Abstract
We investigate the renormalization group flow of the field-dependent Yukawa coupling in the framework of the three flavor quark-meson model. In a conventional perturbative calculation, given that the field rescaling is trivial, the Yukawa coupling does not get renormalized at the one-loop level if it is coupled to an equal number of scalar and pseudoscalar fields. Its field-dependent version, however, does flow with respect to the scale. Using the functional renormalization group technique, we show that it is highly nontrivial how to extract the actual flow of the Yukawa coupling as there are several new chirally invariant operators that get generated by quantum fluctuations in the effective action, which need to be distinguished from that of the Yukawa interaction.
Highlights
One of the merits of the functional renormalization group (FRG) technique is that it allows for calculating the flows of n-point functions nonperturbatively
For the sake of an example, in scalar ðφÞ theories, quantum corrections to the wave function renormalization (Z) typically vanish at the one-loop level, but using the FRG one gets a nonzero contribution once one generalizes the corresponding kinetic term in the effective action as ∼ZðφÞ∂μφ∂μφ and evaluates Z at a symmetry breaking stationary point of the effective action. This procedure is essential, e.g., in two-dimensional systems that undergo topological phase transitions, as the wave function renormalization is known to be diverging in the low temperature phase, which cannot be described in terms of perturbation theory [4]
We raised the question of determining the field dependence of the Yukawa coupling in the three flavor quark-meson model
Summary
One of the merits of the functional renormalization group (FRG) technique is that it allows for calculating the flows of n-point functions nonperturbatively. For the sake of an example, in scalar ðφÞ theories, quantum corrections to the wave function renormalization (Z) typically vanish at the one-loop level, but using the FRG one gets a nonzero contribution once one generalizes the corresponding kinetic term in the effective action as ∼ZðφÞ∂μφ∂μφ and evaluates Z at a symmetry breaking stationary point of the effective action. The essence of the corresponding calculations is that one determines the RG flow of the fermion-fermionmeson proper vertex, defined as δ3Γ=δLψδRψδφ in a given background (Γ being the effective action), and associates it with the flow of the Yukawa coupling itself This obviously works for one flavor models [7,8], and even for the two flavor case [9,10], in particular for models restricted to the σ − π subsector, i.e., with Oð4Þ symmetry in the meson part of the theory. Here we offer a renormalization procedure of the field-dependent Yukawa coupling realizable in any symmetry breaking background through a chirally invariant set of operators.
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