{"paper":{"title":"$A_4$ Modular Flavour Model of Quark Mass Hierarchies close to the Fixed Point $\\tau = i\\infty$","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"M. Tanimoto, S. T. Petcov","submitted_at":"2023-06-09T07:51:36Z","abstract_excerpt":"We study the possibility to generate the quark mass hierarchies as well as the CKM quark mixing and CP violation without fine-tuning in a quark flavour model with modular $A_4$ symmetry. The quark mass hierarchies are considered in the vicinity of the fixed point $\\tau = i\\infty$, $\\tau$ being the vacuum expectation value of the modulus. We consider first a model in which the up-type and down-type quark mass matrices $M_u$ and $M_d$ involve modular forms of level 3 and weights 6, 4 and 2 and each depends on four constant parameters. We also consider the case of $M_u$ and $M_d$ depending on the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.05730","kind":"arxiv","version":2},"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/2306.05730/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"}