Measurement of CP asymmetry in $B^0_s rightarrow D^{mp}_s K^{pm}$ decays

We report on measurements of the time-dependent CP violating observables in $B^0_srightarrow D^{mp}_s K^{pm}$ decays using a dataset corresponding to 1.0 fb$^{-1}$ of pp collisions recorded with the LHCb detector. We find the CP violating observables $C_f=0.53pm0.25pm0.04$, $A^{DeltaGamma}_f=0.37pm0.42pm0.20$, $A^{DeltaGamma}_{bar{f}}=0.20pm0.41pm0.20$, $S_f=-1.09pm0.33pm0.08$, $S_{bar{f}}=-0.36pm0.34pm0.08$, where the uncertainties are statistical and systematic, respectively. Using these observables together with a recent measurement of the $B^0_s$ mixing phase $-2beta_s$ leads to the first extraction of the CKM angle $gamma$ from $B^0_s rightarrow D^{mp}_s K^{pm}$ decays, finding $gamma$ = (115$_{-43}^{+28}$)$^circ$ modulo 180$^circ$ at 68% CL, where the error contains both statistical and systematic uncertainties.

Decay time integrals in neutral meson mixing and their efficient evaluation

In neutral meson mixing, a certain class of convolution integrals is required whose solution involves the error function $mathrm{erf}(z)$ of a complex argument $z$. We show the the general shape of the analytic solution of these integrals, and give expressions which allow the normalisation of these expressions for use in probability density functions. Furthermore, we derive expressions which allow a (decay time) acceptance to be included in these integrals, or allow the calculation of moments. We also describe the implementation of numerical routines which allow the numerical evaluation of $w(z)=e^{-z^2}(1-mathrm{erf}(-iz))$, sometimes also called Faddeeva function, in C++. These new routines improve over the old CERNLIB routine(s) WWERF/CWERF in terms of both speed and accuracy. These new routines are part of the RooFit package, and have been distributed with it since ROOT version 5.34/08.