Indirect CP-Violation in the Neutral Kaon System Beyond Leading Logarithms

Abstract

We have calculated the short distance QCD coefficient \eta_3 of the effective |\Delta S|=2-hamiltonian in the next-to-leading order. Since now all coefficients \eta_1, \eta_2 and \eta_3 are known beyond the leading log approximation, one can achieve a much higher precision in the theoretical analysis of \epsilon_K. The measured value for \epsilon_K$yieldsalowerboundoneachof|V_{cb}|,|V_{ub}/V_{cb}|,thetopquarkmass$m_t$andthenon-perturbativeparameter{B}_{K}asafunctionoftheremainingthreequantities.WediscusstheimplicationsontheCKMphase\delta ,|V_{td}|andthekeyquantityforallCP-violatingprocesses,Im{\lambda }_t=Im[V_{ts}^{\ast }{V}_{td}].ThesequantitiesandtheimprovedWolfensteinparameters\bar{\rho }and\bar{\eta }aretabulatedandtheshapeoftheunitaritytriangleisdiscussed.Wecomparetherangefor|V_{td}|withtheoneobtainedfromtheanalysisof{B}^0--\overline{B^0}mixing.For0.037\le |V_{cb}|\le 0.043,0.06\le |V_{ub}/V_{cb}|\le 0.10and0.65\le B_K\le 0.85wefindfromacombinedanalysisof{ϵ}_{K}andthe{B}^0--\overline{B^0}mixingparamater{x}_d:49^{\circ }\le \delta \le 146^{\circ },7.4\cdot 10^{-3}\le |V_{td}|\le 12.4\cdot 10^{-3},0.85\cdot 10^{-4}\le \text{imag}{\lambda }_t\le 1.60\cdot 10^{-4},-0.36\le \bar{\rho }\le 0.28and0.21\le \bar{\eta }\le \mathrm{0.44.}Wepredictthemassdifferenceofthe$B_s^0$ system to lie in the range 6.5 ps^{-1} \leq \Delta m_{B_s} \leq 28 ps^{-1}. Finally we have a 1995 look at the K_L--K_S mass difference.

Comments: 28 pages in RevTeX, uses epsf. Tables and PostScript figures submitted seperately. A complete PostScript version may be obtained from URL ftp://feynman.t30.physik.tu-muenchen.de/pub/preprints/tum-81-95.ps.gz