One loop corrections to the trilinear self coupling of the Higgs boson in the standard model with inclusion of singlet vector-like top quark

TL;DR

The paper computes the full one-loop corrections to the Higgs trilinear self-coupling in the SM using the zero external momentum (effective potential) approach, obtaining $Γ^{ m{SMoneloop}}_{HHH}$ and the modifier $κ_λ$ with $Γ^{ m{SMoneloop}}_{HHH} = λ_{HHH} + rac{1}{(4π)^2}[... ]$ and $κ_λ = Γ^{ m{SMoneloop}}_{HHH} / λ_{HHH}$; numerically, $Γ^{ m{SMoneloop}}_{HHH} = 175.89$ GeV and $κ_λ = 0.92$ at $μ = m_t$. The study then extends the SM by including a singlet vector-like top partner that mixes with the SM top and derives the one-loop contributions to $κ_λ$ as functions of the partner mass $M_T$ and mixing angle $θ_L$, yielding the full $Γ^{ m{SM+VLQ}}_{HHH}$ in the $ar{MS}$ scheme. Using updated ATLAS bounds on $κ_λ$, the authors map the allowed region in the $M_T$–$s_L$ plane and find an upper bound on $M_T$ of about $2.8$ TeV for plausible mixing, consistent with a perturbative unitarity constraint $M_T \\lesssim 3.4$ TeV at $s_L=0.40$. The work highlights the potential of precision Higgs self-coupling measurements to constrain vector-like quarks and outlines avenues for extending the analysis to more general VLQ representations and higher-order corrections.

Abstract

The complete one loop corrections to the trilinear self coupling of the Higgs boson is firstly evaluated in the Standard Model (SM) by employing the zero momentum approximation. Numerical results of the trilinear self coupling and its modifier $κ_λ$ are obtained. Then we extend the SM by including a singlet vector-like top partner and assume that the top partner only mixes with the top quark, combining with the latest value of the Higgs boson trilinear self coupling modifier $κ_λ$ reported by ATLAS Collaboration, the effects of the mass of the top partner and the mixing parameter on the modifier $κ_λ$ are systematically analyzed. Results indicate that the upper bound of the singlet top partner is about $2800$\,GeV.

Figures (9)

• Figure 1: Three cases in evaluating the trilinear self coupling of the Higgs boson. In diagram (a), there is only one off-shell line in the trilinear self coupling vertex, in diagram (b), there may be two or three off-shell lines in the trilinear self coupling.
• Figure 2: The tree level trilinear self coupling of the Higgs boson in the SM.
• Figure 3: The top quark loop corrections to the trilinear self coupling of the Higgs in the SM.
• Figure 4: The vector boson one loop corrections to the trilinear self coupling of the Higgs boson in the SM, where $V=W,\,Z^{0}$. Diagram (a), there is only $\lambda_{HVV}$ vertex, while diagram (b) there are both $\lambda_{HVV}$ and $\lambda_{HHVV}$ vertexes.
• Figure 5: The Higgs loop corrections to the trilinear self coupling of the Higgs. Diagram (a), there is only trilinear self coupling of the Higgs boson, while in diagram (b), there are both trilinear and quartic self couplings of the Higgs boson.