Heavy-to-light scalar form factors from Muskhelishvili–Omnès dispersion relations

D. -L. Yao; P. Fernandez-Soler; M. Albaladejo; F. -K. Guo; J. Nieves

doi:10.1140/epjc/s10052-018-5790-4

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2018) 78: 310
https://doi.org/10.1140/epjc/s10052-018-5790-4

Regular Article - Theoretical Physics

Heavy-to-light scalar form factors from Muskhelishvili–Omnès dispersion relations

D. -L. Yao¹, P. Fernandez-Soler¹, M. Albaladejo², F. -K. Guo³^,4 and J. Nieves¹^*

¹ Instituto de Física Corpuscular (centro mixto CSIC-UV), Institutos de Investigación de Paterna, Apartado 22085, 46071, Valencia, Spain
² Departamento de Física, Universidad de Murcia, 30071, Murcia, Spain
³ CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Zhong Guan Cun East Street 55, Beijing, 100190, China
⁴ School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

^* e-mail: jmnieves@ific.uv.es

Received: 8 March 2018
Accepted: 8 April 2018
Published online: 18 April 2018

Abstract

By solving the Muskhelishvili–Omnès integral equations, the scalar form factors of the semileptonic heavy meson decays $D\rightarrow \pi \bar{\ell }\nu _\ell$ , $D\rightarrow {\bar{K}} \bar{\ell }\nu _\ell$ , ${\bar{B}}\rightarrow \pi \ell \bar{\nu }_\ell$ and ${\bar{B}}_s\rightarrow K \ell \bar{\nu }_\ell$ are simultaneously studied. As input, we employ unitarized heavy meson–Goldstone boson chiral coupled-channel amplitudes for the energy regions not far from thresholds, while, at high energies, adequate asymptotic conditions are imposed. The scalar form factors are expressed in terms of Omnès matrices multiplied by vector polynomials, which contain some undetermined dispersive subtraction constants. We make use of heavy quark and chiral symmetries to constrain these constants, which are fitted to lattice QCD results both in the charm and the bottom sectors, and in this latter sector to the light-cone sum rule predictions close to $$q^2=0$$ as well. We find a good simultaneous description of the scalar form factors for the four semileptonic decay reactions. From this combined fit, and taking advantage that scalar and vector form factors are equal at , we obtain $|V_{cd}|=0.244\pm 0.022$ , $|V_{cs}|=0.945\pm 0.041$ and $|V_{ub}|=(4.3\pm 0.7)\times 10^{-3}$ for the involved Cabibbo–Kobayashi–Maskawa (CKM) matrix elements. In addition, we predict the following vector form factors at $$q^2=0$$ : $|f_+^{D\rightarrow \eta }(0)|=0.01\pm 0.05$ , $|f_+^{D_s\rightarrow K}(0)|=0.50 \pm 0.08$ , $|f_+^{D_s\rightarrow \eta }(0)|=0.73\pm 0.03$ and $|f_+^{{\bar{B}}\rightarrow \eta }(0)|=0.82 \pm 0.08$ , which might serve as alternatives to determine the CKM elements when experimental measurements of the corresponding differential decay rates become available. Finally, we predict the different form factors above the $$q^2-$$ regions accessible in the semileptonic decays, up to moderate energies amenable to be described using the unitarized coupled-channel chiral approach.