TY - JOUR
T1 - Nambu sum rule in the NJL Models
T2 - From superfluidity to top quark condensation
AU - Volovik, G. E.
AU - Zubkov, M. A.
N1 - Funding Information:
We kindly acknowledge useful remarks by J.D. Bjor ken, D.I. Diakonov, T.W.B. Kibble, F.R. Klinkhamer, S. Nussinov, M.I. Polikarpov, A.M. Polyakov, M. Sha poshnikov, V.I. Shevchenko, T. Vachaspati, M.I. Vy sotsky, and V.I. Zakharov. Wes are very much obliged to V.B. Gavrilov and M.V. Danilov for the explanation of the experimental situation with the search for new par ticles at the LHC. This work was partly supported by the Russian Foundation for Basic Research (project no. 11 02 01227), by the Ministry of Science and Education of the Russian Federation (federal program “Human Capital for Science and Education in Inno vative Russia” and state contract no. 07.514.12.4028, federal program “Research and Development in Pri ority Scientific and Technological Fields in the Rus sian Federation” for 2007–2013). The work of G.E.V. was supported by the Academy of Finland (COE pro gram) and by the EU FP7 program (contract no. 228464 Microkelvin).
PY - 2013/5
Y1 - 2013/5
N2 - It may appear that the recently found resonance at 125 GeV is not the only Higgs boson. We point out the possibility that the Higgs bosons appear in models of top-quark condensation, where the masses of the bosonic excitations are related to the top quark mass by the sum rule similar to the Nambu sum rule of the NJL models [1]. This rule was originally considered by Nambu for superfluid 3He-B and for the BCS model of superconductivity. It relates the two masses of bosonic excitations existing in each channel of Cooper pairing to the fermion mass. An example of the Nambu partners is provided by the amplitude and the phase modes in the BCS model describing Cooper pairing in the s-wave channel. This sum rule suggests the existence of the Nambu partners for the 125 GeV Higgs boson. Their masses can be predicted by the Nambu sum rule under certain circumstances. For example, if there are only two states in the given channel, the mass of the Nambu partner is ∼ 325 GeV. They together satisfy the Nambu sum rule M12 + M22 = 4Mt2, where Mt ∼ 174 GeV is the mass of the top quark. If there are two doubly degenerated states, then the second mass is ∼210 GeV. In this case the Nambu sum rule is 2M12 + 2M22 = 4Mt2. In addition, the properties of the Higgs modes in superfluid 3He-A, where the symmetry breaking is similar to that of the Standard Model of particle physics, suggest the existence of two electrically charged Higgs particles with masses around 245 GeV, which together also obey the Nambu sum rule M+2 + M-2= 4Mt2.
AB - It may appear that the recently found resonance at 125 GeV is not the only Higgs boson. We point out the possibility that the Higgs bosons appear in models of top-quark condensation, where the masses of the bosonic excitations are related to the top quark mass by the sum rule similar to the Nambu sum rule of the NJL models [1]. This rule was originally considered by Nambu for superfluid 3He-B and for the BCS model of superconductivity. It relates the two masses of bosonic excitations existing in each channel of Cooper pairing to the fermion mass. An example of the Nambu partners is provided by the amplitude and the phase modes in the BCS model describing Cooper pairing in the s-wave channel. This sum rule suggests the existence of the Nambu partners for the 125 GeV Higgs boson. Their masses can be predicted by the Nambu sum rule under certain circumstances. For example, if there are only two states in the given channel, the mass of the Nambu partner is ∼ 325 GeV. They together satisfy the Nambu sum rule M12 + M22 = 4Mt2, where Mt ∼ 174 GeV is the mass of the top quark. If there are two doubly degenerated states, then the second mass is ∼210 GeV. In this case the Nambu sum rule is 2M12 + 2M22 = 4Mt2. In addition, the properties of the Higgs modes in superfluid 3He-A, where the symmetry breaking is similar to that of the Standard Model of particle physics, suggest the existence of two electrically charged Higgs particles with masses around 245 GeV, which together also obey the Nambu sum rule M+2 + M-2= 4Mt2.
UR - http://www.scopus.com/inward/record.url?scp=84878118443&partnerID=8YFLogxK
U2 - 10.1134/S0021364013060167
DO - 10.1134/S0021364013060167
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AN - SCOPUS:84878118443
SN - 0021-3640
VL - 97
SP - 301
EP - 306
JO - JETP Letters
JF - JETP Letters
IS - 6
ER -