Differential torsion sensor for direct detection of ultralight vector dark matter

Abstract: Ultralight bosons with masses in the range from $\sim 10^{-22}$ eV/$c^2$ to $\sim 1$ eV/$c^2$, are well-motivated, wave-like dark matter candidates. Particles on the lower-mass end are less explored in experiments due to their vanishingly small mass and weak coupling to the Standard Model. We propose a sensor with dual torsion pendulums for the direct detection of U(1)${B!-!L}$ gauge boson dark matter, which can achieve an enhanced differential torque sensitivity in a frequency band of $\sim 10^{-2}$-$10$ Hz due to its advantages in common-mode rejection and differential angular sensitivity. We describe the design of the differential torsion sensor and present the estimated sensitivity to an ultralight dark matter field coupled to baryon minus lepton ($B!-!L$) number, in a mass range of $\sim 10^{-17}$-$10^{-13}$ eV/$c^2$. Given a setup with meter-scale torsion pendulum beams and kg-scale test masses, the projected constraints on the coupling constant $g{B!-!L}$ can reach $\sim 10^{-27}$ for a boson mass of $\sim 10^{-15}$ eV/$c^2$.