R (cross section ratio)

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

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

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. [ [http://arxiv.org/abs/hep-ph/9502298 S. Eidelman and F. Jegerlehner, Z. Phys. C67 585 (1995).] ] Experimental values have been measured for center-of-mass energies from 400 MeV to 150 GeV. [W.-M. Yao et al., J. Phys. G 33, 1 (2006) Section 40]

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. [W.-M. Yao et al., J. Phys. G 33, 1 (2006) Section 9.7] A naive calculation of R yields

:$R\; =\; 3sum\_q\; e\_q^2,$

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 flavors of the quarks. QCD corrections to this naive formula have been calculated. [S.G. Gorishny "et al.", Phys. Lett. B259 144 (1991)]

Notes