writing change until two particle final states

docs/lecture02.ipynb

@@ -24,7 +24,6 @@
    "cell_type": "markdown",
    "metadata": {
     "editable": true,
-    "jp-MarkdownHeadingCollapsed": true,
     "slideshow": {
      "slide_type": ""
     },
@@ -34,13 +33,6 @@
     "## Experiments and Frames"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "(Particles) Kinematics is understood as the application of special relativity to elementary particle reactions."
-   ]
-  },
   {
    "cell_type": "markdown",
    "metadata": {
@@ -51,7 +43,12 @@
     "tags": []
    },
    "source": [
-    "The 2 standard frames that are commonly used are Center of Mass (CoM) frame and Laboratory (Lab) frame"
+    "Particle kinematics is the application of special relativity to elementary particle reactions.\n",
+    "\n",
+    "Two frames that are commonly used are the Center of Mass (CoM) frame and the laboratory (Lab) frame.\n",
+    "\n",
+    "For a two-particle reaction,\n",
+    "$a+b \\to 1 + ... + n$, the frames satisfy the following relations."
    ]
   },
   {
@@ -64,8 +61,10 @@
     "tags": []
    },
    "source": [
-    "For two particle a and b reation, i.e., \n",
-    "$a+b \\rightarrow 1 + ... + n $, they satisfy:"
+    "- **Lab frame**: $\\vec{p}_b = \\vec{0}$<br>\n",
+    "  Target particle $b$ is at rest, while beam particle $a$ is moving.\n",
+    "- **CoM frame**: $\\vec{p}_a+\\vec{p}_b = \\vec{0}$<br>\n",
+    "  The total momentum is zero, i.e., the momenta of the two initial state particles have opposite direction."
    ]
   },
   {
@@ -78,48 +77,7 @@
     "tags": []
    },
    "source": [
-    "### Lab frame"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "#### $\\vec{p}_b = \\vec{0}$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "which is the frame that the target particle b is at rest, while the beam particle a is moving."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "editable": true,
-    "slideshow": {
-     "slide_type": ""
-    },
-    "tags": []
-   },
-   "source": [
-    "### CoM frame"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "#### $\\vec{p}_a+\\vec{p}_b = \\vec{0}$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "this is the frame that the total moementum is zero, i.e., the two reaction particles has same but opposite direction momentum."
+    "## Two particles Final States"
    ]
   },
   {
@@ -132,14 +90,7 @@
     "tags": []
    },
    "source": [
-    "## Two particles Final States"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### $a+b \\rightarrow 1+2$"
+    "We now see a simple situation of two-body decay ($n=2$), i.e., $a+b \\rightarrow 1+2$"
    ]
   },
   {
@@ -167,11 +118,15 @@
     "tags": []
    },
    "source": [
-    "In the case of the scattering happens in the x-z plane for both frames, the two frames are related by a boost along the z axis.\n",
+    "<!-- In the case of the scattering happens in the x-z plane for both frames, the two frames are related by a boost along the z axis. -->\n",
+    "When we have a final state with two particles ($n=2$), we can define one $xz$ plane that is spanned by the momenta of the two final state particles in the Lab frame. The CoM frame and the Lab frame can now be related by a boost along the $z$-axis (the direction of particle $a$).\n",
     "\n",
-    "$ \\vec{z}$ is parallel to the beam $\\vec{p}_a $\n",
+    "With this definition of the x-z plane, we have:\n",
+    "- $\\vec{z}$ is parallel to the beam $\\vec{p}_a$\n",
+    "- $\\vec{y} $ is parallel to $ \\vec{p}_a \\times \\vec{p}_1$\n",
     "\n",
-    "$ \\vec{y} $ is parallel to $ \\vec{p}_a \\times \\vec{p}_1$"
+    "<!-- $ \\vec{z}$ is parallel to the beam $\\vec{p}_a $\n",
+    "$ \\vec{y} $ is parallel to $ \\vec{p}_a \\times \\vec{p}_1$ -->"
    ]
   },
   {
@@ -2272,6 +2227,10 @@
    "cell_type": "code",
    "execution_count": null,
    "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
     "tags": [
      "hide-input",
      "full-width"