Supergraph Techniques and Two-Loop Beta-Functions for Renormalizable and Non-Renormalizable Operators

Abstract

We present a construction kit for calculating two-loop beta functions in N=1 supersymmetric theories for the operators of the superpotential using supergraph techniques. In particular, it allows to compute the beta functions for every desired, even higher dimensional, operator of the superpotential from the wavefunction renormalization constants of the theory. We apply this method to calculate the two-loop beta functions for the lowest-dimensional effective neutrino mass operator in the Minimal Supersymmetric Standard Model (MSSM) and for the Yukawa couplings in the MSSM extended by singlet superfields and the mass matrix for the latter. Our method can be applied to any N=1 supersymmetric theory.

15 pages, 13 figures; error in two-loop trace terms corrected

References in corpus (7)

• Neutrino Mass Operator Renormalization Revisited
• Classification of Effective Neutrino Mass Operators
• Neutrino Mass Operator Renormalization in Two Higgs Doublet Models and the MSSM
• Predictive Schemes for Bimaximal Neutrino Mixings
• Low energy threshold corrections to neutrino masses and mixing angles
• Family replicated gauge groups and large mixing angle solar neutrino solution
• Renormalization of the neutrino mass matrix

Cited by in corpus (39)

• Theory of Neutrinos: A White Paper
• Flavour physics of leptons and dipole moments
• Running Neutrino Masses, Mixings and CP Phases: Analytical Results and Phenomenological Consequences
• Constructing the large mixing angle MNS matrix in see-saw models with right-handed neutrino dominance
• Running Neutrino Masses, Leptonic Mixing Angles and CP-Violating Phases: From $M_{\mathrm{Z}}$ to ${\Lambda }_{\mathrm{GUT}}$
• Another Look at Minimal Lepton Flavour Violation, l_i -> l_j gamma, Leptogenesis, and the Ratio M_nu/ Lambda_LFV
• From Hierarchical to Partially Degenerate Neutrinos via Type II Upgrade of Type I See-Saw Models
• Third Family Corrections to Quark and Lepton Mixing in SUSY Models with non-Abelian Family Symmetry
• Probing minimal supergravity in the type-I seesaw mechanism with lepton flavour violation at the CERN LHC
• Third Family Corrections to Tri-bimaximal Lepton Mixing and a New Sum Rule
• Renormalization Group Evolution in the type I + II seesaw model
• Neutrino Mass Matrix with Two Zeros and Leptogenesis
• Perturbative Estimates of Lepton Mixing Angles in Unified Models
• Stability of Texture Zeros under Radiative Corrections in See-Saw Models
• Supersymmetric type-III seesaw: lepton flavour violating decays and dark matter
• Radiative Generation of the LMA Solution from Small Solar Neutrino Mixing at the GUT Scale
• Heavy Right-Handed Neutrinos and Dark Matter in the $\nu$CMSSM
• Leptogenesis in Neutrino Textures with Two Zeros
• Constraints on the rare tau decays from mu --> e gamma in the supersymmetric see-saw model
• Confronting SUSY SO(10) with updated Lattice and Neutrino Data
• A Sneutrino NLSP in the $\nu$CMSSM
• Predicting the Sparticle Spectrum from GUTs via SUSY Threshold Corrections with SusyTC
• Quantum corrections to the effective neutrino mass operator in 5D MSSM
• Predictions from High Scale Mixing Unification Hypothesis
• Predicting ${\delta }^{\text{PMNS}}$, ${\theta }_{23}^{\text{PMNS}}$ and fermion mass ratios from flavour GUTs with CSD2
• Lower Bounds on U_{e3}
• The Smallest Neutrino Mass Revisited
• Masses and Mixings in a Grand Unified Toy Model
• Enhanced Tau Lepton Signatures at LHC in Constrained Supersymmetric Seesaw
• No-go limitations on UV completions of the Neutrino Option
• Calculable Cosmological CP Violation and Resonant Leptogenesis
• Nonzero ${\theta }_{13}$ in $SO(3)\to A_4$ lepton models
• Neutrino Masses and Lepton-flavor-violating $\tau$ Decays in the Supersymmetric Left-right Model
• Predictions From High Scale Mixing Unification Hypothesis
• One-Loop Right-Handed Neutrino Threshold Corrections for Two-Loop Running in Supersymmetric Type I Seesaw Models
• Yukawa enhanced electroweak corrections at high energy in the MSSM
• Minimal Lepton Flavor Violation and Renormalization Group Evolution of Lepton Masses and Mixing
• Running of neutrino mass parameters in the Zee model
• Renormalization Group Analysis of Neutrino Mass Parameters