# pylint: disable=arguments-differ, abstract-method, protected-access,
# pylint: disable=too-many-arguments, unbalanced-tuple-unpacking
"""Functions for determining phase space boundaries.
.. seealso:: :doc:`/usage/kinematics`
"""
from __future__ import annotations
import sympy as sp
from ampform.sympy import (
UnevaluatedExpression,
create_expression,
implement_doit_method,
make_commutative,
)
[docs]@make_commutative
@implement_doit_method
class Kibble(UnevaluatedExpression):
"""Kibble function for determining the phase space region."""
def __new__(cls, sigma1, sigma2, sigma3, m0, m1, m2, m3, **hints) -> Kibble:
return create_expression(cls, sigma1, sigma2, sigma3, m0, m1, m2, m3, **hints)
def evaluate(self) -> Kallen:
sigma1, sigma2, sigma3, m0, m1, m2, m3 = self.args
return Kallen(
Kallen(sigma2, m2**2, m0**2), # type: ignore[operator]
Kallen(sigma3, m3**2, m0**2), # type: ignore[operator]
Kallen(sigma1, m1**2, m0**2), # type: ignore[operator]
)
def _latex(self, printer, *args):
sigma1, sigma2, *_ = map(printer._print, self.args)
return Rf"\phi\left({sigma1}, {sigma2}\right)"
[docs]@make_commutative
@implement_doit_method
class Kallen(UnevaluatedExpression):
"""Källén function, used for computing break-up momenta."""
def __new__(cls, x, y, z, **hints) -> Kallen:
return create_expression(cls, x, y, z, **hints)
def evaluate(self) -> sp.Expr:
x, y, z = self.args
return x**2 + y**2 + z**2 - 2 * x * y - 2 * y * z - 2 * z * x # type: ignore[operator]
def _latex(self, printer, *args):
x, y, z = map(printer._print, self.args)
return Rf"\lambda\left({x}, {y}, {z}\right)"
[docs]def is_within_phasespace(
sigma1, sigma2, m0, m1, m2, m3, outside_value=sp.nan
) -> sp.Piecewise:
"""Determine whether a set of masses lie within phase space."""
sigma3 = compute_third_mandelstam(sigma1, sigma2, m0, m1, m2, m3)
kibble = Kibble(sigma1, sigma2, sigma3, m0, m1, m2, m3)
return sp.Piecewise(
(1, sp.LessThan(kibble, 0)),
(outside_value, True),
)
[docs]def compute_third_mandelstam(sigma1, sigma2, m0, m1, m2, m3) -> sp.Add:
"""Compute the third Mandelstam variable in a three-body decay."""
return m0**2 + m1**2 + m2**2 + m3**2 - sigma1 - sigma2
