# Welcome to the PWA Expert System!¶

Warning

The PWA Expert System has been split up into QRules and AmpForm. Please use these packages instead!

The two purposes of the Partial Wave Analysis Expert System are to:

1. validate a particle reaction, based on given information.
E.g.: Can a $$\pi^0$$ decay into 1, 2, 3 $$\gamma$$ particles?

2. create partial wave analysis amplitude models, based on basic information of a reaction, for instance, an amplitude model for $$J/\psi \rightarrow \gamma\pi^0\pi^0$$ in the helicity or canonical formalism.

The user only has to provide a basic information of the particle reaction, such as an initial state and a final state. Helper functions provide easy ways to configure the system, but the user still has full control. The expert system then constructs several hypotheses for what happens during the transition from initial to final state.

## Internal design¶

Internally, the PWA Expert System consists of three major components.

### 1. State Transition Graphs¶

A StateTransitionGraph is a directed graph that consists of nodes and edges. In a directed graph, each edge must be connected to at least one node (in correspondence to Feynman graphs). This way, a graph describes the transition from one state to another.

• The edges correspond to particles/states, in other words a collection of properties such as the quantum numbers that characterize the particle state.

• Each node represents an interaction and contains all information for the transition of this specific step. Most importantly, a node contains a collection of conservation rules that have to be satisfied. An interaction node has $$M$$ ingoing lines and $$N$$ outgoing lines, where $$M,N \in \mathbb{Z}$$, $$M > 0, N > 0$$.

### 2. Conservation Rules¶

The central component of the expert system are the conservation rules. They belong to individual nodes and receive properties about the node itself, as well as properties of the ingoing and outgoing edges of that node. Based on those properties the conservation rules determine whether edges pass or not.

### 3. Solvers¶

The determination of the correct state properties in the graph is done by solvers. New properties are set for intermediate edges and interaction nodes and their validity is checked with the conservation rules.

## Workflow of the Expert System¶

1. Preparation

1.1. Build all possible topologies. A topology is represented by a graph, in which the edges and nodes are empty (no particle information).

1.2. Fill the topology graphs with the user provided information. Typically these are the graph’s ingoing edges (initial state) and outgoing edges (final state).

2. Solving

2.1. Propagate quantum number information through the complete graph while respecting the specified conservation laws. Information like mass is not used in this first solving step.

2.2. Clone graphs while inserting concrete matching particles for the intermediate edges (mainly adds the mass variable).

2.3. Validate the complete graphs, so run all conservation law check that were postponed from the first step.

3. Generate an amplitude model, e.g. helicity or canonical amplitude.