论文标题
低$ x $区域中的重夸克贡献的几何规模
Geometrical scaling of heavy-quark contributions in the low $x$ region
论文作者
论文摘要
我们描述了重夸克结构功能的确定$ f_ {2，l}^{\ mathcal {q} \ bar {\ Mathcal {q}}}} $借助缩放属性。我们观察到，该结构的功能可用于包容性魅力和底部生产，以低$ x $的形式表现出几何缩放。几何缩放意味着重夸克结构功能仅是一个无尺寸变量$τ{\ equiv} q^{2}/q^{2} _ {sat}（x）$的函数。这些结果对于$δ$的任何值都是有效的，为$ x^{ - δ} $在低$ x $下的Parton密度的行为。重夸克结构函数的确定作为质子结构函数的参数化$ f_ {2}（x，x，q^{2}）$及其导数。 $ f_ {2，l}^{\ mathcal {q} \ bar {\ Mathcal {q}}} $的分析表达式在$ f_ {2}（x，x，q^{2}）$的参数的有效参数方面，相对于BDH和ASW模型。为了研究重型夸克的生产过程，我们在DAS方法中使用共线结果。数值计算和与HERA数据的比较表明，建议的方法提供了可靠的$ f_ {2}^{\ Mathcal {q} \ bar {\ Mathcal {Q}}} $，$ r^{c \ bar {c}}在低$ x $的低范围内，低绝对四摩托姆传输平方（$ 4〜 \ mathrm {gev}^{2} <q^{2} <q^{2} <2000〜 \ mathrm {gev}^{2} $）。另外，在Hera Kinematic系列中，$ f_ {2}^{c \ bar {c}}}/f_ {2}^{b \ bar {b}} $，$ f_ {2}}获得$ f_ {2}^{b \ bar {b}}/f_ {2}^{bdhm} $。在LHEC和FCC-EH山脉的过程分析中可以考虑将方法扩展到低和极低的$ x $。
We describe the determination of the heavy quarks structure functions $F_{2,L}^{\mathcal{Q}\bar{\mathcal{Q}}}$ with help of the scaling properties. We observe that the structure functions for inclusive charm and bottom production exhibits geometric scaling at low $x$. The geometrical scaling means that the heavy quark structure function is a function of only one dimensionless variable $τ{\equiv}Q^{2}/Q^{2}_{sat}(x)$ including quark mass. These results are valid for any value of $δ$, being $x^{-δ}$ the behavior of the parton densities at low $x$. The determination of the heavy quark structure function is presented as a parameterization of the proton structure function $F_{2}(x,Q^{2})$ and its derivative. Analytical expressions for $F_{2,L}^{\mathcal{Q}\bar{\mathcal{Q}}}$ in terms of the effective parameters of the parameterization of $F_{2}(x,Q^{2})$ ,with respect to the BDH and ASW models, are presented. To study the heavy quark production processes, we use the collinear results in DAS approach. Numerical calculations and comparison with HERA data demonstrate that the suggested method provides reliable $F_{2}^{\mathcal{Q}\bar{\mathcal{Q}}}$, $R^{c\bar{c}}$ and $σ^{\mathcal{Q}\bar{\mathcal{Q}}}$ at low $x$ in a wide range of the low absolute four-momentum transfers squared ($4~\mathrm{GeV}^{2}<Q^{2}<2000~\mathrm{GeV}^{2}$). Also, in the HERA kinematic range, the ratio of $F_{2}^{c\bar{c}}/F_{2}^{b\bar{b}}$, $F_{2}^{c\bar{c}}/F_{2}^{BDHM}$ and $F_{2}^{b\bar{b}}/F_{2}^{BDHM}$ are obtained. Expanding the method to low and ultra low values of $x$ can be considered in the process analysis of the LHeC and FCC-eh colliders.
