In the Standard Model, all of the properties of the Higgs boson, except its mass, can be calculated from first principles, and the global average measurement of its rest mass is 125.10 ± 0.14 GeV, a precision of about one part per 894.
In the Standard Model, the strength of the interactions of the Higgs boson with the fundamental particles, their so called "Yukawas" is proportional to the rest mass of those particles. The Higgs field also gives mass to the Higgs boson itself in proportion to its rest mass in the Standard Model.
The strength of the coupling of the Higgs boson with itself that is observed experimentally can can compared to a benchmark Standard Model value it has at its measured value, with the value equal to exactly one if the the experimentally measured value matched the predicted one.
If the experimentally measured value were higher, it would be proportionately more than one. If the experimentally measured value were lower, it would be proportionately less than one. It the experimentally measured value were opposite in direction to the exacted value (e.g. by analogy, if the electromagnetic force were repulsive when it was expected to be attractive) then the value is negative.
Tommaso Dorigo reports on the best measurement of the Higgs boson self-coupling to date, from was published by the CMS Collaboration at the Large Hadron Collider (LHC) back in November. Their measurement bounds the Higgs self-coupling to be between -2.7 and 8.6 (relative to a benchmark value of 1.0) within 95% confidence intervals.
This is consistent with the Standard Model prediction, but with lots of uncertainty because it is a hard measurement to make of something that can only happen with any frequency towards the high end of the energy scales that the LHC can produce. Also, while this isn't a terribly tight constraint (many of its interactions are constrained much more tightly), it is sufficiently tight to rule out a large swath of beyond the Standard Model theories that predicted more dramatic deviations from the Standard Model prediction.
Combining the observed strength of all Higgs boson interactions observed to date, in which 1.0 is the Standard Model prediction, the experimentally observed values so far have been 1.13 ± 0.06, a slight tension with the Standard Model prediction, but still remarkably close to properties predicted theoretically in the 1960s, more than half a century ago, when scientists still used slide rules and punch card mainframe computers to do calculations.
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Also, while this isn't a terribly tight constraint (many of its interactions are constrained much more tightly), it is sufficiently tight to rule out a large swath of beyond the Standard Model theories that predicted more dramatic deviations from the Standard Model prediction.
like susy?
Not every kind of SUSY, because it has so many moving parts, by a very broad swath of SUSY theories, mostly because, generically, supersymmetry theories have two or more Higgs doublets, i.e. at a minimum a different mass spin-0 even parity Higgs boson, a spin-0 odd parity Higgs boson, and a pair of positively and negatively charged Higgs bosons with the same electromagnetic charge as a proton and electron respectively, and often additional Higgs bosons in sets of four. These influence the properties of the "regular" Higgs boson.
Also, in general, in supersymmetric theories, sparticles (i.e. the new supersymmetric particles) get their masses through the same Higgs mechanism as the Higgs boson does, through interactions with a Higgs field, and any new particles with masses from that of a muon at about 100 MeV to a mass up to several times the mass of the top quark (mid-hundreds of GeV) is going to dramatically change the relative decay frequencies of the Higgs boson in all of its other channels, all of which are quite tightly constrained. And, of course, sparticles and BSM Higgs bosons are already ruled out over essentially all of the relevant mass range anyway.
So, any SUSY model that works has to have essentially all of its new particles at masses in the several TeV range or more to evade these constraints. And, while there are moving parts that allow you to evade the constraints and do that, the more you do that, the less anything that motivated you to consider SUSY in the first place is addressed. It doesn't solve the hierarchy problem. It doesn't explain any observed phenomena. It doesn't address lepton universality violations. It gets harder and harder to use as an explanation for muon g-2 anomalies. It gets too heavy to provide viable dark matter candidates. It gets very hard to use as a means of coupling constant unification. It is not needed to prevent the Standard Model from predicting unphysical possibilities up to the GUT scale.
It also is a blow, for example, to Technicolor theories (which predict that the Higgs boson is composite even though functionally similar in many respects), ands to theories with extra W' and Z' gauge bosons that aren't many TeV in mass.
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