An early $Z'$ dominance: dark matter, gravitational waves & collider probes

Author(s)

Barman, Basabendu, Das, Nayan, Paul, Partha Kumar, Sahu, Narendra

Abstract

In the minimal anomaly-free gauged B$-$L extension of the Standard Model (SM), we consider a scenario in which the energy density of the new Abelian gauge boson dominates the Universe prior to big bang nucleosynthesis (BBN), resulting in an early matter-dominated (EMD) era. Taking one of the three right-handed neutrinos to be a decaying dark matter (DM) candidate, we investigate its production during this EMD phase. We show that the region of parameter space consistent with the relic abundance lies within the projected sensitivity of several gravitational wave (GW) experiments, where the GW signal arises from cosmic strings formed during the spontaneous breaking of the gauged B$-$L symmetry. We further constrain the viable parameter space using bounds from collider experiments, beam dump experiments, BBN, and ultra high energy neutrino observations, demonstrating the complementarity of multi-messenger probes in exploring physics beyond the SM as well as non-standard cosmological histories prior to BBN.

Figures

Caption

Feynman diagrams corresponding to DM production from $\zbl$ decay (left) and $\zbl$ mediated scattering of the SM particles in the thermal bath (right).

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Left: Evolution of $\zbl$ (blue), radiation (red dashed), DM (green) energy densities along with bath temperature (red solid) and entropy density (black solid), as a function of the scale factor. In all cases we have considered: $\Mzp=10^{4}~{\rm GeV},\,\gbl\simeq 9\times10^{-9},\,\Hin=7.5\times10^5~\text{GeV},\mdm=100\,\text{GeV}$. Right: Same as top panel, but with $\Mzp=300~{\rm GeV},\,\gbl\simeq1.6\times10^{-9},\,\mdm=100\,\text{GeV}$.

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Left: Evolution of $\zbl$ (blue), radiation (red dashed), DM (green) energy densities along with bath temperature (red solid) and entropy density (black solid), as a function of the scale factor. In all cases we have considered: $\Mzp=10^{4}~{\rm GeV},\,\gbl\simeq 9\times10^{-9},\,\Hin=7.5\times10^5~\text{GeV},\mdm=100\,\text{GeV}$. Right: Same as top panel, but with $\Mzp=300~{\rm GeV},\,\gbl\simeq1.6\times10^{-9},\,\mdm=100\,\text{GeV}$.

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Spectrum of GW from CS for the BPs listed in Table~\ref{tab:BP}. The blue, red, magenta, cyan and gray lines represent the amplitude corresponding to BP0 ($G\mu \sim 1.5\times10^{-19})$, BP3 ($G\mu \sim 2\times10^{-15} $), BP4 ($G\mu \sim 2\times10^{-13} $), BP5 ($G\mu \sim 2\times10^{-11} $), and BP6 ($G\mu \sim 2\times10^{-9} $), respectively. The dashed lines distinguish the amplitude of the GW between the standard radiation domination and EMD. The color shaded regions denote current and future sensitivities of various experiments: LIGO~\cite{LIGOScientific:2014pky}, ET~\cite{Punturo_2010}, CE~\cite{LIGOScientific:2016wof}, DECIGO~\cite{Yagi:2011wg}, ultimate DECIGO ~\cite{Seto:2001qf}, BBO~\cite{Seto:2001qf}, LISA~\cite{LISACosmologyWorkingGroup:2022kbp}, $\mu$ARES~\cite{Sesana:2019vho}, THEIA~\cite{Garcia-Bellido:2021zgu} and SKA~\cite{Weltman:2018zrl}.

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{\it Summary of parameter space:} contours of right DM abundance for $\mdm=100$ GeV, where we have fixed two values of the initial Hubble parameter: $\Hin=7.5\times10^5$ GeV (red solid line) and $\Hin=7.5$ GeV (green solid line). Along the blue shaded contour, the observed DM abundance is satisfied for production during RD. The diagonal gray contours represent SNR value $\mathcal{S}=10$, appearing from different GW experiments. All shaded regions are excluded from different experimental observations, as well as theoretical bounds (see text for details). BP1, BP2, BP3 and BP4, from Table \ref{tab:BP} are shown with black star points.

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Same as Fig.~\ref{fig:relicparam}, but for $\mdm=1$ GeV.

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Same as Fig.~\ref{fig:relicparam}, but for $\mdm=4$ PeV to explain the IceCube neutrino events with a decaying DM.