Past exam of the particle physics course of the University of Oxford / 2016 / 1 / 3

The photon propagator gives approximately $d{\sigma }_{\mathrm{NC}}/d{Q}^2\propto 1/(Q^2{)}^2$, whereas a massive W boson gives $d{\sigma }_{\mathrm{CC}}/d{Q}^2\propto 1/(Q^2+M_W^2{)}^2$. Up to different coupling constant values, parton distribution functions and angular factors,Consequently the low-$Q^2$ charged current suppression disappears as $Q^2$ approaches $M_W^2$. The source graph shows comparable cross sections at $Q^2$ of order $10^4{\mathrm{GeV}}^2$, so the relevant mass scale is of order $10^2\mathrm{GeV}$.

A more quantitative, still rough reading uses the $e^{-}p$ ratio $R_1\simeq 0.006$ near $q_1=300{\mathrm{GeV}}^2$ and $R_2\simeq 0.17$ near $q_2=2000{\mathrm{GeV}}^2$, where $q_i$ denotes $Q^2$, not $Q$. If $C$ varies slowly over this interval, set $\kappa =\sqrt{R_2/R_1}{q}_1/q_2$. ThenThe reading is compatible with roughly $70$–$100\mathrm{GeV}$; it is not a precision mass determination. In particular, Z boson exchange contributes to the neutral current at high $Q^2$, and the parton distribution functions do not cancel exactly. Equality of two inclusive cross sections alone does not define $M_W$.