Theory
Threshold effects may be partially spoilt by additional jet radiation: could be interesting to veto additional jets. This is not however naturally done in experiments, which are mostly inclusive over additional jets. Alternatives would be to consider quantities such as pT(ttH) or m(ttH), the latter being mostly insensitive to ISR. In fact the sensitivity seems to be slightly higher for m(ttH) (~10%) than or pT(H) (~6%). Could be studies using MadGraph ?
CMS
H->bb sensitivity decrease above 200 GeV probably due to analysis not being fully optimized yet for high pTH, and includes only resolved decays.
3-bin numbers not always consistent with 2-bin case for bins for extreme bins -- could be due to the fact that the fact that the 2-bin and 3-bin analyses are trained separately.
Would be interesting to estimate sensitivity to H->γγ at higher pT (say where the uncertainty becomes ~100%), to define a BSM bin as for other STXS definitions.
Could have cuts on the b-jets to align better with systematics ? Maybe more appropriate for a differential fiducial measurement.
Could also investigate m(ttH) but worse resolution for H->γγ. Otherwise some kind of H_T, but could be affected by pileup.
Issue with pT(H) is that the main systematics for ttH->bb is from the background where pT(H) is not defined
ATLAS
Some benefit to have same pT(H) boundary as ggF so 120 GeV and 200 GeV, although for the latter ~300-350 may be more adapted since sensitivity is still quite high at 200 GeV. Proposal would be to have a boundary at 120 GeV, dotted boundaries at 60 and 200 GeV, and converge on a further (solid) boundary around 350 GeV. For the latter, also need to agree with ggF to keep the cuts in sync.
H_T and m(ttH) ? More or less extrapolation compared to pT(H), depending on the channel. Would require to define the tops on the theory side, which isn't trivial (could be defined as a truth jet, but at lower pT, may need a large-radius jet to get all the decay products)
Issue with bkg modeling in ttH->bb : need to make sure the binned measurements are not spoilt by increased systematics. However the data-driven systematics determination could work also in a binned situation.
ttH(ML) : can constrain at least the total normalization, and can also have some sensitivity to kinematics through the discriminators.
H_T could be defined as the total H_T of top and Higgs decay products. However needs to decay the top for theory predictions, and perhaps not very closely correlated with experimental observables.
Action items:
Timescale: "soon" for the binning (was due for Moriond...), a bit later for the uncertainties.