R is the ratio of the hadronic cross section to the muon cross section in electron–positron collisions:
R
=
σ
(
0
)
(
e
+
e
−
→
h
a
d
r
o
n
s
)
σ
(
e
+
e
−
→
μ
+
μ
−
)
,
{\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. 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
∑
q
e
q
2
/
e
2
,
{\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. eq 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).
