Unformatted text preview: a. (5 pts) Show that 1 β ( α ) =1 β 2 α 2 + β 3 β 2 2 α + analytic terms in α. b. (10 pts) De²ne the Λparameter by Λ 2 = μ 2 c exp α μ Z α dα β ( α ) with α and c some constants. Show that one can choose α and c such that ln μ 2 Λ 2 = 1 β 2 α μ + β 3 β 2 2 ln( β 2 α μ ) + o ( α μ ) . (1) c. (10 pts) Solve Eq. (1) above for the running coupling α μ ≡ α ( μ 2 ) in terms of ln( μ 2 / Λ 2 ) assuming that ln( μ 2 / Λ 2 ) ± 1 and keeping all terms which decrease with increasing μ 2 less rapidly than ln3 ( μ 2 / Λ 2 ). d. (10 pts) Show that Λ 2 = μ 2 e1 β 2 α μ ( β 2 α μ )β 3 /β 2 2 [1 + o ( α μ )] (2) and prove that this Λ 2 is μindependent. 1...
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 Winter '09
 Kovchegov
 Physics, Particle Physics, Electron, Mass, Work, electron neutrinos

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