Twin modular S4 with SU(5) GUT

We discuss the SU(5) grand unified extension of flavour models with multiple modular symmetries. The proposed model involves two modular S4 groups, one acting in the charged fermion sector, associated with a modulus field value τT with residual $$ {Z}_3^T $$ Z 3 T symmetry, and one acting in the right-handed neutrino sector, associated with another modulus field value τSU with residual $$ {Z}_2^{SU} $$ Z 2 SU symmetry. Quark and lepton mass hierarchies are naturally generated with the help of weightons, which are SM singlet fields, where their non-zero modular weights play the role of Froggatt-Nielsen charges. The model predicts TM1 lepton mixing, and neutrinoless double beta decay at rates close to the sensitivity of current and future experiments, for both normal and inverted orderings, with suppressed corrections from charged lepton mixing due to the triangular form of its Yukawa matrix.

Majorana Fermions in Self-Consistent Effective Hamiltonian Theory

Majorana fermion solution is obtained from the self-consistent effective Hamiltonian theory. The ground state is conjectured to be a non-empty vacuum with 2 fermions, one for each type. The first type is the original charged fermion and the second type the chiral charge-less Majorana fermion. The Marjorana fermion is like a shadow of the first fermion cast by the non-empty vacuum.

Scattering of charged fermion to two-dimensional wormhole with constant axial magnetic flux

Scattering of charged fermion with $$(1+2)$$ ( 1 + 2 ) -dimensional wormhole in the presence of constant axial magnetic flux is explored. By extending the class of fermionic solutions of the Dirac equation in the curved space of wormhole surface to include normal modes with real energy and momentum, we found a quantum selection rule for the scattering of fermion waves to the wormhole. The newly found momentum–angular momentum relation implies that only fermion with the quantized momentum $$k=m'/a\sqrt{q}$$ k = m ′ / a q can be transmitted through the hole. The allowed momentum is proportional to an effective angular momentum quantum number $$m'$$ m ′ and inversely proportional to the radius of the throat of the wormhole a. Flux dependence of the effective angular momentum quantum number permits us to select fermions that can pass through according to their momenta. A conservation law is also naturally enforced in terms of the unitarity condition among the incident, reflected, and transmitted waves. The scattering involving quasinormal modes (QNMs) of fermionic states in the wormhole is subsequently explored. It is found that the transmitted waves through the wormhole for all scenarios involving QNMs are mostly suppressed and decaying in time. In the case of QNMs scattering, the unitarity condition is violated but a more generic relation of the scattering coefficients is established. When the magnetic flux $$\phi =mhc/e$$ ϕ = m h c / e , i.e., quantized in units of the magnetic flux quantum hc/e, the fermion will tunnel through the wormhole with zero reflection.

Masses and electric charges: gauge anomalies and anomalous thresholds

We work out in the forward limit and up to order $$e^6$$ e 6 in perturbation theory the collinear divergences. In this kinematical regime we discover new collinear divergences that we argue can be only cancelled using quantum interference with processes contributing to the gauge anomaly. This rules out the possibility of a quantum consistent and anomaly free theory with massless charges and long range interactions. We use the anomalous threshold singularities to derive a gravitational lower bound on the mass of the lightest charged fermion.

Data driven flavour model

A bottom-up approach has been adopted to identify a flavour model that agrees with present experimental measurements. The charged fermion mass hierarchies suggest that only the top Yukawa term should be present at the renormalisable level. Similarly, describing the lightness of the active neutrinos through the type-I Seesaw mechanism, right-handed neutrino mass terms should also be present at the renormalisable level. The flavour symmetry of the Lagrangian including the fermionic kinetic terms and only the top Yukawa is then a combination of U(2) and U(3) factors. Once considering the Majorana neutrino terms, the associated symmetry is O(3). Lighter charged fermion and active neutrino masses and quark and lepton mixings arise considering specific spurion fields à la Minimal Flavour Violation. The associated phenomenology is investigated and the model turns out to have almost the same flavour protection as the Minimal Flavour Violation in both quark and lepton sectors. Promoting the spurions to dynamical fields, the associated scalar potential is also studied and a minimum is identified such that fermion masses and mixings are correctly reproduced. Very precise predictions for the Majorana phases follow from the minimisation of the scalar potential and thus the neutrinoless-double-beta decay may represent a smoking gun for the model.

Fermions Tunneling and Quantum Corrections for Quintessential Kerr-Newman-AdS Black Hole

This paper is devoted to study charged fermion particles tunneling through the horizon of Kerr-Newman-AdS black hole surrounded by quintessence by using Hamilton-Jacobi ansatz. In our analysis, we investigate Hawking temperature as well as quantum corrected Hawking temperature on account of generalized uncertainty principle. Moreover, we discuss the effects of correction parameter β on the corrected Hawking temperature Te-H, graphically. We conclude that the temperature Te-H vanishes when β=100, whereas for β<100 and β>100, the temperature turns out to be positive and negative, respectively. We observe that the graphs of Te-H w.r.t. quintessence parameter α exhibit behavior only for the particular ranges, i.e., 0<α<1/6, charge 0<Q≤1, and rotation parameter 0<a≤1. For smaller and larger values of negative Λ, as horizon increases, the temperature decreases and increases, respectively.