Full one-loop electroweak radiative corrections to single Higgs production in e+ e-

TL;DR

The paper delivers a complete ${\cal O}(\alpha)$ electroweak treatment of single Higgs production in $e^{+}e^{-}$ collisions, incorporating both Higgs-strahlung and $W$-fusion with hard photon radiation, and validates the computation with a five-parameter non-linear gauge in GRACE-loop. It finds that, at 500 GeV with a light Higgs, the total correction is small in the $\alpha_{\rm QED}$ scheme, while heavier Higgs masses induce larger negative corrections; after isolating universal QED effects, the genuine weak corrections are modest but non-negligible, and the $G_{\mu}$-scheme can obscure high-energy weak effects. The study emphasizes channel-dependent behavior, with large QED corrections in the s-channel and negative weak corrections in the t-channel, and identifies threshold features near $2M_W$, $2M_Z$, and $2m_t$. These results are important for precision Higgs measurements at future linear colliders and for informing refined theoretical predictions, including potential resummation of QED factors and detailed distribution analyses.

Abstract

We present the full ${\cal O}(α)$ electroweak radiative corrections to single Higgs production in \epemt. This takes into account the full one-loop corrections as well as the effects of hard photon radiation. We include both the fusion and Higgs-strahlung processes. The computation is performed with the help of {\tt GRACE-loop} where we have implemented a generalised non-linear gauge fixing condition. The latter includes 5 gauge parameters that can be used for checks on our results. Besides the UV, IR finiteness and gauge parameter independence checks it proves also powerful to test our implementation of the 5-point function. We find that for a 500GeV machine and a light Higgs of mass 150GeV, the total ${\cal O}(α)$ correction is small when the results are expressed in terms of $α_{\rm QED}$. The total correction decreases slightly for higher energies. For moderate centre of mass energies the total ${\cal O}(α)$ decreases as the Higgs mass increases, reaching -10% for $M_H=350$GeV and $\sqrt{s}=500$GeV. In order to quantify the genuine weak corrections we have subtracted the universal virtual and bremsstrahlung correction from the full ${\cal O}(α)$. We find, for $M_H=150$GeV, a weak correction slowly decreasing from -2% to -4% as the energy increases from $\sqrt{s}=300$GeV to $\sqrt{s}=1$TeV after expressing the tree-level results in terms of $G_μ$

Figures (3)

• Figure 1: A small selection of different classes of loop diagrams contributing to $e^{+} e^{-}\; \rightarrow \nu \bar{\nu} H \;$. We keep the same graph numbering as that produced by the system. Graph 1312 belongs to the corrections from self-energies, here both the virtual and counterterm contributions are generated and counted as one diagram. Graph 87 shows a vertex correction. Both graphs can be considered as resonant Higgs-strahlung contributions. Graph 249 represents a box correction, it is a non resonant contribution but applies also to the $\nu_\mu, \nu_\tau$ channels. Graph 486 is also a box correction which is non resonant and applies only to $\nu_e$. Graph 541 and Graph 565 are typical bosonic and fermionic corrections to the $WWH$ vertex for the fusion process. Graph 846 shows a pentagon correction that also applies to $\mu$ and $\tau$ neutrinos, this again can be considered as a non-resonant contribution. Graphs 827 and 828 are pentagons that only contribute to $e^{+} e^{-}\; \rightarrow \nu_e \bar{\nu}_e H \;$.
• Figure 2: The two figures in the first row show the cross section as a function of centre-of-mass energy for a light Higgs of mass $M_H=150$GeV. We show the $s$-channel, $t$-channel and the sum of these (total) cross sections as defined in the text. Both the tree-level (dashed lines) and the full one-loop correction (full lines) are shown. In the second panel we show the relative correction in per-cent. In the second row, the dependence of the cross section as a function of the Higgs mass at a centre-of-mass of $500$GeV is shown.
• Figure 3: Relative weak corrections as defined in the text, for the $t$-channel ($\delta_{W,t-channel}$), $s$-channel ($\delta_{W,s-channel}$)and the whole process ($\delta_{W,total}$). We also show the full ${\cal O}(\alpha)$ correction for the whole process in the first panel. Also shown is the weak correction for the full process expressed in the $G_\mu$ scheme ($\delta^G_{w,total}$), see text.