Effect of2−BExchange in theπωChannel on the Parameters of theρ

We have considered the question of whether the inclusion of the attractive force in the coupled $\pi \omega$ channel due to the exchange of a $2^{-}$ $B$ particle, for which there is some theoretical and experimental evidence, might lessen the discrepancy between the calculated and experimental values of the width of the $\rho$ meson. We follow the procedure of Fulco, Shaw, and Wong in which the matrix $N{D}^{-1\mathrm{}}$ equations are solved with a cutoff adjusted to produce the $\rho$ at its experimental mass. We find that the resulting width is almost totally insensitive to the inclusion of the $B$-exchange force. The insensitivity is due to the fact that, while the Born amplitude for $B$ exchange is positive and of appreciable size, it decreases with energy in such a way that its contribution to the kernel of the integral equation for the $N$ matrix is negative, and the change in the $N$ matrix produced by $B$ exchange is therefore suppressed. The conclusions are independent of the mass and width of the exchanged $2^{-}$ particle.