论文标题
小$ x $的夸克和gluon螺旋进化：修订和更新
Quark and Gluon Helicity Evolution at Small $x$: Revised and Updated
论文作者
论文摘要
我们重新审视了小bjorken- $ x $ gluon和singlet quark螺旋分布（$ s $ channel）形式主义的问题。早期在同一框架中就该主题进行的工作导致了Gluon场力强度$ f^{12} $和Quark“轴向电流” $ {\barψ}γ^+γ^5ψ$ operators（夹在适当的轻孔Wilson线之间）中的“轴向电流” $ {\barψ}γ^+γ^5ψ$。 $α_s\，\ ln^2（1/x）$，$α_s$ the stront耦合常数）。在这项工作中，我们观察到，上述操作员与另一个Gluon操作员的重要混合，$ \ OverLeftarrow {d}^i \，{d}^i $，也夹在轻孔Wilson线之间（带有重复的索引$ i = 1,2 $的重复索引$ i = 1,2 $），在先前的作品中缺少。该操作员具有子eikonal（协变量）阶段的物理含义：其对螺旋性演变的贡献与另一个子欧洲子操作员成正比，$ d^i- \ OverLeftArol {d}^i $，与Jaffe-Manohar Palluons分布有关。在这项工作中，我们将该操作员包括在小$ x $ helicity的演化中，并构建一个新颖的进化，将所有三个操作员混合在一起（$ d^i- \ OverLeftarrow {d}^i $，$ f^{12} $，$ f^{\ bar单座}γ^+γ^5ψ$），概括了先前的结果。我们还以大$ n_c $和大$ n_c \＆n_f $ limits构建了闭合的DLA进化方程，分别具有$ n_c $和$ n_f $的夸克颜色和口味的数字。从数值上求解大$ n_c $方程，我们获得以下小$ x $渐近级和gluon螺旋分布的$Δς$和$Δg$，以及$ g_1 $结构函数，\ [Δς（x，q^2）\simδ（x，x，q^2） g_1（x，q^2）\ sim \ left（\ frac {1} {x} \ right）^{3.66 \，\ sqrt {\ frac {\ frac {α_s\，n_c} {2π}}}}}}}}}，\ \ \ \ \ \]，与早期的工作bybartels，bartels，rys，ermermolaev and rys and rys and rys and rys。
We revisit the problem of small Bjorken-$x$ evolution of the gluon and flavor-singlet quark helicity distributions in the shock wave ($s$-channel) formalism. Earlier works on the subject in the same framework resulted in an evolution equation for the gluon field-strength $F^{12}$ and quark "axial current" ${\barψ}γ^+γ^5ψ$ operators (sandwiched between the appropriate light-cone Wilson lines) in the double-logarithmic approximation (DLA: summing powers of $α_s\,\ln^2(1/x)$ with $α_s$ the strong coupling constant). In this work, we observe that an important mixing of the above operators with another gluon operator, $\overleftarrow{D}^i\,{D}^i$, also sandwiched between the light-cone Wilson lines (with the repeated index $i=1,2$ summed over), was missing in the previous works. This operator has the physical meaning of the sub-eikonal (covariant) phase: its contribution to helicity evolution is shown to be proportional to another sub-eikonal operator, $D^i-\overleftarrow{D}^i$, which is related to the Jaffe-Manohar polarized gluon distribution. In this work we include this operator into small-$x$ helicity evolution, and construct a novel evolution mixing all three operators ($D^i-\overleftarrow{D}^i$, $F^{12}$, and ${\barψ}γ^+γ^5ψ$), generalizing the previous results. We also construct closed DLA evolution equations in the large-$N_c$ and large-$N_c\& N_f$ limits, with $N_c$ and $N_f$ the numbers of quark colors and flavors, respectively. Solving the large-$N_c$ equations numerically we obtain the following small-$x$ asymptotics of the quark and gluon helicity distributions $ΔΣ$ and $ΔG$, along with the $g_1$ structure function, \[ΔΣ(x,Q^2)\simΔG(x,Q^2)\sim g_1(x,Q^2)\sim\left(\frac{1}{x}\right)^{3.66\,\sqrt{\frac{α_s\,N_c}{2π}}},\] in complete agreement with the earlier work by Bartels, Ermolaev and Ryskin.
