Test of the Nonrelativistic Quark Model for "Elementary" Particles: Radiative Decays of Vector Mesons

An experimental test of the nonrelativistic quark model proposed by one of the authors (G.M.) to decribe the internal dynamics of elementary particles is suggested and discussed. The idea is the following: In the nonrelativistic quark model mentioned above, one can obtain not only the ratio $-\frac{3}{2}$ of the magnetic moment of the proton to that of the neutron, but also the absolute value of the magnetic moment of the proton in terms of the quark magnetic moment. By using the value of the quark magnetic moments determined in this way, we calculate the rates of the $M1\mathrm{}$ radiative transitions $V\to P+\gamma$, where $V$ is a vector meson and $P$ a pseudoscalar meson. The following results for the widths are obtained (in MeV): $\omega \to {\pi }^0\gamma \mathrm{}\left(1.17\right)\mathrm{}$; $\omega \to \eta \gamma (6.4\mathrm{}\times {10}^{-3\mathrm{}})$; $\rho \to \pi \gamma (1.2\mathrm{}\times {10}^{-1\mathrm{}})$; ${\rho }_0\to \eta \gamma (4.4\mathrm{}\times {10}^{-2\mathrm{}})$; $K^{*+}\to K^{+}\gamma (7\mathrm{}\times {10}^{-2\mathrm{}})$; $K^{*0\mathrm{}}\to K^0\gamma (2.8\mathrm{}\times {10}^{-1\mathrm{}})$; $\varphi \to \eta \gamma (3.04\mathrm{}\times {10}^{-1\mathrm{}})$. The result for the $\omega$ agrees with the present experimental data, assuming that the ${\pi }^0\gamma$ decay dominates the neutral decay rate of the $\omega$; no experimental data are available for the other decays and it is suggested that the $K^{*0\mathrm{}}\to K^{*}\gamma$ and $\varphi \to \eta \gamma$ decay rates are sufficiently large to deserve a measurement. Two possible reasons for uncertainty are discussed in detail: (a) dependence of the vertex function upon the masses, and (b) choice of the $\omega$ and $\eta$ unitary spin functions.