R (cross section ratio)

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

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

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

[math]\displaystyle{ R = 3\sum_q e_q^2/e^2, }[/math]

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

↑ 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. doi:10.1007/bf01553984. ISSN 0170-9739.
↑ Yao, W-M (2006-07-01). "Review of Particle Physics". Journal of Physics G: Nuclear and Particle Physics 33 (1): 1–1232. doi:10.1088/0954-3899/33/1/001. ISSN 0954-3899. Bibcode: 2006JPhG...33....1Y. Section 40
↑ Yao, W-M (2006-07-01). "Review of Particle Physics". Journal of Physics G: Nuclear and Particle Physics 33 (1): 1–1232. doi:10.1088/0954-3899/33/1/001. ISSN 0954-3899. Bibcode: 2006JPhG...33....1Y. 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.

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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. doi:10.1007/bf01553984. ISSN 0170-9739.

[2] Yao, W-M (2006-07-01). "Review of Particle Physics". Journal of Physics G: Nuclear and Particle Physics 33 (1): 1–1232. doi:10.1088/0954-3899/33/1/001. ISSN 0954-3899. Bibcode: 2006JPhG...33....1Y. Section 40

[3] Yao, W-M (2006-07-01). "Review of Particle Physics". Journal of Physics G: Nuclear and Particle Physics 33 (1): 1–1232. doi:10.1088/0954-3899/33/1/001. ISSN 0954-3899. Bibcode: 2006JPhG...33....1Y. 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.

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R (cross section ratio)

Topic: Physics

Notes