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

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