{"corpus_id":119689358,"paper_sha":"51871e8eb5512f923796e5051bbd2a15f440a041","doi":"10.1007/JHEP12(2011)019","arxiv_id":"1110.2545","pmid":null,"pmcid":null,"mag_id":2083649198,"dblp_id":null,"acl_id":null,"title":"Explicit solutions for effective four- and five-loop QCD running coupling","year":2011,"publication_date":"2011-10-12","venue":"","journal":{"name":"Journal of High Energy Physics","pages":"1-29","volume":"2011"},"journal_issn":null,"journal_title":null,"publication_types":[],"pubmed_pub_types":null,"s2_fields_of_study":["Mathematics","Physics"],"reference_count":21,"citation_count":27,"influential_citation_count":1,"is_open_access":false,"arxiv_categories":["hep-ph","math-ph","math.MP"],"arxiv_license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","arxiv_journal_ref":"JHEP 1112:019,2011","mesh_headings":null,"chemicals":null,"comments_corrections":null,"source_flags":1,"s2_open_access_pdf_url":null,"s2_open_access_landing_url":null,"s2_open_access_license":null,"s2_open_access_status":null,"pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"A bstractWe start with the explicit solution, in terms of the Lambert W function, of the renormalization group equation (RGE) for the gauge coupling in the supersymmetric Yang-Mills theory described by the well-known NSVZ β-function. We then construct a class of β-functions for which the RGE can be solved in terms of the Lambert W function. These β-functions are expressed in terms of a function which is a truncated Laurent series in the inverse u of the gauge coupling a ≡ α/π. The parameters in the Laurent series can be adjusted so that the first coefficients of the Taylor expansion of the β-function in the gauge coupling a reproduce the four-loop or five-loop QCD (or SQCD) β-function.","claims":[{"public_id":"cl_f11404f801bb9a1d10f29a1753d8b321","status":"active","text":"A class of β-functions expressed as a truncated Laurent series in the inverse of the gauge coupling is constructed such that the corresponding renormalization group equation can be solved in terms of the Lambert W function.","confidence":0.88,"contributors":[{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["extraction"],"url":"https://sah.borca.ai/u/322360f1c1"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"},{"id":170,"public_id":"gsgmdx9r6e","public_label":"pupuri (gsgmdx9r6e)","roles":["review"],"url":"https://sah.borca.ai/u/gsgmdx9r6e"}],"url":"https://sah.borca.ai/claims/cl_f11404f801bb9a1d10f29a1753d8b321"},{"public_id":"cl_f84f2ed95d6afff45add35ea1bdfe6e6","status":"active","text":"The parameters of the truncated Laurent series can be adjusted so that the Taylor expansion coefficients of the β-function in the gauge coupling reproduce the four-loop or five-loop QCD (or SQCD) β-function.","confidence":0.85,"contributors":[{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["extraction"],"url":"https://sah.borca.ai/u/322360f1c1"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous 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