Higgs Production and Decay Channels

First of all, the protons circulating in the LHC have to be considered as a bag of quark and gluon components.  Each proton has two valence up quarks and one valence down quark.  At a high fraction of the proton’s momentum, a rule of thumb is to say that each valence quark might have about a third of the proton’s momentum to use in hard elementary particle collisions to produce a massive particle.  So the final 14 TeV center of mass energy collisions might only produce new particles up to 5 TeV in mass or 2.5 TeV in pairs.

However, each component of the proton or “parton” has its own distribution function of momentum as a function of its fraction ‘x’ of the proton’s momentum.  This is called Feynman’s x, after Richard Feynman’s insightful treatment of parton kinematics and dynamics.

The main constituents are the valence quarks, the virtual gluons that they emit, and the quark-antiquark pairs that are formed from the virtual gluons, which also include strange and anti-strange quarks.  The quarks can also emit virtual W bosons, leading to a Higgs production process called W boson fusion.  Here are Feynman diagrams of the various Higgs production processes.  The first is called gluon-gluon fusion.  The top quark t in the loop is virtual.

In W or Z bremsstrahlung the intermediate W or Z are virtual.  The final particles are all real particles.

These are the dominant processes because the Higgs couples proportional to a particles’ mass, and favors the most massive particles which are the top quark at 174 GeV, the W boson at 80 GeV, and the Z boson at 91 GeV.   The upper left diagram is the fusion of gluons to produce a virtual top quark loop, which then produces a real Higgs.  The upper right is the creation and fusion of oppositely charged W’s to a neutral Higgs, or of neutral Z bosons to a Higgs.  In the lower left, gluons each produce a pair of top and anti-top quarks.  The ones that produce the Higgs are virtual, the escaping ones are real.  In the lower right, a virtual W or Z boson decays to a real W or Z boson, respectively, with a real Higgs also.  At the mass of the detected Higgs at 125 GeV,  the gluon gluon fusion is dominant, and the quark-quark and quark-antiquark collisions are about a tenth of that rate.

(Virtual particles do not have the perfect combination of energy and momentum to become real particles, and exist by the Heisenberg Uncertainty Principal over times that are roughly h/(2 pi M c^2)  where h is Planck’s constant and M is the mass of the virtual particle.  The distance that they can traverse is (h c)/(2 pi M c^2) or about (0.2 GeV f)/(Mc^2), where f is a fermi = 10^(-13) cm, and is about the diameter of a proton.  So a virtual particle of Mc^2 = 100 GeV can exist to transit about 2/1,000 of the size of a proton.)

The decay of a Higgs at 125 GeV is proportioned into the following channels:


The 125 GeV Higgs discovered is too light to decay to a pair of top (t) and anti-top quarks.  The next heaviest quark is the bottom at 4.2 GeV, so it decays to a pair of bottom (b) and anti-bottom quarks.   The tau lepton has a mass of 1.8 GeV, and the charm (c) quark has a mass of 1.5 GeV, so these are next among the fermion-antifermion pairs.  The Higgs to WW or ZZ is via a virtual Higgs, since both of these pairs are more massive than a real Higgs at 125 GeV.

Whereas the decay to two photons via a virtual top quark loop is only 0.2%, it is a distinct, clean signature in the detectors, and is carefully studied.





About Dennis SILVERMAN

I am a retired Professor of Physics and Astronomy at U C Irvine. For a decade I have been active in learning about energy and the environment, and in lecturing and attending classes at the Osher Lifelong Learning Institute (OLLI) at UC Irvine.
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