(Solved): (a) A bubble chamber event shows the reaction of a pion hitting a proton at r ...

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(a) A bubble chamber event shows the reaction of a pion hitting a proton at rest according to ${?}^{?}\mathrm{p}??{\mathrm{K}}^0$ followed by the decays $??\mathrm{p}{?}^{?}$and ${\mathrm{K}}^0?{?}^{+}{?}^{?}$. The quark content of the hadrons are: ${?}^{+}(u\stackrel{?}{d}),{?}^{?}(\stackrel{?}{u}d),{\mathrm{K}}^0(d\stackrel{?}{s})$ and $?(uds)$. The respective masses of the particles are $m_{{?}^{\pm }}=140\mathrm{MeV},m_{{\mathrm{K}}^0}=498\mathrm{MeV}$, $m_{?}=1116\mathrm{MeV}$ and $m_p=938\mathrm{MeV}$. The bubble chamber is immersed in a magnetic field. i. Explain briefly how bubble chambers detect the presence of charged particles. ii. Sketch an illustration of this bubble chamber event and explain briefly how information from the bubble chamber is used to distinguish between the tracks associated with the proton and charged pion coming from the decays of the ${\mathrm{K}}^0$ and $?$. iii. Calculate the minimum energy of the initial pion necessary to create the ${\mathrm{K}}^0$ and $?$ particles. iv. Draw the Feynman diagrams, indicating all particles and couplings, of the ${\mathrm{K}}^0?{?}^{+}{?}^{?}$and $??\mathrm{p}{?}^{?}$decays. (b) The ratio of decay rates of the $\mathrm{J}/?(c\stackrel{?}{c})$ particle into gluons and photons, $\frac{?(\mathrm{J}/??\mathrm{gg}?)}{?(\mathrm{J}/??\mathrm{ggg})},$ is proportional to a given function of the electromagnetic and strong coupling strengths, $e$ and $g_{\mathrm{s}}$. Draw the leading-order Feynman diagrams for each decay, indicating the relevant coupling strengths for all vertices. Using these diagrams find how the ratio of rates depends on $e$ and $g_{\mathrm{s}}$. (c) Draw a Feynman diagram of the decay ${?}^{+}?{?}^{+}{?}^0$ indicating all particles, couplings and the colour content of each particle. The quark content of the hadrons are: ${?}^{+}(u\stackrel{?}{d}),{?}^{+}(u\stackrel{?}{d})$ and ${?}^0(d\stackrel{?}{d}$ or $u\stackrel{?}{u})$. Question continued on next page