论文标题
T-ODD领先的Quark tmds in小$ x $
T-odd Leading-Twist Quark TMDs at Small $x$
论文作者
论文摘要
我们研究了非单词t-odd领先Quark横向动量依赖的Parton分布（TMD），Sivers和Boer-Mulders功能的小型$ x $渐近。尽管旋转依赖性的Odderon给出了Quark Sivers功能的领先的小型$ x $渐近学，但我们有兴趣重新审视我们之前考虑的次级校正。我们首先简化了小bjorken $ x $的两个TMD的表达式，然后在大$ n_c $限制中构造由$ n_c $ limit中的由此产生的运算符的小$ x $ Evolution方程，并带有$ n_c $ quark颜色的数量。对于两个TMD，Evolution方程重新恢复了双层参数的所有功率$α_s\，\ ln^2（1/x）$，其中$α_s$是强耦合常数，假定为小。通过数值（用于载体功能）和分析（对于Boer-Mulders功能）求解这些进化方程式，我们到达以下领先的小$ x $ byymptotic，以大$ n_c $：\ begin {align} f_ {align} f_ {align} f_ {1 \：t} k_t^2）\，\ frac {1} {x} + c_1（x，k_t^2）\，\ left（\ frac {1} {x} {x} {x} \ right）^{3.4 \，\ sqrt { h_1^{\ perp \，\ textrm {ns}}（x \ ll 1，k_t^2）＆= c（x，k_t^2）\ left（\ frac {1} {1} {x} {x} {x} \ right）^{ - 1}。 \ notag \ end {align}函数$ c_o（x，k_t^2）$，$ c_1（x，k_t^2）$和$ c（x，k_t^2）$可以很容易地在我们的形式主义中获得：它们是$ x $的$ x $，并不强烈影响$ x $ x $ x $ x $ asmptots，上面是$ x $ x $ x $ assptots。函数$ C_O $以及$ 1/x $ factor源自Odderon Exchange。对于对Quark Sivers功能的子eikonal贡献（带有$ C_1 $的术语），我们的结果取代了由于最近确定的新贡献而在我们先前的工作中获得的结果。
We study the small-$x$ asymptotics of the flavor non-singlet T-odd leading-twist quark transverse momentum dependent parton distributions (TMDs), the Sivers and Boer-Mulders functions. While the leading eikonal small-$x$ asymptotics of the quark Sivers function is given by the spin-dependent odderon, we are interested in revisiting the sub-eikonal correction considered by us earlier. We first simplify the expressions for both TMDs at small Bjorken $x$ and then construct small-$x$ evolution equations for the resulting operators in the large-$N_c$ limit, with $N_c$ the number of quark colors. For both TMDs, the evolution equations resum all powers of the double-logarithmic parameter $α_s \, \ln^2 (1/x)$, where $α_s$ is the strong coupling constant, which is assumed to be small. Solving these evolution equations numerically (for the Sivers function) and analytically (for the Boer-Mulders function) we arrive at the following leading small-$x$ asymptotics of these TMDs at large $N_c$: \begin{align} f_{1 \: T}^{\perp \: NS} (x \ll 1 ,k_T^2) & = C_O (x, k_T^2) \, \frac{1}{x} + C_1 (x, k_T^2) \, \left( \frac{1}{x} \right)^{3.4 \, \sqrt{\frac{α_s \, N_c}{4 π}}} , \notag \\ h_1^{\perp \, \textrm{NS}} (x \ll 1, k_T^2) & = C (x, k_T^2) \left( \frac{1}{x} \right)^{-1}. \notag \end{align} The functions $C_O (x, k_T^2)$, $C_1 (x, k_T^2)$, and $C (x, k_T^2)$ can be readily obtained in our formalism: they are mildly $x$-dependent and do not strongly affect the power-of-$x$ asymptotics shown above. The function $C_O$, along with the $1/x$ factor, arises from the odderon exchange. For the sub-eikonal contribution to the quark Sivers function (the term with $C_1$), our result shown above supersedes the one obtained in our previous work due to the new contributions identified recently.
