Springer : A log story short: running contributions to radiative Higgs decays in the SMEFT

Grojean, Christophe; Guedes, Guilherme; Salla, Gabriel M.; Roosmale Nepveu, Jasper

doi:10.1007/JHEP12(2024)065

Article
Report number	arXiv:2405.20371 ; CERN-TH-2024-075 ; DESY-24-077 ; HU-EP-24/15-RTG
Title	A log story short: running contributions to radiative Higgs decays in the SMEFT
Author(s)	Grojean, Christophe (DESY ; Humboldt U., Berlin ; CERN) ; Guedes, Guilherme (DESY) ; Roosmale Nepveu, Jasper (DESY ; Humboldt U., Berlin) ; Salla, Gabriel M. (DESY ; Sao Paulo U.)
Publication	2024-12-10
Imprint	2024-05-30
Number of pages	50
In:	JHEP 2412 (2024) 065
DOI	10.1007/JHEP12(2024)065
Subject category	hep-ph ; Particle Physics - Phenomenology
Abstract	We investigate the renormalization of the radiative decays of the Higgs to two gauge bosons in the Standard Model Effective Field Theory at mass dimension eight. Given that these are loop-level processes, their one-loop renormalization can be phenomenologically important when triggered by operators generated through the tree-level exchange of heavy particles (assuming a weakly coupled UV model). By computing the tree-level matching conditions of all relevant extensions of the Standard Model, we demonstrate that this effect is indeed present in the $h\to \gamma Z$ decay at dimension eight, even though it is absent at dimension six. In contrast, the $h\to gg$ and $h\to \gamma\gamma$ decays can only be renormalized by operators generated by one-loop processes. For UV models with heavy vectors, this conclusion hinges on the specific form of their interaction with massless gauge bosons which is required for perturbative unitarity. We study the quantitative impact of the possible logarithmic enhancement of $h\to \gamma Z$, and we propose an observable to boost the sensitivity to this effect. Given the expected increased precision of next-generation high-energy experiments, this dimension-eight contribution could be large enough to be probed and could therefore give valuable clues about new physics by revealing some of its structural features manifesting first at dimension eight.
Copyright/License	preprint: (License: CC BY 4.0) publication: © 2024-2025 The Authors (License: CC-BY-4.0), sponsored by SCOAP³

$Plot of the amplitude $\Amp_H$, expanded up to different orders in the triplet mass $M$, normalized by the result in Eq.~\eqref{eq:I}. We emphasize that $\Amp_H$ contains only loop diagrams with at least one heavy particle inside the loop, while the full amplitude is discussed in Section~\ref{sec:5.outlook}.$ $Evaluation of the deviations from the SM value of the $h\to \gamma Z$ decay width (panels \textbf{a} and \textbf{b}) and of the leading term in the expansion of the ratio introduced in Eq.~\eqref{eq:ratio} (panels \textbf{c} and \textbf{d}) as a function of the heavy mass $M$. Panels \textbf{a} and \textbf{c} show the results for the scalar triplet model, while panels \textbf{b} and \textbf{d} are for the scalar triplet plus the charged $SU(2)_L$ singlet vector in the custodial limit, $C_{\phi D}=0$ (further assumptions made during the matching calculation are explained in the text). The dot-dashed green lines represent only the direct contributions at dimension six, resulting from $X^2\phi^2$ operators; the dashed orange lines contain all dimension six terms, including also indirect contributions such as those arising from redefining SM parameters; the dotted red lines correspond to contribution from the dimension-eight logarithm; the solid blue lines are the sum of all of these contributions.$ $Evaluation of the deviations from the SM value of the $h\to \gamma Z$ decay width (panels \textbf{a} and \textbf{b}) and of the leading term in the expansion of the ratio introduced in Eq.~\eqref{eq:ratio} (panels \textbf{c} and \textbf{d}) as a function of the heavy mass $M$. Panels \textbf{a} and \textbf{c} show the results for the scalar triplet model, while panels \textbf{b} and \textbf{d} are for the scalar triplet plus the charged $SU(2)_L$ singlet vector in the custodial limit, $C_{\phi D}=0$ (further assumptions made during the matching calculation are explained in the text). The dot-dashed green lines represent only the direct contributions at dimension six, resulting from $X^2\phi^2$ operators; the dashed orange lines contain all dimension six terms, including also indirect contributions such as those arising from redefining SM parameters; the dotted red lines correspond to contribution from the dimension-eight logarithm; the solid blue lines are the sum of all of these contributions.$ Show more plots

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