  We discuss the prospects to probe the light-quark Yukawa couplings to the
Higgs boson. The Higgs coupling to the charm quark can be probed both via
inclusive and exclusive approaches. On the inclusive frontier, we use our
recently proposed method together with published experimental studies for the
sensitivity of the Higgs coupling to bottom quarks to find that the
high-luminosity LHC can be sensitive to modifications of the charm Yukawa of
the order of a few times its standard model (SM) value. We also present a
preliminary study of this mode for a 100 TeV hadronic machine (with similar
luminosity) and find that the bound can be further improved, possibly within
the reach of the expected signal in the SM. On the exclusive frontier, we use
the recent ATLAS search for charmonia and photon final state. This study yields
the first measurement of the background relevant to these modes. Using this
background measurement we project that at the high-luminosity LHC, unless the
analysis strategy is changed, the sensitivity of the exclusive final state to
the charm Yukawa to the charm Yukawa will be rather poor, of the order of 50
times the SM coupling. We then use a Monte-Carlo study to rescale the above
backgrounds to the h->phi gamma case and obtain a much weaker sensitivity to
the strange Yukawa, of order of 3000 times the SM value. We briefly speculate
what would be required to improve the prospects of the exclusive modes.
