{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T19:48:05Z","timestamp":1767901685429,"version":"3.49.0"},"reference-count":107,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T00:00:00Z","timestamp":1722988800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Research Agency (ANR)","award":["ANR-21-CE31-0002-01"],"award-info":[{"award-number":["ANR-21-CE31-0002-01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The search for New Physics (NP) beyond the Standard Model (SM) has been a central focus of particle physics, including in the context of B-meson decays involving b\u2192s\u2113\u2113 transitions. These transitions, mediated by flavour-changing neutral currents, are highly sensitive to small NP effects due to their suppression in the SM. While direct searches at colliders have not yet led to NP discoveries, indirect probes through semi-leptonic decays have revealed anomalies in observables such as the branching fraction B(B\u2192K\u03bc\u03bc) and the angular observable P5\u2032(B\u2192K\u2217\u03bc\u03bc). In order to assess the observed tensions, it is essential to ensure an accurate SM prediction. In this review, we examine the theoretical basis of the B\u2192K(\u2217)\u2113\u2113 decays, addressing in particular key uncertainties arising from local and non-local form factors. We also discuss the impact of QED corrections to the Wilson coefficients, as well as the effect of CKM matrix elements on the predictions and the tension with the experimental measurements. We discuss the most recent results, highlighting ongoing efforts to refine predictions and to constrain potential signs of NP in these critical decay processes.<\/jats:p>","DOI":"10.3390\/sym16081006","type":"journal-article","created":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T07:01:25Z","timestamp":1723100485000},"page":"1006","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Overview of B\u2192K(\u2217)\u2113\u2113 Theoretical Calculations and Uncertainties"],"prefix":"10.3390","volume":"16","author":[{"given":"Farvah","family":"Mahmoudi","sequence":"first","affiliation":[{"name":"Institut de Physique des 2 Infinis de Lyon, UMR 5822, Universit\u00e9 Claude Bernard Lyon 1, CNRS\/IN2P3, 69622 Villeurbanne, France"},{"name":"Theoretical Physics Department, CERN, CH-1211 Geneva, Switzerland"},{"name":"Institut Universitaire de France (IUF), 75005 Paris, France"}]},{"given":"Yann","family":"Monceaux","sequence":"additional","affiliation":[{"name":"Institut de Physique des 2 Infinis de Lyon, UMR 5822, Universit\u00e9 Claude Bernard Lyon 1, CNRS\/IN2P3, 69622 Villeurbanne, France"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.physletb.2012.08.021","article-title":"Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC","volume":"716","author":"Chatrchyan","year":"2012","journal-title":"Phys. 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