U(3)chiral perturbation theory with infrared regularization

We include the ${\eta }^{\prime }$ in chiral perturbation theory without employing ${1/N}_c$ counting rules. The method is illustrated by calculating the masses and decay constants of the Goldstone boson octet $(\pi ,K,\eta )$ and the singlet ${\eta }^{\prime }$ up to one-loop order. The effective Lagrangian describing the interactions of the ${\eta }^{\prime }$ with the Goldstone boson octet is presented up to fourth chiral order and the loop integrals are evaluated using infrared regularization, which preserves Lorentz and chiral symmetry.