The rare decay $H\to Zγ$ in perturbative QCD

TL;DR

The paper presents an analytic calculation of the two-loop QCD corrections to the heavy-quark loop in the rare Higgs decay $H\to Z\gamma$, extending previous numerical results and providing a full set of master integrals via differential equations in two Landau-type variables. It demonstrates that the small-quark-mass expansion contains only single logarithms at each order, in contrast to $H\to \gamma\gamma$, and shows that running Yukawa couplings resum these logarithms. By exploring renormalization-scheme dependence (OS vs MSbar) for the heavy-quark mass and Yukawa coupling and comparing with independent results, the work delivers precise predictions for the decay width and clarifies the theoretical uncertainties. The analytic master integrals and their GHPL representation also advance related two-loop Higgs processes with full mass dependence, including Higgs-plus-jet production in gluon fusion.

Abstract

The rare Higgs boson decay $H\to Zγ$ is forbidden at tree-level. In the Standard Model, it is loop-mediated through a $W$ boson or a heavy quark. We analytically compute the QCD correction to the heavy quark loop, confirming earlier purely numerical results, that were obtained for on-shell renormalization. The small quark mass expansion of the decay matrix element contains only single-logarithmic contributions at each perturbative order, which is in contrast to the double logarithms observed in $H\to γγ$. We investigate the numerical interplay of bottom and top quark contributions, and the dependence of the result on the renormalization scheme.

Figures (3)

• Figure 1: Example diagrams $(a)$ for the computation of the one-loop amplitudes $A^{(1)}_W$ and $A^{(1)}_q$ and $(b)$ for the computation of the two-loop amplitude $A^{(2)}_q$.
• Figure 2: Two-loop master integrals for the calculation of $A^{(2)}_q$. Dashed lines are massless, whereas internal solid lines denote propagators with mass $m_q$. Double and solid external lines correspond to virtualities $m_H^2$ and $m_Z^2$, respectively. Dotted propagators are taken to be squared.
• Figure 3: Scale variation of the next-to-leading-order decay width $\Gamma^{(2)}$ in the renormalization schemes (a), (b) and (c) for $30\,{\rm GeV}<\mu<300\,{\rm GeV}$.