The original experiment was designed to find it as a proof of antimatter, not dark matter.
the AMS is finally delivering on the promise of its original name when "AM" stood for "antimatter."
When Ting sold NASA and DOE on the AMS, he said it might find runaway particles from oases of antimatter, helping solve a deep riddle. The big bang produced matter and antimatter in equal amounts. Soon after, they began colliding and annihilating each other in puffs of gamma rays. But somehow, matter came to dominate the observable universe. That could be because of some fundamental difference between the two—or maybe it was just a coin flip, where certain regions of space came to be ruled by one or the other. Ting's idea to look for those regions galvanized his critics, who considered it outlandish because clumps of antimatter coexisting with normal galaxies would produce more gamma radiation than astronomers observe. Moreover, large antiparticles could not easily survive the journey to the AMS. But if antimatter were there, the AMS would sniff it out—or so the original pitch went.
But each year has also brought one event or so that for all the world looks like it is curving with charge equal to minus two, Ting says—the expected signature of antihelium. The events could just be heliums bouncing unusually off an atom inside the experiment, leading to a misidentification. But the team has used computers to model all the possible paths a particle could take in the detector. "We still do not see any possible way this could come from any background," Ting says. "Many people in the collaboration think we should publish it."
And seem to be holding up for that, leftover antimatter from the big bang.
You ask:
Why is that? what is the dark matter decay/annihilation that produces that
This is a competing theoretical explanation, based on the theoretical model, example
Galactic Dark Matter (DM) annihilations can produce cosmic-ray anti-nuclei via the nuclear coalescence of the anti-protons and anti-neutrons originated directly from the annihilation process. Since anti-deuterons have been shown to offer a distinctive DM signal, with potentially good prospects of detection in large portions of the DM-particle parameter space, we explore here the production of heavier anti-nuclei, specifically anti-helium
Isn't there any process involving standard model particles that produce anti-helium?
It would be one with very small probabilities because It would have to be a complicated single interaction with 12 quarks and 12 antiquarks, if it were a pair production from a very high energy gamma-field pair production. The models where anti helium coalesces from lower antibaryon number have better probabilities.
Is there any relation with the search for anti-deuteron in dark matter detection experiments?
Anti-deuterons also may appear by coalescence but there are proposals that if dark matter is composed of supersymmetric particles :
measurements of the antiproton cosmic-ray flux at the Earth will be a powerful way to indirectly probe for the existence of supersymmetric relics in the galactic halo. Unfortunately, it is still spoilt by considerable theoretical uncertainties. As shown in this work, searches for low-energy antideuterons appear in the meantime as a plausible alternative, worth being explored. Above a few GeV/n, a dozen spallation antideuterons should be collected by the future AMS experiment on board ISSA. For energies less than about 3 GeV/n, the antideuteron spallation component becomes negligible and may be supplanted by a potential supersymmetric signal. If a few low-energy antideuterons are discovered, this should be seriously taken as a clue for the existence of massive neutralinos in the Milky Way.
It is all very speculative and theoretical.
My question is then, how do these Higgless Theories (that are consistent with what was actually measured at the LHC) work?
Have you looked at the list your link gave for theories without a Higgs field?
If you do you will see a long list of disparate theories that try to model the same data that the standard model,SM, of particle data fits, with various successes as you will see reading the list and its references.
The SM can be thought as a data bank of 99% of measurements and observations at present, and its success is due to also being predictive for new data, as was the discovery of the Higgs boson.
The SM is a quantum field theory, and the introduction of the Higgs field in order to break the symmetry the model has at very high energies , to the mass spectrum we observe in the laboratory, carries with it the necessity of the existence of a Higgs boson, which was a prediction until the Higgs boson was discovered at the LHC.
Alternative theories attempting to model the same data have to embed the SM or show that the SM is derivable from the new theory, in order to fit the existing data.
Each alternate theory works with its own mathematics which cannot be described in a page on a question and answers site.
Best Answer
Depending on what quanta dark matter truly is made of, the Higgs boson may or may not be able to decay into those quanta. Being further nit-picky, at colliders, where the Higgs boson can be studied, dark matter may or may not be produced, the collider experiment will never be able to tell whether a new particle has a long enough lifetime to be the cosmological dark matter. One thus typically refers to such decays as "Higgs to invisible". This avoids the reference to dark matter and would be the right buzz words to use in an internet search.
Yes, there are many dark matter candidates that the Higgs could decay into, yes, experiments at colliders could be able to detect such events, but current searches have not come up with significant discrepancies.
This paper from the CMS collaboration is a nice example to illustrate these points. Their Figure 1 shows some example Feynman diagrams where the Higgs ("H") decays into invisible particles (invisible in CMS, labeled $\chi$) that might be dark matter:
They go on and search their data for such events. Figure 6 from that paper shows what they find:
The colorful areas in the top portion of that figure are various standard model processes that are expected to contribute to this analysis channel. Black dots are their data, which agrees with the sum of the standard model processes. This is again shown in the middle portion where the ratio of the data to the standard model expectation is everywhere about one. The dashed line is the strongest possible amount of decays that they could attribute to the standard model Higgs to decay to some invisible particles.
This then allows them to calculate the largest possible branching ration of Higgs decaying into new beyond-standard model invisible particles, relative to the decay into standard model invisible particles, as being less than 20%, as they show in their Figure 9: