11 TABLE I: The structure functions S$_{0}$ ( x$_{t}$ ′ ) and S$_{0}$ ( x$_{t}$, x$_{t}$ ′ ). TABLE II: The QCD correction factor η$_{t}$ ′ . m$_{t}$ ′ (GeV) 400 600 S$_{0}$ ( x$_{t}$ ′ ) 9.225 17.970 S$_{0}$ ( x$_{t}$, x$_{t}$ ′ ) 4.302 5.225 m$_{t}$ ′ (GeV) 400 600 η$_{t}$ ′ 0.522 0.514 Here η$_{t}$ is the QCD correction factor and its value is 0 . 5765 ± 0 . 0065 [58]. The QCD correction factor η$_{t}$ ′ is given by [59] α$_{s}$ ( µ ) is the running coupling constant at the scale µ at NLO [60]. Here we assume η$_{t}$ ′ = η$_{tt}$ ′ for simplicity. The numerical values of the structure functions S$_{0}$ ( x$_{t}$ ′ ), S$_{0}$ ( x$_{t}$, x$_{t}$ ′ ) and the QCD correction factor η$_{t}$ ′ are given in Table I and Table II respectively for various t ′ mass. Indirect CP violation in K$_{L}$ → ππ is described by the parameter ϵ$_{K}$ , the working formula for it is given by [61] F. Indirect CP violation in K$_{L}$ → ππ η$_{t}$ ′ = ( α$_{s}$ ( m$_{t}$ ) ) 6 / 23 ( α$_{s}$ ( m$_{b}$ ′ ) α$_{s}$ ( m$_{t}$ ) ) 6 / $^{21}$( α$_{s}$ ( m$_{t}$ ′ ) α$_{s}$ ( m$_{b}$ ′ ) ) 6 / 19 . (30) The phase φ$_{ϵ}$ is given by The second term in eq. 31 constitutes a O (5)% correction to ϵ$_{K}$ . In most of the phe- nomenological analysis φ$_{ϵ}$ is taken as π/ 4 and ζ is taken as zero. However ζ = 0 and φ$_{ϵ}$ = (43 . 51 ± 0 . 05) ◦ (33) M ∗ 12 = 〈 ¯ K $^{0}$| H $_{eff}$(Δ S = 2) | K $^{0}$〉 2 m$_{K}$ (32) ϵ$_{K}$ = exp( iφ$_{ϵ}$ ) sin φ$_{ϵ}$ ( Im M k $_{12}$/ Δ M$_{k}$ + ζ ) , (31) where ζ = Im A 0 Re A 0 with A$_{0}$ ≡ A ( K → ( ππ )$_{I}$$_{=0}$ ) and Δ M$_{K}$ denoting the K$_{L}$ − K$_{S}$ mass difference. The off-diagonal element M$_{12}$ in the neutral K -meson mass matrix represents K 0 − ¯ K 0 mixing and is given by