Higgs bosons in particle physics and in condensed matter

TL;DR

This paper explores the analogy between Higgs bosons in particle physics and amplitude modes in condensed matter, proposing a Nambu sum rule that predicts possible additional Higgs particles and discussing implications for the Standard Model.

Contribution

It introduces a novel application of condensed matter Higgs mode analogies to predict new Higgs bosons and their masses within the Standard Model framework.

Findings

Potential existence of a second Higgs boson at 325 GeV.

Possible charged Higgs particles around 245 GeV.

Support for the Nambu sum rule relating Higgs and top quark masses.

Abstract

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. Together they satisfy the Nambu relation $M_{{\rm H}1}^2 + M_{{\rm H}2}^2 = 4 M_{\rm top}^2$, where $M_{\rm top}$ is the top quark mass. Also the properties of the Higgs modes in superfluid $^3$He-A, where the symmetry breaking is similar to that of the Standard Model, suggest the possible existence of two electrically charged Higgs particles with masses $M_{{\rm H}+}=M_{{\rm H}-}\sim 245$ GeV, which together obey the Nambu rule $M_{{\rm H}+}^2 + M_{{\rm H}-}^2 = 4 M_{\rm top}^2$. A certain excess of events at 325 GeV and at 245 GeV has been reported in 2011, though not confirmed in 2012 experiments. Besides, we consider the particular relativistic model of top - quark condensation that suggests the possibility that two twice degenerated Higgs bosons contribute to the Nambu sum rule. This gives the mass around 210 GeV for the Nambu partner of the 125 GeV Higgs boson. We also discuss the other possible lessons from the condensed matter to Standard Model, such as hidden symmetry, where light Higgs emerges as quasi Nambu-Goldstone mode, and the role of broken time reversal symmetry.