* There are new combined limits on dark matter product from the ATLAS and CMS experiments at the Large Hadron Collider (LHC) based upon complete Run I data. No dark matter signal has been observed at the LHC.
The LUX direct dark matter detection experiment still places the most strict bounds on a cross-section of interaction with nucleons for spin independent dark matter (about 10^-45 per cm^2) for dark matter particles of about 10 GeV/c^2 or more of mass. But, for lighter dark matter particles (certainly below 1 GeV), the maximum cross section of interaction with nucleons is set by CMS at about 10^-40 per cm^2 for spin independent dark matter and about 10^-41 per cm^2.
The cross-section of interaction of a neutrino with a nucleon is on the order of 4*10^-39 to 8*10^-39 per cm^2/GeV. Thus, the bounds on dark matter cross-sections of interaction from CMS are comparable to those of neutrinos with hundreds of MeV/c^2 of kinetic energy for dark matter particles up to about 10 GeV. For dark matter particles with masses of 10 GeV or more, exclusion from LUX is comparable to that of neutrinos with less than 10 eV/c^2 of kinetic energy (still relativistic by about three orders of magnitude, but nevertheless a very low energy for a neutrino).
Also, as recently noted, experimental observations of cosmic rays emitted by dwarf galaxies which are dark matter dominated in the dark matter particle theories, place strict bounds on the mean lifetime and dark matter annihilation cross-sections of any potential dark matter particle. Dark matter must have a mean lifetime much longer than the age of the universe and must very rarely annihilate. But, this limitation is more model dependent than some of the other boundaries.
None of these experiments, of course, can rule out any kind of dark matter particles whose only interactions with ordinary matter are via gravity, a particularly simple kind of dark matter model that is increasingly favored.
* Theories with an additional Higgs doublet predict an additional pseudo-scalar neutral Higgs boson, often called A, which could be light. The BESIII collaboration has put increasingly tight boundaries on this possibility in the 212 MeV to 3 GeV mass range, where maximum branching fractions can now be not more than 4.7*10^-6 in J/Psi decays, and is about 100 times smaller than that in parts of that mass range.
Previous experiments have excluded it in other mass ranges for the pseudo-scalar neutral Higgs boson called A. Generally, these experiments rule out light A bosons for masses from about 212 MeV to 9 GeV with significant branching fractions in a quite model independent fashion, and rule out supersymmetric A bosons with masses of less than that of the Z boson (about 90.1 GeV).
There is simply no meaningful experimental evidence to support theories with multiple Higgs doublets, including supersymmetry.
* New, more strict, limits have been set on the maximum magnetic moment of the neutrino.
The scattering of solar neutrinos off electrons in Borexino provides the most stringent restrictions, due to its robust statistics and the low energies observed, below 1 MeV. Our new limit on the effective neutrino magnetic moment which follows from the most recent Borexino data is 3.1 x 10^-11 mu_B at 90% C.L. This corresponds to the individual transition magnetic moment constraints: |Lambda_1| less than 5.6 x10^-11 mu_B, |Lambda_2| less than 4.0 x 10^-11 mu_B, and |Lambda_3| less than 3.1 x 10^-11 mu_B (90% C.L.), irrespective of any complex phase.The Standard Model expectation with a simple Dirac mass neutrino model is 3*10^-19 mu_B. This is non-zero mostly because there is a chance that the neutrino will emit a virtual W boson and a virtual charged lepton that emits a photon at the one loop level. But, it can be much higher (to the point of approaching thresholds of experimental detection) in models where neutrinos have Majorana mass and in supersymmetric models.
Essentially, this is yet more evidence (along with the continuing non-detection of neutrinoless double beta decay) tending to show that violations of baryon number conservation and lepton number conservation are non-existent, or at least virtually non-existent (high energy sphalerons aside) to the point where they are insufficient to account for the baryon asymmetry to the universe, if you assume that the starting point of the universe had matter and antimatter in equal amounts, or was pure energy.
* There are some two sigma tensions between SM predictions and experimental data in the areas of CP violation and the CKM matrix at the LHC, but researchers think that this it is likely that this is due to "penguin pollution" in the Standard Model predicted value (i.e. the impact of often ignored Feynman diagrams that go into the final prediction but are hard to calculate called "penguins" based upon the way that the Feynman diagram that goes into the calculation looks visually). Overall, however, the new data "set strong constraints on models" beyond the Standard model.