Of the Resolution of Pure Quadratic Equations

Euler, Leonard; Hewlett, John

doi:10.1017/cbo9780511693519.058

Cited by 1 publication

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“…The interaction of two photons was first described by Landau and Lifshitz (1) in 1934. Shortly thereafter, Euler and Kockel' 3 ' calculated the cross section for the elastic scattering of light by light, 77 -t 77, and Breit and Wheeler' 4 ' calculated the cross section for the inelastic scattering process 77 -* e*e~. Intense beams of highly energetic photons are required to produce a measurable rate, and consequently the observation of these processes remained experimentally unattainable for several decades.…”

Section: Historical Developmentmentioning

confidence: 99%

“…1.3 gives the amplitude for the process e + e~ -* e*e~X:* M = -e'uip'^uip^vip'^vip^^jT^. (1)(2)(3)(4)(5)(6)(7) In this expression, u and v are the Dirac spinors for the electron and positron, each of the photon propagators contributes a factor of -y, an the process 77 -» -Y. The cross section is then given by:…”

Section: Exact Lowest-order Calculationsmentioning

confidence: 99%

“…This information was recorded on tape with the data, and the result is n £ ± = 1.3 x 10"*. The average vacuum pressure at the IP was approximately 1. x 10 -9 Torr, or 3.2 x 10 7 particles per cm 3 . AZ is taken to be 1 m because beam-gas interactions more than 50 cm from the IP had a negligible probability of passing all cuts.…”

Section: Beam-gas Interactionsmentioning

confidence: 99%

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Resonance production in two-photon interactions

Roe¹

1989

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Resonance production in two-photon interactions is studied using data collected with the ASP detector at the PEP t*e~ storage ring located at the Stanford Linear Accelerator Center. The ASP detector is a non-magnetic lead-glass calorimeter constructed from 632 lead-glass bars. It covers 94% of 4JT in solid angle, extending to witliin 20° of the beamline. Lead-scintillator calorimeters extend the coverage to within 22 mr oi the beamline on both sides. Energy resolution of-3s, where E is the energy is GeV, is achieved for electrons and photons in the lead-glass calorimeter, and particle trajectories are reconstructed with high efficiency. A total luminosity of 108 pb" 1 was collected with the ASP detector at a center-of-mass energy of 29 GeV. The observed process is e*e~-» e*e~7*7*-* e*e~X, where X is a pseudoscalar resonance (J = 0~+) and 7* is a virtual (mass^ 0) photon. The outgoing electrons scatter down the beampipe and are not detected. The observed resonances are the rj and J}' mesons, with masses of 549 and 95S MeV, respectively. They are detected in the 77 decay mode; a total of 23S0 ± 49 i]-* 77 and 56S ± 26 r/-> 77 events are observed. From the number of events, the detection efficiency, and the calculated produc tion cross sections the radiative widths, Tyy, of the T) and 17' were measured and found to be: r 7^(^) = .481 ± .010 ± .047keV r^(ri') = 4.71 ± .22 ± .70keV. These results are in good agreement with the world average values. The radiative width is a probe of the quark content, because photons couple to the quark charge. In the framework of flavor So(3) symmetry of the light (up, down, strange) quarks, the pseudoscalar mixing angle gives the quark content of the T) and rj' mesons. Based on the radiative widths quoted above, the pseudoscalar mixing angle has been determined to be 6 p-19.S ± 2.5°, in agreement with results from J/v decays. iii Acknowledgments I would like to take this opportunity to say a word of thanks. F'rst, to my advisor David Burke, for his advice and support, his boundless energy, etui his enthusiasm for physics. Many thanks are also due to the members of the ASP collaboration, who made this experiment the success it has been and who have been a pleasure to work with. In particular, I acknowledge the camaraderie of my office-mate, Chris Hawkins, who was a ready source of Fortran wit and wisdom. Tom Steele's valuable friendship and T£X-pertise smoothed the waters and made the journey much more pleasant. Thanks also to Lydia Beers, who brightened the way with humor and a friendly smile. Finally, I want to thank my mother for weekly doses of encouragement, my father and brothers for keeping my Alfa Romeo running, and my husband Michael for everything else.

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Section: Historical Developmentmentioning

confidence: 99%

Section: Exact Lowest-order Calculationsmentioning

confidence: 99%