论文标题
小$ x $：通过带回夸克产生的振荡
Helicity at Small $x$: Oscillations Generated by Bringing Back the Quarks
论文作者
论文摘要
我们构建了最近衍生的大型$ n_c \＆n_f $ small- $ x $ x $ helicity Evolution方程的数值解决方案，目的是建立夸克螺旋分布的小$ x $渐近分布，而不是以前在同一框架中探索的大$ n_c $限制。 （这里$ n_c $和$ n_f $是夸克颜色和口味的数字。）虽然大$ n_c $ helicity Evolution仅涉及gluons，但大$ n_c \＆n_f $ Evolution也包括夸克的贡献。我们发现，在进化中添加夸克会使夸克螺旋分布振荡作为$ x $的函数。我们的数值结果以$ n_c \＆n_f $限制导致$ x $ - 依赖性的风味 - 灵巧夸克螺旋分布的依赖性，该分布被\ begin {align}ΔςΔς（x，q^2）\ bigG | _ _ _ { \ frac {1} {x} \ right）^{α_h^q} \，\ cos \ left [ω_q\，\ ln \ left（\ frac {1} {x} {x} \ right） +φ_q\ right]。 \ end {align}功率$α_h^q $表现出弱$ n_f $依赖性，对于所有考虑的$ n_f $值，仍然非常接近$α_H^q（n_f = 0）=（4/\ sqrt {3} {3} {3}）新颖的振荡频率$ω_q$和相移$φ_Q$更大程度地取决于口味$ n_f $（$ω_q_q= 0 $ in pure-Glue lige-n_c $ limit中的$ω_q= 0 $）。 $Δς$的典型振荡时期相当长，涵盖了许多迅速的单位。我们推测我们发现的振荡是否与从数据中提取的奇怪的夸克螺旋分布中看到的$ x $相关的符号变化。
We construct a numerical solution of the recently-derived large-$N_c \& N_f$ small-$x$ helicity evolution equations with the aim to establish the small-$x$ asymptotics of the quark helicity distribution beyond the large-$N_c$ limit explored previously in the same framework. (Here $N_c$ and $N_f$ are the numbers of quark colors and flavors.) While the large-$N_c$ helicity evolution involves gluons only, the large-$N_c \& N_f$ evolution includes contributions from quarks as well. We find that adding quarks to the evolution makes quark helicity distribution oscillate as a function of $x$. Our numerical results in the large-$N_c \& N_f$ limit lead to the $x$-dependence of the flavor-singlet quark helicity distribution which is well-approximated by \begin{align} ΔΣ(x, Q^2)\bigg|_{\mbox{large-}N_c \& N_f} \sim \left( \frac{1}{x} \right)^{α_h^q} \, \cos \left[ ω_q \, \ln \left( \frac{1}{x} \right) + φ_q \right]. \end{align} The power $α_h^q$ exhibits a weak $N_f$-dependence, and, for all $N_f$ values considered, remains very close to $α_h^q (N_f=0) = (4/\sqrt{3}) \sqrt{α_s N_c/(2 π)}$ obtained earlier in the large-$N_c$ limit. The novel oscillation frequency $ω_q$ and phase shift $φ_q$ depend more strongly on the number of flavors $N_f$ (with $ω_q =0$ in the pure-glue large-$N_c$ limit). The typical period of oscillations for $ΔΣ$ is rather long, spanning many units of rapidity. We speculate whether the oscillations we find are related to the sign variation with $x$ seen in the strange quark helicity distribution extracted from the data.
