"""Functions for dynamics lineshapes and kinematics.
.. seealso:: :doc:`/appendix/dynamics`
"""
# pyright: reportPrivateUsage=false
from __future__ import annotations
import sympy as sp
from ampform.kinematics.phasespace import Kallen
from ampform.sympy import (
UnevaluatedExpression,
create_expression,
implement_doit_method,
make_commutative,
)
[docs]@make_commutative
@implement_doit_method
class P(UnevaluatedExpression):
def __new__(cls, s, mi, mj, **hints):
return create_expression(cls, s, mi, mj, **hints)
def evaluate(self):
s, mi, mj = self.args
return sp.sqrt(Kallen(s, mi**2, mj**2)) / (2 * sp.sqrt(s))
def _latex(self, printer, *args):
s, mi, mj = map(printer._print, self.args)
return Rf"p_{{{mi},{mj}}}\left({s}\right)"
[docs]@make_commutative
@implement_doit_method
class Q(UnevaluatedExpression):
def __new__(cls, s, m0, mk, **hints):
return create_expression(cls, s, m0, mk, **hints)
def evaluate(self):
s, m0, mk = self.args
return sp.sqrt(Kallen(s, m0**2, mk**2)) / (2 * m0) # <-- not s!
def _latex(self, printer, *args):
s, m0, mk = map(printer._print, self.args)
return Rf"q_{{{m0},{mk}}}\left({s}\right)"
[docs]@make_commutative
@implement_doit_method
class BreitWignerMinL(UnevaluatedExpression):
def __new__(
cls,
s,
decaying_mass,
spectator_mass,
resonance_mass,
resonance_width,
child2_mass,
child1_mass,
l_dec,
l_prod,
R_dec,
R_prod,
):
return create_expression(
cls,
s,
decaying_mass,
spectator_mass,
resonance_mass,
resonance_width,
child2_mass,
child1_mass,
l_dec,
l_prod,
R_dec,
R_prod,
)
def evaluate(self):
s, m_top, m_spec, m0, Γ0, m1, m2, l_dec, l_prod, R_dec, R_prod = self.args
q = Q(s, m_top, m_spec)
q0 = Q(m0**2, m_top, m_spec)
p = P(s, m1, m2)
p0 = P(m0**2, m1, m2)
width = EnergyDependentWidth(s, m0, Γ0, m1, m2, l_dec, R_dec)
return sp.Mul(
(q / q0) ** l_prod,
BlattWeisskopf(q * R_prod, l_prod) / BlattWeisskopf(q0 * R_prod, l_prod),
1 / (m0**2 - s - sp.I * m0 * width),
(p / p0) ** l_dec,
BlattWeisskopf(p * R_dec, l_dec) / BlattWeisskopf(p0 * R_dec, l_dec),
evaluate=False,
)
def _latex(self, printer, *args) -> str:
s = printer._print(self.args[0])
return Rf"\mathcal{{R}}\left({s}\right)"
[docs]@make_commutative
@implement_doit_method
class BuggBreitWigner(UnevaluatedExpression):
def __new__(cls, s, m0, Γ0, m1, m2, γ):
return create_expression(cls, s, m0, Γ0, m1, m2, γ)
def evaluate(self):
s, m0, Γ0, m1, m2, γ = self.args
s_A = m1**2 - m2**2 / 2 # Adler zero
g_squared = sp.Mul(
(s - s_A) / (m0**2 - s_A),
m0 * Γ0 * sp.exp(-γ * s),
evaluate=False,
)
return 1 / (m0**2 - s - sp.I * g_squared)
def _latex(self, printer, *args) -> str:
s = printer._print(self.args[0], *args)
return Rf"\mathcal{{R}}_\mathrm{{Bugg}}\left({s}\right)"
[docs]@make_commutative
@implement_doit_method
class FlattéSWave(UnevaluatedExpression):
# https://github.com/ComPWA/polarimetry/blob/34f5330/julia/notebooks/model0.jl#L151-L161
def __new__(cls, s, m0, widths, masses1, masses2):
return create_expression(cls, s, m0, widths, masses1, masses2)
def evaluate(self):
s, m0, (Γ1, Γ2), (ma1, mb1), (ma2, mb2) = self.args
p = P(s, ma1, mb1)
p0 = P(m0**2, ma2, mb2)
q = P(s, ma2, mb2)
q0 = P(m0**2, ma2, mb2)
Γ1 *= (p / p0) * m0 / sp.sqrt(s)
Γ2 *= (q / q0) * m0 / sp.sqrt(s)
Γ = Γ1 + Γ2
return 1 / (m0**2 - s - sp.I * m0 * Γ)
def _latex(self, printer, *args) -> str:
s = printer._print(self.args[0])
return Rf"\mathcal{{R}}_\mathrm{{Flatté}}\left({s}\right)"
[docs]@make_commutative
@implement_doit_method
class EnergyDependentWidth(UnevaluatedExpression):
def __new__(cls, s, m0, Γ0, m1, m2, L, R):
return create_expression(cls, s, m0, Γ0, m1, m2, L, R)
def evaluate(self):
s, m0, Γ0, m1, m2, L, R = self.args
p = P(s, m1, m2)
p0 = P(m0**2, m1, m2)
ff = BlattWeisskopf(p * R, L) ** 2
ff0 = BlattWeisskopf(p0 * R, L) ** 2
return sp.Mul(
Γ0,
(p / p0) ** (2 * L + 1),
m0 / sp.sqrt(s),
ff / ff0,
evaluate=False,
)
def _latex(self, printer, *args) -> str:
s = printer._print(self.args[0])
return Rf"\Gamma\left({s}\right)"
[docs]@make_commutative
@implement_doit_method
class BlattWeisskopf(UnevaluatedExpression):
def __new__(cls, z, L, **hints):
return create_expression(cls, z, L, **hints)
def evaluate(self) -> sp.Piecewise:
z, L = self.args
cases = {
0: 1,
1: 1 / (1 + z**2),
2: 1 / (9 + 3 * z**2 + z**4),
}
return sp.Piecewise(
*[(sp.sqrt(expr), sp.Eq(L, l_val)) for l_val, expr in cases.items()]
)
def _latex(self, printer, *args):
z, L = map(printer._print, self.args)
return Rf"F_{{{L}}}\left({z}\right)"
