$K_0^\ast(1430)$ Twist-2 Distribution Amplitude and $B_s,D_s \to K_0^\ast(1430)$ Transition Form Factors

TL;DR

This paper models the $K_0^\ast(1430)$ meson's distribution amplitude using QCD sum rules and a light-cone harmonic oscillator approach, then calculates transition form factors for $B_s,D_s$ decays to this meson, aiding CKM matrix element extraction.

Contribution

It introduces a new LCHO model for the $K_0^\ast(1430)$ leading-twist DA and refines sum rule calculations for its moments, enabling more accurate form factor predictions.

Findings

More accurate $\xi$-moments of the $K_0^\ast(1430)$ DA were obtained.

A novel LCHO model for the DA was established and fitted.

Transition form factors for $B_s,D_s \to K_0^\ast(1430)$ were calculated.

Abstract

Based on the scenario that the $K_0^\ast(1430)$ is viewed as the ground state of $s\bar{q}$ or $q\bar{s}$, we study the $K_0^\ast(1430)$ leading-twist distribution amplitude (DA) $\phi_{2;K_0^\ast}(x,\mu)$ with the QCD sum rules in the framework of background field theory. A more reasonable sum rule formula for $\xi$-moments $\langle\xi^n\rangle_{2;K_0^\ast}$ is suggested, which eliminates the influence brought by the fact that the sum rule of $\langle\xi^0_p\rangle_{3;K_0^\ast}$ cannot be normalized in whole Borel region. More accurate values of the first ten $\xi$-moments, $\langle\xi^n\rangle_{2;K_0^\ast} (n = 1,2,\cdots,10)$, are evaluated. A new light-cone harmonic oscillator (LCHO) model for $K_0^\ast(1430)$ leading-twist DA is established for the first times. By fitting the resulted values of $\langle\xi^n\rangle_{2;K_0^\ast} (n = 1,2,\cdots,10)$ via the least squares method, the behavior of $K_0^\ast(1430)$ leading-twist DA described with LCHO model is determined. Further, by adopting the light-cone QCD sum rules, we calculate the $B_s,D_s \to K_0^\ast(1430)$ transition form factors and branching fractions of the semileptonic decays $B_s,D_s \to K_0^\ast(1430) \ell \nu_\ell$. The corresponding numerical results can be used to extract the Cabibbo-Kobayashi-Maskawa matrix elements by combining the relative experimental data in the future.