Eur. Phys. J. C (2022) 82: 1141
https://doi.org/10.1140/epjc/s10052-022-10984-9

Regular Article - Theoretical Physics

Semileptonic form factors for at nonzero recoil from -flavor lattice QCD

Fermilab Lattice and MILC Collaborations

¹ Department of Computational Mathematics, Science and Engineering, and Department of Physics and Astronomy, Michigan State University, 48824, East Lansing, MI, USA
² Department of Physics and Astronomy, University of Utah, 84112, Salt Lake City, UT, USA
³ Department of Physics, Syracuse University, 13244, Syracuse, NY, USA
⁴ Department of Physics, University of Illinois, 61801, Urbana, IL, USA
⁵ Illinois Center for Advanced Studies of the Universe, University of Illinois, 61801, Urbana, IL, USA
⁶ Departamento de Física Teórica y del Cosmos, Universidad de Granada, 18071, Granada, Spain
⁷ Department of Physics, Indiana University, 47405, Bloomington, IN, USA
⁸ American Physical Society, 11961, Ridge, NY, USA
⁹ Fermi National Accelerator Laboratory, 60510, Batavia, IL, USA
¹⁰ Department of Physics, University of California, 93106, Santa Barbara, CA, USA
¹¹ Department of Physics, University of Arizona, 85721, Tucson, AZ, USA

^s alexv@unizar.es

Received: 13 May 2022
Accepted: 31 October 2022
Published online: 16 December 2022

Abstract

We present the first unquenched lattice-QCD calculation of the form factors for the decay at nonzero recoil. Our analysis includes 15 MILC ensembles with flavors of asqtad sea quarks, with a strange quark mass close to its physical mass. The lattice spacings range from fm down to 0.045 fm, while the ratio between the light- and the strange-quark masses ranges from 0.05 to 0.4. The valence b and c quarks are treated using the Wilson-clover action with the Fermilab interpretation, whereas the light sector employs asqtad staggered fermions. We extrapolate our results to the physical point in the continuum limit using rooted staggered heavy-light meson chiral perturbation theory. Then we apply a model-independent parametrization to extend the form factors to the full kinematic range. With this parametrization we perform a joint lattice-QCD/experiment fit using several experimental datasets to determine the CKM matrix element . We obtain . The first error is theoretical, the second comes from experiment and the last one includes electromagnetic and electroweak uncertainties, with an overall , which illustrates the tensions between the experimental data sets, and between theory and experiment. This result is in agreement with previous exclusive determinations, but the tension with the inclusive determination remains. Finally, we integrate the differential decay rate obtained solely from lattice data to predict , which confirms the current tension between theory and experiment.