C^3ATS: Coupled-Channel effects in the Correlation Analysis Tool using the Schrödinger equation

C^3ATS项目的重点是开发一个c++程序包，该程序包能够数值求解具有N个耦合通道的系统的径向Schrödinger方程，并提供考试中对的相关函数。CATS软件的当前版本已经可用，但它只能提供单通道问题的结果。CATS的输出和扩展C^3ATS的输出是相关函数，它取决于两个主要成分：相互作用和对的发射源，与手边的碰撞系统（pp，p-A或A-A）有关。耦合通道动力学是强相互作用的基本特征，因此预计它与1 fm左右的源尺寸有关（通常在高能pp碰撞中达到）。由于耦合通道的存在可以导致束缚态、分子态和共振的形成，因此需要充分理解耦合通道在强子物理中所起的作用。相对动量空间中的相关函数已被证明对非弹性通道的存在特别敏感，因此可以利用它来研究通过改变源尺寸来研究不同通道之间耦合的影响。除了相互作用之外，关联函数中耦合通道的影响还取决于所谓的转换权重w_j，它与所产生的粒子对产率和所考虑的非弹性通道的运动学性质有关。在这个项目中，我们提出了一个现象学模型，将在C^3ATS扩展中实现，根据统计模型计算和运动部分的传输模型结果相结合来确定这些权重。这两种工具能够在较宽的质心能量范围内（从几个GeV到TeV尺度）提供任何碰撞系统的wj信息。该项目的最终目标是为在奇异区|S|=2,3中重子-重子相互作用和重子-反重子相互作用中主要存在耦合通道的系统提供预测。基于晶格计算、手性方法和介子交换模型的理论模型已经提出，并将使用C^3ATS详细研究耦合通道及其对不同源尺寸的相关函数的影响。

The proposed project C^3ATS focuses on the development of a C++ package able to numerically solve the radial Schrödinger equation for a system with N coupled-channels and to provide the correlation function of the pair in exam. A current version of the software CATS is already available but it can only provide results for single-channel problems. The output of CATS and henc of the extension C^3ATS is the correlation function which depends on two main ingredients: the interaction and the emitting source of pairs, related to the colliding system (pp,p-A or A-A) at hand. The coupled-channels dynamics is a fundamental feature of the strong interaction, hence it is expected to be relevant for source sizes around 1 fm (typically reached in high-energy pp collisions). The full understanding of the role played by coupled-channels in hadron physics is needed since their presence can lead to the formation of bound states, molecular states and resonances. The correlation function in the relative momentum space has proven to be particularly sensitive to the presence of inelastic channels, hence it can be exploited to study the effect of the couplings amongst the different channels by varying the source size. Besides the interaction, the effect of coupled-channels in the correlation function depends also on the so-called conversion weights w_j, connected to the produced particle pair yields and the kinematics properties of the considered inelastic channel. In this project we propose a phenomenological model, to be implemented in the C^3ATS extension, to determine these weights based on the combination of statistical model calculations and transport models results for the kinematic part. These two tools are able to provide the informations on wj for any colliding systems in a wide center-of-mass energy range (from few GeV to the TeV scale).The final goal of the project is to provide predictions for systems with a dominant presence of coupled-channels as baryon-baryon interactions in the strangeness sector |S|=2,3 and baryon-antibaryon interactions. Theoretical models based on lattice calculations, chiral approaches and meson-exchange models are present and with C^3ATS a detailed study of the coupled-channels and their effects on the correlation function for different source sizes will be delivered.