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

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arxiv 2409.09667 v3 pith:Y7PRCLBF submitted 2024-09-15 hep-ph

classification hep-ph
keywords evolutiontwist-3equationspdfsregulatoralphacalculationsdependent
verification ladder T0 review T1 audit T2 compute T3 formal
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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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Cited by 1 Pith paper

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  1. Soft background fields at next-to-leading power in transverse momentum dependent SIDIS with jets

    hep-ph 2025-07 conditional novelty 7.0 of 10

    New next-to-leading-power factorization for SIDIS with jets from a background-field method with explicit soft modes, including operator-level definitions of twist-3 TMDs free of rapidity and endpoint divergences.

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