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| | '''''R''''' is the ratio of the [[hadron]]ic [[cross section (physics)|cross section]] to the [[muon]] cross section in [[electron]]–[[positron]] collisions: |
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| | :<math>R = \frac{\sigma^{(0)}(e^+e^-\rightarrow \mathrm{hadrons})}{\sigma^{(0)}(e^+e^-\rightarrow \mu^+\mu^-)},</math> |
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| | 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]].<ref>[http://arxiv.org/abs/hep-ph/9502298 S. Eidelman and F. Jegerlehner, Z. Phys. '''C67''' 585 (1995).]</ref> Experimental values have been measured for center-of-mass energies from 400 MeV to 150 GeV.<ref>W.-M. Yao et al., J. Phys. G 33, 1 (2006) Section 40</ref> |
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| | ''R'' also provides experimental confirmation of the electric charge of [[quark]]s, in particular the charm quark and bottom quark, and the existence of three quark colors.<ref>W.-M. Yao et al., J. Phys. G 33, 1 (2006) Section 9.7</ref> A simplified calculation of ''R'' yields |
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| | :<math>R = 3\sum_q e_q^2,</math> |
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| | where the sum is over all quark flavors with mass less than the beam energy. ''e<sub>q</sub>'' is the electric charge of the quark, and the factor of 3 accounts for the three colors of the quarks. [[Quantum chromodynamics|QCD]] corrections to this formula have been calculated.<ref>S.G. Gorishny ''et al.'', Phys. Lett. '''B259''' 144 (1991)</ref> |
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| | == Notes == |
| | {{reflist}} |
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| | [[Category:Scattering]] |
| | [[Category:Particle physics]] |
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| | {{particle-stub}} |
Revision as of 09:50, 27 January 2014
R is the ratio of the hadronic cross section to the muon cross section in electron–positron collisions:
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
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]
Notes
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