Systematic Study Of The Mechanism Of Neutrinoless Double β Decay

Neutrinoless double β decay is an attractive topic in particle physics.It could demonstrate whether neutrinos are Dirac fermions or Majorana fermions,and a Majorana neutrino mass term could be generated by the Schechter-Valle black box theorem.Neutrinoless double β decay has not been observed until now.Therefore,theoretically,we need to discuss all possible realizations of neutrinoless double β decay.In this work,we will give a systematic and complete classification of all models contributing to d=7 long-range operators and d=9 short-range operators at one-loop level.The general approach for constructing a model involves the following steps:First,for the given operator,we identify topologies with the same number of outer lines as the number of fields in the operator.Then,the Lorentz nature of each line is specified,i.e.scalars are differentiated from fermions,and we refer to them as diagrams.After that,we construct the UV complete models by specifying the quantum numbers of the external and internal fields.Loop models include free hypercharge parameters,and we need to specify the values of these parameters.Given the quantum numbers of mediators and SM fields,we can check whether there are low-level models.The model meets our expectations only when there are no low-level models,and we call this model the genuine model.In practical progress,as the number of loops increases,the tedium of each step in constructing models grows exponentially.As our work progressed,we gradually developed a tool that helps us to construct models systematically.With the tool,we study the systematical one-loop decomposition of the dimension7 long-range 0vββ decay operators and dimension-9 short-range 0vββ decay operators.With the dimension-7 operators,we find that there are 3 genuine one-loop topologies and 8 diagrams.The procedure to determine the SM quantum number assignments for both external and internal fields is presented.The Majorana neutrino mass in long-range 0vββ decay models is discussed.We also present a one-loop 0vββ decay model that produces Majorana neutrino mass at three-loop level.The phenomenological predictions for light neutrino mass and 0vββ decay half-life time including both mass mechanism and long-range contribution are studied.While in dimension-9,there are 6 genuine topologies that generate 8 diagrams.We also present an example of a 0vββ decay model in which neutrino masses are generated at two-loop level,and the short-range contribution can be comparable with the mass mechanism in some region of parameter space.