CMT150
On Nambu's Fermion-Boson Relations for Superfluid 3He
- Author(s):
J. A. Sauls and Takeshi Mizushima
- Address: Department of Physics & Astronomy, Northwestern University, Evanston, IL 60208
- Date: November 22, 2016
- Journal:
Physical Review B 95, 094515 (2017)
[arXiv]
[DOI]
[PDF]
- Abstract:
Superfluid 3He 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)×
SO(3)→
SO(3).
The Fermions acquire mass, m ≡ ∆, 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,Jz, 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
3He-B is M2 + M2 = 4m2
for each family of Bosonic modes labeled by J, where
M
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→ Tc limits.
We also discuss experimental results, and theoretical analysis, for the masses of the Jc=2±
Higgs modes and the magnitude of the violation of the NSR.
- Comment: 20 pages, 5 figures
- Eprint:
[PDF]
[arXiv]
Return to index