decayamplitude 0.1.0

A tool for modeling of amplitudes using jax

Welcome to the decayamplitude software Project

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Table of Contents

• Installation
• Goal
• Related projects
• How to cite
• License

Installation

pip install decayamplitude

Goal

The software project decayamplitude provides an amplitude package working in tandem with decayangle to build full cascade reaction amplitudes. The main goal is to provide a simple interface to build decay chains and their amplitudes, which can be used in amplitude analyses.

Online Decay Editor

There is a beta version of a web based decay editor, which is hosted here. The Website allows for an easy selection of a decay and resonances. Once finished a script generating an amplitude with decayamplitude can be downloaded. This is usually the easiest and quickest way to get a working amplitude. Explicit lineshapes need then to be defined by the user, where it is marked in the downloaded script.

Usage

from decayamplitude.resonance import Resonance
from decayamplitude.rotation import QN, Angular
from decayamplitude.chain import DecayChain, MultiChain
from decayamplitude.combiner import ChainCombiner




from decayangle.decay_topology import Topology, Node, TopologyCollection

# First we define the final state
final_state_qn = {
        1: QN(1, 1),
        2: QN(2, 1),
        3: QN(0, 1)
    }

# decayangles Topology class is used to generate the angular variables. Be carefull here, as fit results may depend on the ordering. 

topology1 = Topology(
    0,
    decay_topology=((2,3), 1)
)
topology2 = Topology(
    0,
    decay_topology=((1, 2), 3)
)

# alternatively we can use the topology collection to define all topologies automatically
tg = TopologyCollection(
    0,
    [1,2,3]
)
tg.topologies

We now have a basic definition of our decay scheme. But we need resonances to react. In general for a multi body decay we want to define a list of resonances for each isobar. Then let the code figure out all the possible decay chains.

resonances1 = {
    # we need to define resonances for each internal node of the decay chain
    # A resonance needs a node, to which it couples, quantum numbers, a lineshape
    # and a list of argument names, which will be used to map the parameters of the resonance 
    # to the outside, once all our configurations are combined into an amplitude
    (2,3): Resonance(topology1.nodes[(2, 3)], 
                    quantum_numbers=QN(0, -1), 
                    lineshape=BW_lineshape(topology1.nodes[(2, 3)].mass(momenta)), 
                    argnames=["gamma1", "m01"]),

    # since we can not only model decays, but also transitions from 2 particle
        # to many particles
    # Thus we may have to model multiple initial resonances and their production
        # with a lineshape
    # For decays we can use a constant lineshape 
    # The preserve_parity flag controlls which L S couplings will be produced, 
        # if one uses the automated generation of the possible couplings
    # This has no effect if one plugs in couplings by hand
    0: Resonance(Node(0), quantum_numbers=QN(1, 1),
    lineshape=constant_lineshape, 
    argnames=[], 
    preserve_partity=False)

# we use the argnames, to use the same mass for both BW lineshapes, but different widths
resonances2 = {
    (1, 2): Resonance(nodes_2[(1, 2)], quantum_numbers=QN(3, -1), lineshape=BW_lineshape(nodes_2[(1, 2)].mass(momenta)), argnames=["gamma2", "m01"]),
    0: Resonance(Node(0), quantum_numbers=QN(1, 1), lineshape=constant_lineshape, argnames=[], preserve_partity=False)
    }
}

Now we can take the resonance dictionaries and combine them with a topology in order to produce a DecayChain.

chain1 = DecayChain(topology = topology1,
        resonances = resonances1,
        momenta = momenta,
        final_state_qn = final_state_qn)

chain2 = DecayChain(topology = topology2,
        resonances = resonances2,
        momenta = momenta,
        final_state_qn = final_state_qn)

These chains are already able to produce a chain function, which can be evaluated for a given set of parameters.

chain1.chain_function

We can now combine the chains into a ChainCombiner object. This object will internally take care of the alignmeht operations.

combined = ChainCombiner([chain1, chain2])

# we can generate the unpolarized amplitude
unpolarized, argnames = combined.unpolarized_amplitude(combined.generate_couplings())
# unpolarized(*args) will return the amplitude for the given parameters

# we can generate the matix elements depending on the polarization of the particles
polarized, lambdas, argnames = combined.polarized_amplitude(combined.generate_couplings())
# polarized(*lambdas, *args) will return the amplitude for the given parameters and polarization

# here we get a list of aditional function parameters, which represent the polarization of the initial and final state particles
# lambdas = ["h_0", "h_1", "h_2", "h_3"]

# alternatively we can produce all matrix elements at once
matrx_function, matrix_argnames = combined.matrix_function(combined.generate_couplings())
# here we only have the initial state polarization as an additional parameter
# matrix_argnames = ["h_0"] + argnames
# matrx_function(h_0, *args) will return the amplitude for the given parameters and polarization

Related projects

Amplitude analyses dealing with non-zero spin of final-state particles have to implement wigner rotations in some way. However, there are a few projects addressing these rotations explicitly using analytic expressions in DPD paper, derived for three-body decays:

• ThreeBodyDecays.jl,
• SymbolicThreeBodyDecays.jl,
• ComPWA/ampform-dpd.

How to cite

This software package as well as the closely related decayangle should be cited by the accompaning paper Wigner Rotations for Cascade Reactions

License

decayamplitude is distributed under the terms of the MIT license.