Higgs bosons in particle physics and in condensed matter

Understand

Higgs bosons - the amplitude modes - have been experimentally investigated in condensed matter for many years.

• An example is superfluid $^3$He-B, where the broken symmetry leads to 4 Goldstone modes and at least 14 Higgs modes, which are characterized by angular momentum quantum number $J$ and parity.
• Based on the relation $E_{J+}^2+E_{J-}^2=4\Delta^2$ for the energy spectrum of these modes, Yoichiro Nambu proposed the general sum rule, which relates masses of Higgs bosons and masses of fermions.
• If this rule is applicable to Standard Model, one may expect that the observed Higgs boson with mass $M_{{\rm H}1}=125$ GeV has a Nambu partner -- the second Higgs boson with mass $M_{{\rm H}2}=325$ GeV.