QCD Corrections to Associated Higgs Boson Production

TL;DR

This work computes next-to-leading order QCD corrections to associated Higgs production with top quarks in both $e^+e^-$ and hadronic collisions by modeling the Higgs as a radiated parton from a heavy top quark in the regime $M_h \ll M_t$ and $M_h, M_t \ll \sqrt{s}$. The authors derive the Higgs distribution function $f_{t\rightarrow h}(x_h)$ at LO and include ${\cal O}(\alpha_s)$ virtual and real corrections, ensuring infrared cancellation and providing a practical expression for the corrected distribution. They apply this to evaluate cross sections: for $e^+e^-\to t\bar t h^0$ the QCD corrections are mild with a K-factor around $0.94$ at $\sqrt{s}=1$ TeV, while for $pp\to t\bar t h^0$ at the LHC the K-factor ranges from $1.2$ to $1.5$ for an intermediate-mass Higgs ($M_h<180$ GeV), with PDF choices introducing notable uncertainty. Overall, the results highlight the significant impact of QCD corrections on hadronic associated Higgs production and demonstrate the utility and limitations of the effective Higgs approximation.

Abstract

We compute QCD corrections to the processes $e^+e^-\to t \bar t h^0$ and $pp\to t \bar t h^0$ by treating the Higgs boson as a parton which radiates off a heavy quark. This approximatiion is valid in the limits $M_h<<M_t$ and $M_h, M_t<<\sqrt{s}$. The corrections increase the rate for $pp\to t \bar t h^0$ at the LHC by a factor of 1.2 to 1.5 over the lowest order rate for an intermediate mass Higgs boson, $M_h < 180 GeV$. The QCD corrections are small for $e^+e^-\to t \bar t h^0$ at $\sqrt{s}=1 TeV$.

Figures (6)

• Figure 1: Ratio of the radiatively corrected cross section to the lowest order result for $pp\rightarrow h^0$ at the LHC, $\sqrt{s}=14$ TeV, with $\mu=M_h$. This figure uses the $2-$loop value of $\alpha_s(\mu)$ for both the lowest order and the NLO predictions.
• Figure 2: The scattering process $te^-\rightarrow t X$ can be used to extract the Higgs boson structure function $f_{t\rightarrow h}(x_h)$, assuming that the amplitude is dominated by the t-channel Higgs pole.
• Figure 3: Virtual (a) and real (b,c) QCD corrections to be computed in order to obtain the $O(\alpha_s)$ corrections to the structure function $f_{t\rightarrow h}(x_h)$ in the EHA.
• Figure 4: The Higgs distribution function $f_{t\rightarrow h}(x_h)$ in units of $g_t^2/(4\pi)^2$.
• Figure 5: Ratio of the lowest order cross section computed in the EHA for $e^+e^-\rightarrow t\bar{t} h^0$ to the same quantity computed exactly, for intermediate mass Higgs bosons at $\sqrt{s}=1$ TeV.