Higgs coupling constants as a probe of new physics

TL;DR

This work analyzes one-loop corrections to the light Higgs couplings to gauge bosons and to itself within a two-Higgs-doublet model. It disentangles tree-level mixing effects from non-decoupling loop contributions of extra Higgs states, showing that the $hZZ$ coupling remains close to SM values while the $hhh$ coupling can deviate dramatically (up to ~100%) due to heavy-Higgs loops, especially when their masses derive mainly from electroweak symmetry breaking. The study uses an on-shell renormalization framework, applies unitarity and vacuum stability constraints, and explores the SM-like regime and mixing-angle dependencies to map the allowed corrections. The findings imply that precise measurements of both $hZZ$ and $hhh$ at future linear colliders can reveal the presence and nature of an extended Higgs sector, including non-decoupling dynamics, and help distinguish between strongly and weakly coupled THDMs.

Abstract

We study new physics effects on the couplings of weak gauge bosons with the lightest CP-even Higgs boson ($h$), $hZZ$, and the tri-linear coupling of the lightest Higgs boson, $hhh$, at the one loop order, as predicted by the two Higgs doublet model. Those renormalized coupling constants can deviate from the Standard Model (SM) predictions due to two distinct origins; the tree level mixing effect of Higgs bosons and the quantum effect of additional particles in loop diagrams. The latter can be enhanced in the renormalized $hhh$ coupling constant when the additional particles show the non-decoupling property. Therefore, even in the case where the $hZZ$ coupling is close to the SM value, deviation in the $hhh$ coupling from the SM value can become as large as plus 100 percent, while that in the $hZZ$ coupling is at most minus 1 percent level. Such large quantum effect on the Higgs tri-linear coupling is distinguishable from the tree level mixing effect, and is expected to be detectable at a future linear collider.

Figures (10)

• Figure 1: The one-loop contribution of the top quark to the effective $hhh$ coupling as a function of $\sqrt{q^2}$, where $q^\mu$ is the momentum of the off-shell $h$ boson in $h^\ast \to hh$. $\Delta\Gamma_{hhh}^{loop}(q^2)$ is defined by $\Gamma_{hhh}(q^2)-\Gamma_{hhh}^{tree}$ in the SM.
• Figure 2: ($\Delta\lambda_{hhh}^{THDM}/\lambda_{hhh}^{SM}$) is shown as a function of $m_{\Phi} (\equiv m_H^{}=m_A^{}=m_{H^\pm}^{})$. The results of the full one loop calculation are shown as solid curves, while the quartic mass ($m^4_{\Phi}$) contributions, given in Eq. (\ref{['m4THDM']}), are plotted as dotted curves.
• Figure 3: The decoupling behavior of ($\Delta\lambda_{hhh}^{THDM}/\lambda_{hhh}^{SM}$) is shown. The mass of the heavy Higgs bosons $m_{\Phi} (\equiv m_H^{}=m_A^{}=m_{H^\pm}^{})$ is given by $m_{\Phi}^2=\lambda v^2+M^2$.
• Figure 4: The momentum dependence of ($\Delta\lambda_{hhh}^{THDM}/\lambda_{hhh}^{SM}$) is shown, where $\sqrt{q^2}$ is the invariant mass of $h^\ast$ in $h^\ast \to hh$, for each value of $m_\Phi^{}$ ($\equiv m_H^{}=m_A^{}=m_{H^\pm}^{}$) when $m_h=120$ GeV, $\sin(\alpha-\beta)=-1$ and $M=0$.
• Figure 5: Deviation of the one loop renormalized (solid curves) and tree level (dotted curves) form factor $M_1^{hZZ}$ from the SM value is shown as a function of $\delta=\cos^2(\alpha-\beta)$ for various $M$ values. The other parameters are set to be $m_h^{}=120$ GeV, $\tan\beta=2$, and $m_H^{}=m_{H^\pm}^{}=m_A^{}=300$ GeV.