Decay time integrals in neutral meson mixing and their efficient evaluation

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