Past exam of the particle physics course of the University of Oxford / 2021 / 4 / e / Solution

Integrating the distribution in d, use ${\int }_{-1}^1(1+z^2)dz=8/3$ and ${\int }_0^{1}zdz-{\int }_{-1}^{0}zdz=1$. ThereforeSubtract backgrounds and correct the measured forward and backward yields for detector acceptance, charge misidentification and selection efficiency; radiative effects and other mediators must be removed or included in a fit. With $t=\sqrt{4A_{\mathrm{fb}}/3}$ and $r=|g_l/g_r|$, inversion givesA single unpolarized measurement determines the ratio up to $r\leftrightarrow 1/r$. A polarized-beam observable or another signed chiral asymmetry is needed to choose which coupling is larger. Values outside $0\le A_{\mathrm{fb}}\le 3/4$ would contradict this ideal universal single-mediator model, apart from experimental uncertainties.