Signatures of $$A_4$$ symmetry in the charged lepton flavour violating decays in a neutrino mass model

We study the charged lepton flavour violation in a popular neutrino mass model with $$A_4$$ A 4 discrete symmetry. This symmetry requires the presence of multiple Higgs doublets in the model and it also dictates the flavour violating Yukawa couplings of the additional neutral scalars of the model. Such couplings lead to the decays of the neutral mesons, the top quark and the $$\tau $$ τ lepton into charged leptons of different flavours at tree level. The $$A_4$$ A 4 symmetry of the model leads to certain characteristic signatures in these decays. We discuss these signatures and predict the rates for the most favourable charged lepton flavour violating modes.

Symmetries and Their Breaking in the Fundamental Laws of Physics

Symmetries in the Physical Laws of Nature lead to observable effects. Beyond the regularities and conserved magnitudes, the last few decades in particle physics have seen the identification of symmetries, and their well-defined breaking, as the guiding principle for the elementary constituents of matter and their interactions. Flavour SU(3) symmetry of hadrons led to the Quark Model and the antisymmetric requirement under exchange of identical fermions led to the colour degree of freedom. Colour became the generating charge for flavour-independent strong interactions of quarks and gluons in the exact colour SU(3) local gauge symmetry. Parity Violation in weak interactions led us to consider the chiral fields of fermions as the objects with definite transformation properties under the weak isospin SU(2) gauge group of the Unifying Electro-Weak SU(2) × U(1) symmetry, which predicted novel weak neutral current interactions. CP-Violation led to three families of quarks opening the field of Flavour Physics. Time-reversal violation has recently been observed with entangled neutral mesons, compatible with CPT-invariance. The cancellation of gauge anomalies, which would invalidate the gauge symmetry of the quantum field theory, led to Quark–Lepton Symmetry. Neutrinos were postulated in order to save the conservation laws of energy and angular momentum in nuclear beta decay. After the ups and downs of their mass, neutrino oscillations were discovered in 1998, opening a new era about their origin of mass, mixing, discrete symmetries and the possibility of global lepton-number violation through Majorana mass terms and Leptogenesis as the source of the matter–antimatter asymmetry in the universe. The experimental discovery of quarks and leptons and the mediators of their interactions, with physical observables in spectacular agreement with this Standard Theory, is the triumph of Symmetries. The gauge symmetry is exact only when the particles are massless. One needs a subtle breaking of the symmetry, providing the origin of mass without affecting the excellent description of the interactions. This is the Brout–Englert–Higgs Mechanism, which produces the Higgs Boson as a remnant, discovered at CERN in 2012. Open present problems are addressed with by searching the New Physics Beyond-the-Standard-Model.

Dealing with T and CPT violations in mixing as well as direct and indirect CP violations for neutral mesons decaying to two vectors

A large number of observables can be constructed from differential decay rate based on the polarization of final state while considering decay of a neutral meson $$(P^{0} \text { or } {\bar{P}}^{0})$$(P0orP¯0) to two vector particles. But all of these observables are not independent to each other since there are only a few independent theoretical parameters controlling the whole dynamics and therefore various relations among observables emerge. In this paper, we have studied the behaviour of observables for neutral meson decaying to two vectors in presence of $$T$$T and $$C\!P T$$CPT violations in mixing accompanied by both direct and indirect $$C\!P$$CP violations. We have expressed all of the fourteen unknown theoretical parameters for this scenario in terms observables only and constructed the complete set of thirty four relations among observables whose violation would signify the existence of some new Physics involving direct violation of $$C\!P T$$CPT. In addition, using this formalism we have studied three special cases too: (a) SM scenario, (b) SM plus direct $$C\!P$$CP violation (c) SM plus $$T$$T and $$C\!P T$$CPT violation in mixing.