We study the Higgs boson $(h)$ decay to two light jets at the 14 TeV High-Luminosity-LHC (HL-LHC), where a light jet ($j$) represents any non-flavor tagged jet from the observational point of view.
The decay mode $h\to gg$ is chosen as the benchmark since it is the dominant channel in the Standard Model (SM), but the bound obtained is also applicable to the light quarks $(j=u,d,s)$. We estimate the achievable bounds on the decay branching fractions through the associated production $Vh\ (V=W^\pm,Z)$. Events of the Higgs boson decaying into heavy (tagged) or light (un-tagged) jets are correlatively analyzed.
We find that with 3000 fb$^{-1}$ data at the HL-LHC, we should expect approximately $1\sigma$ statistical significance on the SM $Vh(gg)$ signal in this channel. This corresponds to a reachable upper bound ${\rm BR}(h\to jj) \leq 4~ {\rm BR}^{SM}(h\to gg)$ at $95\%$ confidence level.
A consistency fit also leads to an upper bound
${\rm BR}(h\to cc) < 15~ {\rm BR}^{SM}(h\to cc)$ at $95\%$ confidence level.
The estimated bound may be further strengthened by
adopting multiple variable analyses, or adding other production channels.