Search for a stochastic gravitational wave background at 1-5 Hz with Torsion-bar Antenna

We set the first upper limit on the stochastic gravitational wave (GW) background in the frequency range of $1-5\,\mathrm{Hz}$ using a Torsion-bar Antenna (TOBA). A TOBA is a GW detector designed for the detection of low frequency GWs on the ground, with two orthogonal test masses rotated by the incident GWs. We performed a 24-hour observation run using the TOBA and set upper limits, based on frequentist statistics and Bayesian statistics. The most stringent values are $\Omega_\mathrm{gw}h_0^2 \leq 6.0 \times10^{18}$ (frequentist) and $\Omega_\mathrm{gw}h_0^2 \leq 1.2 \times 10^{20}$ (Bayesian) both at $2.58\,\mathrm{Hz}$, where $h_0$ is the Hubble constant in units of $100\,\mathrm{km/s/Mpc}$ and $\Omega_\mathrm{gw}$ is the GW energy density per logarithmic frequency interval in units of the closure density.