Chiral Perturbation Theory for Tensor Mesons

Interactions of $a_2,K_2^{\ast },f_2$ and $f_2^{\mathrm{\prime }}$ tensor-mesons with low-energy $\pi ,K,\eta ,{\eta }^{\mathrm{\prime }}$ pseudo-scalar mesons are constrained by chiral symmetry. We derive a chiral Lagrangian of tensor mesons in which the tensor mesons are treated as heavy non-relativistic matter fields. Using $1\mathrm{/}{N}_c$ counting, we derive relations among unknown couplings of the chiral Lagrangian. Chiral perturbation theory is applied to the tensor-meson mass matrix. At one-loop there are large corrections to the individual tensor meson masses, but the singlet-octet mixing angle remains almost unchanged. We argue that all heavy mesons of spin $\ge 1$ share common feature of chiral dynamics.