diff --git a/lecture2.ipynb b/lecture2.ipynb
index 5b7e40d..474da2f 100644
--- a/lecture2.ipynb
+++ b/lecture2.ipynb
@@ -296,6 +296,24 @@
     "plt.show()"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "aacd8225-ff98-488c-a9d1-7c59e95076e7",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "R12 = 1.74\n",
+    "R23 = 1.53\n",
+    "R31 = 2.45"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -320,9 +338,15 @@
     "ax1.scatter(s12, s23, c=\"black\", s=1e-3)\n",
     "ax1.set_xlabel(R\"$s_{12}\\;\\left[\\mathrm{GeV}^2\\right]$\")\n",
     "ax1.set_ylabel(R\"$s_{23}\\;\\left[\\mathrm{GeV}^2\\right]$\")\n",
+    "ax1.axvline(R12, c=\"C0\", ls=\"dashed\", label=\"$R_{12}$\")\n",
+    "ax1.axhline(R23, c=\"C1\", ls=\"dashed\", label=\"$R_{23}$\")\n",
+    "ax1.legend()\n",
     "ax2.scatter(s31, s12, c=\"black\", s=1e-3)\n",
     "ax2.set_xlabel(R\"$s_{31}\\;\\left[\\mathrm{GeV}^2\\right]$\")\n",
     "ax2.set_ylabel(R\"$s_{12}\\;\\left[\\mathrm{GeV}^2\\right]$\")\n",
+    "ax2.axvline(R31, c=\"C2\", ls=\"dashed\", label=\"$R_{31}$\")\n",
+    "ax2.axhline(R12, c=\"C0\", ls=\"dashed\", label=\"$R_{12}$\")\n",
+    "ax2.legend()\n",
     "fig.tight_layout()\n",
     "plt.show()"
    ]
@@ -417,7 +441,7 @@
     "tags": []
    },
    "source": [
-    "The particle candidates for $R_{12}$, $R_{23}$, and $R_{31}$ are then:"
+    "The particle candidates for $R_{12} \\to \\eta\\pi^0$, $R_{23} \\to \\pi^0 p$, and $R_{31} \\to p\\eta$ are then:"
    ]
   },
   {
@@ -433,7 +457,7 @@
    },
    "outputs": [],
    "source": [
-    "find_candidates(m12_mean, delta=0.01)"
+    "find_candidates(m=np.sqrt(R12), delta=0.01)"
    ]
   },
   {
@@ -449,7 +473,7 @@
    },
    "outputs": [],
    "source": [
-    "find_candidates(m23_mean, delta=0.015)"
+    "find_candidates(m=np.sqrt(R23), delta=0.01)"
    ]
   },
   {
@@ -465,7 +489,233 @@
    },
    "outputs": [],
    "source": [
-    "find_candidates(m31_mean, delta=0.01)"
+    "find_candidates(m=np.sqrt(R31), delta=0.01)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4049d15e-cf9e-4161-b270-e06241ee0279",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "## `Three-particles-2.dat`"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "44163d03-d34f-4b5d-8fc0-1a73f718e363",
+   "metadata": {
+    "editable": true,
+    "mystnb": {
+     "code_prompt_show": "Load data"
+    },
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": [
+     "hide-cell"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "filename2 = gdown.cached_download(\n",
+    "    url=\"https://indico.ific.uv.es/event/6803/contributions/21220/attachments/11209/15511/Three-particles-2.dat\",\n",
+    "    path=\"data/Three-particles-2.dat\",\n",
+    "    md5=\"831aee9fd925c43e8630edc6783ab28d\",\n",
+    "    quiet=True,\n",
+    "    verify=False,\n",
+    ")\n",
+    "data2 = np.loadtxt(filename2)\n",
+    "pa, p1, p2, p3 = (data2[i::4].T for i in range(n_final_state + 1))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "f14f0f0f-c2f2-47a5-9df4-c74ed1431802",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "p0 = p1 + p2 + p3\n",
+    "m0 = mass(p0)\n",
+    "print(f\"{m0.mean():.4g} +/- {m0.std():.4g}\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "3c53c8c1-bce8-4f47-b04c-fea311a36f23",
+   "metadata": {
+    "editable": true,
+    "jupyter": {
+     "source_hidden": true
+    },
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "from IPython.display import Math\n",
+    "\n",
+    "for i, p in enumerate([p0, p1, p2, p3]):\n",
+    "    display(Math(Rf\"m_{i} = {mass(p).mean():.3g}\\text{{ GeV}}\"))\n",
+    "\n",
+    "display(Math(Rf\"m_{{a}} = {mass(pa).mean():.3g}\\text{{ GeV}}\"))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "0fad698b-3112-4329-9a08-b1062fff0ada",
+   "metadata": {
+    "editable": true,
+    "jupyter": {
+     "source_hidden": true
+    },
+    "mystnb": {
+     "code_prompt_show": "Identify final state particles"
+    },
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "from particle import Particle\n",
+    "\n",
+    "\n",
+    "def find_candidates(m: float, delta: float = 0.001) -> list[Particle]:\n",
+    "    return Particle.findall(lambda p: (m - delta) < 1e-3 * p.mass < (m + delta))\n",
+    "\n",
+    "\n",
+    "m1 = mass(p1).mean()\n",
+    "m2 = mass(p2).mean()\n",
+    "m3 = mass(p3).mean()\n",
+    "particles = tuple(find_candidates(m.mean())[0] for m in [m1, m2, m3])\n",
+    "\n",
+    "src = R\"\\text{Final state: }\" + \", \".join(f\"{p.latex_name}\" for p in particles)\n",
+    "Math(src)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f11fc1ae-7459-4ec7-8ce8-3acc737874e7",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "This is again a photon&nbsp;$\\gamma$ hitting a target that produces a meson&nbsp;$\\eta$, pion&nbsp;$\\pi^0$, and proton&nbsp;$p$."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "b95b90b5-99da-4b8b-8aa6-8c4f1d285ee8",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "s12 = mass_squared(p1 + p2)\n",
+    "s23 = mass_squared(p2 + p3)\n",
+    "s31 = mass_squared(p3 + p1)\n",
+    "\n",
+    "m12 = mass(p1 + p2)\n",
+    "m23 = mass(p2 + p3)\n",
+    "m31 = mass(p3 + p1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "5e93638b-fe9a-4ce8-8e3a-5f025a448378",
+   "metadata": {
+    "editable": true,
+    "jupyter": {
+     "source_hidden": true
+    },
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "fig, ax = plt.subplots()\n",
+    "fig.suptitle(\"Dalitz plot – 2D histogram\")\n",
+    "ax.hist2d(s12, s23, bins=100, cmin=1)\n",
+    "ax.set_xlabel(R\"$s_{12}\\;\\left[\\mathrm{GeV}^2\\right]$\")\n",
+    "ax.set_ylabel(R\"$s_{23}\\;\\left[\\mathrm{GeV}^2\\right]$\")\n",
+    "fig.tight_layout()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "3d521919-c81d-4750-874c-81c459d9f130",
+   "metadata": {
+    "editable": true,
+    "jupyter": {
+     "source_hidden": true
+    },
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": [
+     "hide-input",
+     "full-width"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "fig, (ax1, ax2) = plt.subplots(figsize=(10, 4), ncols=2)\n",
+    "fig.suptitle(\"Dalitz plot – scatter plot\")\n",
+    "ax1.scatter(s12, s23, c=\"black\", s=1e-3)\n",
+    "ax1.set_xlabel(R\"$s_{12}\\;\\left[\\mathrm{GeV}^2\\right]$\")\n",
+    "ax1.set_ylabel(R\"$s_{23}\\;\\left[\\mathrm{GeV}^2\\right]$\")\n",
+    "ax1.axvline(R12, c=\"C0\", ls=\"dashed\", label=\"$R_{12}$\")\n",
+    "ax1.axhline(R23, c=\"C1\", ls=\"dashed\", label=\"$R_{23}$\")\n",
+    "ax1.legend()\n",
+    "ax2.scatter(s31, s12, c=\"black\", s=1e-3)\n",
+    "ax2.set_xlabel(R\"$s_{31}\\;\\left[\\mathrm{GeV}^2\\right]$\")\n",
+    "ax2.set_ylabel(R\"$s_{12}\\;\\left[\\mathrm{GeV}^2\\right]$\")\n",
+    "ax2.axvline(R31, c=\"C2\", ls=\"dashed\", label=\"$R_{31}$\")\n",
+    "ax2.axhline(R12, c=\"C0\", ls=\"dashed\", label=\"$R_{12}$\")\n",
+    "ax2.legend()\n",
+    "fig.tight_layout()\n",
+    "plt.show()"
    ]
   }
  ],