R (cross section ratio) explained

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

	\sigma⁽⁰⁾(e^+e^{- →}hadrons)
	\sigma(e^+e^{- →}\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

	2/e
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]

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).

Notes and References

Eidelman . S. . Jegerlehner . F. . Hadronic contributions to (g−2) of the leptons and to the effective fine structure constant α(M_Z²) . Zeitschrift für Physik C . 67 . 4 . 1995 . 0170-9739 . 10.1007/bf01553984 . 585–601. hep-ph/9502298. 15083089 .
Yao . W-M . etal. Review of Particle Physics . Journal of Physics G: Nuclear and Particle Physics . 33 . 1 . 2006-07-01 . 0954-3899 . 10.1088/0954-3899/33/1/001. astro-ph/0601514 . 1–1232. free. 2006JPhG...33....1Y . Section 40
Yao . W-M . etal . Review of Particle Physics . Journal of Physics G: Nuclear and Particle Physics . 33 . 1 . 2006-07-01 . 0954-3899 . 10.1088/0954-3899/33/1/001. astro-ph/0601514 . 1–1232. free. 2006JPhG...33....1Y . Section 9.7
Gorishny . S.G. . Kataev . A.L. . Larin . S.A. . The O(α_S³) corrections to σ_tot (e⁺e⁻ → hadrons) and Γ (τ⁻ → ν_τ + hadrons) in QCD . Physics Letters B . 259 . 1–2 . 1991 . 0370-2693 . 10.1016/0370-2693(91)90149-k . 144–150.