Formation of spin-one mesons by photon-photon fusion

We have observed the formation of two spin-one mesons in \ensuremath{\gamma}\ensuremath{\gamma} fusion reactions in which one photon was highly virtual. The first, consistent with being the ${J}^{\mathrm{PC}}$${=1}^{++}$ ${f}_{1}$(1285), was seen in the final state \ensuremath{\eta}${\ensuremath{\pi}}^{+}$${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}}$ (\ensuremath{\eta}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}), as was the \ensuremath{\eta}'(958). We have previously reported the observation of the second spin-one state, the X(1420), in the final state ${K}^{\ifmmode\pm\else\textpm\fi{}}$${K}_{S}^{0}$${\ensuremath{\pi}}^{\ensuremath{\mp}}$ (${K}_{S}^{0}$\ensuremath{\rightarrow}${\ensuremath{\pi}}^{+}$${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}}$). The formation of this state, which may be the ${f}_{1}$(1420) observed in hadronic interactions, is reanalyzed using a new model and more data. We consider whether the X(1420) could be the partner of the ${f}_{1}$(1285) in the ${J}^{\mathrm{PC}}$${=1}^{++}$ meson nonet. The \ensuremath{\gamma}${\ensuremath{\gamma}}^{\mathrm{*}}$ width of each resonance was determined in several ${Q}^{2}$ bins. Using a model due to Cahn with a \ensuremath{\rho} form factor, we obtained for the coupling parameter \ensuremath{\Gamma}${\ifmmode \tilde{}\else \~{}\fi{}}_{\ensuremath{\gamma}\ensuremath{\gamma}}$(${f}_{1}$(1285)) the value 2.4\ifmmode\pm\else\textpm\fi{}0.5\ifmmode\pm\else\textpm\fi{}0.5 keV.We also found B(X(1420)\ensuremath{\rightarrow}KK\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{\pi})\ensuremath{\Gamma}${\mathrm{\ifmmode \tilde{}\else \~{}\fi{}}}_{\ensuremath{\gamma}\ensuremath{\gamma}}$(X(1420))=1.3\ifmmode\pm\else\textpm\fi{}0.5\ifmmode\pm\else\textpm\fi{}0.3 keV using a \ensuremath{\rho} form factor, or 0.63\ifmmode\pm\else\textpm\fi{}0.24\ifmmode\pm\else\textpm\fi{}0.15 keV using a \ensuremath{\varphi} form factor. The decay distributions of the observed X(1420) events are consistent with a decay proceeding via ${K}^{\mathrm{*}}$(892)K, and favor positive, but do not exclude negative, parity. Assuming that the X(1420) and the ${f}_{1}$(1285) are members of the same qq\ifmmode\bar\else\textasciimacron\fi{} meson nonet and that B(X(1420)\ensuremath{\rightarrow}KK\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{\pi})\ensuremath{\approxeq}1, and using a \ensuremath{\varphi} form factor in the model for X(1420) formation, we determined the singlet-octet mixing angle of that nonet. The result, (45.4\ifmmode\pm\else\textpm\fi{}6.2)\ifmmode^\circ\else\textdegree\fi{}, agrees well with the 42.2\ifmmode^\circ\else\textdegree\fi{} implied by the Gell-Mann--Okubo quadratic mass formula; it is farther from the 35.3\ifmmode^\circ\else\textdegree\fi{} ideal mixing angle. Our results are thus consistent with the X(1420) being the mostly ss\ifmmode\bar\else\textasciimacron\fi{} isoscalar member of the axial-vector qq\ifmmode\bar\else\textasciimacron\fi{} meson nonet; however, we have no evidence contrary to hypotheses that the X(1420) is an exotic ${q}^{2}$q\ifmmode\bar\else\textasciimacron\fi{} $^{2}$ or qq\ifmmode\bar\else\textasciimacron\fi{}g state.