kinematics¶

The create_expressions method forms the bridge between four-momentum data for the decay you are studying and the kinematic variables that are in the HelicityModel. These are invariant mass (see get_invariant_mass_label()) and the \(\theta\) and \(\phi\) helicity angles (see get_helicity_angle_label()).

create_expressions() → Dict[str, Expr][source]¶

permutate_registered_topologies() → None[source]¶

Register permutations of all registered_topologies.

See Extend kinematic variables.

reaction_info: ReactionInfo¶

register_topology(topology: Topology) → None[source]¶

register_transition(transition: StateTransition) → None[source]¶

registered_topologies: Set[Topology]¶

class InvariantMass(momentum: ArraySymbol, **hints: Any)[source]¶

Bases: ampform.kinematics.HasMomentum, ampform.sympy.UnevaluatedExpression

is_extended_real = True¶

class Phi(momentum: ArraySymbol, **hints: Any)[source]¶

Bases: ampform.kinematics.HasMomentum, ampform.sympy.UnevaluatedExpression

is_extended_real = True¶

class RotationY(angle: Expr, **hints: Any)[source]¶

Bases: sympy.core.expr.Expr

property angle¶

as_explicit() → Expr[source]¶

class RotationZ(angle: Symbol, **hints: Any)[source]¶

Bases: sympy.core.expr.Expr

property angle¶

as_explicit() → Expr[source]¶

class Theta(momentum: ArraySymbol, **hints: Any)[source]¶

Bases: ampform.kinematics.HasMomentum, ampform.sympy.UnevaluatedExpression

is_extended_real = True¶

class ThreeMomentumNorm(momentum: ArraySymbol, **hints: Any)[source]¶

Bases: ampform.kinematics.HasMomentum, ampform.sympy.UnevaluatedExpression

is_extended_real = True¶

compute_helicity_angles(four_momenta: Dict[int, ArraySymbol], topology: Topology) → Dict[str, Expr][source]¶

compute_invariant_masses(four_momenta: Dict[int, ArraySymbol], topology: Topology) → Dict[str, Expr][source]¶: Compute the invariant masses for all final state combinations.

create_four_momentum_symbols(topology: Topology) → Dict[int, ArraySymbol][source]¶

determine_attached_final_state(topology: Topology, state_id: int) → List[int][source]¶

Determine all final state particles of a transition.

These are attached downward (forward in time) for a given edge (resembling the root).

Example

For edge 5 in Figure topologies[0], we get:

>>> from qrules.topology import create_isobar_topologies
>>> topologies = create_isobar_topologies(5)
>>> determine_attached_final_state(topologies[0], state_id=5)
[0, 3, 4]

get_helicity_angle_label(topology: Topology, state_id: int) → Tuple[str, str][source]¶

Generate labels that can be used to identify helicity angles.

The generated subscripts describe the decay sequence from the right to the left, separated by commas. Resonance edge IDs are expressed as a sum of the final state IDs that lie below them (see determine_attached_final_state()). The generated label does not state the top-most edge (the initial state).

Example

The following two allowed isobar topologies for a 1-to-5-body decay illustrates how the naming scheme results in a unique label for each of the eight edges in the decay topology. Note that label only uses final state IDs, but still reflects the internal decay topology.

>>> from qrules.topology import create_isobar_topologies
>>> topologies = create_isobar_topologies(5)
>>> topology = topologies[0]
>>> for i in topology.intermediate_edge_ids | topology.outgoing_edge_ids:
...     phi_label, theta_label = get_helicity_angle_label(topology, i)
...     print(f"{i}: '{phi_label}'")
0: 'phi_0,0+3+4'
1: 'phi_1,1+2'
2: 'phi_2,1+2'
3: 'phi_3,3+4,0+3+4'
4: 'phi_4,3+4,0+3+4'
5: 'phi_0+3+4'
6: 'phi_1+2'
7: 'phi_3+4,0+3+4'
>>> topology = topologies[1]
>>> for i in topology.intermediate_edge_ids | topology.outgoing_edge_ids:
...     phi_label, theta_label = get_helicity_angle_label(topology, i)
...     print(f"{i}: '{phi_label}'")
0: 'phi_0,0+1'
1: 'phi_1,0+1'
2: 'phi_2,2+3+4'
3: 'phi_3,3+4,2+3+4'
4: 'phi_4,3+4,2+3+4'
5: 'phi_0+1'
6: 'phi_2+3+4'
7: 'phi_3+4,2+3+4'

Some labels explained:

phi_1+2: edge 6 on the left topology, because for this topology, we have \(p_6=p_1+p_2\).
phi_2+3+4: edge 6 right, because for this topology, \(p_6=p_2+p_3+p_4\).
phi_1,1+2: edge 1 left, because 1 decays from \(p_6=p_1+p_2\).
phi_1,0+1: edge 1 right, because it decays from \(p_5=p_0+p_1\).
phi_4,3+4,2+3+4: edge 4 right, because it decays from edge 7 (\(p_7=p_3+p_4\)), which comes from edge 6 (\(p_7=p_2+p_3+p_4\)).

As noted, the top-most parent (initial state) is not listed in the label.

topologies[0]¶

topologies[1]¶

get_invariant_mass_label(topology: Topology, state_id: int) → str[source]¶

Generate an invariant mass label for a state (edge on a topology).

Example

In the case shown in Figure topologies[0], the invariant mass of state \(5\) is \(m_{034}\), because \(p_5=p_0+p_3+p_4\):

>>> from qrules.topology import create_isobar_topologies
>>> topologies = create_isobar_topologies(5)
>>> get_invariant_mass_label(topologies[0], state_id=5)
'm_034'

Naturally, the ‘invariant’ mass label for a final state is just the mass of the state itself:

>>> get_invariant_mass_label(topologies[0], state_id=1)
'm_1'

implement_latex_subscript(subscript: str) → Callable[[Type[UnevaluatedExpression]], Type[UnevaluatedExpression]][source]¶

AmpForm

kinematics¶