We investigate in detail the charged Higgs production associated with a $W$ boson at electron-positron colliders within the framework of the Type-I two-Higgs-doublet model (THDM). We calculate the integrated cross section at the LO and analyze the dependence of the cross section on the THDM parameters and the colliding energy in a benchmark scenario of the input parameters of Higgs sector. The numerical results show that the integrated cross section is sensitive to the charged Higgs mass, especially in the vicinity of $m_{H^{\pm}} \simeq 184~ {\rm GeV}$ at a $500~ {\rm GeV}$ $e^+e^-$ collider, and decreases consistently as the increment of $\tan\beta$ in the low $\tan\beta$ region. The peak in the colliding energy distribution of the cross section arises from the resonance of loop integrals and its position moves towards low colliding energy as the increment of $m_{H^{\pm}}$. We also study the two-loop NLO QCD corrections to both the integrated cross section and the angular distribution of the charged Higgs boson, and find that the QCD relative correction is also sensitive to the charged Higgs mass and strongly depends on the final-state phase space. For $\tan\beta = 2$, the QCD relative correction at a $500~ {\rm GeV}$ $e^+e^-$ collider varies in the range of $[-10\%,\, 11\%]$ as $m_{H^{\pm}}$ increases from $150$ to $400~ {\rm GeV}$.

中文翻译：

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在电子 I 型 THDM 中对 ${{{e^+e^-}}{{\rightarrow}}{{H^{\pm}}}{{W^{\mp}}}}$ 的 QCD 修正正电子对撞机

我们在 I 型双希格斯双峰模型 (THDM) 的框架内详细研究了与正负电子对撞机中的 $W$ 玻色子相关的带电希格斯产生。我们计算了 LO 处的积分截面，并在 Higgs 扇区输入参数的基准场景中分析了截面对 THDM 参数和碰撞能量的依赖性。数值结果表明积分截面对带电的希格斯质量敏感，尤其是在 $m_{H^{\pm}} \simeq 184~ {\rm GeV}$ 附近 $500~ {\rm GeV }$ $e^+e^-$ 对撞机，并在低 $\tan\beta$ 区域随着 $\tan\beta$ 的增加而持续减少。截面碰撞能量分布的峰值源于环积分的共振，随着$m_{H^{\pm}}$的增加，其位置向低碰撞能量移动。我们还研究了对带电希格斯玻色子的积分截面和角分布的双回路 NLO QCD 校正，发现 QCD 相对校正对带电希格斯玻色子质量也很敏感，并且强烈依赖于终态相位空间。对于$\tan\beta = 2$，QCD 在$500~{\rm GeV}$ $e^+e^-$ collider 处的相对修正在$[-10\%,\, 11\% ]$ 作为 $m_{H^{\pm}}$ 从 $150$ 增加到 $400~ {\rm GeV}$。并发现 QCD 相对校正对带电的希格斯质量也很敏感，并且强烈依赖于终态相空间。对于$\tan\beta = 2$，QCD 在$500~{\rm GeV}$ $e^+e^-$ collider 处的相对修正在$[-10\%,\, 11\% ]$ 作为 $m_{H^{\pm}}$ 从 $150$ 增加到 $400~ {\rm GeV}$。并发现 QCD 相对校正对带电的希格斯质量也很敏感，并且强烈依赖于终态相空间。对于$\tan\beta = 2$，QCD 在$500~{\rm GeV}$ $e^+e^-$ collider 处的相对修正在$[-10\%,\, 11\% ]$ 作为 $m_{H^{\pm}}$ 从 $150$ 增加到 $400~ {\rm GeV}$。