The Anatomy of ϵ/ϵ\epsilon' / \epsilon beyond leading logarithms with improved hadronic matrix elements

Mar, 1993
116 pages
Published in:
  • Nucl.Phys.B 408 (1993) 209-285
e-Print:
Report number:
  • TUM-T31-35-93,
  • MPI-PH-93-11,
  • CERN-TH-6821-93

Citations per year

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Abstract:
We use the recently calculated two--loop anomalous dimensions of current-current operators, QCD and electroweak penguin operators to construct the effective Hamiltonian for ΔS=1\Delta S=1 transitions beyond the leading logarithmic approximation. We solve the renormalization group equations and give the numerical values of Wilson coeff. functions. We propose a new semi-phenomenological approach to hadronic matrix elements which incorporates the data for CPCP-conserving KππK \rightarrow \pi\pi amplitudes and allows to determine the matrix elements of all (VA)(VA)(V-A)\otimes (V-A) operators in any renormalization scheme and do a renormalization group analysis of all hadronic matrix elements Qi(μ)\langle Q_i(\mu) \rangle. We compare critically our treatment of these matrix elements with those given in the literature. We find in the NDR scheme \epe = (6.7 \pm 2.6)\times 10~{-4} in agreement with the experimental findings of E731. We point out however that the increase of Q6\langle Q_6 \rangle by only a factor of two gives \epe = (20.0 \pm 6.5)\times 10~{-4} in agreement with the result of NA31. The dependence of \epe on ΛMSˉ\Lambda_{\bar{MS}}, mtm_t and Q6,8\langle Q_{6,8} \rangle is presented.
  • CP: violation
  • current: flavor changing
  • quantum chromodynamics
  • renormalization group
  • effective Hamiltonian
  • leading logarithm approximation
  • model: weak interaction
  • weak interaction: model
  • CKM matrix matrix
  • operator product expansion