Mixed QCD-EW corrections for Higgs boson production at $e^+e^-$ colliders

TL;DR

This paper calculates the first mixed QCD-electroweak corrections to Higgs production in electron-positron colliders, providing an approximate formula that improves the precision of theoretical predictions crucial for future Higgs property measurements.

Contribution

It introduces the first calculation of mixed QCD-electroweak corrections for Higgs production at $e^+e^-$ colliders and offers an approximate analytic formula valid up to 350 GeV.

Findings

Mixed corrections increase the cross section by about 1.3% at 240 GeV.

Approximate formula matches numerical results well up to 350 GeV.

Corrections are significant for future precision Higgs studies.

Abstract

Since the discovery of the Higgs boson at the Large Hadron Collider, a future electron-position collider has been proposed for precisely studying its properties. We investigate the production of the Higgs boson at such an $e^+e^-$ collider associated with a $Z$ boson, and calculate for the first time the mixed QCD-electroweak corrections to the total cross sections. We provide an approximate analytic formula for the cross section and show that it reproduces the exact numeric results rather well for collider energies up to 350 GeV. We also provide numeric results for $\sqrt{s}=500$ GeV, where the approximate formula is no longer valid. We find that the $\mathcal{O}(\alpha\alpha_s)$ corrections amount to a 1.3% increase of the cross section for a center-of-mass energy around 240 GeV. This is significantly larger than the expected experimental accuracy and has to be included for extracting the properties of the Higgs boson from the measurements of the cross sections in the future.