One-loop Matching of the Type-II Seesaw Model onto the Standard Model Effective Field Theory

Abstract

In this paper, we continue to construct the low-energy effective field theories (EFTs) of the canonical seesaw models, which are natural extensions of the Standard Model (SM) to accommodate tiny but nonzero neutrino masses. Different from three right-handed neutrino singlets in the type-I seesaw model, the Higgs triplet in the type-II seesaw model participates directly in the electroweak gauge interactions, rendering the EFT construction more challenging. By integrating out the heavy Higgs triplet in the functional-integral formalism, we carry out a complete one-loop matching of the type-II seesaw model onto the so-called Standard Model Effective Field Theory (SMEFT). It turns out that 41 dimension-six operators (barring flavor structures and Hermitian conjugates) in the Warsaw basis of the SMEFT can be obtained, covering all those 31 dimension-six operators in the case of type-I seesaw model. The Wilson coefficients for 41 dimension-six operators are computed up to $\mathcal{O}\left(M_{\Delta }^{-2}\right)$ with $M_{\Delta }^{}$ being the mass scale of the Higgs triplet. Moreover, the branching ratios of rare radiative decays of charged leptons $l_{\alpha }^{-}\to l_{\beta }^{-}+\gamma$ are calculated in the EFT and compared with that in the full theory in order to demonstrate the practical application and the correctness of our EFT construction.

arXiv comment37 pages, 3 figures, the version accepted for publication in JHEP; A Mathematica Notebook containing all results for Wilson coefficients is attached in the ancillary files

References in corpus (60)

• Dimension-Six Terms in the Standard Model Lagrangian
• Generating Feynman Diagrams and Amplitudes with FeynArts 3
• FeynRules - Feynman rules made easy
• Asymptotic expansion of Feynman integrals near threshold
• New Developments in FeynCalc 9.0
• Renormalization Group Evolution of the Standard Model Dimension Six Operators III: Gauge Coupling Dependence and Phenomenology
• Renormalization Group Evolution of the Standard Model Dimension Six Operators II: Yukawa Dependence
• Renormalization Group Evolution of the Standard Model Dimension Six Operators I: Formalism and lambda Dependence
• Package-X: A Mathematica package for the analytic calculation of one-loop integrals
• The Standard Model as an Effective Field Theory
• Low energy effects of neutrino masses
• Effective description of general extensions of the Standard Model: the complete tree-level dictionary
• Flavor structures of charged fermions and massive neutrinos
• Stabilization of the Electroweak Vacuum by a Scalar Threshold Effect
• Neutrino Mass Operator Renormalization Revisited
• Dimension-8 Operators in the Standard Model Effective Field Theory
• Extending the Standard Model Effective Field Theory with the Complete Set of Dimension-7 Operators
• Complete Set of Dimension-8 Operators in the Standard Model Effective Field Theory
• Heavy Majorana Neutrinos in the Effective Lagrangian Description: Application to Hadron Colliders
• Operators up to Dimension Seven in Standard Model Effective Field Theory Extended with Sterile Neutrinos
• The mu - e Conversion in Nuclei, mu --> e gamma, mu --> 3e Decays and TeV Scale See-Saw Scenarios of Neutrino Mass Generation
• General Neutrino Interactions from an Effective Field Theory Perspective
• Right-handed neutrino magnetic moments
• The Universal One-Loop Effective Action
• CoDEx: Wilson coefficient calculator connecting SMEFT to UV theory
• Integrating out heavy particles with functional methods: a simplified framework
• Foundation and generalization of the expansion by regions
• FeynHelpers: Connecting FeynCalc to FIRE and Package-X
• Matching scalar leptoquarks to the SMEFT at one loop
• Dimension Seven Operators in Standard Model with Right handed Neutrinos
• Covariant diagrams for one-loop matching
• One-loop Effective Lagrangian for a Standard Model with a Heavy Charged Scalar Singlet
• Complete One-Loop Matching for a Singlet Scalar in the Standard Model EFT
• Extending the Universal One-Loop Effective Action: Heavy-Light Coefficients
• Mixed Heavy-Light Matching in the Universal One-Loop Effective Action
• One-loop effective lagrangians after matching
• Complete Set of Dimension-9 Operators in the Standard Model Effective Field Theory
• An explicit construction of the dimension-9 operator basis in the standard model effective field theory
• Lepton flavor violation in the triplet Higgs model
• Field redefinitions in effective theories at higher orders
• Operator Bases in Effective Field Theories with Sterile Neutrinos: $d\le 9$
• Completing the scalar and fermionic Universal One-Loop Effective Action
• Constraints from muon g-2 and LFV processes in the Higgs Triplet Model
• One-loop matching in the SMEFT extended with a sterile neutrino
• STrEAMlining EFT Matching
• Low Energy Effective Field Theory Operator Basis at $d\le 9$
• Functional Prescription for EFT Matching
• SuperTracer: A Calculator of Functional Supertraces for One-Loop EFT Matching
• One-loop renormalization group equations of the neutrino mass matrix in the triplet seesaw model
• Integrating out heavy fields in the path integral using the background-field method: general formalism
• Complete One-loop Matching of the Type-I Seesaw Model onto the Standard Model Effective Field Theory
• Renormalization Group Evolution of Dimension-seven Operators in Standard Model Effective Field Theory and Relevant Phenomenology
• Renormalization Group Evolution in the type I + II seesaw model
• Neutrino masses in the Standard Model effective field theory
• Effective field theory approach to trans-TeV supersymmetry: covariant matching, Yukawa unification and Higgs couplings
• Lower Limits on $\mu \to e\gamma$ from new Measurements on $U_{e3}$
• Radiative Decays of Charged Leptons in the Seesaw Effective Field Theory with One-loop Matching
• Functional Methods for Heavy Quark Effective Theory
• Radiative decays of charged leptons as constraints of unitarity polygons for active-sterile neutrino mixing and CP violation
• One-Loop Matching Conditions in Neutrino Effective Theory

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• The Standard Model effective field theory at work
• A Proof of Concept for Matchete: An Automated Tool for Matching Effective Theories
• The $\mu$-$\tau$ reflection symmetry of Majorana neutrinos
• Electroweak Phase Transition and Gravitational Waves in the Type-II Seesaw Model
• Neutrino seesaw models at one-loop matching: Discrimination by effective operators
• Introduction to Charged Lepton Flavour Violation
• Integrating out heavy scalars with modified EOMs: matching computation of dimension-eight SMEFT coefficients
• Effective comparison of neutrino-mass models
• Comprehensive Analysis of Charged Lepton Flavour Violation in the Symmetry Protected Type-I Seesaw
• Origin of Neutrino Masses on the Convex Cone of Positivity Bounds
• Lepton-flavour-violating tau decays from triality
• One-loop Matching of Scotogenic Model onto Standard Model Effective Field Theory up to Dimension 7
• Complete One-loop Renormalization-group Equations in the Seesaw Effective Field Theories
• Complete One-loop Structure of the Type-(I+II) Seesaw Effective Field Theory
• Resurrecting the LHC discovery potential in the extended Type-II Seesaw Model
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