$t$-channel Higgs production and constraints on off-shell Higgs couplings

This note is to record an unsucessful idea. I tried hard to persuade myself to write this note as I have spent a significant fraction of time during this summer. For Higgs resonant production and decaying in the $s$ channel, $i \to H \to f$, the cross section is proportional to $y_i^2y_f^2/\Gamma_H$. Thus there is a multi-solution ambiguity on the couplings due to uncertain knowledge on Higgs width. In this work, we study the process $g+q \to g+q+l^++l^-$ with the $t$-channel Higgs boson contribution included. As Higgs boson is not on-shell, this process can be used to measure the Higgs couplings without the ambiguity. Based on the performance of the ATLAS detector in Run~II, the coupling product $y_gy_Z$ can be potentially constrained to be less than 18 times the Standard-Model value for a $p$-$p$ dataset of 140~fb$^{-1}$ at $\sqrt{s}=13$~TeV. Assuming the equality of on-shell couplings and off-shell couplings and combining the on-shell measurements, the width of the Higgs boson is constrained to be less than 1.3~GeV, which is similar to that in the direct measurement. In addition, the interference effect is also analyzed.