Theory determination of form factors at

Marzia Bordone; Martin Jung; Danny van Dyk

doi:10.1140/epjc/s10052-020-7616-4

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2020) 80: 74
https://doi.org/10.1140/epjc/s10052-020-7616-4

Regular Article - Theoretical Physics

Theory determination of $\bar{B} \to D^{()} ℓ^{-} \bar{ν}$ $\varvec{\bar{B}\rightarrow D^{()}\ell ^-\bar{\nu }}$ form factors at $O (1 / m_{c}^{2})$ $\varvec{\mathcal {O}(1/m_c^2)}$

Marzia Bordone¹^a, Martin Jung²^,3 and Danny van Dyk⁴

¹ Universität Siegen, Walter-Flex Straße 3, 57072, Siegen, Germany
² Excellence Cluster Universe, Technische Universität München, Boltzmannstr. 2, 85748, Garching, Germany
³ Dipartimento di Fisica, Università di Torino & INFN, Sezione di Torino, 10125, Turin, Italy
⁴ Technische Universität München, James-Franck-Straße 1, 85748, Garching, Germany

^a marzia.bordone@uni-siegen.de

Received: 10 September 2019
Accepted: 6 January 2020
Published online: 31 January 2020

Abstract

We carry out an analysis of the full set of ten $\bar{B} \to D^{(*)}$ $\bar{B}\rightarrow D^{(*)}$ form factors within the framework of the Heavy-Quark Expansion (HQE) to order $O (α_{s}, 1 / m_{b}, 1 / m_{c}^{2})$ $\mathcal {O}\left( \alpha _s,\,1/m_b,\,1/m_c^2\right)$ , both with and without the use of experimental data. This becomes possible due to a recent calculation of these form factors at and beyond the maximal physical recoil using QCD light-cone sum rules, in combination with constraints from lattice QCD, QCD three-point sum rules and unitarity. We find good agreement amongst the various theoretical results, as well as between the theoretical results and the kinematical distributions in $\bar{B} \to D^{(*)} {e^{-}, μ^{-}} \bar{ν}$ $\bar{B}\rightarrow D^{(*)}\lbrace e^-,\mu ^-\rbrace \bar{\nu }$ measurements. The coefficients entering at the $1 / m_{c}^{2}$ $$1/m_c^2$$ level are found to be of $O (1)$ $\mathcal {O}(1)$ , indicating convergence of the HQE. The phenomenological implications of our study include an updated exclusive determination of $| V_{cb} |$ $|V_{cb}|$ in the HQE, which is compatible with both the exclusive determination using the BGL parametrization and with the inclusive determination. We also revisit predictions for the lepton-flavour universality ratios $R_{D^{(*)}}$ $R_{D^{(*)}}$ , the $τ$ $\tau$ polarization observables $P_{τ}^{D^{(*)}}$ $P_\tau ^{D^{(*)}}$ , and the longitudinal polarization fraction $F_{L}$ $$F_L$$ . Posterior samples for the HQE parameters are provided as ancillary files, allowing for their use in subsequent studies.

© The Author(s) 2020

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