TY - JOUR
T1 - Light scalars in strongly-coupled extra-dimensional theories
AU - Del Debbio, Luigi
AU - Hart, Alistair
AU - Rinaldi, Enrico
N1 - 38 pages (7 pages of Appendix), 10 tables, 21 figures. Minor corrections. Version accepted for publication in JHEP
PY - 2012/7/30
Y1 - 2012/7/30
N2 - The low-energy dynamics of five-dimensional Yang-Mills theories compactified on S^1 can be described by a four-dimensional gauge theory coupled to a scalar field in the adjoint representation of the gauge group. Perturbative calculations suggest that the mass of this elementary scalar field is protected against power divergences, and is controlled by the size of the extra dimension R. As a first step in the study of this phenomenon beyond perturbation theory, we investigate the phase diagram of a SU(2) Yang-Mills theory in five dimensions regularized on anisotropic lattices and we determine the ratios of the relevant physical scales. The lattice system shows a dimensionally reduced phase where the four-dimensional correlation length is much larger than the size of the extra dimension, but still smaller than the four-dimensional volume. In this region of the bare parameter space, at energies below 1/R, the non-perturbative spectrum contains a \emph{light} scalar state. This state has a mass that is independent of the cut-off, and a small overlap with glueball operators. Our results suggest that light scalar fields can be introduced in a lattice theory using compactified extra dimensions, rather than fine tuning the bare mass parameter.
AB - The low-energy dynamics of five-dimensional Yang-Mills theories compactified on S^1 can be described by a four-dimensional gauge theory coupled to a scalar field in the adjoint representation of the gauge group. Perturbative calculations suggest that the mass of this elementary scalar field is protected against power divergences, and is controlled by the size of the extra dimension R. As a first step in the study of this phenomenon beyond perturbation theory, we investigate the phase diagram of a SU(2) Yang-Mills theory in five dimensions regularized on anisotropic lattices and we determine the ratios of the relevant physical scales. The lattice system shows a dimensionally reduced phase where the four-dimensional correlation length is much larger than the size of the extra dimension, but still smaller than the four-dimensional volume. In this region of the bare parameter space, at energies below 1/R, the non-perturbative spectrum contains a \emph{light} scalar state. This state has a mass that is independent of the cut-off, and a small overlap with glueball operators. Our results suggest that light scalar fields can be introduced in a lattice theory using compactified extra dimensions, rather than fine tuning the bare mass parameter.
KW - hep-lat
KW - hep-ph
U2 - 10.1007/JHEP07(2012)178
DO - 10.1007/JHEP07(2012)178
M3 - Article
VL - 2012
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
SN - 1126-6708
IS - 7
M1 - 178
ER -