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things before visulization
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@shenvitor
shenvitor committed Aug 30, 2024
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"import os\n",
"import warnings\n",
"\n",
"import numpy as np\n",
"import sympy as sp\n",
"from ampform.io import aslatex\n",
"from ampform.kinematics.angles import Phi, Theta\n",
"from ampform.kinematics.lorentz import (\n",
" ArrayMultiplication,\n",
" ArraySize,\n",
" BoostZMatrix,\n",
" Energy,\n",
" EuclideanNorm,\n",
" FourMomentumSymbol,\n",
" RotationYMatrix,\n",
" RotationZMatrix,\n",
" ThreeMomentum,\n",
" three_momentum_norm,\n",
")\n",
"from ampform.sympy import unevaluated\n",
"from ampform.sympy._array_expressions import ArraySum\n",
"from IPython.display import Latex\n",
"from tensorwaves.data import (\n",
" SympyDataTransformer,\n",
" TFPhaseSpaceGenerator,\n",
" TFUniformRealNumberGenerator,\n",
")\n",
"\n",
"STATIC_PAGE = \"EXECUTE_NB\" in os.environ\n",
"\n",
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"intensity_expr = sp.Abs(A12 + A23 + A31) ** 2\n",
"intensity_expr"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Phase Space Generation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Mass for $p\\gamma$ system"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"E_lab_gamma = 8.5\n",
"m_proton = 0.938\n",
"m_0 = np.sqrt(2 * E_lab_gamma * m_proton + m_proton**2)\n",
"m_lambda = 1.12\n",
"m_k = 0.494\n",
"m_pi = 0.135\n",
"m_0"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"rng = TFUniformRealNumberGenerator(seed=0)\n",
"phsp_generator = TFPhaseSpaceGenerator(\n",
" initial_state_mass=m_0,\n",
" final_state_masses={1: m_k, 2: m_pi, 3: m_lambda},\n",
")\n",
"phsp_momenta = phsp_generator.generate(500_000, rng)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Kinematic variables"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"tags": [
"hide-input"
]
},
"outputs": [],
"source": [
"@unevaluated\n",
"class SquaredInvariantMass(sp.Expr):\n",
" momentum: sp.Basic\n",
" _latex_repr_ = \"m_{{{momentum}}}^2\"\n",
"\n",
" def evaluate(self) -> sp.Expr:\n",
" p = self.momentum\n",
" p_xyz = ThreeMomentum(p)\n",
" return Energy(p) ** 2 - EuclideanNorm(p_xyz) ** 2\n",
"\n",
"\n",
"def formulate_helicity_angles(\n",
" pi: FourMomentumSymbol, pj: FourMomentumSymbol\n",
") -> tuple[Theta, Phi]:\n",
" pij = ArraySum(pi, pj)\n",
" beta = three_momentum_norm(pij) / Energy(pij)\n",
" Rz = RotationZMatrix(-Phi(pij), n_events=ArraySize(Phi(pij)))\n",
" Ry = RotationYMatrix(-Theta(pij), n_events=ArraySize(Theta(pij)))\n",
" Bz = BoostZMatrix(beta, n_events=ArraySize(beta))\n",
" pi_boosted = ArrayMultiplication(Bz, Ry, Rz, pi)\n",
" return Theta(pi_boosted), Phi(pi_boosted)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"p1 = FourMomentumSymbol(\"p1\", shape=[])\n",
"p2 = FourMomentumSymbol(\"p2\", shape=[])\n",
"p3 = FourMomentumSymbol(\"p3\", shape=[])\n",
"p12 = ArraySum(p1, p2)\n",
"p23 = ArraySum(p2, p3)\n",
"p31 = ArraySum(p3, p1)\n",
"\n",
"theta1_expr, phi1_expr = formulate_helicity_angles(p1, p2)\n",
"theta2_expr, phi2_expr = formulate_helicity_angles(p2, p3)\n",
"theta3_expr, phi3_expr = formulate_helicity_angles(p3, p1)\n",
"\n",
"s12_expr = SquaredInvariantMass(p12)\n",
"s23_expr = SquaredInvariantMass(p23)\n",
"s31_expr = SquaredInvariantMass(p31)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"kinematic_variables = {\n",
" theta1: theta1_expr,\n",
" theta2: theta2_expr,\n",
" theta3: theta3_expr,\n",
" phi1: phi1_expr,\n",
" phi2: phi2_expr,\n",
" phi3: phi3_expr,\n",
" s12: s12_expr,\n",
" s23: s23_expr,\n",
" s31: s31_expr,\n",
"}\n",
"\n",
"Latex(aslatex(kinematic_variables))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"helicity_transformer = SympyDataTransformer.from_sympy(\n",
" kinematic_variables, backend=\"jax\"\n",
")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"phsp = helicity_transformer(phsp_momenta)\n",
"list(phsp)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Parameters"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"jupyter": {
"source_hidden": true
},
"tags": [
"hide-input",
"scroll-input"
]
},
"outputs": [],
"source": [
"a_vals = [0, 1.0, 3.0, 3.5, 2.0] # Slight adjustment to emphasize higher waves\n",
"b_vals = [0, -1.0, 3.5, 0.5, 0] # Adjust for new final state coupling\n",
"c_vals = [0, 0, 3.0, 0, 0] # Adjust if more s-wave or p-wave is expected\n",
"\n",
"m_Kstar2_val = 1.43\n",
"m_Sigma_val = 1.385\n",
"m_Nstar_val = 1.71\n",
"\n",
"Gamma_Kstar2_val = 0.62\n",
"Gamma_Sigma_val = 0.2\n",
"Gamma_Nstar_val = 0.27\n",
"\n",
"l12_val = 2 # I still use 2 assuming K^*_2\n",
"l23_val = 1\n",
"l31_val = 0\n",
"\n",
"parameters_default = {\n",
" m_Kstar2: m_Kstar2_val,\n",
" m_Sigma: m_Sigma_val,\n",
" m_Nstar: m_Nstar_val,\n",
" Gamma_Kstar2: Gamma_Kstar2_val,\n",
" Gamma_Sigma: Gamma_Sigma_val,\n",
" Gamma_Nstar: Gamma_Nstar_val,\n",
" l12: l12_val,\n",
" l23: l23_val,\n",
" l31: l31_val,\n",
"}\n",
"\n",
"a_dict = {a[i]: a_vals[i + l_max] for i in range(-l_max, l_max + 1)}\n",
"b_dict = {b[i]: b_vals[i + l_max] for i in range(-l_max, l_max + 1)}\n",
"c_dict = {c[i]: c_vals[i + l_max] for i in range(-l_max, l_max + 1)}\n",
"parameters_default.update(a_dict)\n",
"parameters_default.update(b_dict)\n",
"parameters_default.update(c_dict)\n",
"\n",
"Latex(aslatex(parameters_default))"
]
}
],
"metadata": {
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