Sterile neutrinos and effective field theory

Sterile neutrinos are gauge-singlet fields that can have Majorana masses. They interact with the Standard-Model fields through Yukawa couplings and higher-dimensional gauge-invariant operators. In the framework of neutrino extended Standard Model Effective Field Theory, we study the effect of sterile neutrinos on neutrinoless double beta decay, lepton-number-violating kaon decay and displaced-vertex search at the collider. We use Chiral Effective Field theory to connect physics at the level of quarks and gulons to physics at the hadronic level in terms of pions and nucleons. The expression for neutrinoless double beta decay is given in terms of phase-space factors, hadronic low-energy constatnts, neutrino masses, nuclear matrix elements and the Wilson coefficients of higher-dimensional operators for various isotopes. We also do a similar study on kaon decay. If sterile neutrinos are long-lived, their decay lead to displaced vertices that can be reconstructed. We investigate such sterile neutrinos at Belle II and LHC experiments. By using these experiments, we can probe beyond-the-Standard-Model physics to a very high scale e.g. 100 TeV.