Motivated by the first search for the rare charged-current B decay to four leptons, $$\ell \bar{\nu }_\ell \ell ^{(\prime )} \bar{\ell }^{(\prime )}$$ , we calculate the decay amplitude with factorization methods. We obtain the $$B\rightarrow \gamma ^*$$ form factors, which depend on the invariant masses of the two lepton pairs, at leading power in an expansion in $$\Lambda _\mathrm{QCD}/m_b$$ to next-to-leading order in $$\alpha _s$$ , and at $$\mathcal {O}(\alpha _s^0)$$ at next-to-leading power. Our calculations predict branching fractions of a few times $$10^{-8}$$ in the $$\ell ^{(\prime )} \bar{\ell }^{(\prime )}$$ mass-squared bin up to $$q^2=1~$$ GeV $$^2$$ with $$n_+q>3~$$ GeV. The branching fraction rapidly drops with increasing $$q^2$$ . An important further motivation for this investigation has been to explore the sensitivity of the decay rate to the inverse moment $$\lambda _B$$ of the leading-twist B meson light-cone distribution amplitude. We find that in the small- $$q^2$$ bin, the sensitivity to $$\lambda _B$$ is almost comparable to $$B^- \rightarrow \mathrm {\ell }^- \bar{\nu }_{\mathrm {\ell }}\gamma $$ when $$\lambda _B$$ is small, but with an added uncertainty from the light-meson intermediate resonance contribution. The sensitivity degrades with larger $$q^2$$ .
{ "_oai": { "updated": "2021-09-28T01:17:57Z", "id": "oai:repo.scoap3.org:63573", "sets": [ "EPJC" ] }, "authors": [ { "affiliations": [ { "country": "Germany", "value": "Physik Department T31, Technische Universit\u00e4t M\u00fcnchen, James-Franck-Stra\u00dfe 1, Garching, 85748, Germany", "organization": "Technische Universit\u00e4t M\u00fcnchen" } ], "surname": "Beneke", "given_names": "Martin", "full_name": "Beneke, Martin" }, { "affiliations": [ { "country": "Germany", "value": "Physik Department T31, Technische Universit\u00e4t M\u00fcnchen, James-Franck-Stra\u00dfe 1, Garching, 85748, Germany", "organization": "Technische Universit\u00e4t M\u00fcnchen" } ], "surname": "B\u00f6er", "email": "philipp.boeer@tum.de", "full_name": "B\u00f6er, Philipp", "given_names": "Philipp" }, { "affiliations": [ { "country": "Germany", "value": "Physik Department T31, Technische Universit\u00e4t M\u00fcnchen, James-Franck-Stra\u00dfe 1, Garching, 85748, Germany", "organization": "Technische Universit\u00e4t M\u00fcnchen" } ], "surname": "Rigatos", "given_names": "Panagiotis", "full_name": "Rigatos, Panagiotis" }, { "affiliations": [ { "country": "Netherlands", "value": "Gravitational Waves and Fundamental Physics (GWFP), Maastricht University, Duboisdomein 30, Maastricht, 6229 GT, The Netherlands", "organization": "Maastricht University" }, { "country": "Netherlands", "value": "Nikhef, Science Park 105, Amsterdam, 1098 XG, The Netherlands", "organization": "Nikhef" } ], "surname": "Vos", "given_names": "K.", "full_name": "Vos, K." } ], "titles": [ { "source": "Springer", "title": "QCD factorization of the four-lepton decay $$B^-\\rightarrow \\ell \\bar{\\nu }_\\ell \\ell ^{(\\prime )} \\bar{\\ell }^{(\\prime )}$$ <math> <mrow> <msup> <mi>B</mi> <mo>-</mo> </msup> <mo>\u2192</mo> <mi>\u2113</mi> <msub> <mover> <mrow> <mi>\u03bd</mi> </mrow> <mrow> <mo>\u00af</mo> </mrow> </mover> <mi>\u2113</mi> </msub> <msup> <mi>\u2113</mi> <mrow> <mo>(</mo> <mo>\u2032</mo> <mo>)</mo> </mrow> </msup> <msup> <mover> <mrow> <mi>\u2113</mi> </mrow> <mrow> <mo>\u00af</mo> </mrow> </mover> <mrow> <mo>(</mo> <mo>\u2032</mo> <mo>)</mo> </mrow> </msup> </mrow> </math>" } ], "dois": [ { "value": "10.1140/epjc/s10052-021-09388-y" } ], "publication_info": [ { "page_end": "15", "journal_title": "European Physical Journal C", "material": "article", "journal_volume": "81", "artid": "s10052-021-09388-y", "year": 2021, "page_start": "1", "journal_issue": "7" } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "acquisition_source": { "date": "2021-09-28T00:32:23.206196", "source": "Springer", "method": "Springer", "submission_number": "36fba5861ff311ecb53772fd3742099d" }, "page_nr": [ 15 ], "license": [ { "url": "https://creativecommons.org/licenses//by/4.0", "license": "CC-BY-4.0" } ], "copyright": [ { "holder": "The Author(s)", "year": "2021" } ], "control_number": "63573", "record_creation_date": "2021-07-21T18:30:26.797502", "_files": [ { "checksum": "md5:2665c9e438e25457cd443dc6ebf9dced", "filetype": "xml", "bucket": "3ade2695-6e50-4423-9320-f9718f87bba5", "version_id": "9d1e25c7-bf2b-41db-a11d-445cbec15fd9", "key": "10.1140/epjc/s10052-021-09388-y.xml", "size": 30588 }, { "checksum": "md5:8f5e0ac1af8b0922601d035e3891d9cf", "filetype": "pdf/a", "bucket": "3ade2695-6e50-4423-9320-f9718f87bba5", "version_id": "44ebcc55-789b-4c63-a3e1-5a6cc9ca3296", "key": "10.1140/epjc/s10052-021-09388-y_a.pdf", "size": 1598159 } ], "collections": [ { "primary": "European Physical Journal C" } ], "abstracts": [ { "source": "Springer", "value": "Motivated by the first search for the rare charged-current B decay to four leptons, $$\\ell \\bar{\\nu }_\\ell \\ell ^{(\\prime )} \\bar{\\ell }^{(\\prime )}$$ <math> <mrow> <mi>\u2113</mi> <msub> <mover> <mrow> <mi>\u03bd</mi> </mrow> <mrow> <mo>\u00af</mo> </mrow> </mover> <mi>\u2113</mi> </msub> <msup> <mi>\u2113</mi> <mrow> <mo>(</mo> <mo>\u2032</mo> <mo>)</mo> </mrow> </msup> <msup> <mover> <mrow> <mi>\u2113</mi> </mrow> <mrow> <mo>\u00af</mo> </mrow> </mover> <mrow> <mo>(</mo> <mo>\u2032</mo> <mo>)</mo> </mrow> </msup> </mrow> </math> , we calculate the decay amplitude with factorization methods. We obtain the $$B\\rightarrow \\gamma ^*$$ <math> <mrow> <mi>B</mi> <mo>\u2192</mo> <msup> <mi>\u03b3</mi> <mo>\u2217</mo> </msup> </mrow> </math> form factors, which depend on the invariant masses of the two lepton pairs, at leading power in an expansion in $$\\Lambda _\\mathrm{QCD}/m_b$$ <math> <mrow> <msub> <mi>\u039b</mi> <mi>QCD</mi> </msub> <mo>/</mo> <msub> <mi>m</mi> <mi>b</mi> </msub> </mrow> </math> to next-to-leading order in $$\\alpha _s$$ <math> <msub> <mi>\u03b1</mi> <mi>s</mi> </msub> </math> , and at $$\\mathcal {O}(\\alpha _s^0)$$ <math> <mrow> <mi>O</mi> <mo>(</mo> <msubsup> <mi>\u03b1</mi> <mi>s</mi> <mn>0</mn> </msubsup> <mo>)</mo> </mrow> </math> at next-to-leading power. Our calculations predict branching fractions of a few times $$10^{-8}$$ <math> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>8</mn> </mrow> </msup> </math> in the $$\\ell ^{(\\prime )} \\bar{\\ell }^{(\\prime )}$$ <math> <mrow> <msup> <mi>\u2113</mi> <mrow> <mo>(</mo> <mo>\u2032</mo> <mo>)</mo> </mrow> </msup> <msup> <mover> <mrow> <mi>\u2113</mi> </mrow> <mrow> <mo>\u00af</mo> </mrow> </mover> <mrow> <mo>(</mo> <mo>\u2032</mo> <mo>)</mo> </mrow> </msup> </mrow> </math> mass-squared bin up to $$q^2=1~$$ <math> <mrow> <msup> <mi>q</mi> <mn>2</mn> </msup> <mo>=</mo> <mn>1</mn> <mspace width=\"3.33333pt\"></mspace> </mrow> </math> GeV $$^2$$ <math> <msup> <mrow></mrow> <mn>2</mn> </msup> </math> with $$n_+q>3~$$ <math> <mrow> <msub> <mi>n</mi> <mo>+</mo> </msub> <mi>q</mi> <mo>></mo> <mn>3</mn> <mspace width=\"3.33333pt\"></mspace> </mrow> </math> GeV. The branching fraction rapidly drops with increasing $$q^2$$ <math> <msup> <mi>q</mi> <mn>2</mn> </msup> </math> . An important further motivation for this investigation has been to explore the sensitivity of the decay rate to the inverse moment $$\\lambda _B$$ <math> <msub> <mi>\u03bb</mi> <mi>B</mi> </msub> </math> of the leading-twist B meson light-cone distribution amplitude. We find that in the small- $$q^2$$ <math> <msup> <mi>q</mi> <mn>2</mn> </msup> </math> bin, the sensitivity to $$\\lambda _B$$ <math> <msub> <mi>\u03bb</mi> <mi>B</mi> </msub> </math> is almost comparable to $$B^- \\rightarrow \\mathrm {\\ell }^- \\bar{\\nu }_{\\mathrm {\\ell }}\\gamma $$ <math> <mrow> <msup> <mi>B</mi> <mo>-</mo> </msup> <mo>\u2192</mo> <msup> <mrow> <mi>\u2113</mi> </mrow> <mo>-</mo> </msup> <msub> <mover> <mrow> <mi>\u03bd</mi> </mrow> <mrow> <mo>\u00af</mo> </mrow> </mover> <mi>\u2113</mi> </msub> <mi>\u03b3</mi> </mrow> </math> when $$\\lambda _B$$ <math> <msub> <mi>\u03bb</mi> <mi>B</mi> </msub> </math> is small, but with an added uncertainty from the light-meson intermediate resonance contribution. The sensitivity degrades with larger $$q^2$$ <math> <msup> <mi>q</mi> <mn>2</mn> </msup> </math> ." } ], "imprints": [ { "date": "2021-07-21", "publisher": "Springer" } ] }