$B_{(s)} \to S(a_0(1450), K_0^*(1430), f_0(1500))$ helicity form factors within QCD light-cone sum rules

TL;DR

This work computes the helicity form factors for $B_{(s)}$ decays into heavy scalar mesons $S=a_0(1450), K_0^*(1430), f_0(1500)$ using QCD light-cone sum rules with conventional $q\bar{q}$ structure. It includes next-to-leading order QCD corrections and twist-3 light-cone distribution amplitudes, and extrapolates the form factors over the full $q^2$ range via a simplified $z$-series expansion. The authors then derive differential decay widths, branching ratios, and lepton polarization observables for semi-leptonic, FCNC, and neutrino modes, finding overall consistency with some methods while highlighting large current uncertainties in scalar-meson structure. These results provide theoretical benchmarks to interpret future measurements and to probe the underlying nature of light scalar mesons.

Abstract

In this paper, we investigate the helicity form factors (HFFs) of the $B_{(s)}$-meson decay into a scalar meson with a mass larger than 1~GeV, {\it i.e.,} $B \to a_0(1450)$, $B_{(s)} \to K_0^*(1430)$ and $B_{s} \to f_0(1500)$ by using light-cone sum rules approach. We take the standard currents for correlation functions. To enhance the precision of our calculations, we incorporate the next-to-leading order (NLO) corrections and retain the scalar meson twist-3 light-cone distribution amplitudes. Furthermore, we extend the HFFs to the entire physical $q^2$ region employing a simplified $z$-series expansion. At the point of $q^2=1\rm{~GeV^2}$, all NLO contributions to the HFFs are negative, with the maximum contribution around $25\%$. Then, as applications of these HFFs, we analyze the differential decay widths, branching ratios, and lepton polarization asymmetries for the semi-leptonic $B_{(s)} \to S \ell \barν_\ell$, FCNC $B_{(s)} \to S \ell \bar{\ell}$ and rare $B_{(s)} \to S ν\barν$ decays. Our results are consistent with existing studies within uncertainties. The current data still suffer from large uncertainties and need to be measured more precisely, which can lead to a better understanding of the fundamental properties of light scalar mesons.

Figures (7)

• Figure 1: Twist-2 and 3 distribution amplitudes of $a_0(1450), f_0(1500), K^*_0(1430)$-mesons at the scale $\mu$ =1 GeV. The solid lines are the central values, and the shaded bands are used for the corresponding errors.
• Figure 2: The center values for $B_{(s)} \to a_0(1450), f_0(1500), K^*_0(1430)$ HFFs with respect to Borel parameter for the four different $q^2$ values.
• Figure 3: The variation of the HFFs for the semi-leptonic transitions $B_{(s)} \to a_0(1450), f_0(1500), K^*_0(1430)$ with the threshold parameter $s_0$ at a fixed value of the Borel parameter $M^2$.
• Figure 4: HFFs for the semi-leptonic transitions $B_{(s)} \to a_0(1450), f_0(1500), K^*_0(1430)$ across the entire physical region. The solid lines represent the central values, and the shaded bands indicate the corresponding uncertainties obtained by varying the input parameters such as $m_b,~m_{B_{(s)}},~f_{B_{(s)}}$, $m_S,~M^2,~s_0,~\phi_{2;S}(u,\mu),~\psi_{3;S}^{s}(u,\mu),~\psi_{3;S}^{\sigma}(u,\mu),\cdots$, which have been added up in quadrature.
• Figure 5: The differential decay widths for the FCCC semi-leptonic decays $B \to a_0(1450)\ell\bar{\nu}_\ell$, $B_s \to K_0^*(1430)\ell\bar{\nu}_\ell$, FCNC semi-leptonic decays $B_s \to f_0(1500)\ell^+\ell^-$, $B_{(s)} \to K_0^*(1430)\ell^+\ell^-$, which the lepton are taken as $e,\mu, \tau$. The solid lines are the central values, and the shaded bands are used for the corresponding errors.