* A new Snowmass paper on Baryon Number Violation, something that has never been observed and is largely ruled out by the Standard Model.
But, the theoretical motivation for finding it to explain matter-antimatter asymmetry in the universe, is great, although there is no sign of it so far.
The most obvious place to look is proton decay, which has a minimum half-life of longer than 1.4* 10^34 years for one of the two most common decay modes that could exist if it was allowed, and 5.9*10^33 years for the other. Predictably, beyond the Standard Model theories contemplate proton decay rates just a little bit beyond what can currently be measured experimentally. Other searches such as neutron-antineutron oscillation have also come up empty.
The paper urges continued searches for proton decay and new neutron-antineutron searches.
The paper doesn't really discuss it, but looking anew at the Standard Model v. SUSY gauge unification graphs that extrapolate the running of the coupling constants of the three Standard Model forces at high energies, I am struck by how powerful a tool that could be to prove or falsify a lot of BSM physics. While SUSY merely bends the strong force and electromagnetic force coupling constants a bit at high energies (aka modifies their "beta functions"), it actually changes the direction of the running of the weak force coupling constant at high energies, starting around 1 TeV-10 TeV. This seems like a credible target to measure in my lifetime or at least my children's lifetimes. State of the art theoretical calculations of the Standard Model runnings of these coupling constants can be found here.
Experimental measurements of the strong force coupling constant apparently only reach up to the single digit GeV scale (at least as of 2007), although some experiments seem to reach considerably further but in a less definitive way, and the LHC has also expanded the envelope a bit. This study from 2009 seems to be one of the stronger bounds on strong force coupling constant running deviations from the Standard Model expectation. This talk shows experimental results for the strong force coupling constant running up to about 200 GeV. A 2012 experiment found no deviation in the running of the strong force coupling constant up to 600 GeV. A fair amount of active research on the QCD coupling constant running, however, is concerned not with the UV limit, but the IR limit.
Standard Model running of the weak force coupling constants had been confirmed up to about 100 GeV as of 2009. Electromagnetic coupling constant running has apparently been measured up to 21 TeV as of 2006 at LEP.
* The new Snowmass paper on Charge Leptons looks at two issues. Lepton Flavor Violating (LFV) Processes and Lepton Flavor Conserving Processes. Flavor violation in Charge Lepton processes is predicted by the Standard Model to exist at an undetectable 10^-56 branching ratio of muon decays if neutrinos have a Dirac nature and the PMNS matrix elements are at approximately current experimental levels. But, many beyond the Standard Model theories predict greater lepton flavor violation. Various mid-budget physics experiments are looking for and contemplated that would search for LFV.
A second part of the paper on Lepton Flavor Conserving Processes mostly focuses on the prospects of further research regarding anomalous magnetic moments (g-2) and electric dipole moments (EDM), of the three charged leptons to rule out or confirm the existence of BSM phenomena at energy scales impossible to reach directly in near term big budget collider experiments.
Aside: the arvix HEP-Experiment category really conflates two entirely different kinds of papers. Those that propose new experiments, and those the report the results of existing experiments. It would be nice if the system could categorize the two kinds of papers separately.
Also, notably, both of these papers are suggesting medium budget physics that may be attractive alternatives to a next generation LHC. Getting fundamental physics funds out of a single basket seems wise, even if the LHC may have been the right tool for today.
It is also remarkable how tight the measurements of quantities like the electron EDM, the muon g-2, the lower limit on the mean lifetime of the proton, and the existence of lepton flavor violating processes already is with current experimental work. There is simply not a lot of wiggle room for alternatives to the Standard Model to fit themselves into given the extreme precision of some of the measurements that have been made already, particularly those involving electroweak processes.