Physics: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. 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.[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(MZ2)". 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(αS3) corrections to σtot (e+e− → 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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