Dark matter constraints on low mass and weakly coupled <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mo>−</mml:mo><mml:mi>L</mml:mi></mml:math> gauge boson

Abstract

We investigate constraints on the new $B\ensuremath{-}L$ gauge boson (${Z}_{BL}$) mass and coupling (${g}_{BL}$) in a $U(1{)}_{B\ensuremath{-}L}$ extension of the standard model (SM) with an SM singlet Dirac fermion ($\ensuremath{\zeta}$) as dark matter (DM). The DM particle $\ensuremath{\zeta}$ has an arbitrary $B\ensuremath{-}L$ charge $Q$ chosen to guarantee its stability. We focus on the small ${Z}_{BL}$ mass and small ${g}_{BL}$ regions of the model, and find new constraints for the cases where the DM relic abundance arises from thermal freeze-out as well as freeze-in mechanisms. In the thermal freeze-out case, the dark matter coupling is given by ${g}_{\ensuremath{\zeta}}\ensuremath{\equiv}{g}_{BL}Q\ensuremath{\simeq}0.016\sqrt{{m}_{\ensuremath{\zeta}}[\mathrm{GeV}]}$ to reproduce the observed DM relic density and ${g}_{BL}\ensuremath{\ge}2.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}\sqrt{{m}_{\ensuremath{\zeta}}[\mathrm{GeV}]}$ for the DM particle to be in thermal equilibrium prior to freeze-out. Combined with the direct dark matter detection constraints and the indirect constraints from cosmic microwave background and AMS-02 measurements, discussed in earlier papers, we find that the allowed mass regions are limited to be ${m}_{\ensuremath{\zeta}}\ensuremath{\gtrsim}200\text{ }\text{ }\mathrm{GeV}$ and ${M}_{{Z}_{BL}}\ensuremath{\gtrsim}10\text{ }\text{ }\mathrm{GeV}$. We then discuss the lower ${g}_{BL}$ values where the freeze-in scenario operates and find the following relic density constraints on parameters depending on the ${g}_{BL}$ range and dark matter mass: Case (A): for ${g}_{BL}\ensuremath{\ge}2.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}\sqrt{{m}_{\ensuremath{\zeta}}[\mathrm{GeV}]}$, one has ${g}_{\ensuremath{\zeta}}^{2}{g}_{BL}^{2}+\frac{0.82}{1.2}{g}_{\ensuremath{\zeta}}^{4}\ensuremath{\simeq}8.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}$; and Case (B): for ${g}_{BL}&lt;2.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}\sqrt{{m}_{\ensuremath{\zeta}}[\mathrm{GeV}]}$, there are two separate constraints depending on ${m}_{\ensuremath{\zeta}}$. Case (B1): for ${m}_{\ensuremath{\zeta}}\ensuremath{\lesssim}2.5\text{ }\text{ }\mathrm{TeV}$, we find ${g}_{\ensuremath{\zeta}}^{2}{g}_{BL}^{2}\ensuremath{\simeq}8.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}(\frac{{m}_{\ensuremath{\zeta}}}{2.5\text{ }\text{ }\mathrm{TeV}})$; and Case (B2): for ${m}_{\ensuremath{\zeta}}\ensuremath{\gtrsim}2.5\text{ }\text{ }\mathrm{TeV}$, we have ${g}_{\ensuremath{\zeta}}^{2}{g}_{BL}^{2}\ensuremath{\simeq}8.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}$. For this case, we display the various parameter regions of the model that can be probed by a variety of ``Lifetime Frontier'' experiments such as FASER, FASER2, Belle II, SHiP, and LDMX.

Topics & Concepts