Higgs self-coupling beta-function in the Standard Model at three loops

Abstract

We present the results for three-loop beta-function for the Higgs self-coupling calculated within the unbroken phase of the Standard Model. We also provide the expression for three-loop beta-function of the Higgs mass parameter, which is obtained as a by-product of our main calculation. Our results coincide with that of recent paper arXiv:1303.2890. In addition, the expression for the Higgs field anomalous dimension is given.

Figures (1)

• Figure 1: For the calculation of the beta-function of the Higgs self-coupling we evaluate all diagrams included in Fig. $a$. For the calculation of the beta-function of the Higgs mass parameter we should insert the mass operator into self-energy diagrams for Higgs fields. Effectively the mass operator is equivalent to the quartic Higgs vertices with two external Higgs fields $[\phi^{+}\phi^{-}]$. All diagrams corresponding to Fig. $b$ should be multiplied by the factor $1/2$.