Abstract
We investigate some higher-loop structural properties of the function in asymptotically free vectorial gauge theories. Our main focus is on theories with fermion contents that lead to an infrared (IR) zero in . We present analytic and numerical calculations of the value of the gauge coupling where reaches a minimum, the value of at this minimum, and the slope of at the IR zero, at two-, three-, and four-loop order. The slope of at the IR zero is relevant for estimates of a dilaton mass in quasiconformal gauge theories. Some inequalities are derived concerning the dependence of the above quantities on loop order. A general inequality is derived concerning the dependence of the shift of the IR zero of , from the -loop to the ()-loop order, on the sign of the ()-loop coefficient in . Some results are also given for gauge theories with supersymmetry.
- Received 14 January 2013
DOI:https://doi.org/10.1103/PhysRevD.87.105005
© 2013 American Physical Society