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Non-adiabatic evolution of dark sector in the presence of $U(1)_{L_μ-L_τ}$ gauge symmetry

In secluded dark sector scenario, the connection between the visible and the dark sector can be established through a portal coupling and its presence opens up the possibility of non-adiabatic evolution of the dark sector. To study the non-adiabatic evolution of the dark sector, we have considered a $U(1)_{L_μ- L_τ} \otimes U(1)_X$ extension of the standard model (SM). Here the dark sector is charged only under $U(1)_X$ gauge symmetry whereas the SM fields are singlet under this symmetry. Due to the presence of tree-level kinetic mixing between $U(1)_X$ and $U(1)_{L_μ- L_τ}$ gauge bosons, the dark sector evolves non-adiabatically and thermal equilibrium between the visible and dark sector is governed by the portal coupling. Depending on the values of the portal coupling ($ε$), dark sector gauge coupling ($g_X$), mass of the dark matter ($m_χ$) and mass of the dark vector boson ($m_{Z^\prime}$), we study the temperature evolution of the dark sector as well as the various non-equilibrium stages of the dark sector in detail. Furthermore we have also investigated the constraints on the model parameters from various laboratory and astrophysical searches. We have found that the parameter space for the non-adiabatic evolution of dark sector is significantly constrained for $m_{Z^\prime}$ $\lesssim 100 \, {\rm MeV}$ from the observations of beam dump experiments, stellar cooling etc. The relic density satisfied region of our parameter space is consistent with the bounds from direct detection, and self interaction of dark matter (SIDM) for the mass ratio $r \equiv m_{Z^\prime}/m_χ= 10^{-3}$ and these bounds will be more relaxed for larger values of $r$. However the constraints from measurement of diffuse $γ$-ray background flux and cosmic microwave background (CMB) anisotropy are strongest for $r = 10^{-1}$ and for smaller values of $r$, they are not significant.