R (cross section ratio)

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

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

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

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

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.^[4]

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).

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