We have systematically studied the S-wave pseudoscalar meson and heavy vector meson scattering lengths to the third order with the chiral perturbation theory, which will be helpful to reveal their strong interaction. For comparison, we have presented the numerical results of the scattering lengths (1) in the framework of the heavy meson chiral perturbation theory and (2) in the framework of the infrared regularization. The chiral expansion converges well in some channels.

10 pages, 1 figures, 4 tables. Corrected typos, Improved numerical results, and More dicussions. Accepted for publication by Phys.Rev.D