Past exam of the particle physics course of the University of Oxford / 2017 / 3 / c / Solution

Restore the unit conversion in the phase,Equivalently use mass units $\mathrm{eV}/c^2$ and energies in $\mathrm{eV}$, with $\hslash c=1.97327\times 10^{-7}\mathrm{eV}\mathrm{m}$. The numerical conversion factor isThusThe familiar coefficient $1.267$ uses $L$ in metres and $E$ in MeV, or kilometres and GeV; it would be a factor of one thousand too small with the units requested here.^[ref] The quoted differences with units ${\mathrm{eV}}^2$ are interpreted as squared-mass differences, despite the source's abbreviated $\Delta m_{ij}$ notation.