Extended investigation of the twelve-flavor β-function

Zoltán Fodor,Kieran Holland,Julius Kuti,Dániel Nógrádi,Chik Him Wong

doi:10.1016/j.physletb.2018.02.008

Abstract

We report new results from high precision analysis of an important BSM gauge theory with twelve massless fermion flavors in the fundamental representation of the SU(3) color gauge group. The range of the renormalized gauge coupling is extended from our earlier work [1] to probe the existence of an infrared fixed point (IRFP) in the β-function reported at two different locations, originally in [2] and at a new location in [3]. We find no evidence for the IRFP of the β-function in the extended range of the renormalized gauge coupling, in disagreement with [2,3]. New arguments to guard the existence of the IRFP remain unconvincing [4], including recent claims of an IRFP with ten massless fermion flavors [5,6] which we also rule out. Predictions of the recently completed 5-loop QCD β-function for general flavor number are discussed in this context.

Highlights

We report new results from high precision analysis of an important BSM gauge theory with twelve massless fermion flavors in the fundamental representation of the SU(3) color gauge group
The relocation of the infrared fixed point (IRFP) followed the announcement of a new IRFP with ten massless fermion flavors in the fundamental representation of the SU(3) color gauge group [5, 6]
The claim in [5, 6] would imply that the theory with twelve flavors must be conformal and the lower edge of the conformal window (CW) of multi-flavor BSM theories with fermions in the fundamental representation would be located below ten flavors

Summary

History of the IRFP with 12 massless fermions

A conformal infrared fixed point (IRFP) of the β-function was reported earlier with critical gauge coupling g2∗ ≈ 6.2 and interpreted as conformal behavior of the much studied BSM gauge theory with twelve massless fermions in the fundamental representation of the SU(3) color gauge group [2]. This result was claimed to confirm the original finding of the IRFP in [7, 8].

Scale-dependent β-function on the lattice

High precision twelve-flavor analysis in large volumes

Ten-flavor preview with conclusions