Muon_mass_Fit_using_SciPy_added_by_J_Dolen.ipynb

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        "# Calculating Invariant Mass\n",
        "\n",
        "This activity uses data from the [CMS detector](https://cms.cern/detector) at CERN in Geneva, Switzerland. We've used this in [Quarknet's Data Camp at Fermilab](https://quarknet.org/page/data-camp-description) for several years to help teachers learn about particle physics.  \n",
        "\n",
        "To get started,\n",
        "- You won't hurt anything by experimenting. If you break it, close the tab and open the activity again to start over.\n",
        "- Is this your first time? Need a refresher? Try the 5-minute [Intro to Coding activity](./intro.ipynb) and come back here.\n",
        "\n",
        "When you're ready, run each code cell until you get down to **Part One**."
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        "# imports some software packages we'll use\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib as mpl\n",
        "import matplotlib.pyplot as plt"
      ]
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        "# a hashtag tells the program \"don't read the rest of the line\"\n",
        "# That way we can write \"comments\" to humans trying to figure out what the code does\n",
        "\n",
        "data = pd.read_csv('https://github.com/QuarkNet-HEP/coding-camp/raw/main/data/muons.csv')\n",
        "# units in these files are energy, E (in GeV) and momentum, p (in GeV/c)\n",
        "\n",
        "# The .head(n) command displays the first n rows of a file.\n",
        "data.head(3)"
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              "(475465, 6)"
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        "# .shape displays the (number of rows , number of columns)\n",
        "data.shape"
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        "## Part One\n",
        "Get acquainted with this data set. It represents muons produced in a proton-proton collision (called an *event*). Look at the cells above to find the answers to the following questions:\n",
        "- In the table above, what do you think each of the column headings represent? After you discuss with your partner, take a look at the [key](https://github.com/QuarkNet-HEP/coding-camp/blob/main/CMS_data_headings.md).\n",
        "- How many events does this data set contain?"
      ]
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      "source": [
        "## Part Two\n",
        "Each muon has momentum and since they travel in 3 dimensions the momentum has three components. You can calculate the total momentum with the Pythogorean Theorem:  \n",
        "- In 2 dimensions, it's the familiar:  \n",
        "|p|<sup>2</sup> = p<sub>x</sub><sup>2</sup> + p<sub>y</sub><sup>2</sup>  \n",
        "  \n",
        "  \n",
        "- In 3 dimensions, it looks like:  \n",
        "|p|<sup>2</sup> = p<sub>x</sub><sup>2</sup> + p<sub>y</sub><sup>2</sup> + p<sub>z</sub><sup>2</sup>  \n",
        "  \n",
        "  \n",
        "<img src=\"https://upload.wikimedia.org/wikipedia/commons/thumb/6/64/Coord_XYZ.svg/2000px-Coord_XYZ.svg.png\" alt=\"Drawing\" width=\"200\" height=\"200\"/>  \n",
        "\n",
        "Try editing the code in the cell below to calculate the muon's total momentum.\n",
        "\n",
        "When you're ready, scroll down to **Part 3**."
      ]
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              "      Run     Event         E       px        py        pz        pT  \\\n",
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              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-7fefe7be-8695-4ce5-adfa-9b00968ef16f button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-7fefe7be-8695-4ce5-adfa-9b00968ef16f');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-7b077008-a06a-4da3-ab0b-e6956f6380e3\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-7b077008-a06a-4da3-ab0b-e6956f6380e3')\"\n",
              "            title=\"Suggest charts\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "     width=\"24px\">\n",
              "    <g>\n",
              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-7b077008-a06a-4da3-ab0b-e6956f6380e3 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "data"
            }
          },
          "metadata": {},
          "execution_count": 4
        }
      ],
      "source": [
        "# You can specify a column by data['column name']\n",
        "# This adds a column and fills it with E+px^2 for each event\n",
        "data['pT'] =  np.sqrt( data['px']**2  + data['py']**2)\n",
        "data['p'] =  np.sqrt( data['px']**2  + data['py']**2+ data['pz']**2)\n",
        "data.head(3)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4MXlLaWNjv1F"
      },
      "source": [
        "## Part Three\n",
        "Here's where special relativity comes in. A particle's **energy** is due to both it's **mass** and **momentum**. This equation is also similar to the Pythagoream theorem:  \n",
        "\n",
        "<center>energy<sup>2</sup> = mass<sup>2</sup> + momentum<sup>2</sup></center>  \n",
        "\n",
        "*Mass* in this equation is called the particle's *invariant mass* because it is a value all observers would agree on, regardless of their reference frame. The code below creates a column for the mass of the muon, but the equation isn't quite right.  \n",
        "- Edit the code in the cell below to *really* calculate the muon's mass.  \n",
        "- How could your equation produce some imaginary numbers?  \n",
        "\n",
        "When you're ready, scroll down to **Part 4**."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "1sgk3CLRjv1A",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 178
        },
        "outputId": "eebb7e6b-6b29-4abd-a90b-69c677450f61"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/dist-packages/pandas/core/arraylike.py:396: RuntimeWarning: invalid value encountered in sqrt\n",
            "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "      Run     Event         E       px        py        pz        pT  \\\n",
              "0  165617  74601703   9.69873 -9.51043  0.366205   1.86329  9.517478   \n",
              "1  165617  75100943   6.20385 -4.26661  0.456545  -4.47930  4.290967   \n",
              "2  165617  75587682  19.28920 -4.21208 -0.651623  18.81210  4.262186   \n",
              "\n",
              "           p      mass  \n",
              "0   9.698156  0.105495  \n",
              "1   6.202945  0.105982  \n",
              "2  19.288892  0.109086  "
            ],
            "text/html": [
              "\n",
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              "      <td>0.366205</td>\n",
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              "      <td>9.698156</td>\n",
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              "      <td>6.20385</td>\n",
              "      <td>-4.26661</td>\n",
              "      <td>0.456545</td>\n",
              "      <td>-4.47930</td>\n",
              "      <td>4.290967</td>\n",
              "      <td>6.202945</td>\n",
              "      <td>0.105982</td>\n",
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              "      <td>19.28920</td>\n",
              "      <td>-4.21208</td>\n",
              "      <td>-0.651623</td>\n",
              "      <td>18.81210</td>\n",
              "      <td>4.262186</td>\n",
              "      <td>19.288892</td>\n",
              "      <td>0.109086</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-5615aa51-304f-4763-8d78-a7037dd83770')\"\n",
              "            title=\"Convert this dataframe to an interactive table.\"\n",
              "            style=\"display:none;\">\n",
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              "  </svg>\n",
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              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
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              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-5615aa51-304f-4763-8d78-a7037dd83770 button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-5615aa51-304f-4763-8d78-a7037dd83770');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
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              "\n",
              "\n",
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              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
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              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-4665225f-d467-4572-b4d8-97ff0f1d5404 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "data"
            }
          },
          "metadata": {},
          "execution_count": 5
        }
      ],
      "source": [
        "data['mass'] = np.sqrt(data['E']**2 - data['p']**2) # this also calculates nothing useful\n",
        "data = data.fillna(0) # fills in a zero for any imaginary values your caluclation might produce\n",
        "data.head(3)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-scsKIdKjv1G",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "outputId": "8f9b8254-d0c3-4892-bc7c-12d562ff0932"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "plt.hist(data['mass'], bins=100, range=[0.105,0.1065], log=False)  # makes the histogram\n",
        "plt.title(\"Muon Mass Peak\")\n",
        "plt.xlabel(\"Mass (in GeV/c^2)\")\n",
        "plt.ylabel(\"number of events\")\n",
        "plt.grid(False);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zlF-KDk0jv1K"
      },
      "source": [
        "## Part Four\n",
        "The code above may take a few moments to run since it's grabbing a pretty big data set (>400,000 events!?). When it's finished, you'll see a histogram of the invariant mass values you calucalted for muon 1 in each event. This is called a *mass plot*.  \n",
        "- You'll probably need to adjust the histogram's range and number of bins to see a clear peak. The x-value of that peak occurs at the invariant mass of the particle (in this case, a muon).\n",
        "- Based on your histogram, what value does the muon's invariant mass seem to be?\n",
        "- Try replacing the histogram's title and x-axis label to something better.  \n",
        "\n",
        "## Part Five  \n",
        "Now that you've analyzed your own huge set of particle collision events, here are some follow-up questions:\n",
        "- How does the value you calculated compare to the accepted mass of the [muon](https://en.wikipedia.org/wiki/Muon)? Is it very different, if so why might that be?\n",
        "- Why doesn't energy have x, y, and z components like momentum?\n",
        "- How does E<sup>2</sup> - p<sup>2</sup> give you a unit of mass<sup>2</sup>?\n",
        "\n",
        "## More Tools  \n",
        "The cells below show some more advanced techniques.  "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "3Zq2yLC0jv1L"
      },
      "outputs": [],
      "source": [
        "# run this command to make your plots look like they're from xkcd.com\n",
        "plt.xkcd();\n",
        "# then re-execute your code to make a plot and see it xkcd-ified."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "SIbaFNC1jv1Q"
      },
      "outputs": [],
      "source": [
        "# run this cell to make normal-looking plots again\n",
        "mpl.rcdefaults()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Mj5aIoG4jv1U"
      },
      "source": [
        "A professional physicist would usually fit a theoretical curve to the mass plot to identify the particle's invariant mass. For reconstructing more complex particle decays they'd use a [relativistic Breit-Wigner](https://en.wikipedia.org/wiki/Relativistic_Breit%E2%80%93Wigner_distribution) curve, but we'll try it here just for practice.  \n",
        "- First, choose some parameters for the curve based on where the peak is on your histogram and how wide it looks.  \n",
        "- Then, run the code and keep adjusting the parameters until the curve tightly fits the peak."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "LOaKSIAWjv1U",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 410
        },
        "outputId": "476da8ef-dd63-408a-8fd8-5a379dba49a5"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 600x400 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Fit \"by hand\"\n",
        "\n",
        "# set the Breit-Wigner parameters\n",
        "xmin = 0.105  # lower bound for your plot\n",
        "xmax = 0.1065  # upper bound for your plot\n",
        "particle_mass = .10565 # the x-value of the peak\n",
        "width = .00073 # width of the peak halfway up; a.k.a. \"full width at half max\" or FWHM\n",
        "K = 0.00002  # a constant that affects the height of the curve, you'll need to tinker with this some\n",
        "\n",
        "# calculate the Breit-Wigner curve\n",
        "x = np.arange(xmin, xmax, (xmax-xmin)/200) # makes a series of equally spaced x-values\n",
        "y = K / ((x**2 - particle_mass**2)**2 + (particle_mass*width)**2) # calculates the y-values for the B-W curve\n",
        "\n",
        "# make the plot\n",
        "fig, ax = plt.subplots(1,1, figsize=(6,4))\n",
        "ax.hist(data['mass'], bins=100, range=[xmin,xmax], log=False)  # plots the histogram\n",
        "ax.plot(x, y, color='r')  # plots the curve\n",
        "plt.title(\"Muon Mass Peak\")\n",
        "plt.xlabel(\"Mass (in GeV/c^2)\")\n",
        "plt.ylabel(\"number of events\")\n",
        "plt.grid(True);"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Fit using SciPy added by J. Dolen\n",
        "# Example of how to fit a histogram with a relativistic Breit-Wigner function using scipy\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.optimize import curve_fit\n",
        "\n",
        "# Note: Normally we do this to plot a histogram:\n",
        "#    plt.hist(s, bins=100, normed=True, histtype='step',color='blue')\n",
        "#\n",
        "# In order to fit the histogram, we need to know the location of each bin and the entries in each bin\n",
        "#   To do this we can ask that the plot return a tuple of this data (n,bins,patches) when we make the plot:\n",
        "\n",
        "(n,bins,patches) = plt.hist(data['mass'], bins=100, range=[xmin,xmax], log=False)\n",
        "\n",
        "#  Reference:\n",
        "#      ( http://matplotlib.org/api/pyplot_api.html?highlight=hist#matplotlib.pyplot.hist\n",
        "#    n = array containing the number of entries in each bin\n",
        "#    bins = array containing the locations of the bin edges (so the length is nbins +1)\n",
        "\n",
        "print(\"n=\",n)\n",
        "print(\"bins=\",bins)\n",
        "print(\"patches=\",patches)\n",
        "\n",
        "# To fit we need an array of bin centers. The array returned above contains the bin edge locations. We can calculate the bin center locations as follows:\n",
        "bin_centers = 0.5*(bins[1:] + bins[:-1])\n",
        "\n",
        "# define the function used in the fit. In this case we use the relativistic Breit-Wigner function from above\n",
        "def f(x, particle_mass, width, K):\n",
        "    return K / ((x**2 - particle_mass**2)**2 + (particle_mass*width)**2)\n",
        "\n",
        "# Before performing the fit we typically provide the fitting algorithm some ballpark values for the fit parameters.\n",
        "# Above you were asked to do your best to fit the histogram \"by hand\". These values will be a good guess for the fit:\n",
        "\n",
        "guess_particle_mass = .1 # the x-value of the peak\n",
        "guess_width = .0008 # width of the peak halfway up; a.k.a. \"full width at half max\" or FWHM\n",
        "guess_K = 0.000025  # a constant that affects the height of the curve, you'll need to tinker with this some\n",
        "\n",
        "# Perform the fit using scipy.optimize.curve_fit\n",
        "#   https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html\n",
        "#   scipy.optimize.curve_fit(f, xdata, ydata, p0=None, sigma=None, absolute_sigma=False, check_finite=None, bounds=(-inf, inf), method=None, jac=None, *, full_output=False, nan_policy=None, **kwargs)\n",
        "#   p0 is a list containing the initial guesses for the function parameters\n",
        "popt, pcov = curve_fit(f, bin_centers, n, p0 = [guess_particle_mass, guess_width, guess_K])\n",
        "\n",
        "# curve_fit returns popt which is an array of final fit parameters determined by the fit\n",
        "fit_result_particle_mass = popt[0]\n",
        "fit_result_width         = popt[1]\n",
        "fit_result_K             = popt[2]\n",
        "\n",
        "# Print the fit result parameters to the screen\n",
        "print(\"*\"*50)\n",
        "print(\"fit_result_particle_mass = \" , fit_result_particle_mass)\n",
        "print(\"fit_result_width         = \" , np.fabs(fit_result_width)     )\n",
        "print(\"fit_result_K             = \" , fit_result_K    )\n",
        "print(\"*\"*50)\n",
        "\n",
        "# Plot the fit on top of the histogram.\n",
        "#  feed the fit function the bin center locations and the fit parameter and plot the values\n",
        "plt.plot(bin_centers, f(bin_centers,  fit_result_particle_mass, fit_result_width , fit_result_K ), 'r')\n",
        "plt.title(\"Muon Mass Peak\")\n",
        "plt.xlabel(\"Mass (in GeV/c^2)\")\n",
        "plt.ylabel(\"number of events\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 958
        },
        "id": "AZFiYXfVk0Ho",
        "outputId": "ff2f3ef8-163d-4b1f-a135-24edd04dcdfa"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "n= [ 553.  620.  617.  665.  694.  755.  835.  823.  916.  955. 1019. 1076.\n",
            " 1189. 1205. 1298. 1364. 1428. 1456. 1692. 1616. 1715. 1811. 1911. 2067.\n",
            " 2070. 2143. 2249. 2414. 2412. 2544. 2602. 2653. 2758. 2805. 2857. 2948.\n",
            " 3020. 3061. 3003. 3224. 3210. 3221. 3161. 3191. 3278. 3206. 3235. 3031.\n",
            " 3203. 3125. 3004. 3010. 2994. 2933. 2787. 2752. 2694. 2557. 2509. 2449.\n",
            " 2278. 2206. 2193. 2128. 1979. 1917. 1789. 1775. 1690. 1599. 1487. 1388.\n",
            " 1393. 1307. 1148. 1191. 1087.  998.  910.  901.  837.  846.  709.  680.\n",
            "  627.  632.  573.  577.  557.  491.  477.  474.  426.  419.  386.  405.\n",
            "  373.  358.  363.  319.]\n",
            "bins= [0.105    0.105015 0.10503  0.105045 0.10506  0.105075 0.10509  0.105105\n",
            " 0.10512  0.105135 0.10515  0.105165 0.10518  0.105195 0.10521  0.105225\n",
            " 0.10524  0.105255 0.10527  0.105285 0.1053   0.105315 0.10533  0.105345\n",
            " 0.10536  0.105375 0.10539  0.105405 0.10542  0.105435 0.10545  0.105465\n",
            " 0.10548  0.105495 0.10551  0.105525 0.10554  0.105555 0.10557  0.105585\n",
            " 0.1056   0.105615 0.10563  0.105645 0.10566  0.105675 0.10569  0.105705\n",
            " 0.10572  0.105735 0.10575  0.105765 0.10578  0.105795 0.10581  0.105825\n",
            " 0.10584  0.105855 0.10587  0.105885 0.1059   0.105915 0.10593  0.105945\n",
            " 0.10596  0.105975 0.10599  0.106005 0.10602  0.106035 0.10605  0.106065\n",
            " 0.10608  0.106095 0.10611  0.106125 0.10614  0.106155 0.10617  0.106185\n",
            " 0.1062   0.106215 0.10623  0.106245 0.10626  0.106275 0.10629  0.106305\n",
            " 0.10632  0.106335 0.10635  0.106365 0.10638  0.106395 0.10641  0.106425\n",
            " 0.10644  0.106455 0.10647  0.106485 0.1065  ]\n",
            "patches= <BarContainer object of 100 artists>\n",
            "**************************************************\n",
            "fit_result_particle_mass =  0.1056581768956351\n",
            "fit_result_width         =  0.0006918478473722942\n",
            "fit_result_K             =  1.7861722413545983e-05\n",
            "**************************************************\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DcA5-9bPjv1a"
      },
      "source": [
        "If you finally have a curve that pretty closely fits the peak in your histogram, take a look at the parameters you set. We can use those to determine the particle's mass and lifetime. The invariant mass of the particle is your *particle_mass*. The particle's mean lifetime is h-bar/width.  \n",
        "- How do the values below compare with the accepted values for mass and lifetime of the muon?  \n",
        "They probably don't agree very well because we're applying the Breit-Wigner curve to a particle we observed (not valid) instead of one we're trying to reconstruct from analyzing its decay products. If you ever find yourself doing a *mass reconstruction* to discover a short-lived particle by its decay products, this will might be useful."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "nfxSGutbjv1a",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "dad47877-e340-4e10-ab9b-80fc1107aaf9"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "mass =  0.10565  GeV/c^2\n",
            "mean lifetime =  4.281144e-05  seconds\n"
          ]
        }
      ],
      "source": [
        "print(\"mass = \", np.round(particle_mass,6), \" GeV/c^2\")\n",
        "hbar = 6.582e-25      # in GeV*s\n",
        "width = np.fabs(fit_result_width)/3e8**2\n",
        "print(\"mean lifetime = \", np.format_float_scientific(hbar/(2*width),6), \" seconds\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "collapsed": true,
        "id": "IckJMDaijv1f"
      },
      "source": [
        "---  \n",
        "## Saving Your Work  \n",
        "This is running on a Google server on a distant planet and deletes what you've done when you close this tab. To save your work for later use or analysis you have a few options:  \n",
        "- File > \"Save a copy in Drive\" will save it to you Google Drive in a folder called \"Collaboratory\". You can run it later from there.  \n",
        "- File > \"Download .ipynb\" to save to your computer (and run with Jupyter software later)  \n",
        "- File > Print to ... um ... print.  \n",
        "- To save an image of a graph or chart, right-click on it and select Save Image as ...  \n",
        "\n",
        "## Credits\n",
        "This notebook was designed by [Quarknet](https://quarknet.org/) Teaching and Learning Fellow [Adam LaMee](https://adamlamee.github.io/) and UCF Physics undergrad Brooke Emison. The handy csv files were created from the CMS Run2011A primary datasets and converted from ROOT format by the masterful [Tom McCauley](https://github.com/tpmccauley). More can be found on the [CERN OpenData](http://opendata.cern.ch/?ln=en) site, like [here](http://opendata.cern.ch/record/545). The 3D vector image can be found on [WikiMedia Commons](https://commons.wikimedia.org/wiki/File:Coord_XYZ.svg). Finally, thanks to the great folks at [Binder](https://mybinder.org/) and [Google Colaboratory](https://colab.research.google.com/notebooks/intro.ipynb) for making this notebook interactive without you needing to download it or install [Jupyter](https://jupyter.org/) on your own device. Find more activities and license info at [CODINGinK12.org](http://www.codingink12.org)."
      ]
    }
  ],
  "metadata": {
    "anaconda-cloud": {},
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3 (ipykernel)",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.9.7"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}