{"paper":{"title":"Galaxy bias renormalization: Two-loop Power Spectrum, One-loop Trispectrum and Bispectrum","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc","hep-th"],"primary_cat":"astro-ph.CO","authors_text":"Henrique Rubira, Mathias Garny, Thomas Bakx, Zvonimir Vlah","submitted_at":"2026-06-30T07:54:28Z","abstract_excerpt":"We present a complete treatment of fifth-order renormalized galaxy bias at the one- and two-loop level in real space, including gradient corrections to deterministic bias operators at next-to-leading order. We then provide a complete computation of the two-loop power spectrum as well as the one-loop bispectrum and trispectrum of biased tracers, and demonstrate how to jointly model these statistics in a fully renormalized framework. These statistics also require stochastic renormalization of products of two, three or four operators at coincidence, which we include at leading order in gradients "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.31280","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/2606.31280/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"}