Decay time integrals in neutral meson mixing and their efficient evaluation
Decay time integrals in neutral meson mixing and their efficient evaluation
复制标题
中性介子混合中的衰减时间积分及其高效评估
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
M. Schiller
中科院分区：
文献类型：
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作者：
T. M. Karbach;G. Raven;M. Schiller
在中性介子混合中，需要一类卷积积分，其解涉及复宗量z的误差函数mathrm{erf}（z）。我们展示了这些积分的解析解的一般形状，并给出了允许这些表达式归一化以用于概率密度函数的表达式。此外，我们推导出表达式，允许（衰减时间）接受这些积分，或允许计算的时刻。
我们还描述了数值例程的实现，该例程允许在C++中对$w（z）=e^{-z^2}（1-mathrm{erf}（-iz））$进行数值计算，有时也称为Faddeeva函数。这些新例程在速度和准确性方面都优于旧的CERNLIB例程WWERF/CWEF。这些新的例程是RooFit包的一部分，并且从ROOT版本5.34/08开始就随它一起分发。
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.