Infrared fixed point of SU(2) gauge theory with six flavors

Abstract

We compute the running of the coupling in SU(2) gauge theory with six fermions in the fundamental representation of the gauge group. We find a strong evidence that this theory has an infrared stable fixed point at strong coupling and measure also the anomalous dimension of the fermion mass operator at the fixed point. This theory therefore likely lies close to the boundary of the conformal window and will display novel infrared dynamics if coupled with the electroweak sector of the Standard Model.

Infrared Behaviour of SU(2) Gauge Theory with $N_f$ fundamental flavours

“…Because of the finite size effects and poor signal at the IRFP caused by g 2 GF − g 2 * ∼ 0, exact numbers cannot be extracted using this method. On the right side of Fig 2 we present this method for the N f = 6 model and we can see that the finite-size scaling method develops a maximum that agrees with the measurement obtained from the slope of the β -function [9,10].…”

“…We do not plot the recent 5-loop result [18] as not only does it not have an IRFP with these numbers of fermions, it also develops two separate conformal windows in SU(2) models clearly indicating a breaking of perturbation theory at high couplings [9]. As can be seen from Fig 1, the N f = 6 theory has an IRFP at g 2 * = 14.5(4) +0.4 −1.2 [9] and the N f = 8 theory has an IRFP at g 2 * = 8.24(59) +0.97 −1.64 [8]. Here the first set of errors is the statistical error for the chosen set of discretizations and the second set gives the variation between different discretization choices.…”

“…τ 0 defines an empirical O(a 2 ) improvement for the gradient flow coupling [16]. We choose τ 0 = 0.025log(1+2g 2 GF ) for N f = 6 [9] and τ 0 = 0.06log(1+g 2 GF ) for N f = 8 [8]. In [10] we employ alternative O(a 2 ) improvement by combining clover and plaquette measurements of E(t) with empirical coefficient X [17].…”

Phase of confined electroweak force in the early Universe

“…A theory with N f < 11 has β g < 0, and this perturbative analysis suggests that such a theory is strongly coupled in the IR; that is, g 2 /4π grows as large as 4π as the energy scale decreases toward Λ W . This perturbative analysis is confirmed by numerical lattice studies for small N f while N f = 6 is marginal and near the conformal window [28][29][30][31][32].…”

“…However, this simple model has been studied using non-perturbative, numerical lattice techniques [33,34] for N f = 2 (see also Refs. [28][29][30][31][32]). Those studies conclude that SU(2N f ) ψ is broken to Sp(2N f ) ψ , which is the naive expectation from chiral symmetry breaking in analogy with QCD [35,36].…”