Constraining scalar-tensor theories by neutron star-balck hole gravitational wave events

With the continuous upgrade of detectors, more and more gravitational wave (GW) events were captured by the LIGO Scientific Collaboration and Virgo Collaboration (LVC), which offers a new avenue to test General Relativity and explore the nature of gravity. Although, various model-independent tests have been performed by LVC in previous works, it is still interesting to ask what constraints on specific models can be placed by current GW observations. In this work, we focus on three models of scalar-tensor theories, the Brans-Dicke theory (BD), the theory with scalarization phenomena proposed by Damour and Esposito-Far\`{e}se (DEF), and Screened Modified Gravity (SMG). From all 4 possible NSBH events so far, we use two of them to place the constraints. The other two are excluded in this work due to the possible unphysical deviations. We consider the inspiral range with the cutoff frequency at the innermost stable circular orbit and add a modification of dipole radiation into the waveform template. The scalar charges of neutron stars in the dipole term are derived by solving the Tolman-Oppenheimer-Volkoff equations for different equations-of-states. The constraints are obtained by performing the full Bayesian inference with the help of the open source software \texttt{Bilby}. The results show that the constraints given by GWs are comparable with those given by pulsar timing experiments for DEF theory, but are not competitive with the current solar system constraints for BD and SMG theories.