Abstract
We present a lattice study of a Nambu Jona-Lasinio (NJL) model using Wilson fermions. Four fermion interactions are a natural part of several extensions of the Standard Model, appearing as a low energy description of a more fundamental theory. In models of dynamical electroweak symmetry breaking they are used to endow the Standard Model fermions with masses. In infrared conformal models these interaction, when sufficiently strong, can alter the dynamics of the fixed point, turning the theory into a (near) conformal model with desirable features for model building. As a first step toward the nonperturbative study of these models, we study the phase space of the ungauged NJL model.
Highlights
It has been recently shown that gauge Yukawa theories, similar to the Standard Model, even when manifestly perturbative, can abide compositeness conditions [1].1 It was shown that, in certain regions of the gauge Yukawa parameter space, the Higgs-like state is not a propagating degree of freedom at high energies but a low-energy manifestation of an effective four-fermion interaction
We have studied the phase space of the Nambu–JonaLasinio model with Wilson fermions
By measuring the expectation values of the auxiliary fields hσi and hπi, related respectively to the chiral condensate and a flavorparity breaking condensate, we were able to identify the critical lines with zero quark mass
Summary
It has been recently shown that gauge Yukawa theories, similar to the Standard Model, even when manifestly perturbative, can abide compositeness conditions [1].1 It was shown that, in certain regions of the gauge Yukawa parameter space, the Higgs-like state is not a propagating degree of freedom at high energies but a low-energy manifestation of an effective four-fermion interaction. [19] bypassed these hurdles by constructing a successful example of partial compositeness that makes use of both TC fermions and TC scalars The dynamics of these theories is that large anomalous dimensions are no longer needed, one can give masses to all the fermions of the Standard Model, no new model building is required, and they greatly widen the spectrum of theories to investigate on the lattice. According to Holdom [20], a model of walking dynamics with a large mass anomalous dimension can enhance the SM fermion mass term dynamically It was later suggested [21] that walking dynamics could be achieved by having the third, Nambu–Jona-Lasinio (NJL) type, term induce chiral symmetry breaking in an otherwise infrared conformal technicolor model [21,22]. This work is a necessary initial step towards a systematic study of four-fermion interactions and their impact on models of dynamical symmetry breaking
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