We show within proton hot spot picture that the exclusive vector meson production in electron-proton deeply inelastic scattering is sensitive to the individual width of the constituent quarks of the proton. For comparison, we calculate the exclusive $J/\mathrm{\Psi }$ production cross-sections in three cases, ${\mathrm{B}}_{\mathrm{u}}\ge {\mathrm{B}}_{\mathrm{d}}$, ${\mathrm{B}}_{\mathrm{u}}<{\mathrm{B}}_{\mathrm{d}}$ and ${\mathrm{B}}_{\mathrm{u}}\ne {\mathrm{B}}_{\mathrm{u}}^{\prime }\ne {\mathrm{B}}_{\mathrm{d}}$, where the ${\mathrm{B}}_{\mathrm{u}}$, ${\mathrm{B}}_{\mathrm{u}}^{\prime }$ and ${\mathrm{B}}_{\mathrm{d}}$ denote the widths of two up quarks and a down quark. We find that only results calculated with ${\mathrm{B}}_{\mathrm{u}}\ge {\mathrm{B}}_{\mathrm{d}}$ can give a reasonable description of the exclusive $J/\mathrm{\Psi }$ production cross-section data at HERA. To test that our results are independent of the details of the model, we retain the average width of the three constituent quarks unchanged and compute the exclusive $J/\mathrm{\Psi }$ production cross-sections with contribution weight by setting different proportional coefficients (${\mathrm{W}}_{\mathrm{u}}$ and ${\mathrm{W}}_{\mathrm{d}}$) for the up and down quarks, respectively. It shows that the results calculated with ${\mathrm{W}}_{\mathrm{u}}\ge {\mathrm{W}}_{\mathrm{d}}$ can well reproduce the exclusive $J/\mathrm{\Psi }$ production data at HERA, while the opposite case cannot describe the HERA data. These interesting findings seem to indicate that the up quark has more gluons around it than the down quark at high energy although the spatial distribution of gluons fluctuates event-by-event. To ensure the relevant results independent of the species of the vector meson, we also calculate the ρ production cross-sections with the same group of parameters used in the exclusive $J/\mathrm{\Psi }$ production and compare the predictions with the HERA data. It shows that all the results computed in the exclusive ρ productions are consistent with the findings obtained in the exclusive $J/\mathrm{\Psi }$ productions.

我们在质子热点图中显示，电子-质子深度非弹性散射中唯一的矢量介子产生对质子组成夸克的个体宽度敏感。为了进行比较，我们计算了 ${\mathrm{B}}_{\mathrm{u}}\ge {\mathrm{B}}_{\mathrm{d}}$ 、 ${\mathrm{B}}_{\mathrm{u}}<{\mathrm{B}}_{\mathrm{d}}$ 和 ${\mathrm{B}}_{\mathrm{u}}\ne {\mathrm{B}}_{\mathrm{u}}^{\prime }\ne {\mathrm{B}}_{\mathrm{d}}$ 三种情况下的排他 $J/\mathrm{\Psi }$ 生产横截面，其中 ${\mathrm{B}}_{\mathrm{u}}$ 、 ${\mathrm{B}}_{\mathrm{u}}^{\prime }$ 和 ${\mathrm{B}}_{\mathrm{d}}$ 表示两个上夸克和一个下夸克的宽度。我们发现，只有使用 ${\mathrm{B}}_{\mathrm{u}}\ge {\mathrm{B}}_{\mathrm{d}}$ 计算的结果才能合理描述HERA独有的 $J/\mathrm{\Psi }$ 生产截面数据。为了测试我们的结果独立于模型的细节，我们保持三个组成夸克的平均宽度不变，并通过设置不同的比例系数（< b10> 和 ${\mathrm{W}}_{\mathrm{d}}$ ) 分别表示上夸克和下夸克。表明 ${\mathrm{W}}_{\mathrm{u}}\ge {\mathrm{W}}_{\mathrm{d}}$ 计算的结果可以很好地再现HERA独有的 $J/\mathrm{\Psi }$ 生产数据，而相反的情况无法描述HERA数据。这些有趣的发现似乎表明，尽管胶子的空间分布随事件而波动，但在高能下，上夸克周围的胶子比下夸克更多。为了确保相关结果独立于矢量介子的种类，我们还使用独家 $J/\mathrm{\Psi }$ 生产中使用的同一组参数计算 ρ 生产横截面，并将预测与 HERA 数据进行比较。它表明，在独家 ρ 产生式中计算的所有结果与在独家 $J/\mathrm{\Psi }$ 产生式中获得的结果一致。