Abstract
In this paper, we accomplish the complete one-loop matching of the type-I seesaw model onto the Standard Model Effective Field Theory (SMEFT), by integrating out three heavy Majorana neutrinos with the functional approach. It turns out that only 31 dimension-six operators (barring flavor structures and Hermitian conjugates) in the Warsaw basis of the SMEFT can be obtained, and most of them appear at the one-loop level. The Wilson coefficients of these 31 dimension-six operators are computed up to mathcal{O} (M−2) with M being the mass scale of heavy Majorana neutrinos. As the effects of heavy Majorana neutrinos are encoded in the Wilson coefficients of these higher-dimensional operators, a complete one-loop matching is useful to explore the low-energy phenomenological consequences of the type-I seesaw model. In addition, the threshold corrections to the couplings in the Standard Model and to the coefficient of the dimension-five operator are also discussed.
Highlights
Can match it onto the Standard Model Effective Field Theory (SMEFT) by integrating out the heavy degrees of freedom to study its low-energy consequences
The compelling experimental evidence for neutrino masses and lepton flavor mixing indicates that the SM is incomplete and serves only as an EFT at the electroweak scale
It is useful to establish the low-energy EFT of the type-I seesaw model by integrating out the heavy Majorana neutrinos and their impact is encoded in the Wilson coefficients of higher-dimensional operators
Summary
We set up the framework of the functional approach to perform the tree-level and one-loop matchings between the low-energy EFT and an UV theory by integrating out the heavy degrees of freedom. This framework has been first presented in ref. LUV together with the source terms around the classical background fields up to the second order of quantum fields, and obtain. To obtain the local functionals, one can expand Φc [φB] to a given order in 1/M and denote the local one by Φc [φB], where M represents the mass scale of heavy fields that is considered to be extremely high. It is worthwhile to mention that the separation of the tree- and one-loop-level contributions and the loop counting in the UV theory are unambiguous
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