Electroweak Effective Operators and Higgs Physics

TL;DR

This work analyzes a dimension-6 electroweak EFT for Higgs-gauge interactions, focusing on a reduced operator basis that affects gauge boson propagators and Higgs couplings. It shows that, once MSbar renormalization is correctly applied, the leading logarithmic oblique corrections cancel, leaving finite contributions that yield weak bounds on loop-induced operators; tree-level operators remain tightly constrained by precision data. The authors quantify how Higgs decay channels (e.g., $H\to WW$, $H\to \gamma\gamma$, $H\to Z\gamma$) complement oblique constraints, with explicit expressions linking decay rates to the operator coefficients. They also bridge operator bases (HISZ and SILH) and highlight the importance of scheme choices in interpreting EFT limits for electroweak and Higgs phenomenology.

Abstract

We derive bounds from oblique parameters on the dimension-6 operators of an effective field theory of electroweak gauge bosons and the Higgs doublet. The loop- induced contributions to the S, T, and U oblique parameters are sensitive to these contributions and we pay particular attention to the role of renormalization when computing loop corrections in the effective theory. Limits on the coefficients of the effective theory from loop contributions to oblique parameters yield complementary information to direct Higgs production measurements.

Figures (6)

• Figure 1: Limits from the oblique parameters on $f_{\Phi, 1}$ and $f_{BW}$ for $\Lambda=1~TeV$. These operators contribute at tree level and are significantly restricted. The curves (from outer to inner) are 99, 95, and 68 $\%$ confidence level.
• Figure 2: (a) Limits from the oblique parameters on $f_{BB}$ and $f_{WW}$ for $\Lambda=1~TeV$, using the leading logarithmic results of Eq. \ref{['numll']}. The curves (from outer to inner) are 99, 95, and 68 $\%$ confidence level. (b) Same as (a) except using the renormalized values of the coefficients, $f_{BB}(m_Z)$ and $f_{WW}(m_Z)$, Eqs. \ref{['rennumb']} and \ref{['obfin']}.
• Figure 3: (a) Limits from the oblique parameters on $f_{W}$ and $f_{WW}$ for $\Lambda=1~TeV$, using the leading logarithmic results of Eq. \ref{['numll']}. The curves (from outer to inner) are 99, 95, and 68 $\%$ confidence level. (b) Same as (a) except using the renormalized values of the coefficients, $f_{W}(m_Z)$ and $f_{WW}(m_Z)$, Eqs. \ref{['rennumb']} and \ref{['obfin']}.
• Figure 4: $95\%$ confidence level limits from the measurement of gluon fusion production with $H\rightarrow W^+W^-$ (black band), compared with the inferred limits from the oblique parameters.
• Figure 5: Comparison of limits from oblique parameters (blue bands) and $95\%$ confidence level limits from the measurement of gluon fusion production and the subsequent $H\rightarrow \gamma \gamma$ decay (red vertical line).