Meson-meson scattering in the quark model: Spin dependence and exotic channels

We apply a quark interchange model to spin-dependent and exotic meson-meson scattering. The model includes the complete set of standard quark model forces, including one-gluon exchange spin orbit and tensor and scalar confinement spin orbit. Scattering amplitudes derived assuming simple harmonic oscillator (SHO) and Coulomb plus linear plus hyperfine meson wave functions are compared. In $I=2\mathrm{}$ $\pi \pi$ we find approximate agreement with the S-wave phase shift from threshold to 1.5 GeV, where we predict an extremum that is supported by the data. Near threshold we find a rapid energy dependence that may reconcile theoretical estimates of small scattering lengths with experimental indications of larger ones based on extrapolation of measurements at moderate $k_{\pi }^2.$ In pseudoscalar-vector scattering we find that the quark-quark $L\cdot S$ and T forces map onto $L\cdot S$ and T meson-meson interactions, and the P-wave $L\cdot S$ force is large. Finally we consider scattering in $J^{{\mathrm{PC}}_n}$ exotic channels, and note that some of the “Deck effect” mechanisms suggested as possible nonresonant origins of the ${\pi }_1\mathrm{}\left(1400\right)\mathrm{}$ signal are not viable in this model.