of additional measurements which will remove discrete ambiguities.
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