arXiv subjects

N. Razzaghi

Publications and source records attributed to N. Razzaghi.

8 recordsLinked to original sources

arXiv2026

Open Path Geometric Phases in Three Flavor Neutrino Oscillations through Layered Matter

We present a gauge invariant formulation of open path geometric phases in the context of three flavor neutrino oscillations traversing nonuniform matter. In contrast to the standard Berry phase, which is intrinsically associated with closed adiabatic cycles, neutrino propagation from source to detector typically traces an open trajectory within the parameter space of matter dependent Hamiltonians. We derive this formalism within a layered matter framework, where each discrete layer is characterized by a constant density and a local matter eigenbasis. The total evolution operator is expressed as a path ordered product of dynamical propagation factors and interface matrices that bridge adjacent matter eigenbases. This construction naturally yields geometric phase chains composed of endpoint projections and interface overlaps. We demonstrate that these chains remain invariant under arbitrary local rephasings of the instantaneous matter eigenstates, thereby resolving the gauge dependence ambiguity typically associated with open path transport. The proposed formalism elucidates the noncommutative nature of flavor evolution in layered media, illustrating that profiles with identical column densities but distinct ordering can yield different transition amplitudes. Furthermore, we analyze the influence of the Dirac CP phase, showing that it deforms the geometry of matter eigenbasis transport without being equivalent to the geometric phase itself. In the continuous limit, finite interface overlaps converge to Berry connection factors, while endpoint projections remain indispensable for ensuring open path gauge invariance. We discuss the phenomenological implications of this structure, emphasizing that geometric phases are not independent observables but contribute to transition probabilities via interference among coherent propagation chains.

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arXiv2026

Breaking the Democratic Limit in the Generalized Friedberg-Lee Model: Implications for Neutrino Masses and Mixing

We investigate a generalized Friedberg--Lee (FL) framework for neutrino masses, focusing on the singular parameter space at Point D ($α= β= -1/3$). At this limit, the neutrino mass matrix exhibits a democratic texture governed by the $S_3$ permutation symmetry. Although theoretically profound, the exact democratic limit is phenomenologically excluded as it predicts a degenerate mass spectrum and a vanishing reactor angle ($θ_{13}=0$). To reconcile this high-symmetry limit with experimental observations, we introduce a minimal and systematic perturbation that preserves the Twisted Friedberg--Lee (TFL) symmetry. This mechanism effectively lifts the mass degeneracy and breaks the magic and $μ$--$τ$ symmetries in a controlled manner. Our derivation avoids \textit{ad hoc} parameters, establishing a robust framework that yields a realistic inverted mass hierarchy ($m_3=0$), a non-zero $θ_{13}$, and intrinsic CP violation. We demonstrate that the model predicts maximal atmospheric mixing and a significant Dirac CP phase. The obtained numerical ranges for the neutrino masses and the Jarlskog invariant show excellent agreement with global fit data, providing a theoretically motivated foundation for neutrino flavor physics within the TFL scheme.

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arXiv2023

Neutrino mixing matrix and masses at a particular point of the generalized Fridberg-Lee model

We propose the generalized Friedberg-Lee model neutrino mass model at a particular point (point D at which $α=β=-\frac{1}{3}$) where at this point, the generalized Fridberg-Lee model is converted to the Democratic mass matrix with the $S_3$ symmetry. The Democratic texture has an experimentally unfavored degenerate mass spectrum on the base of the tribimaximal mixing matrix $(U_{TBM})$. We modify the Democratic mass matrix, at point D, to obtain a nondegenerate mass spectrum by adding the breaking mass term as preserving the twisted Fridberg-Lee symmetry. Although the mixing matrix is still $(U_{TBM})$, where leads to $θ_{13}=0$ which is not consistent with the results from Daya Bay and RENO experiments that have established a nonzero value for $θ_{13}$. preserving the leading behavior of $U$ as tribimaximal, and we apply the Broken Democratic neutrino mass texture as a mass matrix at point D. Subsequently, we characterize a minimal perturbation mass matrix which is responsible for a nonzero $θ_{13}$ along with CP violation parameters, besides the solar neutrino mass splitting has been resulted from it. Let us mention that, unlike other investigations, the perturbation matrix is not adopted on an ad hoc basis, but is generated only in one step by the rules of perturbation method that we will describe. Subsequently, we develop the following results to the literature: (a) we obtain the corresponding neutrino mixing matrix of the generalized Fridberg-Lee model at point D with $θ_{23}=\fracπ{4}$ and non-zero $δ$; (b) the ordering of the neutrino masses is inverted; (c) we also obtain the allowed range of the mass parameters, the Dirac phase and the Jarlskog parameter which are consistence with the available experimental data.

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arXiv2022

The special Two zeros texture based on $A_4$ symmetry and perturbation method

The current study aimed to investigate the special case of two zeros in a Majorana neutrino mass matrix based on $A_4$ symmetry, where charged lepton mass matrix is diagonal. The texture $M_ν^{S_7}$ with $(μ, μ)$ and $(τ,τ)$ vanishing element of mass matrix has magic and $μ-τ$ symmetry, with a tribimaximal form of the mixing matrix which leads to $θ_{13}=0$ that it is not consistent with experimental data and does not seem to be allowed. Since $θ_{13}$ is small compared to other neutrino mixing angles, we show that $θ_{13}$, and $δ$ could be obtained by using a complex symmetrical perturbation in the mass basis and also could be shown that $δm^2\equiv~m_2^2-m^2_1\neq0$ affecting the atmospheric mixing angle. We find that for the complex perturbation mass matrix, only the results of the case I, $Δ<0$ and $\textit{Re}(α)<0$, are consistent with experimental data. Furthermore, the allowed range of our parameter space and complex element of perturbation are found which led to finding the deviation of $θ_{23}$ from $45^\circ$ where this deviation is in line with the experimental data which indicate the accuracy of our model and its results. Our prediction is inverted mass ordering in the Case I. The results of the case II, $Δ>0$ and $\textit{Re}(α)>0$, are ruled out.

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arXiv2022

Generating CP violation from a modified Fridberg-Lee model

The overall characteristics of the solar and atmospheric neutrino oscillations are approximately consistent with a tribimaximal form of the mixing matrix $U$ of the lepton sector. Exact tribimaximal mixing leads to $θ_{13}=0$. However, the results from the Daya Bay and RENO experiments have established, such that in comparison to the other neutrino mixing angles, $θ_{13}$ is small. Moreover, the atmospheric and solar mass splitting differ by two orders of magnitude. These significant differences constitutes the great enthusiasm and main motivation for our research herein reported. Keeping the leading behavior of U as tribimaximal. We would make a response to the following questions: at some level, whether or not the small parameters such as the solar neutrino mass splitting and $U_{e3}$, which vanish in a new framework, can be interpreted as a modified FL neutrino mass model? Subsequently, a minimal single perturbation leads to nonzero values for both of them? Our minimal perturbation matrix is constructed solely from computing the third mass eigenstate, using the rules of perturbation theory. Let us point out that in contrast with~\cite{my}, this matrix is not ad hoc assumed, but is instead built following a series of steps we will outline. Also in compared to the original FL neutrino mass model which generalize it by inserting phase factors, our work is more accurate. Subsequently, we produce the following results that add new contributions to the literature: a) we obtain a realistic neutrino mixing matrix with $δ\neq0$ and $θ_{23}=45^\circ$; b) the solar mass splitting term is dominated by an imaginary term, which could induce the existence of Majorana neutrinos, along with explaining a large CP violation in nature.

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arXiv2022

Two-zero textures based on $A_4$ symmetry and unimodular mixing matrix

Applying the $A_4$ symmetry in the scenario of unimodular second scheme of trimaximal $TM_2$ mixing matrix, where the charged lepton mass matrix is diagonal and the nature of neutrinos are Majorana, we investigate and analyze feasible two zeros neutrino mass matrices. Among the seven possible two-zero textures with $A_4$ symmetry, we have found that only two textures, namely the texture with $(e, e)$ and $(e,μ)$ vanishing element of mass matrix and its permutation, are consistent with the experimental data in the non-perturbation method. We also obtain new significant relations between phases of our model, namely $ρ+σ=ϕ\pmπ$ and $\sin^2{θ_{13}}=\frac{2}{3}R_ν$ where $R_ν=\frac{δm^2}{Δm^2}$. Subsequently, by admitting the experimental ranges of $R_ν$, we retrieve the allowed range of the unknown phase $ϕ$. Such a procedure assist us to determine the ranges of all the neutrino observable parameters, the masses of neutrinos, the CP-violating phases and $J$ parameter as well as to predict the normal hierarchy for the neutrino mass. Finally, we show that our predictions with respect to our herewith reported specific textures are consistent with the corresponding data reported from neutrino oscillation, cosmic microwave background and neutrinoless double beta decay experiments.

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arXiv2016

Neutrino mixing matrix and masses from a generalized Friedberg-Lee model

The overall characteristics of the solar and atmospheric neutrino oscillation are approximately consistent with a tribimaximal form of the mixing matrix $U$ of the lepton sector. Exact tribimaximal mixing leads to $θ_{13}=0$. However, recent results from Daya Bay and RENO experiments have established a nonzero value for $θ_{13}$. Keeping the leading behavior of $U$ as tribimaximal, we use a generalized Fridberg-Lee neutrino mass model along with a complementary ansatz to incorporate a nonzero $θ_{13}$ along with CP violation. We generalize this model in two stages: In the first stage we assume $μ-τ$ symmetry and add imaginary components which leads to nonzero phases. In the second stage we add a perturbation with real components which breaks the $μ-τ$ symmetry and this leads to a nonzero value for $θ_{13}$. The combination of these two generalizations leads to CP violation. Using only two of the experimental data, we can fix all of the parameters of our model and predict not only values for the other experimental data, which agree well with the available data, but also the masses of neutrinos and the CP violating phases and parameters. These predictions include the following: $\langle m_{ν_e} \rangle\approx(0.033-0.037)~eV$, $\langle m_{ν_μ} \rangle\approx(0.043-0.048)~ eV$, $\langle m_{ν_τ} \rangle\approx(0.046-0.051)~ eV$, and $59.21^{\circ}\lesssim δ\lesssim 59.34^{\circ}$

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arXiv2012

Generalized Friedberg-Lee model for CP violation in neutrino physics

We propose a phenomenological model of Dirac neutrino mass operator based on the Fridberg-Lee (FL) neutrino mass model to include CP violation. By considering the most general set of complex coefficients, and imposing the condition that the mass eigenvalues are real, we find a neutrino mass matrix which is non-hermitian, symmetric and magic. In particular, we find that the requirement of obtaining real mass eigenvalues by transferring the residual phases to the mass eigenstates self-consistently, dictates the following relationship between the imaginary part of the mass matrix elements $B$ and the parameters of the FL model: $B=\pm\sqrt{3/4(a-b_{r})^{2}\sin^{2}2θ_{13}\cos^{2}θ_{12}}$. We obtain inverted neutrino mass hierarchy, $m_{3}=0$. Making a correspondence between our model and the experimental data produces stringent conditions on the parameters as follows: $35.06^{\circ}\lesssimθ_{12}\lesssim36.27^{\circ}$, $θ_{23}= 45^{\circ}$, $7.27^{\circ}\lesssimθ_{13}\lesssim11.09^{\circ}$, and $82.03^{\circ}\lesssimδ\lesssim85.37^{\circ}$. We get mildly broken $μ-τ$ symmetry, which reduces the resultant neutrino mixing pattern from tribimaximal (TBM) to trimaximal (TM). The CP violation as measured by the Jarlskog parameter is restricted by $0.027\lesssim J\lesssim0.044$.

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