DalitzPlotDKpipi

#Dalitz plot simulation for a $D^{+}→k^{-}\pi^{+} \pi^{+}$ decay 19/11/2023,

Author: Elser Lopez, Contact: [email protected]

General information

This code makes a Montecarlo simulation through the Metropolis-Hastings algorithm, following the equations for a three body decay showing into the PDG Kinematics review, and using the masses as: $M=m_{D}=1870$ MeV, $m_1=m_{k^{-}}=494$ MeV, $m_{k^{*0}}=890$ MeV, $m_{2}=m_{3}=m_{\pi^{+}}=140$ MeV.

On the other hand, the aceptance ratio uses the probability amplitud as

$|{\overline{\mathcal{M}}(m_{12_{i→j}})}|^2=A^2 \dfrac{m_{k^{}}^4}{(m_{12_{j}}^2-m_{k^{}}^2)^2 +m_{k^{}}^2\Gamma_{k^{}}^2 }$,

where $A^2=2.18 \times 10^{-17}$ and $Γ_{k*}=50$ MeV.

In order to run this code you need the following Python Libraries:

• numpy
• random
• matplotlib
• mpl_scatter_density

This code saves two figures corresponding to the Dalitz plot from the equations and a Dalitz plot from the Montecarlo simulation. The first one is called "DalitzPlot.pdf" and the second "DalitzPlotMontecarlo.pdf"

Finally, this code was built using Python 3.10.12; Other versions may not work.