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R (cross section ratio)

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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).

Notes

  1. Eidelman, S.; Jegerlehner, F. (1995). "Hadronic contributions to (g−2) of the leptons and to the effective fine structure constant α(MZ)". Zeitschrift für Physik C. 67 (4): 585–601. arXiv:hep-ph/9502298. doi:10.1007/bf01553984. ISSN 0170-9739. S2CID 15083089.
  2. Yao, W-M; et al. (2006-07-01). "Review of Particle Physics". Journal of Physics G: Nuclear and Particle Physics. 33 (1): 1–1232. arXiv:astro-ph/0601514. Bibcode:2006JPhG...33....1Y. doi:10.1088/0954-3899/33/1/001. ISSN 0954-3899. Section 40
  3. Yao, W-M; et al. (2006-07-01). "Review of Particle Physics". Journal of Physics G: Nuclear and Particle Physics. 33 (1): 1–1232. arXiv:astro-ph/0601514. Bibcode:2006JPhG...33....1Y. doi:10.1088/0954-3899/33/1/001. ISSN 0954-3899. Section 9.7
  4. Gorishny, S.G.; Kataev, A.L.; Larin, S.A. (1991). "The O(αS) corrections to σtot (ee → hadrons) and Γ (τ → ντ + hadrons) in QCD". Physics Letters B. 259 (1–2): 144–150. doi:10.1016/0370-2693(91)90149-k. ISSN 0370-2693.


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