Asymptotically free four-Fermi theory in 4 dimensions at the z=3 Lifshitz-like fixed point
- Department of Theoretical Physics, Tata Institute of Fundamental Research, Mumbai 400 005 (India)
We show that a Nambu-Jona-Lasinio type four-fermion coupling at the z=3 Lifshitz-like fixed point in 3+1 dimensions is asymptotically free and generates a mass scale dynamically. This result is nonperturbative in the limit of a large number of fermion species. The theory is ultraviolet complete and at low energies exhibits Lorentz invariance as an emergent spacetime symmetry. Many of our results generalize to z=d in odd d spatial dimensions; z=d=1 corresponds to the Gross-Neveu model. The above mechanism of mass generation has potential applications to the fermion mass problem and to dynamical electroweak symmetry breaking. We present a scenario in which a composite Higgs field arises from a condensate of these fermions, which then couples to quarks and leptons of the standard model. Such a scenario could eliminate the need for the Higgs potential and the associated hierarchy problem. We also show that the axial anomaly formula at z=3 coincides with the usual one in the relativistic domain.
- OSTI ID:
- 21313408
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 80, Issue 10; Other Information: DOI: 10.1103/PhysRevD.80.105018; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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MASS
POTENTIALS
QUARKS
RELATIVISTIC RANGE
SIMULATION
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STANDARD MODEL
SYMMETRY
SYMMETRY BREAKING
WEINBERG-SALAM GAUGE MODEL