Amplitudes explicit form

ComPWA · Sep 6, 2024 · 514907e · 514907e
1 parent 6307f25
commit 514907e
Showing 1 changed file with 146 additions and 8 deletions.
diff --git a/docs/lambda-k-pi/manual-dpd.ipynb b/docs/lambda-k-pi/manual-dpd.ipynb
@@ -54,9 +54,11 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "metadata": {
+    "jp-MarkdownHeadingCollapsed": true
+   },
    "source": [
-    "# Reaction "
+    "## Reaction "
    ]
   },
   {
@@ -206,7 +208,17 @@
    "outputs": [],
    "source": [
     "half = sp.Rational(1, 2)\n",
-    "\n",
+    "three_half = sp.Rational(3, 2)\n",
+    "five_half = sp.Rational(5, 2)\n",
+    "seven_half = sp.Rational(7, 2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
     "A1 = sp.IndexedBase(\"A^1\")\n",
     "A2 = sp.IndexedBase(\"A^2\")\n",
     "A3 = sp.IndexedBase(\"A^3\")\n",
@@ -303,16 +315,41 @@
     "    m_k = sp.Symbol(rf\"m_{{{resonance_name}}}\")\n",
     "    gamma_k = sp.Symbol(rf\"\\Gamma_{{{resonance_name}}}\")\n",
     "    theta23, phi23 = sp.symbols(r\"theta_23 phi_23\")  # noqa: F841\n",
-    "    s23, lambda_R = sp.symbols(r\"s_{23} \\lambda_K^*\")\n",
+    "    s23, lambda_R = sp.symbols(r\"s_{23} \\lambda_{K^*}\")\n",
     "    delta = sp.KroneckerDelta(-half, lambda_R + half)\n",
     "    d_k = Wigner.d(1, lambda_R, 0, theta23)\n",
     "    return sp.Sum(\n",
     "        (gamma_k * m_k * delta * c_k * d_k / (-sp.I * gamma_k * m_k + m_k**2 - s23)),\n",
     "        (lambda_R, -lambda_r_value, lambda_r_value),\n",
-    "    )\n",
-    "\n",
-    "\n",
-    "formualte_A1(\"K^{*}(1410)\", 1)"
+    "    )"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "A1 = (\n",
+    "    formualte_A1(\"K^{*}(1410)^+\", 1)\n",
+    "    + formualte_A1(\"K^{*}(1680)^+\", 1)\n",
+    "    + formualte_A1(\"K^{*}(892)^+\", 1)\n",
+    "    + formualte_A1(\"K^{*}_0(1430)^+\", 0)\n",
+    "    + formualte_A1(\"K^{*}_0(700)\", 0)\n",
+    "    + formualte_A1(\"K^{*}_2(1430)\", 2)\n",
+    "    + formualte_A1(\"K^{*}_3(1780)\", 3)\n",
+    "    + formualte_A1(\"K^{*}_4(2045)\", 4)\n",
+    ")\n",
+    "A1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "Math(aslatex(A1, terms_per_line=1))"
    ]
   },
   {
@@ -345,6 +382,57 @@
     "A2_expr"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def formualte_A2(resonance_name, lambda_r_value):  # noqa: N802\n",
+    "    c_k = sp.Symbol(rf\"C_{{{resonance_name}}}\")\n",
+    "    m_k = sp.Symbol(rf\"m_{{{resonance_name}}}\")\n",
+    "    gamma_k = sp.Symbol(rf\"\\Gamma_{{{resonance_name}}}\")\n",
+    "    theta31, phi31 = sp.symbols(r\"theta_31 phi_31\")  # noqa: F841\n",
+    "    s31, lambda_R = sp.symbols(r\"s_{31} \\lambda_{\\Sigma^*}\")\n",
+    "    delta = sp.KroneckerDelta(-half, lambda_R + half)\n",
+    "    d_k = Wigner.d(1, lambda_R, 0, theta31)\n",
+    "    return sp.Sum(\n",
+    "        (gamma_k * m_k * delta * c_k * d_k / (-sp.I * gamma_k * m_k + m_k**2 - s31)),\n",
+    "        (lambda_R, -lambda_r_value, lambda_r_value),\n",
+    "    )\n",
+    "\n",
+    "\n",
+    "formualte_A2(r\"\\Sigma(1385)^0\", three_half)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "A2 = (\n",
+    "    formualte_A2(r\"\\Sigma(1385)^0\", three_half)\n",
+    "    + formualte_A2(r\"\\Sigma(1660)^0\", half)\n",
+    "    + formualte_A2(r\"\\Sigma(1670)^0\", three_half)\n",
+    "    + formualte_A2(r\"\\Sigma(1750)^0\", half)\n",
+    "    + formualte_A2(r\"\\Sigma(1775)^0\", five_half)\n",
+    "    + formualte_A2(r\"\\Sigma(1915)^0\", five_half)\n",
+    "    + formualte_A2(r\"\\Sigma(1940)^0\", three_half)\n",
+    "    + formualte_A2(r\"\\Sigma(2030)^0\", seven_half)\n",
+    ")\n",
+    "A2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "Math(aslatex(A2, terms_per_line=1))"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -367,6 +455,56 @@
     ")\n",
     "A3_expr"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def formualte_A3(resonance_name, lambda_r_value):  # noqa: N802\n",
+    "    c_k = sp.Symbol(rf\"C_{{{resonance_name}}}\")\n",
+    "    m_k = sp.Symbol(rf\"m_{{{resonance_name}}}\")\n",
+    "    gamma_k = sp.Symbol(rf\"\\Gamma_{{{resonance_name}}}\")\n",
+    "    theta12, phi12 = sp.symbols(r\"theta_12 phi_12\")  # noqa: F841\n",
+    "    s12, lambda_R = sp.symbols(r\"s_{12} \\lambda_{N^*}\")\n",
+    "    delta = sp.KroneckerDelta(half, lambda_R + half)\n",
+    "    d_k = Wigner.d(1, lambda_R, 0, theta12)\n",
+    "    return sp.Sum(\n",
+    "        (gamma_k * m_k * delta * c_k * d_k / (-sp.I * gamma_k * m_k + m_k**2 - s12)),\n",
+    "        (lambda_R, -lambda_r_value, lambda_r_value),\n",
+    "    )\n",
+    "\n",
+    "\n",
+    "formualte_A3(\"N(1650)^0\", half)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "A3 = (\n",
+    "    formualte_A3(\"N(1650)^+\", half)\n",
+    "    + formualte_A3(\"N(1675)^+\", five_half)\n",
+    "    + formualte_A3(\"N(1680)^+\", five_half)\n",
+    "    + formualte_A3(\"N(1700)^+\", three_half)\n",
+    "    + formualte_A3(\"N(1710)^+\", half)\n",
+    "    + formualte_A3(\"N(1720)^+\", three_half)\n",
+    "    + formualte_A3(\"N(2190)^+\", seven_half)\n",
+    ")\n",
+    "A3"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "Math(aslatex(A3, terms_per_line=1))"
+   ]
   }
  ],
  "metadata": {