\beta-function for the Higgs self-interaction in the Standard Model at three-loop level

Abstract

We analytically compute the QCD, electroweak, Higgs and third generation Yukawa contributions to the \beta-function for the Higgs self-coupling as well as for the Higgs mass parameter in the unbroken phase of the Standard Model at three-loop level.

Comments: v2: minor improvements, references added v3: A bug in the numerical analysis is corrected, which changes some terms in Eqs. (3.6), (3.7), (3.9) and (3.10). The overall effect of these terms to the evolution of the Higgs quartic coupling at large scales remains small. The analytical results stay untouched. Three figures are added