With the first round of experimental talks complete, now we have some theory to discuss the implications.
10:45am: Carlos Wagner, "Low Energy Supersymmetry and Higgs Physics"
Large variations of Higgs couplings still allowed, for certain values of large. So it is worth studying what kind of variations are possible in motivated BSM.
SUSY of course recovers the SM Higgs phenomenology in the decoupling limit.
While we need large stop mixing, there is no lower limit on the stop masses from the Higgs mass.
Large mixing decouples light stop from Higgs, so corrections to gluon fusion smaller than might be expected.
An upper bound on the stop mass from the Higgs mass of about 10 TeV; higher loops suppress stop contributions to Higgs mass. Not quite sure what the assumptions here are.
Non-SM Higgs has tan β-enanced couplings to down-type quarks. SUSY breaking induces diagonal couplings; loop suppression can be offset with this enhancement. So constrained by SUSY searches.
This talk feels like a number of unrelated points. There's no consistent narrative.
Final point is about a small excess in light staus, that we saw in the SUSY session yesterday. Carlos has promoted light staus in line with the diphoton excess. I'm reminded of some of the efforts to look at the WW cross section excess I saw talks on at Brookhaven back in May.
11:20am: Lawrence Hall, "TeV-Scale Superpartners from the Multiverse"
Discovery of perturbative Higgs and no BSM is, historically speaking, a surprise. Either (almost) natural physics will show up soon, or naturalness is flawed. Hence the multiverse of the title. Claimed that the multiverse can explain tuning and size of both cosmological constant and Higgs VEV; can it say anything about the SUSY scale?
Conclusion is that even though we have (multi)-TeV superpartners, they likely will not show up at the LHC.
Note that natural SUSY has drifted over the years. Originally, natural superpartners were 50-150 GeV.
Important threshold was the '04 invention of split SUSY; anthropic arguments much older ('79 review in astro!) but this was first real application to particle BSM.
CC. paper hep-th/0702115 to look up on explaining the last factor of one-thousand in fine tuning.
Argument on fine tuning with VEV based on decay of complex nuclei runs on similar form to Weinberg's original CC argument.
What, then, of SUSY masses? Need probability distribution for SUSY scale, including fine tuning if scale much larger than VEV. One possible class of distributions lead to run away, strongly preferring all SUSY partners at the GUT scale. In this case, to fit the observed Higgs mass we need tan β = 1, suggesting a symmetry at the GUT scale between the tow Higgs doublets. Uncertainties on this measurement look key to resolve if this is actually consistent with measurements. Top mass measurement dominates.
Alternatively, use multiverse arguments for vacuum lifetime. This argument is entirely consistent but unconvincing.
Need for one heavy quark, and two light quarks/one light lepton? See hep-ph/0608121.
An alternative to high-scale SUSY is hat the probability distribution for the SUSY scale pushes to high values, but there is an upper limit from some anthropic arguments. Suggested one is that you get too much dark matter at high scales. Possible but highly debated point. If we accept it, it suggests an LSP mass of one to a few TeV. "Unnatural TeV SUSY". Two cases, depending on how gaugino masses are generated; either gauginos comparable to sfermions, or there is a one-loop suppression in gaugino masses.
This idea has a number of different names (Spread, Mini-Split, etc). It is attractive because it gives the right Higgs mass without effort. Interesting Wino DM phenomenology as sfermions get heavy, in particular non-thermal DM from freeze-in.
Summary: the multiverse is a horrible possibility. But we must consider it seriously. Several possibilities about where SUSY might live based on simple multiverse models. Superpartners could be just outside the reach of the LHC.
11:55am: Roberto Contino, "Higgs compositeness: current status and future strategies"
Analogy of Higgs in WW scattering to sigma in pi-pi scattering raises question of why Higgs is narrow and light; sigma is (relatively) heavy and broad. Explanation is that Higgs must be pNGB itself. Note that this implies that the Higgs production amplitudes will grow with energy.
Can observed Higgs be composite? Higgs potential finite and features explicit breaking of Goldstone symmetry. You need at least two such breakings that cancel against each other, introducing an irreducible fine-tuning of order v2/f2. If EWSB is triggered at quadratic order in the spurions, we predict a too-heavy Higgs of ~300 GeV. One way around this is to make tR fully composite; this predicts lighter Higgses, closer to the observation. The top partners have to be not too heavy, not too strongly coupled in this scenario.
Alternatively, EWSB can come in at quartic order in the spurions. This works for fundamental tops but requires more fine tuning.
Composite Higgs has non-standard couplings to W, Z. This runs into constraints from EWPT. Coupling must agree with SM at 5% level; though this can be relaxed by the contribution from heavy states. Particularly, negative contributions to S-parameter from fermion partners is key. Also, contributions to both S and T parameters simultaneously eases limits a lot.
Another obvious limit comes from direct searches for top partners. LHC limits now run to around 700-800 GeV. Much of the natural parameter space in simplified models is ruled out by this.
Higgs measurements place limits, but not as severe as you might think. Goldstone symmetry reduces corrections to couplings to photons, gluons. Higgs decay to photon+Z might be smoking gun signal.
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