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

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) ${\varphi }_{2;K_0^{\ast }}(x,\mu )$ with the QCD sum rules in the framework of background field theory. A more reasonable sum rule formula for $\xi$-moments $⟨{\xi }^n{⟩}_{2;K_0^{\ast }}$ is suggested, which eliminates the influence brought by the fact that the sum rule of $⟨{\xi }_p^0{⟩}_{3;K_0^{\ast }}$ cannot be normalized in whole Borel region. More accurate values of the first ten $\xi$-moments, $⟨{\xi }^n{⟩}_{2;K_0^{\ast }}(n=1,2,\cdots ,10)$, 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 $⟨{\xi }^n{⟩}_{2;K_0^{\ast }}(n=1,2,\cdots ,10)$ 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.

Comments: 16 pages, 4 figures