Past exam of the sub-atomic physics course of the University of Oxford / 2016 / 4 / d

Under the stipulated peak-energy approximation, set $E=m_V$ separately for $V=W,Z$ in the supplied Breit-Wigner resonance cross section. For a spin-one resonance,Define the measured ratio as $R=\sigma (W\to \ell \nu )/\sigma (Z\to \ell \ell )$. With the known production prefactor ratio neglected as instructed, the spin factors cancel andSolving for the positive physical width givesIf the production prefactors are retained as $C_W,C_Z$, multiply the quantity under the square root by $C_W/C_Z$. The partial decay widths in this extraction are calculated inputs, while the total decay width being inferred need not be fixed to its Standard Model value.

The peak and integrated resonance width dependence explains why the square root is essential to the specified peak approximation. An energy-integrated narrow-width cross section contains one inverse power of the total decay width, because integrating over the resonance supplies a factor proportional to its width. That different observable leads to a different extraction formula. Real hadron-collider analyses also include parton distribution functions and the energy convolution; the present result follows the explicit approximation in the source.