Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Running of neutrino mass parameters in the Zee model

Michael A. Schmidt, James Vandeleur

TL;DR

The paper analyzes quantum corrections to neutrino mass parameters in the Zee model using a two-stage EFT approach, deriving 1-loop matching conditions for Zee $\rightarrow$ 2HDM EFT and 2HDM EFT $\rightarrow$ SMEFT, and studying RG running of Weinberg-type operators. It demonstrates that neutrino masses in the SMEFT are generated primarily by RG running in the 2HDM EFT rather than direct high-scale matching, with large logs controlled by the scale separation $m_h \gg m_{H_2} \gg m_{h_{\rm SM}}$. Through four benchmark UV scenarios, the authors show that running can significantly affect $\Delta m_{21}^2$, $\Delta m_{3l}^2$, and PMNS parameters, and that the solar CP phase $\delta$ is particularly sensitive to UV inputs. The work highlights the necessity of EFT treatments and RG corrections in precision neutrino phenomenology for radiative mass models and suggests that similar running effects will occur in other radiative scenarios such as the scotogenic model.

Abstract

We analyse the size of quantum corrections in the Zee model using effective field theory techniques. We derive the relevant 1-loop matching conditions and use them together with the existing renormalisation group equations in the two Higgs doublet model to calculate quantum corrections to the neutrino mass squared differences, mixing angles, and phases. Using four benchmark scenarios, we demonstrate when quantum corrections have to be included in studies of neutrino mass parameters in the Zee model.

Running of neutrino mass parameters in the Zee model

TL;DR

The paper analyzes quantum corrections to neutrino mass parameters in the Zee model using a two-stage EFT approach, deriving 1-loop matching conditions for Zee 2HDM EFT and 2HDM EFT SMEFT, and studying RG running of Weinberg-type operators. It demonstrates that neutrino masses in the SMEFT are generated primarily by RG running in the 2HDM EFT rather than direct high-scale matching, with large logs controlled by the scale separation . Through four benchmark UV scenarios, the authors show that running can significantly affect , , and PMNS parameters, and that the solar CP phase is particularly sensitive to UV inputs. The work highlights the necessity of EFT treatments and RG corrections in precision neutrino phenomenology for radiative mass models and suggests that similar running effects will occur in other radiative scenarios such as the scotogenic model.

Abstract

We analyse the size of quantum corrections in the Zee model using effective field theory techniques. We derive the relevant 1-loop matching conditions and use them together with the existing renormalisation group equations in the two Higgs doublet model to calculate quantum corrections to the neutrino mass squared differences, mixing angles, and phases. Using four benchmark scenarios, we demonstrate when quantum corrections have to be included in studies of neutrino mass parameters in the Zee model.

Paper Structure

This paper contains 26 sections, 67 equations, 12 figures, 3 tables.

Table of Contents

  1. Introduction
  2. The Zee and two Higgs doublet models (2HDM)
  3. Perturbativity and stability of the potential.
  4. Heavy mass scales in the Higgs sector
  5. Lepton sector and neutrino mass parameters
  6. EFT calculation of neutrino mass matrix
  7. EFT Matching
  8. Renormalisation group running
  9. Numeric Calculations
  10. Phenomenological constraints
  11. Calculation framework
  12. Benchmark cases
  13. Benchmark 1: Minimally constrained case (Ye1 < Ye2, alpha=1)
  14. Benchmark 2: Variations of the Yukawa couplings in the UV.
  15. Benchmark 3: (alpha = 0)
  16. ...and 11 more sections

Figures (12)

  • Figure 1: 1-loop Feynman diagrams that generate neutrino masses in the Zee model. In the Higgs basis, only the diagrams with $H_1$ on the external legs survive with the $H_2$ internal propagator. The diagram on the right is the flavour-space transpose of the one on the left.
  • Figure 2: Tree and 1-loop level contributions from the Zee model to the Weinberg like $\kappa^{ij}$ in the 2HDM EFT. Different choices of fields of a diagram are indicated with slashes, e.g. there are three self energy insertions for diagram (c) with $h$, $H_1$ or $H_2$ in the loop and quartic couplings $\lambda_h$, $\lambda_8$ and $\lambda_9$, respectively.
  • Figure 3: Tree level contribution in the Zee model to the quartic couplings $\lambda_3$ and $\lambda_4$ in the 2HDM EFT.
  • Figure 4: Tree and 1-loop level contributions from the 2HDM EFT to the SMEFT Weinberg operator $C$.
  • Figure 5: Running of $\kappa^{11}$, $\kappa^{12}$, $Y_e^1$ and $Y_e^2$ in the 2HDM EFT for the first set of high-scale benchmark parameters. The real component of the diagonal elements of each parameter matrix is plotted. The values of the Weinberg-like operator $\kappa$ are multiplied by $v^2$ to represent the scale of the resulting neutrino masses.
  • ...and 7 more figures