Abstract
We have simulated the SU(4) lattice gauge theory coupled to dynamical fermions in the fundamental and two-index antisymmetric (sextet) representations simultaneously. Such theories arise naturally in the context of composite Higgs models that include a partially composite top quark. We describe the low-lying meson spectrum of the theory and fit the pseudoscalar masses and decay constants to chiral perturbation theory. We infer as well the mass and decay constant of the Goldstone boson corresponding to the nonanomalous U(1) symmetry of the model. Our results are broadly consistent with large-${N}_{c}$ scaling and vector-meson dominance.
Highlights
Gauge theories coupled simultaneously to more than one fermion representation—“multirep” theories—open a new dimension in the study of gauge dynamics
We have simulated the SU(4) lattice gauge theory coupled to dynamical fermions in the fundamental and two-index antisymmetric representations simultaneously
Q2 N2c þ where p is some characteristic exponent determined by large-Nc considerations, and the Qi are a set of expansion coefficients
Summary
Gauge theories coupled simultaneously to more than one fermion representation—“multirep” theories—open a new dimension in the study of gauge dynamics. We have already explored the mesonic and baryonic spectrum of the SU(4) gauge theories with only fundamental [9] or only sextet fermions [10].2 Those results fit nicely into the body of work on QCD and its generalizations to larger values of Nc. The analysis there, similar to QCD studies, related the gauge coupling β and hopping parameter κ to a physical scale r1 (the Sommer scale) and the quark mass mq, and used the latter as an abscissa for plotting particle masses and decay constants. This form of χPT provides formulas for masses, decay constants, and chiral condensates at next-to-leading order, with m4 and m6 as independent variables These formulas contain an important qualitatively new piece of physics compared to QCD—communication between the different species. Appendix D contains a calculation of perturbative Z-factors for the nHYP lattice action with dislocation suppression
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