Complete two-loop Yukawa-induced running of the Higgs-gluon coupling in SMEFT

TL;DR

This work completes the two-loop renormalisation group evolution for the SMEFT Higgs-gluon coupling $O_{HG}$ by deriving Yukawa-induced running from class 3 and class 7 operators in the Warsaw basis. The authors provide the explicit two-loop RGE, examine scheme dependencies, and validate the result with independent computations. They then quantify the phenomenological impact via Higgs data fits, using both bottom-up Wilson coefficient analyses and top-down vector-like quark UV models, showing that two-loop running can tighten or shift bounds on certain operators, particularly those with top Yukawa couplings. The results offer a more complete and precise framework for SMEFT analyses of Higgs production and decays across energy scales, enabling more reliable connections between high-scale new physics and LHC observables.

Abstract

We compute the two-loop renormalisation group equation for the effective Higgs to gluon coupling in Standard Model Effective Field Theory. Concretely, we present the contributions generated by the operators belonging to class 3 and 7 in the Warsaw basis, completing the two-loop renormalization program of the Higgs-gluon coupling proportional to the top Yukawa coupling for potentially tree-level generated operators. We investigate the phenomenological impact of the contributions in fits to Higgs data both in a bottom-up approach and a top-down approach in terms of UV models with vector-like quarks.

Figures (7)

• Figure 1: Sample of the diagrams with a single insertion of the operator $\mathcal{O}_{Ht} ^{}$ which vanish because of kinematics, see main text for details. We use a thick (thin) line to denote a left-(right-)handed field, a dashed line to denote the Higgs doublet, a black square to denote an insertion of $\mathcal{O}_{Ht} ^{}$ and a black dot to denote a SM vertex insertion.
• Figure 2: Sample of the two-loop order diagrams with a single insertion of the operator $\mathcal{O}_{Ht} ^{}$. We use a thick (thin) line to denote a left-(right-)handed field, a dashed line to denote the Higgs doublet, a black square to denote an insertion of $\mathcal{O}_{Ht} ^{}$, a black dot to denote a SM vertex insertion and a white star to denote the Yukawa coupling counterterm.
• Figure 3: Sample of the two-loop order diagrams with a single insertion of the operators $\mathcal{O}_{H\Box} ^{}$ and $\mathcal{O}_{HD} ^{}$. We use a thick (thin) line to denote a left-(right-)handed field, a dashed line to denote the Higgs doublet, a white square to denote an insertion of $\mathcal{O}_{H\Box} ^{}$ and $\mathcal{O}_{HD} ^{}$ and a black dot to denote a SM vertex insertion.
• Figure 4: Allowed ranges at $2\sigma$ for the WCs obtained by performing one parameter fits. The yellow (orange) line is obtained by considering one-loop (two-loop) running effects.
• Figure 5: Allowed regions at $2\sigma$ obtained via a two parameter fit including one-loop (in yellow) and two-loop (in orange) running effects. We consider in pairs the operators belonging to class 3 and to class 7. For class 7, we further separate between the cases in which the quarks in the operators are the doublets or the singlets under SU(2)$_{\rm L}$.