https://doi.org/10.1140/epjc/s10052-022-11050-0
Regular Article - Theoretical Physics
Exclusive determinations of 
and 
through unitarity
1
Physics Department, INFN Sezione di Roma La Sapienza, Piazzale Aldo Moro 5, 00185, Rome, Italy
2
Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tre, Via della Vasca Navale 84, 00146, Rome, Italy
3
Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126, Pisa, Italy
4
Istituto Nazionale di Fisica Nucleare, Sezione di Pisa, Largo Bruno Pontecorvo 3, 56127, Pisa, Italy
Received:
20
January
2022
Accepted:
21
November
2022
Published online:
1
December
2022
In this work we apply the Dispersive Matrix (DM) method of Di Carlo et al. (Phys Rev D 104:054502, 2021) and Martinelli et al. (Phys Rev D 105:034503, 2022) to the lattice computations of the Form Factors (FFs) entering the semileptonic 
decays, recently produced by the FNAL/MILC Collaborations (Fermilab Lattice, MILC collaboration, Semileptonic form factors for 
at nonzero recoil from 2 + 1-flavor lattice QCD. arXiv:2105.14019) at small, but non-vanishing values of the recoil variable (
). Thanks to the DM method we obtain the FFs in the whole kinematical range accessible to the decay in a completely model-independent and non-perturbative way, implementing exactly both unitarity and kinematical constraints. Using our theoretical bands of the FFs we extract from the experimental data and compute the theoretical value of 
. Our final result for reads 
, compatible with the most recent inclusive estimate at the 
level. Moreover, we obtain the pure theoretical value 
, which is compatible with the experimental world average at the 
level.
© The Author(s) 2022
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