The LEP fit to the resonance with three light neutrino species gives ,

PHYSICS · Subjective · Fermi University Physics · Particle Physics & Quantum Fields · Particles, interactions and experiment · Electroweak theory and the Standard Model

Symmetry and Flavour, Ch Resonances: the relativistic Breit-Wigner, unitarity and the Z line shape

Problem

The LEP fit to the

Z

resonance with three light neutrino species gives

M_Z = 91.1876\,\mathrm{GeV}

\Gamma_{ee} = 83.91\,\mathrm{MeV}

\Gamma_{\rm had} = 1744.4\,\mathrm{MeV}

and

\Gamma_Z = 2495.5\,\mathrm{MeV}

, giving the peak hadronic cross section

\sigma^0_{\rm had} = 12\pi\Gamma_{ee}\Gamma_{\rm had}/(M_Z^2\Gamma_Z^2) = 41.50\,\mathrm{nb}

. Each additional light neutrino species coupling to the

Z

as the known ones do adds a further invisible partial width of

165.9\,\mathrm{MeV}

\Gamma_Z

, while

\Gamma_{ee}

and

\Gamma_{\rm had}

are unchanged (they do not depend on the number of neutrino species). Predict the peak hadronic cross section

\sigma^0_{\rm had}

that would have been measured if there were four light neutrino species rather than three.

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