The slope of the time-dependent asymmetry, ΔYK+K- and ΔYπ+π-, in D0 → K+K- and D0 → π+π- decays

The most precise measurement of the the slope of the time-dependent asymmetry defined by the parameter Delta Y-f (f = K+K-, pi(+)pi(-)), of the decay rates of D-0 and D-0 mesons into the final states in the decays D-0 -> K+K- and D-0 -> pi(+)pi(-) were recently reported by LHCb collaboration with the values of Delta YK+K- = (-2 . 3 +/- 1.5 +/- 0.3) x 10(-4) and Delta Y pi+pi- = (-4.0 +/- 2.8 +/- 0.4) x 10(-4). In this study, we have obtained Delta YK+K- = (-2.27 +/- 1.12) x 10(-4 )and Delta Y pi+pi- = (-3.15 +/- 1.72) x 10(-4) where Delta Y constrains possible CP violation. The CP violation in the decays D-0 -> K+K- and D-0 -> pi(+)pi(-) have been calculated under the factorization approach. These decay modes include a current-current tree and penguin diagrams that their amplitudes are considered separately, by introducing strong and weak phases with the delta and phi parameters, respectively. We have obtained for both of decays delta(1) = 0 degrees, delta(2) = (90.04 +/- 0.01)degrees, phi(1) = 0 degrees and phi(2) = (68.48 +/- 1.55)degrees. The CP asymmetries are calculated to be A(CP)(K+K-) = (+0.03 +/- 0.02)% and A(CP) (pi(+)pi(-)) = (+0.03 +/- 0.01)% at mu = 1 GeV. Finally, from the sum of the amplitudes, we have calculated the total amplitude and obtained comparable results with experimental values for the branching ratios of decays.