Quantum Chromodynamics with Eight and Twelve Degenerate Quark Flavors on the Lattice

About this book

This thesis is concerned with the behavior of non-abelian gauge theories with many flavors of fermions. In perturbation theory, an infrared fixed point is predicted to exist, and theories become conformal in the low energy limit, in non-abelian gauge theories with the number of fermions just below the threshold of losing asymptotic freedom. With the number of fermion flavors even smaller than the number required for conformal behavior, the coupling constant is expected to run slowly or "walk". However, the exact number of fermion flavors that is required for the conformal behavior is unknown. This thesis probes for non-perturbative evidence for such behavior by simulating SU(3) gauge theories on the lattice with eight and twelve degenerate fermions in the fundamental representation. The naive staggered fermion action with the DBW2 gauge action is used in the simulations. The exact RHMC algorithm with the Omelyan integrator is used for simulating all eight-flavor gauge configurations and twelve-flavor gauge configurations with large masses, mq ≥ 0.01. For the other twelve-flavor simulations with smaller masses, mq transition. All the evidences gathered in this thesis support the argument that theories of both eight and twelve flavors of fermion in the fundamental representation of SU(3) gauge group are consistent with the behavior one would expected from a theory with spontaneously broken chiral symmetry. The strongest supporting evidence is the linearity of mÏ€2 ∝ mq at zero temperatures and the existence of a chiral symmetry restoring transition at finite temperatures. We note that other lattice simulations, also exploring the hadronic observables, arrive at a similar conclusion, while simulations of the running of the coupling have claimed that the 12 flavor theory is conformal.