Twist-3 light-cone distribution amplitudes of the scalar mesons within the QCD sum rules and their application to the B→SB \to S transition form factors

We investigate the twist-3 light-cone distribution amplitudes (LCDAs) of the scalar mesons $a_0$, $K^{\ast}_0$ and $f_0$ within the QCD sum rules. The QCD sum rules are improved by a consistent treatment of the sizable $s$-quark mass effects within the framework of the background field approach. Adopting the valence quark component $(\bar{q}_1 q_2)$ as the dominant structure of the scalar mesons, our estimation for their masses are close to the measured $a_0(1450)$, $K^{\ast}_0(1430)$ and $f_0(1710)$. From the sum rules, we obtain the first two non-zero moments of the twist-3 LCDAs $\phi^{s,\sigma}_{a_0}$: $\langle \xi_{s,a_0}^{2(4)} \rangle=0.369 \;(0.245)$ and $\langle \xi_{\sigma,a_0}^{2(4)} \rangle=0.203 \;(0.093)$; those of the twist-3 LCDAs $\phi_{K^*_0}^{s,\sigma}$: $\langle \xi_{s,K^{\ast}_0}^{1(2)} \rangle =0.004\;(0.355)$ and $\langle \xi_{\sigma,K^{\ast}_0}^{1(2)} \rangle =0.018\;(0.207)$; and those of the twist-3 LCDAs $\phi_{f_0}^{s,\sigma}$: $\langle \xi_{s,f_0}^{2(4)} \rangle=0.335 \;(0.212)$ and $\langle \xi_{\sigma,f_0}^{2(4)} \rangle=0.196 \; (0.088)$, respectively. As an application of those twist-3 LCDAs, we study the $B \to S$ transition form factors by introducing proper chiral currents into the correlator, which is constructed such that the twist-3 LCDAs give dominant contribution and the twist-2 LCDAs make negligible contribution. Our results of the $B \to S$ transition form factors at the large recoil region $q^2 \simeq 0$ are consistent with those obtained in the literature, which inversely shows the present twist-3 LCDAs are acceptable.Comment: 14 pages, 12 figures, 7 table

Study on the Effect of Regional Water Pollution—Take Huaxi River in Chongqing as an Example

Water pollution management plays a crucial role in China’s ecological environment development. It has evolved from being solely the responsibility of the government to a collaborative effort involving multiple entities. This paper presents findings from a field survey conducted around the collaborative capacity and effectiveness of wastewater treatment in Huaxi River, Chongqing. The study collected 427 valid questionnaires and employed SPSS26.0 software and AMOS24.0 software, utilizing structural equation modelling and regression analysis to verify the relationship between the variables. The results highlight that synergy mechanism acts as a mediating variable between synergy capability and synergy governance effect, underscoring the role of mechanism in the relationship between capability and governance effect. The conclusion emphasizes the importance of enhancing synergistic capacity and synergistic mechanism to effectively promote synergistic governance effect in the water pollution management of Huaxi River in Chongqing. This can be achieved by improving the abilities of multiple stakeholders in managing water pollution, enhancing cooperation among parties, and encouraging participation of social organizations, the public, and enterprises in the management process to achieve sustainable development of ecological civilization