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^{-}\rightarrow \mathrm {hadrons} )}{\sigma ^{(0)}(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

R=3\sum _{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 colors of the quarks. QCD corrections to this formula have been calculated.[4]

Notes

Eidelman, S.; Jegerlehner, F. (1995). "Hadronic contributions to (g−2) of the leptons and to the effective fine structure constant α(M_Z²)". Zeitschrift für Physik C. 67 (4): 585–601. arXiv:hep-ph/9502298. doi:10.1007/bf01553984. ISSN 0170-9739.
Yao, W-M; et al. (2006-07-01). "Review of Particle Physics". Journal of Physics G: Nuclear and Particle Physics. 33 (1): 1–1232. Bibcode:2006JPhG...33....1Y. doi:10.1088/0954-3899/33/1/001. ISSN 0954-3899. Section 40
Yao, W-M; et al. (2006-07-01). "Review of Particle Physics". Journal of Physics G: Nuclear and Particle Physics. 33 (1): 1–1232. Bibcode:2006JPhG...33....1Y. doi:10.1088/0954-3899/33/1/001. ISSN 0954-3899. Section 9.7
Gorishny, S.G.; Kataev, A.L.; Larin, S.A. (1991). "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): 144–150. doi:10.1016/0370-2693(91)90149-k. ISSN 0370-2693.

gollark: Oh, so it just combusts toast. I see.

gollark: I mean, I'm pretty sure you need to actually have some sort of physical burning thing for that.

gollark: But *can* it throw fire?

gollark: The hypertoaster is electrical though, flamethrowers mostly run on chemical means.

gollark: Every house has both, but they could share a lot of components surely, as the main goal is to warm stuff up.

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[1] Eidelman, S.; Jegerlehner, F. (1995). "Hadronic contributions to (g−2) of the leptons and to the effective fine structure constant α(M_Z²)". Zeitschrift für Physik C. 67 (4): 585–601. arXiv:hep-ph/9502298. doi:10.1007/bf01553984. ISSN 0170-9739.

[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. 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. 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(α_S³) corrections to σ_tot (e⁺e⁻ → hadrons) and Γ (τ⁻ → ν_τ + hadrons) in QCD". Physics Letters B. 259 (1–2): 144–150. doi:10.1016/0370-2693(91)90149-k. ISSN 0370-2693.