https://doi.org/10.1140/epjc/s10052-020-7850-9
Regular Article - Theoretical Physics
Heavy-Quark expansion for 
form factors and unitarity bounds beyond the 
limit
1
Universität Siegen, Walter-Flex Straße 3, 57072, Siegen, Germany
2
Technische Universität München, James-Franck-Straße 1, 85748, Garching, Germany
3
Dipartimento di Fisica, Università di Torino & INFN, Sezione di Torino, 10125, Torino, Italy
* e-mail: marzia.bordone@uni-siegen.de
Received:
17
January
2020
Accepted:
16
March
2020
Published online:
29
April
2020
We carry out a comprehensive analysis of the full set of 
form factors for spectator quarks 
within the framework of the Heavy-Quark expansion (HQE) to order 
. In addition to the available lattice QCD calculations we make use of two new sets of theoretical constraints: we produce for the first time numerical predictions for the full set of 
form factors using Light-Cone sum rules with 
-meson distribution amplitudes. Furthermore, we reassess the QCD three-point sum rule results for the Isgur-Wise functions entering all our form factors for both 
and 
spectator quarks. These additional constraints allow us to go beyond the commonly used assumption of 
symmetry for the 
form factors, especially in the unitarity constraints which we impose throughout our analysis. We find the coefficients of the IW functions emerging at 
to be consistent with the naive 
expectation, indicating a good convergence of the HQE. While we do not find significant SU(3) breaking, the explicit treatment of as compared to a simple symmetry assumption renders the unitarity constraints more effective. We find that the (pseudo)scalar bounds are saturated to a large degree, which affects our theory predictions. We analyze the phenomenological consequences of our improved form factors by extracting 
from 
decays and producing theoretical predictions for the lepton-flavour universality ratios R(D), 
, 
and 
, as well as the 
- and 
polarization fractions for the 
modes.
© The Author(s), 2020
