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arXiv 2303.16339hep-phnucl-th
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从低能质子光锥波函数的演化中导出高能偶极散射振幅

High-energy dipole scattering amplitude from evolution of low-energy proton light-cone wave functions

Adrian Dumitru, Heikki Mäntysaari, Risto Paatelainen

备注：
11 pages, 10 figures. Obtained dipole-proton amplitudes at different x are included in the ancillary files, v2 matches published version
发表信息：
Phys. Rev. D 107, 114024 (2023)
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AI总结：

本文基于低能质子光锥波函数构建BK演化方程的初始条件，通过拟合耦合常数较好描述了HERA的粲截面数据，但拟合优度表明仍需系统性改进。

摘要：

在平均场近似下，小偶极在高能下的前向散射振幅由Balitsky-Kovchegov（BK）演化方程给出。该方程需要一个初始条件 $N(r; x_0)$，用于描述大小为 $r$ 的偶极与在动量分数 $x_0$ 处被探测的靶发生散射的过程。我们没有使用在 $x\ll x_0$ 的高能数据上调整的特设参数化，而是尝试构建一个与质子的低能、大 $x$ 性质相一致的初始散射振幅。我们从文献中的非微扰三夸克光锥模型波函数出发。我们加入了由于发射一个胶子而产生的 ${\cal O}(g)$ 阶修正，以及由于交换一个胶子而产生的 ${\cal O}(g^2)$ 阶虚修正，这些修正在具有精确运动学的光锥微扰理论中计算得出。我们提供了 $x_0=0.01 - 0.05$ 时所得 $N(r; x_0)$ 的数值数据以及解析参数化。在领头对数（LL）近似下向更低 $x$ 求解BK方程，通过拟合一个参数即耦合常数 $α_s\simeq 0.2$，我们较好地描述了HERA实验中测量到的深度非弹性散射中的粲截面。然而，由于无法在 $x_0$ 处调整初始振幅，对高精度数据的拟合结果为 $χ^2/N_\text{dof} = 2.3$（$N_\text{dof} =38$），这提供了明确的统计证据，表明需要进行系统性改进，例如对光子波函数、演化方程和初始条件的改进。

英文摘要：

The forward scattering amplitude of a small dipole at high energies is given in the mean field approximation by the Balitsky-Kovchegov (BK) evolution equation. It requires an initial condition $N(r; x_0)$ describing the scattering of a dipole with size $r$ off the target that is probed at momentum fraction $x_0$. Rather than using ad hoc parameterizations tuned to high-energy data at $x\ll x_0$, here we attempt to construct an initial scattering amplitude that is consistent with low-energy, large-$x$ properties of the proton. We start from a non-perturbative three quark light-cone model wave function from the literature. We add ${\cal O}(g)$ corrections due to the emission of a gluon, and ${\cal O}(g^2)$ virtual corrections due to the exchange of a gluon, computed in light-cone perturbation theory with exact kinematics. We provide numerical data as well as analytic parameterizations of the resulting $N(r; x_0)$ for $x_0=0.01 - 0.05$. Solving the BK equation in the leading logarithmic (LL) approximation towards lower $x$, we obtain a fair description of the charm cross section in deeply inelastic scattering measured at HERA by fitting one parameter, the coupling constant $α_s\simeq 0.2$. However, without the option to tune the initial amplitude at $x_0$, the fit of the high precision data results in $χ^2/N_\text{dof} = 2.3$ at $N_\text{dof} =38$, providing clear statistical evidence for the need of systematic improvement e.g. of the photon wave function, evolution equation, and initial condition.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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