Custom topologies

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Custom topologies#

As illustrated in Generate transitions, the StateTransitionManager offers you a bit more flexibility than the façade function generate_transitions() used in the main Usage page. In this notebook, we go one step further, by specifying a custom Topology via StateTransitionManager.topologies.

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from IPython.display import Markdown

import qrules
from qrules import InteractionType, StateTransitionManager
from qrules.topology import Edge, Topology

2-to-2 topology#

As a simple example, we start with a 2-to-2 scattering topology. We define it as follows:

topology = Topology(
    nodes=range(2),
    edges=enumerate(
        [
            Edge(None, 0),
            Edge(None, 0),
            Edge(1, None),
            Edge(1, None),
            Edge(0, 1),
        ],
        -2,
    ),
)

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source = qrules.io.asmermaid(
    topology,
    markdown=True,
    render_initial_state_id=True,
    render_node=True,
    render_resonance_id=True,
)
Markdown(source)

        flowchart LR
    n_0["$$0$$"]
    n_1["$$1$$"]
    B["$$-2$$"]
    A["$$-1$$"]
    N0(("$$(0)$$"))
    N1(("$$(1)$$"))
    n_2("$$2$$")
    B --- N0
    A --- N0
    N1 --- n_0
    N1 --- n_1
    N0 --- n_2
    n_2 --- N1

First, we construct a StateTransitionManager for the transition \(K^-K^+ \to \pi^+\pi^-\). The constructed Topology can then be inserted via its topologies attribute:

stm = StateTransitionManager(
    initial_state=["K-", "K+"],
    final_state=["pi-", "pi+"],
    formalism="canonical",
)
stm.set_allowed_interaction_types([InteractionType.STRONG, InteractionType.EM])
stm.topologies = (topology,)  # tuple is immutable

For the rest, the process is just the same as in Generate transitions:

problem_sets = stm.create_problem_sets()
reaction_kk = stm.find_solutions(problem_sets)

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source = qrules.io.asmermaid(reaction_kk, collapse_graphs=True, markdown=True)
Markdown(source)

        flowchart LR
    T0_0["$$0: \pi^{-}$$"]
    T0_1["$$1: \pi^{+}$$"]
    T0_B["$$K^{-}$$"]
    T0_A["$$K^{+}$$"]
    T0_N0@{ shape: text, label: " " }
    T0_N1@{ shape: text, label: " " }
    T0_2("$$\begin{array}{ll} a_{0}(980)^{0} & \omega(782) \\\ a_{0}(1450)^{0} & \omega(1420) \\\ f_{0}(500) & \rho(770)^{0} \\\ f_{0}(980) & \rho(1450)^{0} \\\ f_{0}(1370) & \rho(1700)^{0} \\\ f_{0}(2020) &  \end{array}$$")
    T0_B --- T0_N0
    T0_A --- T0_N0
    T0_N1 --- T0_0
    T0_N1 --- T0_1
    T0_N0 --- T0_2
    T0_2 --- T0_N1

Warning

It is not yet possible to give the initial state a certain energy. So some collider process like \(e^-e^+\to\pi^+\pi\) does not result in a large number of resonances.

stm.initial_state = ["e-", "e+"]
problem_sets = stm.create_problem_sets()
reaction_ep = stm.find_solutions(problem_sets)

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source = qrules.io.asmermaid(reaction_ep, collapse_graphs=True, markdown=True)
Markdown(source)

        flowchart LR
    T0_0["$$0: \pi^{-}$$"]
    T0_1["$$1: \pi^{+}$$"]
    T0_B["$$e^{-}$$"]
    T0_A["$$e^{+}$$"]
    T0_N0@{ shape: text, label: " " }
    T0_N1@{ shape: text, label: " " }
    T0_2("$$f_{0}(500)$$")
    T0_B --- T0_N0
    T0_A --- T0_N0
    T0_N1 --- T0_0
    T0_N1 --- T0_1
    T0_N0 --- T0_2
    T0_2 --- T0_N1

What can do at most, is switch off MassConservation, either through the constructor of the StateTransitionManager, or by modifying ProblemSet.

stm = StateTransitionManager(
    initial_state=["e-", "e+"],
    final_state=["pi-", "pi+"],
    formalism="canonical",
    mass_conservation_factor=None,
)
stm.set_allowed_interaction_types([InteractionType.STRONG, InteractionType.EM])
stm.topologies = (topology,)
problem_sets = stm.create_problem_sets()
reaction_ep_no_mass = stm.find_solutions(problem_sets)

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source = qrules.io.asmermaid(reaction_ep_no_mass, collapse_graphs=True, markdown=True)
Markdown(source)

        flowchart LR
    T0_0["$$0: \pi^{-}$$"]
    T0_1["$$1: \pi^{+}$$"]
    T0_B["$$e^{-}$$"]
    T0_A["$$e^{+}$$"]
    T0_N0@{ shape: text, label: " " }
    T0_N1@{ shape: text, label: " " }
    T0_2("$$\begin{array}{llllll} a_{0}(980)^{0} & f_{0}(980) & \omega(782) & \psi(3770) & \rho(1700)^{0} & \Upsilon(11020) \\\ a_{0}(1450)^{0} & f_{0}(1370) & \omega(1420) & \psi(4040) & \Upsilon(1S) &  \\\ \chi_{c0}(1P) & f_{0}(1500) & \omega(1650) & \psi(4160) & \Upsilon(2S) &  \\\ \chi_{b0}(1P) & f_{0}(1710) & \phi(1020) & \psi(4415) & \Upsilon(3S) &  \\\ \chi_{b0}(2P) & f_{0}(2020) & \phi(1680) & \rho(770)^{0} & \Upsilon(4S) &  \\\ f_{0}(500) & J/\psi(1S) & \psi(2S) & \rho(1450)^{0} & \Upsilon(10860) &  \end{array}$$")
    T0_B --- T0_N0
    T0_A --- T0_N0
    T0_N1 --- T0_0
    T0_N1 --- T0_1
    T0_N0 --- T0_2
    T0_2 --- T0_N1
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