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Register a new userComment on the article by D. Borah and B. Karmakar Linear seesaw for Dirac neutrinos with A4 flavour symmetry, Phys. Lett. B789 (2019) 59-70, arXiv: 1806.10685
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D. Borah and B. Karmakar in Phys. Lett. B789 (2019) have proposed an A4 flavoured linear seesaw model to realise light Dirac neutrinos. In this comment article, we show that some neutrino Yukawa interactions were missed in the model, thus implying that a different formula would be needed to determine the effective neutrino mass matrix, with significantly different results. Our result shows that, unlike stated in Phys. Lett. B789 (2019), that the inverted neutrino mass spectrum is not ruled out.
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In this paper we reply to the comment presented in [1]. In that work the author raises several points about the geometric phase for neutrinos discussed in [2]. He affirms that the calculation is flawed due to incorrect application of the definition of noncyclic geometric phase and the omission of one term in Wolfenstein effective Hamiltonian. He claims that the results are neither gauge invariant nor lepton field rephasing invariant and presents an alternative calculation, solely in order to demonstrate that the Majorana CP-violating phase enters the geometric phase essentially by lepton field rephasing transformation. Finally he claims that the nontrivial dependence of geometric phase on Majorana CP-violating phase presented in [2] is unphysical and thus unmeasurable. We discuss each of the points raised in [1] and show that they are incorrect. In particular, we introduce geometric invariants which are gauge and reparametrization invariants and show that the omitted term in the Wolfenstein effective Hamiltonian has no effect on them. We prove that the appearance of the Majorana phase cannot be ascribed to a lepton field rephasing transformation and thus the incorrectness of the claim of unphysicality and unmeasurability of the geometric phase. In the end we show that the calculation presented in [1] is inconsistent and based on the erroneous assumption and implementation of the wavefunction collapse. We remark that the geometric invariants defined in the present paper show a difference between Dirac and Majorana neutrinos, since they depend on the CP-violating Majorana phase.
In the cross section for single-inclusive jet production in electron-nucleon collisions, the distribution of a quark in an electron appears at next-to-next-to-leading order. The numerical calculations in Ref. [1] were carried out using a perturbative approximation for the distribution of a quark in an electron. We point out that that distribution receives nonperturbative QCD contributions that invalidate the perturbative approximation. Those nonperturbative effects enter into cross sections for hard-scattering processes through resolved-electron contributions and can be taken into account by determining the distribution of a quark in an electron phenomenologically.
We offer a clarification of the significance of the indicated paper of H. Cheng. Chengs conclusions about the attractive nature of Casimir forces between parallel plates are valid beyond the particular model in which he derived them; they are likely to be relevant to other recent literature on the effects of hidden dimensions on Casimir forces.
In this communication we refute a criticism concerning results of our work [3] that was presented in references [1] and [2].
In this work, we present a comparative study of the three of the seesaw models, viz., type II, inverse and linear seesaw models, to investigate about light neutrino masses and mixings, flavour structure, neutrinoless double beta decay ($ 0 u beta beta $) and charged lepton flavour violation (cLFV) decay ($murightarrow egamma$). We consider the $ A_{4} $ flavour symmetry, while some other symmetries, like $U(1)_{X}$, $Z_4$ and $Z_5$ are also included to forbid unwanted terms in the Lagrangian. Taking into account the present experimental data for the known light neutrino parameters from recent global fit data, we compute the currently unknown neutrino parameters such as the lightest neutrino mass ($m_1$), CPV phase (Dirac and Majorana), and effective light neutrino mass in the neutrinoless double beta decay, by considering different VEV alignments of the triplet scalar flavon fields. We also elucidate on the octant of atmospheric neutrino mixing angle, $theta_{23}$, in the light of our predicted results. Finally, we present the region of parameter spaces of $m_1$, CPV phases, octant of $theta_{23}$ and effective mass measurable in of neutrino less double beta decay experiments, that can be tested in future experiments. We observe that the branching ratio of ($murightarrow egamma$) can help discriminate the three seesaw models. Further, the favoured Octant of the atmospheric mixing angle $theta_{23}$ changes with the VEV alignment of the triplet flavon field - i.e., the internal flavour structure of the neutrinos is reflected in their composition (mixing). The constant F determining the scale of flavour symmetry breaking, seesaw scale and coupling constants of the three seesaw models has also been computed, which puts a constraint among them allowed by the present experimental results.
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