R2 vertices for the effective ggH theory

TL;DR

The paper addresses missing ${\\rm R_2}$ rational terms for NLO Higgs production via gluon fusion in the heavy-top effective theory. It computes the complete set of ${\\rm R_2}$ Feynman rules generated by the dimension-five operator ${\\mathcal L}_{\\rm eff}=-{\\frac{1}{4}} A H G^a_{\\mu\\nu} G^{a,\\mu\\nu}$ with ${A}= {\\frac{\\alpha_S}{3\\pi v}}\\left(1+{\\frac{11}{4}}{\\frac{\\alpha_S}{\\pi}}\\right)$, including the five interactions $Hgg$, $Hggg$, $Hgggg$, $Hq\\bar q$, and $Hq\\bar q g$, and verified by two independent computational approaches. It presents explicit tensor structures $V^{\\mu_1\\mu_2\\mu_3}_{m_1 m_2 m_3}$ and $X^{\\mu_1\\mu_2\\mu_3\\mu_4}_{m_1 m_2 m_3 m_4}$ and a color decomposition in traces of adjoint and fundamental generators, showing that $\\lambda_{\\rm HV}$-dependence resides entirely in ${\\rm R_2}$ and cancels in physical amplitudes. These R2 rules enable fully automatic four-dimensional NLO calculations for Higgs phenomenology at the LHC, particularly for Higgs plus jets, by providing the missing ingredient for methods such as OPP, Open Loops, and FDR.

Abstract

We list all possible R2 Feynman rules needed in NLO computations involving couplings of Higgs and gluons mediated by an infinitely heavy top loop. They provide the rational contribution generated by the (d-4)-dimensional part of the amplitude, paving the way for four-dimensional automatic NLO methods in Higgs phenomenology.

Figures (1)

• Figure 1: The ${\rm R_2}$ vertices generated by the effective Lagrangian in eq. (\ref{['efflagr']}). All momenta are incoming, $N_c$ is the number of colors and $\lambda_{\rm HV}= 1~(\lambda_{\rm HV}=0)$ in Dimensional Regularization (Reduction). Quarks are massless and the dashed line represents the Higgs field. The tensors $V^{\mu_1 \mu_2 \mu_3}_{m_1 m_2 m_3}(p_1, p_2, p_3)$ and $X^{\mu_1 \mu_2 \mu_3 \mu_4}_{m_1 m_2 m_3 m_4}$ are defined in the text.