Precision measurements of indirect $CP$ violation in the charm sector with LHCb

<!--HTML-->A study of indirect $CP$ violation in $D$$^{0}$ mesons is presented through a measurement of the asymmetry of the effective decay widths of $D$$^{0}$ and $\bar{D}$$^{0}$ mesons. This observable, known as $A$$_{Γ}$, is measured in decays to the $CP$ eigenstates $K$+$K$− and $\pi$$^{+}$$\pi$$^{-}$ using data collected in $pp$ collisions by the LHCb experiment in 2012 with an integrated luminosity of 1.9 fb$^{−1}$ . The results are combined with a previously published LHCb measurement using 1 fb$^{−1}$ of data collected in 2011 to yield average values of, <br><br>$A$$_{Γ}$($K$ +$K$ − ) = (−0.14 ± 0.37 ± 0.10) × 10$^{−3}$, <p>$A$$_{Γ}$($\pi$+$\pi$−) = ( 0.14 ± 0.63 ± 0.15) × 10$^{−3}$,<br><br>where the first quoted uncertainty is statistical, and the second systematic. The results show no evidence of $CP$ violation and improve on the precision of the previous best measurements by nearly a factor of two. where the first quoted uncertainty is statistical, and the second systematic. The results show no evidence of $CP$ violation and improve on the precision of the previous best measurements by nearly a factor of two. New methods are presented for measuring the $D$$^{0}$ meson lifetime that rely on updated LHCb data acquisition techniques, which collect large datasets while reducing time-dependent biases. Many measurements of indirect $CP$ violation observables depend on precision measurements of meson lifetimes. Furthermore, the large datasets being collected by LHCb necessitate faster analysis techniques such that results can keep pace with the magnitude of acquired data. The methods presented employ a binned fit, where the main method separates an intractable background with a simple selection requirement and a second potential method investigates novel machine learning classification algorithms.