In the standard model, the Higgs gives mass to the W and Z bosons and to the fermions, but in different ways. Theoretically you could have a Higgs which does the first but not the second (in which case the fermions must get their masses in some other way); this is called a "fermiophobic" Higgs. Today, a paper claims that a fermiophobic Higgs is favored by experiment.
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