{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"critpt","formal_name":"CritPt","introduction":"CritPt evaluates scientific understanding and multi-step reasoning and computation on research-level physics problems. Its public dataset contains 70 challenges with problem descriptions and code templates.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://critpt.com/","indexing_mode":"noindex","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[]}},"task_id":"b886e409-9498-52b8-afb5-011b0496a07a","task_key":"train--Challenge~5f57~5fmain","task_revision_id":"2","upstream_id":"Challenge_57_main","short_description":"Consider a vector field $A^\\mu$ coupled to the standard model $B-L$ current…","config":"","split":"train","body":"{\"code_template\":\"def answer():\\n    r\\\"\\\"\\\"\\n    Return the values of the smallest $\\\\epsilon_{B-L}$ for three scenarios.\\n\\n    Inputs\\n    ----------\\n    None\\n\\n    Outputs\\n    ----------\\n    eps_B_L_min: list[float],\\n          smallest $\\\\epsilon_{B-L}$ it can probe at $250\\\\,\\\\text{Hz}$ with an observation time of $13$ years and SNR of $1$\\n          for scenarios where $\\\\delta q=\\\\{0.074, 6\\\\times 10^{-3}, 5\\\\times 10^{-4}\\\\}$.\\n    \\\"\\\"\\\"\\n\\n    # ------------------ FILL IN YOUR RESULTS BELOW ------------------\\n    eps_B_L_min = ...\\n    # ---------------------------------------------------------------\\n\\n    return eps_B_L_min\",\"problem_description\":\"\\n\\n# Problem setup:\\nConsider a vector field $A^\\\\mu$ coupled to the standard model $B-L$ current $J^\\\\mu_{B-L}$ through $\\\\mathcal{L}\\\\supset -\\\\epsilon_{B-L}eJ^\\\\mu_{B-L} A_\\\\mu$. If the vector field makes up all the dark matter, the local dark matter density indicates that the field could exert a measurable force on mirrors in laser interferometers, with sufficiently large coupling. Consider LIGO, with a strain sensitivity of $3\\\\times 10^{-24}\\\\, \\\\text{Hz}^{-1/2}$ at frequency $250\\\\,\\\\text{Hz}$.\\n\\n# Main problem:\\n\\nTake the dark charge $Q_D$ to mass $M$ radio to be $\\\\frac{Q_D}{M}\\\\sim \\\\frac{0.5}{m_n}$ for the inner mirrors, where $m_n$ is the mass of a neutron. We introduce a doped outer mirror, resulting in a differential forced between the inner and outer mirror. We assume the outer mirror gains an additiona $\\\\delta \\\\left(\\\\frac{Q_D}{M}\\\\right)\\\\sim \\\\frac{\\\\delta q}{m_n}$, where $m_n$ is the mass of a neutron. With an observation time of $13$ years and SNR of $1$, what is the smallest $\\\\epsilon_{B-L}$ it can probe at $250\\\\,\\\\text{Hz}$? Provide answers for scenarios where $\\\\delta q=\\\\{0.074, 6\\\\times 10^{-3}, 5\\\\times 10^{-4}\\\\}$.\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://critpt.com/","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}