Top Quark Mediated Higgs Decay into Hadrons to Order alpha(s)**5

TL;DR

This work provides the analytic ${\cal O}(\alpha_s^5)$ correction to the SM Higgs decay width into gluons in the region $M_H<2M_t$. By integrating out the top quark, the authors formulate an effective Lagrangian and compute the absorptive part ${\rm Im}\,\Pi^{GG}$ to four loops, yielding a detailed $K$-factor expansion up to NNNLO. Numerical evaluation for $M_t=175$ GeV, $M_H=120$ GeV, and $\alpha_s^{(5)}(M_H)/\pi=0.0363$ shows a moderate last-term contribution but a substantial stabilization of the residual scale dependence. The result reduces the theoretical uncertainty in Higgs hadronic decays and informs precision Higgs phenomenology at the LHC, illustrating the power of combining diagrammatic generation, the Baikov method, and high-precision reconstruction in multi-loop QCD. The study highlights the continued importance of high-order QCD corrections for accurate Higgs coupling analyses.

Abstract

We present in analytic form the O(alpha_s^5) correction to the H->gg partial width of the standard-model Higgs boson with intermediate mass M_H<2M_t. Its knowledge is useful because the O(alpha_s^4) correction is sizeable (around 20%). For M_H=120 GeV, the resulting QCD correction factor reads 1 + (215/12) alpha_s^(5)(M_H)/pi + 152.5 (alpha_s^(5)(M_H)/pi)^2 + 381.5 (alpha_s^(5)(M_H)/pi)^3 \approx 1+0.65+0.20+0.02. The new four-loop correction increases the total Higgs-boson hadronic width by a small amount of order 1 promille and stabilizes significantly the residual scale dependence.