R (cross section ratio)

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

$R={\frac {\sigma ^{(0)}(e^{+}e^{-}\rightarrow \mathrm {hadrons} )}{\sigma ^{(0)}(e^{+}e^{-}\rightarrow \mu ^{+}\mu ^{-})}},$

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

$R=3\sum _{q}e_{q}^{2},$

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.