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.^[1] Experimental values have been measured for center-of-mass energies from 400 MeV to 150 GeV.^[2]

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.^[3] 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.^[4]

Notes

1. S. Eidelman and F. Jegerlehner, Z. Phys. C67 585 (1995).
2. W.-M. Yao et al., J. Phys. G 33, 1 (2006) Section 40
3. W.-M. Yao et al., J. Phys. G 33, 1 (2006) Section 9.7
4. S.G. Gorishny et al., Phys. Lett. B259 144 (1991)