Diffractive production of vector mesons in muon-proton scattering at 150 and 100 GeV

We have studied the production of $\rho$ and $\phi$ mesons from muon scattering on a liquidhydrogen target at 150 and 100 GeV. For the $\rho$ we observe a skewed mass distribution which becomes somewhat more normal with increasing $Q^2$ (the square of the four-momentum transferred from the muon), and an exponential distribution in $t$ (the square of the four-momentum transferred to the target proton) with a slope which is consistent with a slight decrease as $Q^2$ increases. The dependence of the cross section on $Q^2$ follows that of the square of the $\rho$ propagator with little contribution from longitudinal $\rho$ production. The angular distribution of the $\rho$ decay confirms the smallness of the contribution from longitudinal $\rho$ production at our energies. The cross section when extrapolated to $Q^2=0\mathrm{}$ agrees with that measured in real photoproduction. The decay angular distribution of the $\rho$ decay shows that $s$-channel helicity is largely conserved, although we detect a helicity-single-flip contribution at the 10-15% level. Natural-parity exchange in the $t$ channel dominates, and the transverse and longitudinal amplitudes are found to be in phase. These characteristics are consistent with the diffractive nature of the vectordominance model. The $t$ distribution of $\phi$ production is also exponential, although less steep than that for the $\rho$. We observe an elastically produced four-pion state at a mass of approximately 1600 MeV. We identify this state with the ${\rho }^{\prime }\mathrm{}\left(1600\right)\mathrm{}$, and find it to be produced with a distribution exponential in $t$.