Higgs Bosons in Particle Physics and in Condensed Matter

Volovik, G. E.; Zubkov, M. A.

doi:10.1007/s10909-013-0905-7

Cited by 68 publications

(73 citation statements)

References 55 publications

(96 reference statements)

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“…Based on the NSR for a NJL-type theory of top quark condensation, the authors suggest the possibility that there may be a partner to the Higgs Boson with a mass of 125 GeV -e.g. a Higgs partner near 270 GeV, 18,20 analogous to the Higgs partners for the J = 2 Bosonic spectrum of 3 He-B. Here we point out that estimates of the mass of a Higgs partner based on such sum rules may be imprecise because the NSR is generally violated.…”

Section: Nambu's Mass Relationsmentioning

confidence: 85%

“…Thus, the J c = 2 ± Higgs modes obey the NSR in the weakcoupling limit of the TDGL theory. 12,18,20 However, the NSR is violated by strong-coupling corrections to the Higgs masses, shown in Fig. 2 as a function of pressure for the strong-coupling β parameters shown in Fig.…”

Section: 31mentioning

confidence: 97%

“…2.2 of Ref. 20). Based on the NSR for a NJL-type theory of top quark condensation, the authors suggest the possibility that there may be a partner to the Higgs Boson with a mass of 125 GeV -e.g.…”

Section: Nambu's Mass Relationsmentioning

confidence: 99%

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On the Nambu fermion-boson relations for superfluidHe3

Sauls

Mizushima

2017

Phys. Rev. B

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Superfluid 3 He is a spin-triplet (S = 1), p-wave (L = 1) BCS condensate of Cooper pairs with total angular momentum J = 0 in the ground state. In addition to the breaking of U(1) gauge symmetry, separate spin or orbital rotation symmetry is broken to the maximal sub-group, SO(3) S × SO(3) L → SO(3) J . The Fermions acquire mass, m F ≡ ∆, where ∆ is the BCS gap. There are also 18 Bosonic excitations -4 Nambu-Goldstone (NG) modes and 14 massive amplitude Higgs (AH) modes. The Bosonic modes are labeled by the total angular momentum, J ∈ {0, 1, 2}, and parity under particle-hole symmetry, c = ±1. For each pair of angular momentum quantum numbers, J, J z , there are two Bosonic partners with c = ±1. Based this spectrum Nambu proposed a sum rule connecting the Fermion and Boson masses for BCS type theories, which for 3 He-B is M 2 J, + + M 2 J, − = 4m 2 F for each family of Bosonic modes labeled by J, where M J, c is the mass of the Bosonic mode with quantum numbers (J, c). Nambu's sum rule (NSR) has recently been discussed in the context of Nambu-Jona-Lasinio models for physics beyond the standard model to speculate on possible partners to the recently discovered Higgs Boson at higher energies. Here we point out that Nambu's Fermion-Boson mass relations are not exact. Corrections to the Bosonic masses from (i) leading order strong-coupling corrections to BCS theory, and (ii) polarization of the parent Fermionic vacuum lead to violations of the sum-rule. Results for these mass corrections are given in both the T → 0 and T → T c limits. We also discuss experimental results, and theoretical analysis, for the masses of the J c = 2 ± Higgs modes and the magnitude of the violation of the NSR. I. INTRODUCTIONOne of the key features of spontaneous symmetry breaking in condensed matter and quantum field theory is the emergence of new elementary quanta -phonons in crystalline solids, magnons in ferromagnets, the Higgs and gauge bosons of the standard model. In the latter example, spontaneous symmetry breaking (SSB) in the BCS theory of superconductivity played an important role in theoretical models for the mass spectrum of elementary particles. [1][2][3] In BCS superfluids the binding of Fermions into Cooper pairs leads to an energy gap, ∆, in the Fermion spectrum, i.e. Fermions in the broken symmetry phase (Bogoliubov quasiparticles) acquire a mass m F = ∆, while condensation of Cooper pairs leads to the breaking of global U(1) gauge symmetry, the generator being particle number. The latter also implies that the Bogoliubov Fermions are no longer particle number (Fermion "charge") eigenstates, but coherent superpositions of normal-state particles and holes. Charge conservation is ensured by an additional contribution to the charge current -a collective mode of the broken symmetry phase. This massless Bosonic excitation of the phase of condensate amplitude 4,5 is the NambuGoldstone (NG) mode associated with broken U(1) symmetry, and is manifest as a phonon in neutral superfluid 3 He. II. NAMBU'S MASS RELATIONSNambu and Jona...

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Section: Nambu's Mass Relationsmentioning

confidence: 85%

Section: 31mentioning

confidence: 97%

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On the Nambu fermion-boson relations for superfluidHe3

Sauls

Mizushima

2017

Phys. Rev. B

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“…The states of the B phase are classified by total angular momentum quantum numbers (J) of 0, 1 and 2. The J = 2 state comprises bosons that are analogous to the famous Higgs boson 14 . A remarkable finding is that the broken symmetry of the B phase, and its J = 2 state, enable the propagation of transverse sound waves 15,16 -a feature that was unheard of in liquids and was often assumed to be a property only of rigid solids.…”

Section: Eighty Years Of Superfluiditymentioning

confidence: 99%

Eighty years of superfluidity

Halperin¹

2018

Nature

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“…We set = a = 1 throughout the paper except in Figures. While the purpose in the present paper is to discuss the effect of inhomogeneity in J (α) j on collective modes in the superfluid phase, here we briefly review properties of ground states and collective modes of the BoseHubbard model (1) in the case that the system is homogeneous (J (α) j = J, µ j = µ). When the filling factor n (the number of atoms per site) is non-integer, the ground state is always a superfluid phase.…”

Section: Modelmentioning

confidence: 99%

Localized Higgs modes of superfluid Bose gases in optical lattices: A Gutzwiller mean-field study

Danshita

Tsuchiya

2017

Phys. Rev. A

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We study effects of a potential barrier on collective modes of superfluid Bose gases in optical lattices. We assume that the barrier is created by local suppression of the hopping amplitude. When the system is in a close vicinity of the Mott transition at commensurate fillings, where an approximate particle-hole symmetry emerges, there exist bound states of Higgs amplitude mode that are localized around the barrier. By applying the Gutzwiller mean-field approximation to the Bose-Hubbard model, we analyze properties of normal modes of the system with a special focus on the Higgs bound states. We show that when the system becomes away from the Mott transition point, the Higgs bound states turn into quasi-bound states due to inevitable breaking of the particlehole symmetry. We use a stabilization method to compute the resonance energy and line width of the quasi-bound states. We compare the results obtained by the Gutzwiller approach with those by the Ginzburg-Landau theory. We find that the Higgs bound states survive even in a parameter region far from the Mott transition, where the Ginzburg-Landau theory fails.

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Higgs Bosons in Particle Physics and in Condensed Matter

Cited by 68 publications

References 55 publications

On the Nambu fermion-boson relations for superfluidHe3

On the Nambu fermion-boson relations for superfluidHe3

Eighty years of superfluidity

Localized Higgs modes of superfluid Bose gases in optical lattices: A Gutzwiller mean-field study

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