Mixed $\text{QCD}\otimes \text{EW}$ corrections to charged Higgs pair production in THDM at electron-positron colliders

Abstract

We calculate the two-loop mixed QCD$\otimes$EW corrections for the charged Higgs boson pair production within the framework of four types of Two Higgs Doublet Models (THDMs) with the $Z_2$ symmetry. We analyze in detail the dependences of our results on physical parameters, including the charged Higgs mass, $\tan {\hat{I}}^2$, the scattering angle, and the colliding energy. It is noticeable that the mixed QCD$\otimes$EW relative correction is independent of the scattering angle due to the topology of Feynman diagrams at $O(\hat{I}\pm \hat{I}{\pm }_s)$. Numerical results in most allowed regions of four types of THDMs are provided in the density plots on the $m_{H^{\pm }}$-$\tan {\hat{I}}^2$ plane. For type-I and type-X, the mixed QCD$\otimes$EW relative correction varies slightly near $1\%$ except in the vicinity of resonance. For type-II and type-Y, the corrections increase consistently in large $\tan {\hat{I}}^2$ region and reach up to $11.5\%$ at $\tan {\hat{I}}^2=50$. We also compute the $O(\hat{I}\pm )$ corrections to obtain the corrected cross section up to $O(\hat{I}\pm \hat{I}{\pm }_s)$. The numerical results show that the corrected cross section can be larger than $80\mathrm{fb}$ in some parameter space region for type-I and type-X THDMs.

26 pages, 7 figures