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Renormalization of dimension-six operators relevant for the Higgs decays $h\rightarrow γγ,γZ$

J. Elias-Miro, J. R. Espinosa, E. Masso, A. Pomarol

TL;DR

Using an effective field theory with a structured dimension-six operator basis, the paper analyzes RG running for Higgs decays h → γγ and h → γZ. It demonstrates that tree-level current-current operators do not produce log-enhanced mixing into the one-loop suppressed operators that govern these decays, and that only one-loop suppressed operators and fermion dipoles contribute to the running at one loop. The authors provide explicit leading-log expressions for the relevant anomalous dimensions, show that a basis choice can yield a simple block-diagonal RG structure, and discuss implications for the S parameter and for translating between operator bases. These results constrain potential new physics effects in Higgs decays and clarify apparent discrepancies with partial-basis analyses.

Abstract

The discovery of the Higgs boson has opened a new window to test the SM through the measurements of its couplings. Of particular interest is the measured Higgs coupling to photons which arises in the SM at the one-loop level, and can then be significantly affected by new physics. We calculate the one-loop renormalization of the dimension-six operators relevant for $h\rightarrow γγ, γZ$, which can be potentially important since it could, in principle, give log-enhanced contributions from operator mixing. We find however that there is no mixing from any current-current operator that could lead to this log-enhanced effect. We show how the right choice of operator basis can make this calculation simple. We then conclude that $h\rightarrow γγ, γZ$ can only be affected by RG mixing from operators whose Wilson coefficients are expected to be of one-loop size, among them fermion dipole-moment operators which we have also included.

Renormalization of dimension-six operators relevant for the Higgs decays $h\rightarrow γγ,γZ$

TL;DR

Using an effective field theory with a structured dimension-six operator basis, the paper analyzes RG running for Higgs decays h → γγ and h → γZ. It demonstrates that tree-level current-current operators do not produce log-enhanced mixing into the one-loop suppressed operators that govern these decays, and that only one-loop suppressed operators and fermion dipoles contribute to the running at one loop. The authors provide explicit leading-log expressions for the relevant anomalous dimensions, show that a basis choice can yield a simple block-diagonal RG structure, and discuss implications for the S parameter and for translating between operator bases. These results constrain potential new physics effects in Higgs decays and clarify apparent discrepancies with partial-basis analyses.

Abstract

The discovery of the Higgs boson has opened a new window to test the SM through the measurements of its couplings. Of particular interest is the measured Higgs coupling to photons which arises in the SM at the one-loop level, and can then be significantly affected by new physics. We calculate the one-loop renormalization of the dimension-six operators relevant for , which can be potentially important since it could, in principle, give log-enhanced contributions from operator mixing. We find however that there is no mixing from any current-current operator that could lead to this log-enhanced effect. We show how the right choice of operator basis can make this calculation simple. We then conclude that can only be affected by RG mixing from operators whose Wilson coefficients are expected to be of one-loop size, among them fermion dipole-moment operators which we have also included.

Paper Structure

This paper contains 9 sections, 56 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Dimension-six operator basis
  3. Non-renormalization of $\hbox{\boldmath{$h\rightarrow \gamma\gamma,\gamma Z$}}$ from current- current operators
  4. The importance of the choice of basis
  5. Renormalization group equation for $\hbox{\boldmath{$\kappa_{\gamma\gamma}$}}$ and $\hbox{\boldmath{$\kappa_{\gamma\widetilde{\gamma}}$}}$
  6. RGEs for $\hbox{\boldmath{$\kappa_{\gamma Z}$}}$ and $\hbox{\boldmath{$\kappa_{\gamma\widetilde{Z}}$}}$ and a new basis
  7. Dipole operators
  8. The ${\hbox{\boldmath{$S$}}}$ parameter
  9. Conclusions

Figures (1)

  • Figure 1: The only two diagrams that could give a contribution (at one loop) from ${\cal O}_{WW}$, ${\cal O}_{BB}$ and ${\cal O}_{WB}$ (with coefficient generically denoted as $c_{VV'}$ in the figure) to the renormalization of ${\cal O}_{HW}$ and ${\cal O}_{HB}$ (or to ${\cal O}_W$ and ${\cal O}_B$).