Higgs boson production at $\mu^+ \mu^+$ colliders

TL;DR

This paper investigates Higgs boson production at high-energy $^+^+$ colliders, revealing that higher-order processes mediated by photons and Z bosons dominate at high energies, leading to significant production rates comparable to $^+^-$ colliders.

Contribution

It demonstrates that higher-order $^+^+$ collider processes have large cross sections due to $(\,\log s)^3$ growth, highlighting their importance in Higgs production.

Findings

Higher-order processes dominate at high energies.

Cross sections grow as $(\log s)^3$, surpassing leading-order expectations.

Higgs production rates are comparable to $^+^-$ colliders at 10 TeV.

Abstract

We study Higgs boson production at $\mu^+ \mu^+$ colliders at high energy. Since both initial-state particles are positively charged, there is no $W$ boson fusion at the leading order, as it requires a $W^+ W^-$ pair. However, we find that the cross section of the higher-order, $\gamma$- and $Z$-mediated $W$ boson fusion process is large at high center-of-mass energies $\sqrt s$, growing as $(\log s)^3$. This is in contrast to the $\log s$ behavior of the leading-order $W$ boson fusion. Thus, even though it is a higher-order process, the rate of Higgs boson production for 10 TeV energies at $\mu^+ \mu^+$ colliders with polarized beams can be as high as about half of the one at $\mu^+ \mu^-$ colliders, assuming the same integrated luminosity. To calculate the cross section of this process accurately, we carefully treat the collinear emission of the photon in the intermediate state. The thereby obtained large cross section furthermore shows the significance of Higgs production with an extra $W$ boson in the final state also at $\mu^+ \mu^-$ and $e^+ e^-$ colliders.