Inclusive electron-positron annihilation into hadrons (${\sigma }_h(s)$)

At leading electromagnetic order and with negligible electron mass, the photon-channel relativistic cross-section is ${\sigma }_h=4{\pi }^2\alpha {\rho }_h=16{\pi }^3{\alpha }^2{\rho }_J/s$, in the stated hadronic photon spectral density and hadronic electromagnetic-current spectral density conventions. Initial electron and positron spins are averaged; final hadronic states are summed inclusively. Electroweak channels beyond photon exchange are separate contributions.

The hadronic R ratio normalizes the photon-channel hadronic relativistic cross-section to the leading massless muon-pair value. The free active-quark result is $R=N_c{\sum }_f{Q}_f^2$. It depends on flavor charges as well as the number of active flavors; it is not simply $N_c{N}_f$.