Past exam of the particle and nuclear physics course of the University of Cambridge / 2022 / Section B / 6 / d

For (i), CP symmetry relates the negative- and positive-pion radiative channels to excellent accuracy. The original positive-pion table therefore predictsThe comparison requires the same photon-energy and event-selection definition. The table attaches an unexplained footnote to this radiative channel; it does not specify those cuts in the supplied excerpt. An arbitrarily soft photon is not a separately infrared-finite exclusive observable, so the numerical value must retain the table's definition.

Part (ii) contains an apparent notation error in the original PDF as well as the TeX: it prints $e^{-}{\nu }_e{e}^{-}{e}^{+}$, rather than $e^{-}{\bar{\nu }}_e{e}^{-}{e}^{+}$. Taken literally, the charged leptons carry net electron-family lepton number $2-1=+1$, and the printed ${\nu }_e$ adds another $+1$. The initial pion has zero lepton number. This is a $\Delta L_e=2$ channel, not the charge conjugate of the listed positive-pion decay. In the ordinary lepton-number-conserving Standard Model approximation,Allowing lepton-number-violating masses for Majorana neutrinos would require additional physical assumptions and does not justify assigning the tabulated number to that channel.

For the likely intended charge-conjugate process, the prediction is insteadThis distinction follows from a lepton-number test of a decay channel; replacing the printed neutrino by an antineutrino must be stated explicitly.