One of the Grieg subjects which seems to be of the immediate common
interest in Bergen and Warsaw is h->tau tau decay. On the experimental
side, I understand that uncertainities in this measurement are still
substantial and require more work and bigger statistics. This of
course provide also opportunities - larger error bars still allow for
deviations from the SM, in particular in CP violating phases of the
couplings. On the theoretical side, it seems that new CP phases in the
tau couplings are particularly advantageous in explaining bariogenesis
- see e.g. recent paper 2003.00099, directly related to this subject.

Therefore, perhaps we can start a common project here, in my feeling
it can be advanced fairly quickly as we all already have experience in
the topic.

First, one the theory side one can calculate h->2 tau decay in the
universal setup, I mean SM extended by higher order operators up to
dimension-6 ("SMEFT"). This covers all potential SM extensions. First
one needs to go through the operator basis, find those contributing to
this process at tree and likely also 1-loop level (this is because
tree level operators can be suppressed for some reasons and in this
case 1-loop contributions may be comparable). Then, calculate the most
general matrix element, BR and various distributions - here
experimental input is required, which types of distributions can be
actually measured.  Also, in the context of the CP violation, knowing
the analytical form of the SMEFT amplitude one can try to find more
"special" observables (asymmetries, some combinations of
measurements?) particularly sensitive to given coupling or given
complex phase.

Comparing theoretical formulae with data, one can find bounds on the
SMEFT couplings (Wilson coefficients of dim-6 operators), both on
their real and complex parts. Here experimental input is crucial,
perhaps also adapting your analysis and Monte Carlo's to make
determination of various Wilson coefficients more accurate. I do not
have enough experience here to propose anything more specific yet, at
least not before theoretical calculations are done.  Again, on theory
side, dim-6 operators may contribute to many processes, so Wilson
coefficients may be also bounded by other measurements, not just
h->tau tau (EDM's for sure! - but also others) - and such constraints
could be combined with h->tau tau analysis for more stringent limits.

Finally, knowing universal EFT bounds one can use them in twofold way.
First, still within EFT approach, one can check if the obtained bounds
on CP phases allow for efficient baryogenesis (something a la analysis
of 2003.00099, but perhaps more general, with more operators and new
constraints). Second, one can consider how EFT bounds translate into
allowed couplings of the chosen specific complete UV models.  Such
models usually in their low energy limit lead to correlations between
EFT couplings, so some bounds may become tighter than in the case of
fully general SMEFT. Or may be we get some other ideas, they usually
appear when working on the project...