Abstract
Abstract We present analytical results for the QCD β-function extended to the gaugeless limit of the unbroken phase of the Standard Model at four-loop level. Apart from the strong coupling itself we include the top-Yukawa contribution and the Higgs self-coupling. We observe a numerically small non-naive γ 5 contribution at order y t 4 g s 4 , a feature not encountered in lower loop orders. We discuss the treatment of γ5 which is more involved than in previous calculations at three-loop level.
Highlights
The evolution of the quartic Higgs self-coupling has received a lot of interest because of its close connection to the question of vacuum stability in the Standard Model
We present analytical results for the QCD β-function extended to the gaugeless limit of the unbroken phase of the Standard Model at four-loop level
In this paper we extend the QCD β-function to the gaugeless limit of the SM, i.e. we include the dependence on the top-Yukawa coupling yt and the quartic Higgs self-coupling λ
Summary
2.1 Gaugeless limit of the SM The Lagrangian of the SM in the unbroken phase can be decomposed into. The scalar part LΦ contains the kinetic term for the scalar field Φ, its potential and its coupling to the electroweak gauge bosons through the covariant derivative. In the gaugeless limit we neglect two smaller gauge couplings g2 and g1 (electroweak sector). The left- and right-handed parts of the quark fields and vertices participating in the Yukawa interaction are renormalized differently. ΔLYukawa = −δZ1(tbΦ)yt (tPRt) Φ∗2 + (tPLt) Φ2 − ̄bPRt Φ∗1 − (tPLb) Φ1 , δLΦ = δZ2(2Φ)∂μΦ†∂μΦ − m2 δZΦ2 Φ†Φ + δZ1(4Φ). All these renormalization constants were computed at three-loop level in the course of the calculations in [5].
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