R (cross section ratio)

R is the ratio of the hadronic cross section to the muon cross section in electron–positron collisions:

$R=\frac{{\sigma }^{(0)}(e^{+}{e}^{-}\to \mathrm{h}\mathrm{a}\mathrm{d}\mathrm{r}\mathrm{o}\mathrm{n}\mathrm{s})}{\sigma (e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-})},$

where the superscript (0) indicates that the cross section has been corrected for initial state radiation. R is an important input in the calculation of the anomalous magnetic dipole moment. Experimental values have been measured for center-of-mass energies from 400 MeV to 150 GeV.

R also provides experimental confirmation of the electric charge of quarks, in particular the charm quark and bottom quark, and the existence of three quark colors. A simplified calculation of R yields

$R=3\sum _q{e}_q^2/e^2,$

where the sum is over all quark flavors with mass less than the beam energy. e_q is the electric charge of the quark, and the factor of 3 accounts for the three colors of the quarks. QCD corrections to this formula have been calculated.

Usually, the denominator in R is not the actual experimental μμ cross section, but the off-resonance theoretical QED cross-section: this makes resonances more visibly dramatic than normalization by the μμ cross section, which is also greatly enhanced at these resonances (hadronic states, and Z boson).

Notes

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