**11:00 am: Testing the Higgs boson through pair production,**

*Roberto Contino***Why is double-Higgs production so important? Can measure new couplings inaccessible to single-Higgs processes, in particular self-coupling and HHVV couplings. These are (further) essential tests of Higgs as a single doublet. Most importantly, they will probe EWSB dynamics at higher energies.**

Natural language to probed these couplings is EW EFT. Couplings written so SM contribution is one, deviation due to heavy physics ~ g

^{2}/m

^{2}.

*Single*-Higgs couplings constrained to deviate from SM by less than ~30%. This points to a gap between SM and NP (little hierarchy).

Double-Higgs couplings as probe of strength of EWSB: If not in SM, as known, Goldstone self-coupling diverges at high energy (grows like s/v

^{2}). Speed at which this grows proportional to shift in Higgs coupling, and correspondingly scale of strong interactions inversely proportional to this deviation. Hence standard argument for probing cut-off to EFT using measurements of higher-dimensional couplings. The advantage of double-Higgs production is that the couplings are proportional to v

^{2}/f

^{2}rather than v/f as for single-Higgs couplings.

*i.e.*Greater sensitivity.

Additionally, combining observation of deviation with non-observations of new states gives lower bounds on NP couplings.

To no surprise, Contino seems to be assuming a strongly coupled high-energy theory.

Example based on VBF to hh to 4b or bbττ. Needs lots of luminosity (3ab

^{-1}). Some sensitivity, what scale is probed? Looks like very low scales,

*f*less than a TeV? Corresponds to Λ ~ 6 TeV.

To now surprise, can do better at linear colliders.

**11:30 am: CP Violation in 3-body Higgs decays,**

*Adam Falkowski***New title!**

In SM, there are no CP-violating couplings (at tree level). But already at dim-6 with over 2000 operators the possibility exists. The induced CP-violating gauge couplings are currently very weakly constrained, especially compared to their very small (3-loop) SM values.

An important indirect constraints comes from EDMs, but this assumes Higgs couples to light generations, something we cannot directly probe in the near future. A semi-direct probe comes from kinematic distributions of Higgs final states.

Direct observables (CP violation in decays) done to death in flavour physics, but apparently ignored in Higgs physics. Examination of effect in specific decay to Zγ. Leads to forward-backward asymmetry in Z decay products. Direction is defined by photon, so no problems from symmetry of LHC initial state.

Symmetric and anti-symmetric amplitudes both dominant on the

*Z*pole, suppression by width/mass~0.07 which is not too small. Asymmetry of order a few to 10% allowed so far.

Seeing this is pretty hard. Even symmetric component of decay unseen yet. Even for 3ab

^{-1}, only have significance order 1 for 10% asymmetry. Can we do better with more intelligent tools? Work in progress.

Looking for asymmetry at linear collider problematic due to need to produce hZ, rather than h. Asymmetry exists directly in that channel, but additional suppression.

**12:00 pm: Implications of the Higgs signal for BSM physics,**

*Georg Ralf Weiglein***What do we know already? Mass as precision observable, though this means we need to worry about systematics. Spin strongly preferred to be zero; though wiggle room if two overlapping signals we would like to exclude.**

Note: need to improve Mh to match expected accuracy (at ILC) in Br(h to ZZ)!

There is no such thing as a model-independent measurement of a coupling. Even with σ times Br, measurements so far use SM Higgs properties to cut down background. With no measurement of total cross section (impossible at LHC) can only constrain ratios of couplings, though this is not necessarily a bad thing.

A general study should be sufficiently general yet feasible to constrain. It also needs to include SM precision corrections.

Largest deviations in Higgs couplings in generic 2HDM in couplings to b/τ, which is unfortunate as they are the hardest to constrain.

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