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Dispersion relations for $B^- \to \ell^- \bar{\nu}_\ell \ell^{\prime-} \ell^{\prime+}$ form factors

Authors :
Kürten, Stephan
Zanke, Marvin
Kubis, Bastian
van Dyk, Danny
Source :
Phys.Rev.D 107 (2023) 5, 053006
Publication Year :
2022

Abstract

Using dispersive methods, we study the $B \to \gamma^*$ form factors underlying the decay $B^- \to \ell^- \bar{\nu}_\ell \ell^{\prime-} \ell^{\prime+}$. We discuss the ambiguity that arises from a separation of the full $B^- \to \ell^- \bar{\nu}_\ell \ell^{\prime-} \ell^{\prime+}$ amplitude into a hadronic tensor and a final-state-radiation piece, including effects from nonvanishing lepton masses. For the eligibility of a dispersive treatment, we propose a decomposition of the hadronic part that leads to four form factors that are free of kinematic singularities. By establishing a set of dispersion relations, we then relate the $B \to \gamma^*$ form factors to the well-known $B \to V$, $V=\omega(782),\rho(770)$, analogues. Using the combination of a series expansion in a conformal variable and a vector-meson-dominance ansatz to parameterize the $B \to \gamma^*$ form factors, we infer the values of the associated unknown parameters from the available input on $B \to V$. The phenomenological application of our formalism includes the determination of the branching ratios and forward-backward asymmetries of the process $B^- \to \ell^- \bar{\nu}_\ell \ell^{\prime-} \ell^{\prime+}$ for the two lightest leptons.<br />Comment: 23 pages, 6 figures, 5 tables; v2: branching ratios with tau leptons included, version published in Phys. Rev. D

Details

Database :
arXiv
Journal :
Phys.Rev.D 107 (2023) 5, 053006
Publication Type :
Report
Accession number :
edsarx.2210.09832
Document Type :
Working Paper
Full Text :
https://doi.org/10.1103/PhysRevD.107.053006