{"paper":{"title":"VacuumTunneling: A package to solve bounce equation with renormalization factor","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["astro-ph.CO"],"primary_cat":"hep-ph","authors_text":"Banghui Hua, Jiang Zhu","submitted_at":"2025-01-25T14:50:37Z","abstract_excerpt":"The Vacuum tunneling rate $\\Gamma$ from the effective action is a key to studying the cosmological first-order phase transition(FOPT). One solid way to compute the $\\Gamma$ is to start with the derivative expansion of the effective action and solve the bounce equation numerically. In this process, the renormalization factor $Z$ of the tunneling field may play a center rule, which is not considered in existing packages. Therefore, we present a \\texttt{Mathematica} package \\vt to compute the bounce action with or without the renormalization factor. Applying the \\vt package, we find that the pres"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.15236","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.15236/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}