The leptonic decay of neutral vector (J^P C=1^–)mesons can be pictured as proceeding via a virtu

Step 1: Identify the quark content of each meson and the charge of each quark. - The $rho$ meson

Question

The leptonic decay of neutral vector $\left(J^{P C}=1^{--}\right)$mesons can be pictured as proceeding via a virtual photon, $$ \mathrm{V}(\mathrm{q} \overline{\mathrm{q}}) \rightarrow \gamma \rightarrow \mathrm{e}^{+} \mathrm{e}^{-} . $$ The technique for calculating such amplitudes will be explained in succeeding chapters. Here, it suffices to note that the $\mathrm{V}-\gamma$ coupling is proportional to the charge of the quark q. Neglecting a possible dependence on the vector meson mass, show that the leptonic decay widths are in the ratios $$ \rho: \omega: \phi: \psi=9: 1: 2: 8 \text {. } $$

    The leptonic decay of neutral vector $\left(J^{P C}=1^{--}\right)$mesons can be pictured as proceeding via a virtual photon,
$$
\mathrm{V}(\mathrm{q} \overline{\mathrm{q}}) \rightarrow \gamma \rightarrow \mathrm{e}^{+} \mathrm{e}^{-} .
$$

The technique for calculating such amplitudes will be explained in succeeding chapters. Here, it suffices to note that the $\mathrm{V}-\gamma$ coupling is proportional to the charge of the quark q. Neglecting a possible dependence on the vector meson mass, show that the leptonic decay widths are in the ratios
$$
\rho: \omega: \phi: \psi=9: 1: 2: 8 \text {. }
$$

Quarks and leptons: introductory course in modern particle physics

Francis Halzen, Alan… 1st Edition

Chapter 2, Problem 25

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Step 1

- The $\rho$ meson is made up of either up and anti-up quarks $(u\bar{u})$ or down and anti-down quarks $(d\bar{d})$. The charge of the up quark $(u)$ is $+\frac{2}{3}$ and the charge of the down quark $(d)$ is $-\frac{1}{3}$. - The $\omega$ meson is also made up Show more…

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The leptonic decay of neutral vector $\left(J^{P C}=1^{--}\right)$mesons can be pictured as proceeding via a virtual photon, $$ \mathrm{V}(\mathrm{q} \overline{\mathrm{q}}) \rightarrow \gamma \rightarrow \mathrm{e}^{+} \mathrm{e}^{-} . $$ The technique for calculating such amplitudes will be explained in succeeding chapters. Here, it suffices to note that the $\mathrm{V}-\gamma$ coupling is proportional to the charge of the quark q. Neglecting a possible dependence on the vector meson mass, show that the leptonic decay widths are in the ratios $$ \rho: \omega: \phi: \psi=9: 1: 2: 8 \text {. } $$

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