论文标题
中间$ x $的质子质子的夸克和gluon纠缠
Quark and gluon entanglement in the proton on the light cone at intermediate $x$
论文作者
论文摘要
在QCD中，带有$ n_c $颜色的抗对称性价夸克色彩空间singlet状态$ \simε_{i_1 \ cdots i_ {n_c}} | i_1，\ cdots，i_ {n_c} \ rangle $的proton的proton的proton的密度$ n_单一颜色的自由度，δ_{ij} $。它的eigenvalues的简化频谱，$λ_i= 1/n_c $，纯度$ \ mathrm {tr} 〜ρ^2 = 1/n_c $，以及von〜neumann entropy $ s_ \ s_ \ mathrm {vn} = \ log log（n_c）$ coldate commim insimal entancim enterancemal enterancemal enterancemal enterancemal enterancemal enterancemal coloremal coloremal colorest。另一方面，对于$ n_c \ to \ infty $，质子的空间波函数将由平均场确定的价值夸克波函数（E. Witten，nucl。Phys。B160（1979）p。57），而没有空间自由度的范围。 Brodsky和Schlumpf使用简单的三夸克模型轻波函数的$ N_C = 3 $计算的模型计算预测了空间自由度的百分比纠缠百分比。使用轻束扰动理论，我们还得出了与四个parton $ | QQQG \ rangle $ fock状态相关的密度矩阵。追踪夸克，我们为Gluon的自由度构建了降低的密度矩阵，该矩阵编码其与来源的纠缠。我们的表达式提供了密度矩阵的依赖性，用于gluon轻曲线动量的软截止$ x $，以及界线和紫外线调节器。以简单的近似值获得的数值结果表明，与三个夸克fock状态的夸克相比，Gluon（$ x_g <\ langle x_q \ rangle $）更强。
In QCD with $N_c$ colors the anti-symmetric valence quark color space singlet state $\sim ε_{i_1\cdots i_{N_c}} |i_1,\cdots, i_{N_c}\rangle$ of the proton corresponds to the reduced density matrix $ρ_{ij}=(1/N_c) δ_{ij}$ for a single color degree of freedom. Its degenerate spectrum of eigenvalues, $λ_i=1/N_c$, the purity $\mathrm{tr}~ρ^2 = 1/N_c$, and the von~Neumann entropy $S_\mathrm{vN}=\log(N_c)$ all indicate maximal entanglement of color. On the other hand, for $N_c\to\infty$ the spatial wave function of the proton factorizes into valence quark wave functions determined by a mean field (E. Witten, Nucl. Phys. B 160 (1979) p. 57) where there is no entanglement of spatial degrees of freedom. A model calculation at $N_c=3$ using a simple three quark model light-front wave function by Brodsky and Schlumpf, predicts percent level entanglement of spatial degrees of freedom. Using light-cone perturbation theory we also derive the density matrix associated with the four parton $|qqqg\rangle$ Fock state. Tracing out the quarks, we construct the reduced density matrix for the degrees of freedom of the gluon, which encodes its entanglement with the sources. Our expressions provide the dependence of the density matrix on the soft cutoff $x$ for the gluon light-cone momentum, and on the collinear and ultraviolet regulators. Numerical results obtained in a simple approximation indicate stronger entanglement for the gluon (with $x_g < \langle x_q\rangle$) than for quarks in the three quark Fock state.
