Taking a clue from the minimal structure of texture 4-zero Hermitian mass matrices, which are very successful in accommodating quark mixing data, we propose a form of texture 2-zero complex symmetric neutrino mass matrix with only one phase parameter. This minimal mass matrix not only accommodates the available neutrino oscillation data, but also makes interesting predictions for the unknown parameters like the lightest neutrino mass <inline-formula><tex-math id='TM0001' notation='LaTeX'>$m_{\nu _1}$</tex-math></inline-formula> (for normal ordering), Jarlskog&#8217;s rephasing-invariant <inline-formula><tex-math id='TM0002' notation='LaTeX'>$J_{\mathrm{ CP}}$</tex-math></inline-formula>, the Dirac-type CP-violating phase <inline-formula><tex-math id='TM0003' notation='LaTeX'>$\delta _{\mathrm{ CP}}$</tex-math></inline-formula>, and the effective neutrino mass <inline-formula><tex-math id='TM0004' notation='LaTeX'>$\langle m_{ee} \rangle $</tex-math></inline-formula>. We also explore the correlations between the parameters of the model, which lead us to minimizing the parameters further.

India

Manoj Kumar

Nikhila Awasthi

Monika Randhawa

Manmohan Gupta

Minimal Structure for Neutrino Mass Matrix

Abstract Using unitarity, unlike the approaches available in the literature, we construct 9 independent representations of the Cabibbo–Kobayashi–Maskawa) CKM matrix starting with each of the 9 elements of the matrix. The relationship of these independently constructed representations with those already available in the literature is compared and discussed. Further, the implications of these representations are explored for some of the CKM parameters such as , J and . Interestingly, we find that the PDG representation which is equivalent to our first representation seems to be most appropriate to incorporate the hierarchy of the elements of the CKM matrix as well as to describe the related phenomenology.

Gurjit Kaur

Aakriti Bagai

Gulsheen Ahuja

Revisiting Representations of Quark Mixing Matrix

Fritzsch–Xing matrices are a particular class of texture 4 zero hermitian quark mass matrices, known to be successful in accommodating the quark mixing data. In the present work, it is shown that these texture 4-zero matrices with only one phase parameter, unlike the usually considered two phase parameters, are not only consistent with the latest experimental quark mixing data, but also predict the CP violation parameters, J and corresponding phase  $$\delta $$  <math> <mi>δ</mi> </math>  , in agreement with the recent global analyses. We also show that the mass matrix elements do not exhibit a strong hierarchy and there is a strong correlation between some of the mass matrix elements of up and down sector. A precision measurement of  $$\delta $$  <math> <mi>δ</mi> </math>   as well as small quark masses would have the potential to constrain the phase structure of the matrices further.

Minimizing the phase structure of quark mass matrices

Abstract An attempt has been made to carry out a detailed analysis of quark mass matrices having structure beyond the minimal texture. In particular, keeping in mind precision measurements of Cabibbo–Kobayashi–Maskawa parameters as well as refinements in the ranges of light quark masses, we have examined the viability of all possible combinations of Hermitian texture 5 zero quark mass matrices. Interestingly, one finds that all these possibilities are now excluded by the present quark mixing data, thereby having important implications for model building.

Shivali Kaundal

Going beyond the minimal texture of quark mass matrices in the era of precision measurements

Abstract We have carried out an extensive analysis of all possible minimal texture quark mass matrices implying 169 texture-6 zero combinations. One finds that all these combinations are ruled out: a good number of these analytically, the other possibilities being excluded by the present quark mixing data. Interestingly, even if there are future changes in the ranges of the light quark masses, these conclusions remain valid.

Minimal texture of quark mass matrices and precision CKM measurements

We point out a potential relevance between the Krein–Gupta–Bleuler (KGB) vacuum leading to a fully covariant quantum field theory for gravity in de Sitter (dS) spacetime and the observable smallness of the cosmological constant. This may provide a formulation of linear quantum gravity in a framework amenable to developing a more complete theory determining the value of the cosmological constant.

China

Hamed Pejhan

Japan

Kazuharu Bamba

Iran

Mohammad Enayati

Surena Rahbardehghan

A small non-vanishing cosmological constant from the Krein–Gupta–Bleuler vacuum

In the light of refined and large measurements of the reactor mixing angle 13 , we have revisited the texture three- and two-zero neutrino mass matrices in the flavor basis. For Majorana neutrinos, it has been explicitly shown that all the texture three-zero mass matrices remain ruled out. Further, for both normal and inverted mass ordering, for the texture two-zero neutrino mass matrices one finds interesting constraints on the Dirac-like CP-violating phase and Majorana phases and .

Madan Singh

Revisiting the texture zero neutrino mass matrices

In this paper, vacuum expectation value (VEV) of the energy–momentum tensor for a conformally coupled scalar field in de Sitter space–time is investigated through the Krein–Gupta–Bleuler construction. This construction has already been successfully applied to the de Sitter minimally coupled massless scalar field and massless spin-2 field to obtain a causal and fully covariant quantum field on de Sitter background. We also consider the effects of boundary conditions. In this respect, Casimir energy–momentum tensor induced by Dirichlet boundary condition on a curved brane is evaluated.

S. Rahbardehghan

H. Pejhan

The Krein–Gupta–Bleuler quantization in de Sitter space–time; Casimir energy–momentum tensor for a curved brane

The implications of the recently measured leptonic mixing angle as well as the other two mixing angles have been examined for Fritzsch-like mass matrices with minimal texture for Dirac neutrinos. Interestingly, the existing data seem to rule out this texture-specific case of Dirac neutrinos for normal/inverted hierarchies as well as degenerate scenarios of masses.