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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. 

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Indirect CP violation in K$_{L}$ → ππ is described by the parameter ϵ$_{K}$ , the working formula for it is given by [61] 

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 

The phase φ$_{ϵ}$ is given by 

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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 

