Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userAnalysis of four-zero textures in $3+1$ framework
100
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The presence of a zero texture in the neutrino mass matrix can indicate the presence of an underlying symmetry which can generate neutrino mass and mixing. In this paper, for the first time we study the four-zero textures of the low energy neutrino mass matrix in the presence of an extra light-sterile neutrino i.e., the 3+1 neutrino scheme. In our analysis we find that out of the 210 possible four-zero textures only 15 textures are allowed. We divide the allowed four-zero textures into two classes -- class $A$ in which the value of mass matrix element $M_{ee}$ is zero and class $B$ in which $M_{ee}$ is non-zero. In this way we obtain ten possible four-zero textures in class $A$ and five possible four-zero textures in class $B$. In our analysis we find that, for normal hierarchy the allowed number of textures in class $A$ ($B$) is nine (three). For the case of inverted hierarchy we find that, two textures in class $A$ are disallowed and these textures are different from the disallowed textures for normal hierarchy in class $A$. However, we find that all the five textures in class $B$ are allowed for the inverted hierarchy. Based on analytic expressions for the elements $M_{alphabeta}$, we discuss the reasons for certain textures being disallowed. We also discuss the correlations between the different parameters of the allowed textures. Finally, we present the implications of our study on experimental searches for neutrinoless double beta decay.
rate research
Read More
We investigate, within the Type I seesaw framework, the physical implications of zero textures in the Yukawa couplings which generate the neutrino Dirac mass matrix $m_D$. It is shown that four is the maximal number of texture zeroes compatible with the observed leptonic mixing and the assumption that no neutrino mass vanishes. We classify all allowed four-zero textures of $m_D$ into two categories with three classes each. We show that the different classes, in general, admit CP violation both at low and high energies. We further present the constraints obtained for low energy physics in each case. The r^ ole of these zero textures in establishing a connection between leptogenesis and low energy data is analysed in detail. It is shown that it is possible in all cases to completely specify the parameters relevant for leptogenesis in terms of light neutrino masses and leptonic mixing together with the unknown heavy neutrino masses.
For type I seesaw and in the basis where the charged lepton and heavy right-handed neutrino mass matrices are real and diagonal, four has been shown to be the maximum number of zeros allowed in the neutrino Yukawa coupling matrix $Y_ u$. These four zero textures have been classified into two distinct categories. We investigate certain phenomenological consequences of these textures within a supersymmetric framework. This is done by using conditions implied on elements of the neutrino Majorana mass matrix for textures of each category in $Y_ u$. These conditions turn out to be stable under radiative corrections. Including the effective mass, which appears in neutrinoless double beta decay, along with the usual neutrino masses, mixing angles and phases, it is shown analytically and through scatter plots how restricted regions in the seesaw parameter space are selected by these conditions. We also make consequential statements on the yet unobserved radiative lepton flavor violating decays such as $mu to e gamma$. All these decay amplitudes are proportional to the moduli of entries of the neutrino Majorana mass matrix. We also show under which conditions the low energy CP violation, showing up in neutrino oscillations, is directly linked to the CP violation required for producing successful flavor dependent and flavor independent lepton asymmetries during leptogenesis.
We investigate Linear and Inverse seesaw mechanisms with maximal zero textures of the constituent matrices subjected to the assumption of non-zero eigenvalues for the neutrino mass matrix $m_ u$ and charged lepton mass matrix $m_e$. If we restrict to the minimally parametrized non-singular `$m_e$ (i.e., with maximum number of zeros) it gives rise to only 6 possible textures of $m_e$. Non-zero determinant of $m_ u$ dictates six possible textures of the constituent matrices. We ask in this minimalistic approach, what are the phenomenologically allowed maximum zero textures are possible. It turns out that Inverse seesaw leads to 7 allowed two-zero textures while the Linear seesaw leads to only one. In Inverse seesaw, we show that 2 is the maximum number of independent zeros that can be inserted into $mu_S$ to obtain all 7 viable two-zero textures of $m_ u$. On the other hand, in Linear seesaw mechanism, the minimal scheme allows maximum 5 zeros to be accommodated in `$m$ so as to obtain viable effective neutrino mass matrices ($m_ u$). Interestingly, we find that our minimalistic approach in Inverse seesaw leads to a realization of all the phenomenologically allowed two-zero textures whereas in Linear seesaw only one such texture is viable. Next our numerical analysis shows that none of the two-zero textures give rise to enough CP violation or significant $delta_{CP}$. Therefore, if $delta_{CP}=pi/2$ is established, our minimalistic scheme may still be viable provided we allow more number of parameters in `$m_e$.
Hadronic matrix elements of local four-quark operators play a central role in non-leptonic kaon decays, while vacuum matrix elements involving the same kind of operators appear in inclusive dispersion relations, such as those relevant in $tau$-decay analyses. Using an $SU(3)_Lotimes SU(3)_R$ decomposition of the operators, we derive generic relations between these matrix elements, extending well-known results that link observables in the two different sectors. Two relevant phenomenological applications are presented. First, we determine the electroweak-penguin contribution to the kaon CP-violating ratio $varepsilon/varepsilon$, using the measured hadronic spectral functions in $tau$ decay. Second, we fit our $SU(3)$ dynamical parameters to the most recent lattice data on $Ktopipi$ matrix elements. The comparison of this numerical fit with results from previous analytical approaches provides an interesting anatomy of the $Delta I = frac{1}{2}$ enhancement, confirming old suggestions about its underlying dynamical origin.
The inverse neutrino seesaw, characterised by only one source of lepton number violation at an ultralight $O$(keV) scale and observable new phenomena at TeV energies accessible to the LHC, is considered. Maximal zero textures of the $3times 3$ lighter and heavier Dirac mass matrices of neutral leptons, appearing in the Lagarangian for such an inverse seesaw, are studied within the framework of $mutau$ symmetry in a specified weak basis. That symmetry ensures the identity of the positions of maximal zeros of the heavy neutrino mass matrix and its inverse. It then suffices to study the maximal zeros of the lighter Dirac mass matrix and those of the inverse of the heavier one since they come in a product. The observed absence of any unmixed neutrino flavour and the assumption of no strictly massless physical neutrino state allow only eight $4$-zero $times$ $4$-zero, eight $4$-zero $times$ $6$-zero and eight $6$-zero $times$ $4$-zero combinations. The additional requirement of leptogenesis is shown to eliminate the last sixteen textures. The surviving eight $4$-zero $times$ $4$-zero textures are subjected to the most general explicit $mutau$ symmetry breaking terms in the Lagrangian in order to accommodate the nonzero value of $theta_{13}$ in the observed range. A full diagonalisation is then carried out. On numerical comparison with all extant and relevant neutrino (antineutrino) data, seven of these eight combination textures in five neutrino matrix forms are found to be allowed, leading to five distinct neutrino mass matrices. Two of these permit only a normal (and the other three only an inverted) mass ordering of the light neutrinos.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
