No Sign Of Higgs-Portal Dark Matter

The CMS experiment at the Large Hadron Collider (LHC) has found no evidence for Higgs boson decays into non-Standard Model particles that are "invisible" to its detectors such as dark matter (inferred from conservation of mass-energy and momentum in Higgs boson decays). The ATLAS experiment concurs in results it released in April of last year.

So, if dark matter exists, it probably does not get its mass via the Higgs mechanism the way that fundamental particles in the Standard Model (with the possible exception of neutrinos) do.

There is still a lot that the experiments conducted so far can't rule out in a model independent fashion, not because there is any sign that they are present, as because the measurements just aren't precise enough so far.

But, if a beyond the Standard Model particle had a coupling with the Higgs boson, called a Yukawa, proportional to its rest mass, as the other Standard Model particles do, this new particle would have a profound impact on the relative proportion of all of the decay products of a Higgs boson that are observed, which is largely a function of the mass of the Higgs boson, the masses of the Standard Model fundamental particles, and their spins (quarks and leptons have spin 1/2 and Standard Model fundamental bosons other than the Higgs boson have spin 1). 

This plays out to produce the chart below for various hypothetical Higgs boson masses, which shows the percentage of decays which are of a particular type on the Y-axis and the mass of the Higgs boson on the X axis (with the real Higgs boson having a mass of about 125 GeV).

Numerically, the decays of a 125 GeV Higgs boson in the Standard Model are approximately as follows:

b-quark pairs, 58%

W boson pairs, 21.3%

gluon pairs, 8%

tau-lepton pairs, 6.3%

c-quark pairs, 3%

Z boson pairs, 2.8%

photon pairs, 0.2%

muon pairs, 0.02%

The total does not add to 100% due to rounding errors and due to omitted low probability decays such as electron-positron pairs, strange quark pairs, down quark pairs, up quark pairs, and some asymmetric boson pairs.

Several the decay channels of the Higgs boson have been observed and are tolerably close to the expected values in the chart above (specifically decays to ZZ, two photons, WW, bb, two tau leptons, and two muons). Lines don't appear for the decays of a Higgs boson to quark-antiquark pairs for strange, down and up quarks, to muon-antimuon pairs, or to electron-positron pairs, because such decays are expected to be profoundly more rare than the decays depicted due to their small rest masses.

So, while a Higgs boson could have up to 18% invisible decays that are unaccounted for in a model-independent analysis, the observed decays actually place far more strict limitations upon what couplings a "vanilla" new particle with the Higgs boson could have, and as a result, on what its Higgs field coupling derived mass could be. For example, if the new "invisible" particle had a mass of 2 GeV or more, it would profoundly throw off the branching fractions of b quarks, c quarks and tau leptons from the Higgs boson.

The exclusion is strongest for fermion (e.g. spin-1/2 or spin-3/2) dark matter or other beyond the Standard Model fermions that couple to the Higgs boson in the standard way in the mass range from significantly less than the charm quark rest mass (about 1.27 GeV) up to half of the Higgs boson mass (about 62.5 GeV). 

It is also significant for spin-1 bosons with masses similar to the 80-90 GeV masses of the W and Z bosons, although even a light spin-1 boson that derived its mass from the Higgs field should have been enough to throw the other branching fractions off significantly.

But, the exclusion from Higgs boson decay data so far isn't particularly strong for fermion dark matter or other beyond the Standard Model fermions that couple to the Higgs boson in the standard way with masses of less than or equal to the mass of strange quarks and muons (i.e. less than about 100 MeV and probably significantly less given the dimuon channel decays identified by the CMS experiment) which would occur in less than 0.1% of Higgs boson decays.

The exclusion also isn't particularly strong for dark matter particles with more than half of the Higgs boson mass (i.e. more than 63 GeV), which would be mass-energy conservation prohibited in Higgs boson decay end states. But this exclusion on the high mass end of possible new particle masses is also conservatively low, because, particles more massive than that which couple to the Higgs field can still leave a detectible effect in collider experiments. 

In particular, evidence for the top quark coupling to the Higgs boson has been found at the LHC. So, we'd expect heavy fermionic dark matter that gets its mass from the Higgs field to have a mass of more than the approximately 173 GeV mass of the top quark in order go undetected. 

Also, in theory, a new particle deriving its mass from the Higgs field with a mass greater than the top quark and the usual coupling strength proportional to its rest mass would also make the universe profoundly unstable at energies well below the energies that colliders have explored already. See Arianna Braconi, Mu-Chun Chen, Geoffrey Gaswint, "Revisiting Electroweak Phase Transition with Varying Yukawa Coupling Constants" (October 5, 2018).

There are other non-particle physics considerations from astronomy that further tend to disfavor such a heavy dark matter particle mass, although not as definitively.

So, the LHC based exclusions for Higgs portal dark matter are powerful is disfavoring a supersymmetric WIMP candidate with a mass in the range of 1 GeV to 1000 GeV that direct detection experiments also powerfully disfavor. 

Image from here. The dotted blue line labeled Z portal Cx=1 in the chart below is basically equivalent to the cross-section of interaction with nucleons of ordinary Standard Model neutrinos. A femtobarn (fb) is 10^-39 cm^2. An attobarn (ab) is 10^-42 cm^2. A zeptobarn (zb) is 10^-45 cm^2. A yoctobarn (yb) is 10^-48 cm^2.

But the LHC isn't very useful in ruling out fermion dark matter candidates that are electromagnetically neutral and don't interact via the strong force (which other experiments also strongly rule out over a much larger mass range), but do interact in the usual way with the Higgs field, that have masses of  significantly less than 100 MeV, a mass range in which direct detection detection experiments (whose sensitivity falls off dramatically below 1 GeV) are also not very powerful at ruling out dark matter candidates.

For example, neither the LHC nor the direct detection experiments are helpful in ruling out a warm dark matter candidate with a mass in the 1-20 keV range favored by astronomy observations, even if it gets it mass from the Higgs field and has weak force interactions.

Also, the LHC provides no insight regarding, and can't confirm or deny the existence of, dark matter particle candidates that don't interact at all via any of the three Standard Model forces and have mass due to mechanisms other than their interactions with the Higgs field.

The source for this analysis above is as follows (via Sabine Hossenfelder's twitter feed):

The physicists in the CMS collaboration considered recently the complete data collected during the Run 2 operations of the LHC and extensively searched for presence of events corresponding to invisibly decaying Higgs boson. However there was no hint for the presence of any signal, only the known stuff, the backgrounds of the expected amounts! Too bad, indeed.

The negative result, however, is very important for our efforts in understanding the properties of the Higgs boson. It showed that the Higgs boson cannot decay invisibly more often than in 18% of the cases. This number is actually quite large, when compared to the decay into, say a pair of photons which is easy to identify in the experiment, but occurs only about twice in thousand decays. The LHC experiments are looking forward eagerly to having more data to see if Nature does allow such "invisible" decays of the Higgs boson, but are simply more rare. Not the least at all, such results from the LHC are actually interpreted in terms of interaction probability of dark matter with ordinary matter. This depends on the mass of the dark matter particle and thus absence of "invisible" decay of the Higgs boson rules out the existence of such particles in a complementary way to the dedicated searches for dark matter in non-accelerator experiments.

From the CMS experiment (discussing this paper). 

The charts below are from the paper. The first one is the percentage of invisible decays. The mean expected percentage consistent with the data is about 8% but the results are consistent with zero.

The second looks at exclusions of parameter spaces for Higgs portal dark matter candidates by cross-section of interaction (on the Y-axis) and particle mass (on the X-axis). The exclusion is particularly strong, relative to direct exclusion experiments in the sub-1 GeV mass range. The scalar dark matter exclusions shown is for bosonic dark matter with a Higgs field interaction of the mass shown on the X-axis and spin-0.