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This note is to record an unsucessful idea. I tried hard to persuade myselfto write this note as I have spent a significant fraction of time during thissummer. 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 thereis a multi-solution ambiguity on the couplings due to uncertain knowledge onHiggs 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 couplingproduct $y_gy_Z$ can be potentially constrained to be less than 18 times theStandard-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-shellcouplings and combining the on-shell measurements, the width of the Higgs bosonis constrained to be less than 1.3~GeV, which is similar to that in the directmeasurement.  In addition, the interference effect is also analyzed.

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