Neutrinoless double-beta decay. A brief review

In this brief review we discuss the generation of Majorana neutrino masses through the see-saw mechanism, the theory of neutrinoless double-beta decay, the implications of neutrino oscillation data for the effective Majorana mass, taking into account the recent Daya Bay measurement of theta_13, and the interpretation of the results of neutrinoless double-beta decay experiments.Comment: 22 page

Soft breaking of Lμ−LτL_\mu-L_\tau symmetry: Light neutrino spectrum and Leptogenesis

Continuous $U(1)_{L_\mu-L_\tau}$ symmetry can generate quasi degenerate mass spectrum for both left handed light and right handed heavy Majorana neutrinos assuming that the symmetry preserving non zero parameters are nearly same. There is an accidental $\mu\tau$ exchange symmetry in the light and heavy neutrino Majorana mass terms. This implies $\theta_{13}=0$ and $\theta_{23}=\frac{\pi}{4}$. In addition it generates another zero mixing angle and one zero mass difference. We restrict ourselves to type-I See-Saw mechanism for generation of light neutrino mass. We have found that under $U(1)_{L_\mu-L_\tau}$ symmetry cosmological lepton asymmetry vanishes. We break $U(1)_{L_\mu-L_\tau}$ such a way that the $\mu\tau$ exchange symmetry preserves in the neutrino sector. We have seen that light neutrino phenomenology can be explained under soft breaking of this symmetry. We have observed that softness of this symmetry breaking depends on the degeneracy of the light neutrino mass spectrum. Quasi-degeneracy of right handed neutrino mass spectrum opens an option for resonant leptogenesis. The degeneracy of the right handed neutrino mass spectrum is restricted through light neutrino data. We observed that for generation of right sized baryon asymmetry common neutrino mass scale $m_0$ have to be of the order of $\sqrt{\Delta m^2_{\rm atm}}$ and corresponding right handed neutrino mass scale have to be nearly $10^{13}$ GeV. We also have discussed the effect of RG evolution on light neutrino spectrum and also on baryon asymmetry.Comment: 21 pages, no figure, Revised with the comments on RG effec

Neutrino Mixing and Quark-Lepton Complementarity

As a result of identification of the solution to the solar neutrino problem, a rather precise relation theta_{sun} + theta_C = pi/4 between the leptonic 1-2 mixing angle theta_{sun} and the Cabibbo angle has emerged. It would mean that the lepton and the quark mixing angles add up to the maximal, suggesting a deep structure by which quarks and leptons are interrelated. We refer the relation ``quark-lepton complementarity'' (QLC) in this paper. We formulate general conditions under which the QLC relation is realized. We then present several scenarios which lead to the relation and elaborate on phenomenological consequences which can be tested by the future experiments. We also discuss implications of the QLC relation for the quark-lepton symmetry and the mechanism of neutrino mass generation.Comment: 22 pages, version to be published in Phys. Rev.

Icosahedral (A5) Family Symmetry and the Golden Ratio Prediction for Solar Neutrino Mixing

We investigate the possibility of using icosahedral symmetry as a family symmetry group in the lepton sector. The rotational icosahedral group, which is isomorphic to A5, the alternating group of five elements, provides a natural context in which to explore (among other possibilities) the intriguing hypothesis that the solar neutrino mixing angle is governed by the golden ratio. We present a basic toolbox for model-building using icosahedral symmetry, including explicit representation matrices and tensor product rules. As a simple application, we construct a minimal model at tree level in which the solar angle is related to the golden ratio, the atmospheric angle is maximal, and the reactor angle vanishes to leading order. The approach provides a rich setting in which to investigate the flavor puzzle of the Standard Model.Comment: 22 pages, version to be published in Phys. Rev.

Flavor Delta(54) in SU(5) SUSY Model

We design a supersymmetric SU (5) GUT model using \Delta (54), a finite non-abelian subgroup of SU (3)f . Heavy right handed neutrinos are introduced which transform as three-dimensional repre-sentation of our chosen family group. The model successfully reproduces the mass hierarchical mass structures of the Standard Model, and the CKM mixing matrix. It then provides predictions for the light neutrino with a normal hierarchy and masses such that m{\nu},1 \approx 5\times10-3 eV, m{\nu}, 2 \approx 1\times 10-2 eV, and m{\nu},3 \approx 5 \times 10-2 eV. We also provide predictions for masses of the heavy neutrinos, and correc- tions to the tri-bimaximal matrix that fit within experimental limits, e.g. a reactor angle of -7.31o. A simple modification to our model is introduced at the end and is shown to also produce predictions that fall well within those limits.Comment: 22 page

On the New Conditions for a Total Neutrino Conversion in a Medium

We show that the arguments forming the basis for the claim that the conditions for total neutrino conversion derived and studied in detail in [1,2] ``are just the conditions of the parametric resonance of neutrino oscillations supplemented by the requirement that the parametric enhancement be complete'', given in [4] have flaws which make the claim physically questionable. We show also that in the case of the transitions in the Earth of the Earth-core-crossing solar and atmospheric neutrinos the peaks in the relevant transitions probabilities $P_{a b}$, associated with the new conditions, $max P_{a b} = 1$, are of physical relevance - in contrast to what is suggested in [4]. Actually, the enhancement of $P_{a b}$ in any region of the corresponding parameter space are essentially determined by these absolute maxima of $P_{a b}$. We comment on few other aspects of the results derived in [1,2,3] which have been misunderstood and/or misinterpreted in [4].Comment: 8 pages, late

A question of hierarchy: matter effects with atmospheric neutrinos and anti-neutrinos

It is by now established that neutrinos mix, have (different) non-zero masses, and therefore oscillate. The oscillation parameters themselves, however, are not all well-known. An open problem is that of the neutrino mass hierarchy. We study the possibility of determining the neutrino mass hierarchy with atmospheric neutrinos using an iron calorimeter detector capable of charge identification such as the proposed MONOLITH and ICAL/INO detectors. We find that such detectors are sensitive to the sign of the mass-squared difference, \delta_{32} = m_3^2 - m_2^2, provided the as-yet unknown mixing angle between the first and third generations, \theta_{13}, is greater than 6 degrees (\sin^2 2\theta_{13} > 0.04). A result with a significance greater than 90% CL requires large exposures (more than 500 kton-years) as well as good energy and angular resolution of the detected muons (better than 15%), especially for small \theta_{13}. Hence obtaining definitive results with such a detector is difficult, unless \theta_{13} turns out to be large. In contrast, such detectors can establish a clear oscillation pattern in atmospheric neutrinos in about 150 kton-years, therefore determining the absolute value of \delta_{32} and \sin^2 2 \theta_{23} to within 10%.Comment: 36 pages revtex with 14 eps figures; new section on statistical significance when detector resolution is include

What Happens If an Unbroken Flavor Symmetry Exists?

Without assuming any specific flavor symmetry and/or any specific mass matrix forms, it is demonstrated that if a flavor symmetry (a discrete symmetry, a U(1) symmetry, and so on) exists, we cannot obtain the CKM quark mixing matrix $V$ and the MNS lepton mixing matrix $U$ except for those between two families for the case with the completely undegenerated fermion masses, so that we can never give the observed CKM and MNS mixings. Only in the limit of $m_{\nu 1} =m_{\nu 2}$ ($m_d=m_s$), we can obtain three family mixing with an interesting constraint $U_{e3}=0$ ($V_{ub}=0$).Comment: 10 pages, no figure, title and presentation change

Testing Supersymmetry with Lepton Flavor Violating tau and mu decays

In this work the following lepton flavor violating $\tau$ and $\mu$ decays are studied: $\tau^- \to \mu^- \mu^- \mu^+$, $\tau^- \to e^- e^- e^+$, $\mu^- \to e^- e^- e^+$, $\tau^- \to \mu^- \gamma$, $\tau^- \to e^- \gamma$ and $\mu^- \to e^- \gamma$. We work in a supersymmetric scenario consisting of the minimal supersymmetric standard model particle content, extended by the addition of three heavy right handed Majorana neutrinos and their supersymmetric partners, and where the generation of neutrino masses is done via the seesaw mechanism. Within this context, a significant lepton flavor mixing is generated in the slepton sector due to the Yukawa neutrino couplings, which is transmited from the high to the low energies via the renormalization group equations. This slepton mixing then generates via loops of supersymmetric particles significant contributions to the rates of $l_j \to 3 l_i$ and the correlated $l_j \to l_i \gamma$ decays. We analize here in full detail these rates in terms of the relevant input parameters, which are the usual minimal supergravity parameters and the seesaw parameters. For the $l_j \to 3 l_i$ decays, a full one-loop analytical computation of all the contributing supersymmetric loops is presented. This completes and corrects previous computations in the literature. In the numerical analysis compatibility with the most recent experimental upper bounds on all these $\tau$ and $\mu$ decays, with the neutrino data, and with the present lower bounds on the supersymmetric particle masses are required. Two typical scenarios with degenerate and hierarchical heavy neutrinos are considered. We will show here that the minimal supergravity and seesaw parameters do get important restrictions from these $\tau$ and $\mu$ decays in the hierarchical neutrino case.Comment: Version to appear in Physical Review