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FEAT: define RelativisticBreitWigner and FormFactor
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@redeboer
redeboer committed Apr 27, 2024
1 parent 9f1d987 commit b9dc49c
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126 changes: 29 additions & 97 deletions docs/jpsi2ksp.ipynb
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Expand Up @@ -31,23 +31,24 @@
"import logging\n",
"import os\n",
"import warnings\n",
"from typing import TYPE_CHECKING, Any\n",
"from typing import TYPE_CHECKING\n",
"\n",
"import graphviz\n",
"import jax.numpy as jnp\n",
"import matplotlib.pyplot as plt\n",
"import qrules\n",
"import sympy as sp\n",
"from ampform.dynamics import EnergyDependentWidth, formulate_form_factor\n",
"from ampform.dynamics import BlattWeisskopfSquared, EnergyDependentWidth\n",
"from ampform.kinematics.phasespace import compute_third_mandelstam\n",
"from ampform.sympy import perform_cached_doit, unevaluated\n",
"from ampform.sympy import perform_cached_doit\n",
"from IPython.display import Latex, Markdown\n",
"from tensorwaves.data.transform import SympyDataTransformer\n",
"from tqdm.auto import tqdm\n",
"\n",
"from ampform_dpd import DalitzPlotDecompositionBuilder, get_particle\n",
"from ampform_dpd.adapter.qrules import normalize_state_ids, to_three_body_decay\n",
"from ampform_dpd.decay import IsobarNode, Particle, ThreeBodyDecayChain\n",
"from ampform_dpd.dynamics import FormFactor, RelativisticBreitWigner\n",
"from ampform_dpd.io import (\n",
" as_markdown_table,\n",
" aslatex,\n",
Expand All @@ -68,7 +69,9 @@
},
{
"cell_type": "markdown",
"metadata": {},
"metadata": {
"jp-MarkdownHeadingCollapsed": true
},
"source": [
"## Decay definition"
]
Expand Down Expand Up @@ -158,7 +161,9 @@
},
{
"cell_type": "markdown",
"metadata": {},
"metadata": {
"jp-MarkdownHeadingCollapsed": true
},
"source": [
"## Lineshapes for dynamics"
]
Expand All @@ -172,13 +177,6 @@
":::"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the following, we define the **relativistic Breit-Wigner function** as:"
]
},
{
"cell_type": "code",
"execution_count": null,
Expand All @@ -187,48 +185,20 @@
"source_hidden": true
},
"tags": [
"hide-input"
"hide-input",
"full-width"
]
},
"outputs": [],
"source": [
"@unevaluated\n",
"class RelativisticBreitWigner(sp.Expr):\n",
" s: Any\n",
" mass0: Any\n",
" gamma0: Any\n",
" m1: Any\n",
" m2: Any\n",
" angular_momentum: Any\n",
" meson_radius: Any\n",
" _latex_repr_ = (\n",
" R\"\\mathcal{{R}}_{{{angular_momentum}}}\\left({s}, {mass0}, {gamma0}\\right)\"\n",
" )\n",
"\n",
" def evaluate(self):\n",
" s, m0, w0, m1, m2, angular_momentum, meson_radius = self.args\n",
" width = EnergyDependentWidth(\n",
" s=s,\n",
" mass0=m0,\n",
" gamma0=w0,\n",
" m_a=m1,\n",
" m_b=m2,\n",
" angular_momentum=angular_momentum,\n",
" meson_radius=meson_radius,\n",
" name=Rf\"\\Gamma_{{{sp.latex(angular_momentum)}}}\",\n",
" )\n",
" return (m0 * w0) / (m0**2 - s - width * m0 * sp.I)\n",
"\n",
"\n",
"bw = RelativisticBreitWigner(*sp.symbols(\"s m0 Gamma0 m1 m2 L R\"))\n",
"Latex(aslatex({bw: bw.doit(deep=False)}))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"with $\\Gamma_0(s)$ a {class}`~ampform.dynamics.EnergyDependentWidth`, and we define the **form factor** as:"
"s, m0, w0, m1, m2, L, R, z = sp.symbols(\"s m0 Gamma0 m1 m2 L R z\")\n",
"exprs = [\n",
" RelativisticBreitWigner(s, m0, w0, m1, m2, L, R),\n",
" EnergyDependentWidth(s, m0, w0, m1, m2, L, R),\n",
" FormFactor(s, m1, m2, L, R),\n",
" BlattWeisskopfSquared(z, L),\n",
"]\n",
"Latex(aslatex({e: e.doit(deep=False) for e in exprs}))"
]
},
{
Expand All @@ -238,50 +208,8 @@
"jupyter": {
"source_hidden": true
},
"tags": [
"hide-input"
]
},
"outputs": [],
"source": [
"@unevaluated\n",
"class FormFactor(sp.Expr):\n",
" s: Any\n",
" m1: Any\n",
" m2: Any\n",
" angular_momentum: Any\n",
" meson_radius: Any\n",
"\n",
" _latex_repr_ = R\"\\mathcal{{F}}_{{{angular_momentum}}}\\left({s}, {m1}, {m2}\\right)\"\n",
"\n",
" def evaluate(self):\n",
" s, m1, m2, angular_momentum, meson_radius = self.args\n",
" return formulate_form_factor(\n",
" s=s,\n",
" m_a=m1,\n",
" m_b=m2,\n",
" angular_momentum=angular_momentum,\n",
" meson_radius=meson_radius,\n",
" )\n",
"\n",
"\n",
"ff = FormFactor(*sp.symbols(\"s m1 m2 L R\"))\n",
"Latex(aslatex({ff: ff.doit(deep=False)}))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here, $B_L^2$ is a {class}`~ampform.dynamics.BlattWeisskopfSquared`."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"jupyter": {
"source_hidden": true
"mystnb": {
"code_prompt_show": "Define dynamics builder functions"
},
"tags": [
"hide-input",
Expand Down Expand Up @@ -400,7 +328,9 @@
},
{
"cell_type": "markdown",
"metadata": {},
"metadata": {
"jp-MarkdownHeadingCollapsed": true
},
"source": [
"## Model formulation"
]
Expand Down Expand Up @@ -473,12 +403,14 @@
},
"outputs": [],
"source": [
"Latex(aslatex(model.amplitudes))"
"Latex(aslatex({k: v for k, v in model.amplitudes.items() if v}))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"metadata": {
"jp-MarkdownHeadingCollapsed": true
},
"source": [
"## Preparing for input data"
]
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52 changes: 52 additions & 0 deletions src/ampform_dpd/dynamics/__init__.py
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Original file line number Diff line number Diff line change
Expand Up @@ -5,10 +5,41 @@
from typing import Any

import sympy as sp
from ampform.dynamics import formulate_form_factor
from ampform.kinematics.phasespace import Kallen
from ampform.sympy import unevaluated


@unevaluated
class RelativisticBreitWigner(sp.Expr):
s: Any
mass0: Any
gamma0: Any
m1: Any
m2: Any
angular_momentum: Any
meson_radius: Any
_latex_repr_ = (
R"\mathcal{{R}}_{{{angular_momentum}}}\left({s}, {mass0}, {gamma0}\right)"
)

def evaluate(self):
from ampform.dynamics import EnergyDependentWidth # noqa: PLC0415

s, m0, w0, m1, m2, angular_momentum, meson_radius = self.args
width = EnergyDependentWidth(
s=s,
mass0=m0,
gamma0=w0,
m_a=m1,
m_b=m2,
angular_momentum=angular_momentum,
meson_radius=meson_radius,
name=Rf"\Gamma_{{{sp.latex(angular_momentum)}}}",
)
return (m0 * w0) / (m0**2 - s - width * m0 * sp.I)


@unevaluated
class P(sp.Expr):
s: Any
Expand Down Expand Up @@ -150,3 +181,24 @@ def evaluate(self) -> sp.Piecewise:
return sp.Piecewise(*[
(sp.sqrt(expr), sp.Eq(L, l_val)) for l_val, expr in cases.items()
])


@unevaluated
class FormFactor(sp.Expr):
s: Any
m1: Any
m2: Any
angular_momentum: Any
meson_radius: Any

_latex_repr_ = R"\mathcal{{F}}_{{{angular_momentum}}}\left({s}, {m1}, {m2}\right)"

def evaluate(self):
s, m1, m2, angular_momentum, meson_radius = self.args
return formulate_form_factor(
s=s,
m_a=m1,
m_b=m2,
angular_momentum=angular_momentum,
meson_radius=meson_radius,
)

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