We consider a model in which Goldstone bosons, described by a SU(N) chiral nonlinear σ model, are coupled to an N-plet of colored fermions by means of a Yukawa interaction. We study the one-loop renormalization group flow and show that the non-Gaussian UV fixed point, which is present in the purely bosonic model, is lost because of fermion loop effects unless N is sufficiently large. We then add four-fermion contact interactions to the Lagrangian and show that in this case there exist several non-Gaussian fixed points. The strength of the contact interactions, predicted by the requirement that the theory flows towards a fixed point in the UV, is compared to the current experimental bounds. This toy model could provide an important building block of an asymptotically safe model of the weak interactions.

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Persistent URL dx.doi.org/10.1016/j.physletb.2011.10.029
Journal Physics Letters B
Citation
Bazzocchi, F. (F.), Fabbrichesi, M. (M.), Percacci, R. (R.), Tonero, A, & Vecchi, L. (L.). (2011). Fermions and Goldstone bosons in an asymptotically safe model. Physics Letters B, 705(4), 388–392. doi:10.1016/j.physletb.2011.10.029