Solution (source code)

= Solution

For the <neutral strange B meson>, a charged-current tree amplitude has $\bar b\to\bar cW^+$ followed by $W^+\to c\bar s$, while the initial $s$ is a spectator. The $c\bar c$ pair forms the <J psi meson> and the $s\bar s$ pair forms the <phi meson>. Charge and <quark> flavour flow are conserved at each vertex except for the permitted weak flavour change. <antiquark> arrows point opposite their physical propagation direction.

\Image[/past-exam-of-the-particle-and-nuclear-physics-course-of-the-university-of-cambridge/2013/paper-1-bs-decay.png]
{title=Original quark-level charged-current contribution to the neutral strange B-meson decay; arrows show fermion flow}

Useful reconstruction modes are \b[$J/\psi\to\mu^+\mu^-$ or $e^+e^-$], through a <virtual photon>, and \b[$\phi\to K^+K^-$], a strong decay. The latter is the largest individual $\phi$ mode, with $K_L^0K_S^0$ also important. For the $J/\psi$, the <inclusive branching fraction versus reconstruction mode> distinction matters: hadronic decays dominate inclusively, principally through three <gluons>; each charged-lepton pair accounts for about 6%, not most decays. The charm pair lies below open-charm threshold. These distinctions are confirmed by the official particle listings.<Review of Particle Physics by Particle Data Group (2022)>[J/psi(1S) listing, p. 2, decay modes; phi(1020) listing, p. 4, decay modes]{ref}