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How is it possible that a higgs at ~125 GeV can decay into 2 W bosons @ ~ 80 GeV a piece (for example)? Shouldn't a particle only be allowed to decay to lighter particles + energy? Diagram copied from this question

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The decay channels of the Higgs boson on your graph contain decays to virtual particles as well. In particular, one talks about $ZZ^*$ and $WW^*$ decays, too. The asterisk means that the particular particle which carries the asterisk is virtual. Its being virtual means that its energy and momentum don't have to obey $$E^2-p^2c^2=m_0^2c^4$$ i.e. they can be "off-shell" but being off-shell requires that the particle fails to exist "permanently" or for extended periods of time. Virtual particles may only exist for a very limited period of time which is even shorter if the particles are "very off-shell".

Because one of the particles is off-shell, its energy may be very small, even as small as zero (or slightly negative), so the total energy of the pair with one real particle and one virtual particle may be "just above" the rest mass of the W-boson or Z-boson for the decay to be sufficiently likely.

The virtual W-bosons and Z-bosons nevertheless decay to similar products as physical (on-shell) W-bosons and Z-bosons. In principle, the energy of a virtual particle may be negative (or there may be decays to two virtual particles) so the decay rate isn't strictly zero even for Higgs masses below the W-boson or Z-boson mass, respectively. Nevertheless, the $WW^*$ or $ZZ^*$ branching ratio rapidly increases above the single W-boson or Z-boson mass.

That's not the case of decays to quark pairs which only becomes significant if both quarks are on-shell. For example, the $t\bar t$ decay channel would only kick for a Higgs mass above 350 GeV, twice the top quark mass. Also, the parametric description of the shape of the branching ratio near the "threshold" (minimum allowed Higgs mass or energy for which the decay is possible) would differ between bosons and fermions.

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