RESUMEN
We consider the Sudakov form factor in planar N=4 supersymmetric Yang-Mills theory in the off shell kinematical regime, which can be achieved by considering the theory on its Coulomb branch. We demonstrate that for up to three loops both the infrared-divergent as well as the finite terms do exponentiate, with the coefficient accompanying log^{2}(m^{2}) determined by the octagon anomalous dimension Γ_{oct}. This behavior is in stark contrast to previous conjectural accounts in the literature. Together with the finite terms we observe that for up to three loops the logarithm of the Sudakov form factor is identical to twice the logarithm of the null octagon O_{0}, which was recently introduced within the context of integrability-based approaches to four point correlation functions with infinitely large R charges. The null octagon O_{0} is known in a closed form for all values of the 't Hooft coupling constant and kinematical parameters. We conjecture that the relation between O_{0} and the off shell Sudakov form factor will hold to all loop orders.
RESUMEN
We perform a manifestly gauge-independent analysis of the vacuum stability in the standard model including two-loop matching, three-loop renormalization group evolution, and pure QCD corrections through four loops. All these ingredients are exact, except that light-fermion masses are neglected. We in turn apply the criterion of nullifying the Higgs self-coupling and its beta function in the modified minimal-subtraction scheme and a recently proposed consistent method for determining the true minimum of the effective Higgs potential that also avoids gauge dependence. Exploiting our knowledge of the Higgs-boson mass, we derive an upper bound on the pole mass of the top quark by requiring that the standard model be stable all the way up to the Planck mass scale and conservatively estimate the theoretical uncertainty. This bound is compatible with the Monte Carlo mass quoted by the Particle Data Group at the 1.3σ level.
