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• W2551933222 abstract "Superfluid $^{3}mathrm{He}$ 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 subgroup $mathrm{SO}{(3)}_{S}ifmmodetimeselsetexttimesfi{}mathrm{SO}{(3)}_{L}ensuremath{rightarrow}{mathrm{SO}(3)}_{J}$. The fermions acquire mass ${m}_{F}ensuremath{equiv}mathrm{ensuremath{Delta}}$, where $mathrm{ensuremath{Delta}}$ is the BCS gap. There are also 18 bosonic excitations: 4 Nambu-Goldstone modes and 14 massive amplitude Higgs modes. The bosonic modes are labeled by the total angular momentum $Jensuremath{in}{0,1,2}$, and parity under particle-hole symmetry $mathrm{c}=ifmmodepmelsetextpmfi{}1$. For each pair of angular momentum quantum numbers $J,{J}_{z}$, there are two bosonic partners with $mathrm{c}=ifmmodepmelsetextpmfi{}1$. Based on this spectrum, Nambu proposed a sum rule connecting the fermion and boson masses for BCS-type theories, which for $^{3}mathrm{He}text{ensuremath{-}}B$ is ${M}_{J,+}^{2}+{M}_{J,ensuremath{-}}^{2}=4{m}_{F}^{2}$ for each family of bosonic modes labeled by $J$, where ${M}_{J,c}$ is the mass of the bosonic mode with quantum numbers $(J,mathrm{c})$. The Nambu 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 the Nambu 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 $Tensuremath{rightarrow}0$ and $Tensuremath{rightarrow}{T}_{c}$ limits. We also discuss experimental results, and theoretical analysis, for the masses of the ${J}^{text{c}}={2}^{ifmmodepmelsetextpmfi{}}$ Higgs modes and the magnitude of the violation of the NSR." @default.
• W2551933222 created "2016-11-30" @default.
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• W2551933222 date "2017-03-22" @default.
• W2551933222 modified "2023-10-18" @default.
• W2551933222 title "On the Nambu fermion-boson relations for superfluidHe3" @default.
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• W2551933222 doi "https://doi.org/10.1103/physrevb.95.094515" @default.
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