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arXiv 2102.03989hep-ph
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一种改进的光锥谐振子模型及其对π介子超前扭转分布振幅的计算

An improved light-cone harmonic oscillator model for the pionic leading-twist distribution amplitude

Tao Zhong, Zhi-Hao Zhu, Hai-Bing Fu, Xing-Gang Wu, Tao Huang

备注：
15 pages, 6 figures, matches the version to appear in PRD
发表信息：
Phys. Rev. D 104, 016021 (2021)
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摘要：

本文通过对传统光锥谐振子模型的改进，在重构函数$φ_{2;π}(x)$的基础上，研究了π介子导扭分布振幅$ϕ_{2;π}(x,μ)$。为了约束模型参数，我们在QCD背景场论求和规则（BFTSR）的框架下计算了它的矩$\langleξ^n\rangle_{2;π}|_μ$，直到$10^{\rm th}$阶。考虑到$0^{\rm th}$矩$\langleξ^0\rangle_{2;π}|_μ$的求和规则不能归一化的事实，我们提出了一个更合理的$\langleξ^n\rangle_{2;π}|_μ$求和规则公式。然后，我们在初始尺度$μ_0 = 1~{\rm GeV}$下用$n=(2,4,6,8,10)$获得$\langleξ^n\rangle_{2;π}|_{μ_0}$的值。前两个矩为：$\langle ξ^2\rangle_{2;π}|_{μ_0} = 0.271 \pm 0.013$、$\langleξ^4\rangle_{2;π}|_{μ_0} = 0.138 \pm 0.010$ ;相应的Gegenbauer矩分别为$a^{2;π}_2(μ_0) = 0.206 \pm 0.038$、$a^{2;π}_4(μ_0) = 0.047 \pm 0.011$。在对矩$\langleξ^n\rangle_{2;π}|_μ$进行拟合后，利用最小二乘法得到了合适的模型参数。扭曲2 π DA的结果更接近AdS/QCD和晶格结果，但比Dyson-Schwinger方程的结果窄。此外，我们利用光锥求和规则计算了π介子-光子跃迁形状因子（TFF）和$B\toπ$ TFF，与实验和理论结果一致。

英文摘要：

In this paper, we study the pion leading-twist distribution amplitude $ϕ_{2;π}(x,μ)$ by improving the traditional light-cone harmonic oscillator model within the reconstruction of the function $φ_{2;π}(x)$. In order to constraining the model parameters, we calculate its moments $\langleξ^n\rangle_{2;π}|_μ$ in the framework of QCD background field theory sum rule (BFTSR) up to $10^{\rm th}$ order. Considering the fact that the sum rule of the $0^{\rm th}$ moment $\langleξ^0\rangle_{2;π}|_μ$ cannot be normalized, we suggest a more reasonable sum rule formula for $\langleξ^n\rangle_{2;π}|_μ$. Then, we obtain the values of $\langleξ^n\rangle_{2;π}|_{μ_0}$ with $n=(2,4,6,8,10)$ at the initial scale $μ_0 = 1~{\rm GeV}$. The first two moments are: $\langle ξ^2\rangle_{2;π}|_{μ_0} = 0.271 \pm 0.013$, $\langleξ^4\rangle_{2;π}|_{μ_0} = 0.138 \pm 0.010$; and the corresponding Gegenbauer moments are $a^{2;π}_2(μ_0) = 0.206 \pm 0.038$, $a^{2;π}_4(μ_0) = 0.047 \pm 0.011$, respectively. After fitting the moments $\langleξ^n\rangle_{2;π}|_μ$, we obtained the appropriate model parameters by using the least square method. The resultant behavior for twist-2 pion DA is more closely to the AdS/QCD and lattice result, but is narrower than that by Dyson-Schwinger equation. Furthermore, we calculate the pion-photon transition form factors (TFF) and $B\toπ$ TFF within light-cone sum rule approach, which are conform with experimental and theoretical results.

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