An Analytic Formula and an Upper Bound for ε/ε in the Standard Model
نویسندگان
چکیده
Using the idea of the penguin box expansion we find an analytic expression for ε/ε in the Standard Model as a function of mt, ms(mc) and two non-perturbative parameters B (1/2) 6 and B (3/2) 8 . This formula includes next-to-leading QCD/QED short distance effects calculated recently by means of the operator product expansion and renormalization group techniques. We also derive an analytic expression for the upper bound on ε/ε as a function of |Vcb|, |Vub/Vcb|, BK and other relevant parameters. Numerical examples of the bound are given. ∗Supported by the German Bundesministerium für Forschung und Technologie under contract 06 TM 732 and by the CEC Science project SC1-CT91-0729. email: [email protected] and [email protected] This year [1] we have analyzed the CP violating ratio ε/ε in the Standard Model including leading and next-to-leading logarithmic contributions to the Wilson coefficient functions of the relevant local operators. Another next-toleading order analysis of ε/ε can be found in [2]. Imposing the constraints from the CP conserving K → ππ data on the hadronic matrix elements of these operators we have given numerical results for ε/ε as a function of ΛMS, mt and two non-perturbative parameters B (1/2) 6 and B (3/2) 8 which cannot be fixed by the CP conserving data at present. These two parameters are defined by 〈Q6(mc)〉0 ≡ B (1/2) 6 〈Q6(mc)〉 (vac) 0 〈Q8(mc)〉2 ≡ B (3/2) 8 〈Q8(mc)〉 (vac) 2 , (1) where
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