Kinetic mixing between a Higgs boson and a nearly degenerate dark scalar: Oscillations and displaced vertices

Extensions beyond the standard model allow for a gauge singlet scalar to be kinetically coupled with the Higgs. We consider kinetic mixing between a dark scalar gauge singlet nearly degenerate with the Higgs, focusing on the dynamical aspects of the mixing phenomena. The renormalization program is carried out by obtaining the one-loop effective action which yields an effective non-Hermitian Hamiltonian to study the dynamics of mixing. The scalar Higgs becomes a coherent superposition of the mass eigenstates, thus kinetic mixing leads to oscillations and common decay channels in striking similarity with neutral meson mixing. Near degeneracy yields an enhancement of the kinetic coupling. For small kinetic mixing we find that the mass eigenstates feature different lifetimes which result in a wide separation of time scales of evolution along with important coherence aspects from dark scalar-Higgs interference. The wide separation of scales is manifest as displaced decay vertices which could potentially be a telltale experimental signal of kinetic mixing.

Figure 1

${\mathcal{P}}_{\varphi \to \varphi }(t)$, the solid line corresponds to ${ϵ}_R={10}^{-3},\eta =2\times {10}^{-3}$, the dashed line shows Higss decay without mixing (${ϵ}_R=0$). The rightmost figure displays the dynamics on the longest time scale. The lowest figure displays ${\mathcal{P}}_{\varphi \to \chi }(t)$.

Figure 2

$\ln ({\mathcal{P}}_{\varphi \to \varphi }(t))$, the solid line corresponds to ${ϵ}_R={10}^{-3},\eta =2\times {10}^{-3}$, the dashed line shows Higss decay without mixing (${ϵ}_R=0$).

Figure 3

$\ln ({\mathcal{P}}_{\varphi \to \varphi }(t))$, the solid line corresponds to ${ϵ}_R={10}^{-3},\eta =0.077$, corresponding $M_{\chi }=135\mathrm{GeV}$, $g_1^1\simeq 2\times {10}^{-9},g_2^2\simeq 4\times {10}^{-5}$, the dashed line shows Higss decay without mixing (${ϵ}_R=0$). At early times the Higgs-like mode dominates, at intermediate times the interference between Higgs and dark-like modes dominates and the dark-like mode dominates at late times (see text).