2017/09/30 by Yannick Meurice, Y. Meurice · 16 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Fermion #Gauge theory #Lattice (music) #Mathematical physics #Particle physics #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Sigma model #U-1 #hep-lat #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.96.114507
published in Physical review. D/Physical review. D. 96(11) (American Physical Society) · 6 pages, 2 figures, uses revtex, references added
arxiv created 2017/11/01 · openalex publication_date 2017/12/11 · arxiv updated 2017/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We consider a linear sigma model describing 2Nf2 bosons (\ensuremathσ, a0, \ensuremathη^\ensuremath' and \mathbf\ensuremathπ) as an approximate effective theory for a SU(3) local gauge theory with Nf Dirac fermions in the fundamental representation. The model has a renormalizable U(Nf)L\ensuremath\bigotimesU(Nf)R invariant part, which has an approximate O(2Nf2) symmetry, and two additional terms, one describing the effects of a SU(Nf)V invariant mass term and the other the effects of the axial anomaly. We calculate the spectrum for arbitrary Nf. Using preliminary and published lattice results from the LatKMI collaboration, we found combinations of the masses that vary slowly with the explicit chiral symmetry breaking and Nf. This suggests that the anomaly term plays a leading role in the mass spectrum and that simple formulas such as M_\ensuremathσ2\ensuremath≃(2/Nf\ensuremath-C_\ensuremathσ)M_\ensuremathη^\ensuremath'2 should apply in the chiral limit. Lattice measurements of M_\ensuremathη^\ensuremath'2 and of approximate constants such as C_\ensuremathσ could help in locating the boundary of the conformal window. We show that our calculation can be adapted for arbitrary representations of the gauge group and in particular to the minimal model with two sextets, where similar patterns are likely to apply.