Renormalization Group Evolution of Dimension-seven Operators in Standard Model Effective Field Theory and Relevant Phenomenology

Abstract

We showed in a previous publication that there are six independent dimension-seven operators violating both lepton and baryon numbers ($L=-B=1$) and twelve ones violating lepton but preserving baryon number ($L=2,B=0$) in standard model effective field theory, and we calculated one-loop renormalization for the former six operators. In this work we continue our efforts on renormalization of the operators. It turns out this could become subtle because the operators are connected by nontrivial relations when fermion flavors are counted. This kind of relations does not appear in lower dimensional operators. We show how we can extract anomalous dimension matrix for a flavor-specified basis of operators from counterterms computed for the above flavor-blind operators without introducing singular inverse Yukawa coupling matrices. As a phenomenological application, we investigate renormalization group effects on nuclear neutrinoless double $\beta$ decay. We also discuss very briefly its analog in the meson sector, $K^{\pm }\to {\pi }^{\mp }{\mu }^{\pm }{\mu }^{\pm }$, and indicate potential difficulties to compute its decay width.

v1: 18 pages, 2 figures, 5 tables. v2: 21 pages, 3 figures, 5 tables, to appear in jhep; minor revisions made without changing results: (1) corrected typos; (2) added clarifying statements and three refs; (3) Appendix expanded by an explicit example of calculation; (4) corrected an error in eq. (13), thanks to the referee; (5) replaced fig. 2 due to a numerical problem

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• Heavy Majorana Neutrinos in the Effective Lagrangian Description: Application to Hadron Colliders
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Cited by in corpus (5)

• General neutrino interactions with sterile neutrinos in light of coherent neutrino-nucleus scattering and meson invisible decays
• Long-distance Contributions to Neutrinoless Double Beta Decay ${\pi }^{-}\to {\pi }^{+}ee$
• One-loop running of dimension-six Higgs-neutrino operators and implications of a large neutrino dipole moment
• One-loop Matching of the Type-II Seesaw Model onto the Standard Model Effective Field Theory
• Complete One-loop Renormalization-group Equations in the Seesaw Effective Field Theories