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arXiv · 2409.09667

Evolution of unpolarized transverse momentum dependent parton distributions of twist-3

Xue-Tao Liu·Ping-An Liu·Yu-Lu Liu·An-Ping Chen
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Abstract

We revisit the calculation of the evolution equations for four unpolarized twist-3 transverse momentum dependent (TMD) parton distribution functions (PDFs) at $\mathcal {O}(\alpha_s)$. Unlike the existing calculations in the literature, which are based on the background field method, we derive the evolution equations directly through diagram expansion. Additionally, instead of using the $\delta$ regulator, we employ the exponential regulator to regularize the rapidity divergences. We find that the evolutions of the four twist-3 TMD PDFs are governed by eight homogeneous equations. Our evolution kernels agree with one set of results in the literature, but differ from another by a sign. Considering the advantages of the exponential regulator in high-order perturbative calculations, our results are crucial for computing the twist-3 TMD PDFs at $\mathcal {O}(\alpha_s^2)$.

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Xue-Tao Liu, Ping-An Liu, Yu-Lu Liu, An-Ping Chen. 2024-09-15. Evolution of unpolarized transverse momentum dependent parton distributions of twist-3. https://doi.org/10.1103/sz46-x2sk

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