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$B_c \to J/ψ$螺旋度形状因子和$B_c^+ \to J/ψ+(P, V, \ell^+ ν_\ell)$衰变

$B_c \to J/ψ$ helicity form factors and the $B_c^+ \to J/ψ+(P, V, \ell^+ ν_\ell)$ decays

Wei Cheng, Yi Zhang, Long Zeng, Hai-Bing Fu, Xing-Gang Wu

备注：
10 pages, 4 figures, published version
发表信息：
Chin. Phys. C 46, 053103 (2022)
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摘要：

在本文中，我们计算$B_c\to J/ψ$螺旋形状因子（HFFs）的扭曲-4精度使用光锥求和规则（LCSR）的方法。在将这些HFF外推到物理允许的$q^2$区域后，我们研究了$B^+_c$介子二体衰变和半轻子衰变$B_c^+ \to J/ψ+(P, V, \ell^+ ν_\ell)$，其中$P/V$分别代表轻赝标/矢量介子。通过使用CKM矩阵元和来自Particle Data Group的$B_c$寿命可以导出分支分数，并且我们获得${\cal B}(B_c^+ \to J/ψπ^+)=(0.136^{+0.002}_{-0.002})\%$、${\cal B}(B_c^+ \to J/ψK^+)=(0.010^{+0.000}_{-0.000})\%$、${\cal B}(B_c^+ \to J/ψρ^+) =(0.768^{+0.029}_{-0.033})\%$、${\cal B}(B_c^+ \to J/ψK^{\ast +})=(0.043^{+0.001}_{-0.001})\%$、${\cal B}(B_c^+ \to J/ψμ^+ν_μ)=(2.802^{+0.526}_{-0.675})\%$和${\cal B}(B_c^+ \to J/ψτ^+ν_τ)=(0.559^{+0.131}_{-0.170})\%$。然后，我们获得了${\cal R}_{π^+/μ^+ν_μ} = 0.048^{+ 0.009}_{-0.012}$和${\cal R}_{K^+ / π^+} = 0.075^{+0.005}_{-0.005}$，它们在$1σ$误差范围内与LHCb测量值一致。我们还获得了${\cal R}_{J/ψ}=0.199^{+ 0.060}_{-0.077}$，它像其他的理论预测，是一致的LHCb测量值$2σ$ -误差。这意味着LCSR方法下的HFF也适用于$B^+_c$介子二体衰变和半轻子衰变$B_c^+ \to J/ψ+(P, V, \ell^+ ν_\ell)$，而LCSR方法下的HFF则意味着$B_c\to J/ψ\ell^+ ν_\ell$半轻子衰变可能存在新的物理机制.

英文摘要：

In this paper, we calculate the $B_c\to J/ψ$ helicity form factors (HFFs) up to twist-4 accuracy by using the light-cone sum rules (LCSR) approach. After extrapolating those HFFs to the physically allowable $q^2$ region, we investigate the $B^+_c$-meson two-body decays and semi-leptonic decays $B_c^+ \to J/ψ+(P, V, \ell^+ ν_\ell)$ with $P/V$ stands for light pseudoscalar/vector meson, respectively. The branching fractions can be derived by using the CKM matrix element and the $B_c$ lifetime from the Particle Data Group, and we obtain ${\cal B}(B_c^+ \to J/ψπ^+)=(0.136^{+0.002}_{-0.002})\%$, ${\cal B}(B_c^+ \to J/ψK^+)=(0.010^{+0.000}_{-0.000})\%$, ${\cal B}(B_c^+ \to J/ψρ^+) =(0.768^{+0.029}_{-0.033})\%$, ${\cal B}(B_c^+ \to J/ψK^{\ast +})=(0.043^{+0.001}_{-0.001})\%$, ${\cal B}(B_c^+ \to J/ψμ^+ν_μ)=(2.802^{+0.526}_{-0.675})\%$ and ${\cal B}(B_c^+ \to J/ψτ^+ν_τ)=(0.559^{+0.131}_{-0.170})\%$. We then obtain ${\cal R}_{π^+/μ^+ν_μ} = 0.048^{+ 0.009}_{-0.012}$ and ${\cal R}_{K^+ / π^+} = 0.075^{+0.005}_{-0.005}$, which agree with the LHCb measured value within $1σ$-error. We also obtain ${\cal R}_{J/ψ}=0.199^{+ 0.060}_{-0.077}$, which like other theoretical predictions, is consistent with the LHCb measured value within $2σ$-error. Those imply that the HFFs under the LCSR approach are also applicable to the $B^+_c$ meson two-body decays and semi-leptonic decays $B_c^+ \to J/ψ+(P, V, \ell^+ ν_\ell)$, and the HFFs obtained by using LCSR in a new way implies that there may be new physics in the $B_c\to J/ψ\ell^+ ν_\ell$ semi-leptonic decays.

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