Fractional dynamics as source of CP violation in the Standard Model

The origin of CP violation in K-meson channels and the strong CP problem are long-standing puzzles of the Standard Model. Building on our recent contributions$^{1), 2)}$ we find that breaking of CP symmetry is a direct manifestation of fractional dynamics and non-equilibrium phenomena in particle physics. Our results are summarized below: \[ \left| \varepsilon_K \right|_{EXP} =(2.280\pm 0.013)\times 10^{-3}, \quad \left| \varepsilon_K \right|_{THEOR} =2.162\times 10^{-3} \] \[ \left| {\varepsilon_K}^{'} \right|_{EXP} =(3.878\pm 0.16)\times 10^{-6}, \quad \left| {\varepsilon_K}^{'} \right|_{THEOR} =4.670\times 10^{-6} \] \[ (\theta _{QCD} )_{EXP} <10^{-10}, \quad (\theta _{QCD} )_{THEOR} <3.491\times 10^{-10} \] Here, $\left| \varepsilon_K \right|$, $\left| {\varepsilon_K}^{'} \right|$ are the two CP parameters describing the K-meson sector and $\theta _{QCD} $ the CP term associated with the vacuum structure of Quantum Chromodynamics. 1) E. Goldfain, Communications in Nonlinear Science and Numerical Simulation,~Volume 13, Issue 3,~June 2008, Pages 666-676 2) E. Goldfain, Communications in Nonlinear Science and Numerical Simulation,~Volume 13, Issue 7,~September 2008, Pages 1397-1404