Abstract
Abstract
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 [1, 2], we are interested in revisiting the sub-eikonal correction considered by us earlier in [3]. 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-Nc limit, with Nc the number of quark colors. For both TMDs, the evolution equations resum all powers of the double-logarithmic parameter αs ln2(1/x), where αs 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 Nc:$$ {\displaystyle \begin{array}{l}{f}_{1T}^{\perp NS}\left(x\ll 1,{k}_T^2\right)={C}_O\left(x,{k}_T^2\right)\frac{1}{x}+{C}_1\left(x,{k}_T^2\right){\left(\frac{1}{x}\right)}^{3.4\sqrt{\frac{\alpha_s{N}_c}{4\pi }}}\\ {}{h}_1^{\perp \textrm{NS}}\left(x\ll 1,{k}_T^2\right)=C\left(x,{k}_T^2\right){\left(\frac{1}{x}\right)}^{-1}.\end{array}} $$
f
1
T
⊥
NS
x
≪
1
k
T
2
=
C
O
x
k
T
2
1
x
+
C
1
x
k
T
2
1
x
3.4
α
s
N
c
4
π
h
1
⊥
NS
x
≪
1
k
T
2
=
C
x
k
T
2
1
x
−
1
.
The functions CO(x,$$ {k}_T^2 $$
k
T
2
), C1(x,$$ {k}_T^2 $$
k
T
2
), and C(x,$$ {k}_T^2 $$
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 CO, along with the 1/x factor, arises from the odderon exchange. For the sub-eikonal contribution to the quark Sivers function (the term with C1), our result shown above supersedes the one obtained in [3] due to the new contributions identified recently in [4].
Publisher
Springer Science and Business Media LLC
Subject
Nuclear and High Energy Physics
Cited by
11 articles.
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