Anatomy of the Quasi-PDF with a Transverse-Momentum Cutoff
Abstract
The quasi-PDF is fundamentally different from the light-cone PDF, and large-momentum effective theory relates the two through perturbative matching. This has required considerable effort. One of the difficulties in matching is that no single renormalization scheme has been agreed upon for the quasi-PDF, and the resulting variety of prescriptions can obscure the physics underlying the matching. We study how the choice of scheme affects the renormalized quasi-PDF and the matching coefficient, and how the two are related, aiming to identify a scheme in which this dependence becomes transparent. As a first attempt, we consider the transverse-momentum cutoff scheme. It is not used in practice, since a hard momentum cutoff breaks Lorentz invariance, and it has generally been treated as an illustrative example exhibiting the linear divergence of the spatial Wilson line. A careful study, however, reveals a richer structure than expected. The ultraviolet divergence in this scheme depends not only on the cutoff itself, but also on an independent divergence associated with the momentum fraction of the quasi-PDF. Disentangling these two ultraviolet structures, and following the disentangling through the explicit one-loop calculation, uncovers further structure along the way. Once the ultraviolet contributions are correctly separated and assigned to the renormalization counterterm, a finite ambiguity remains, and we use it to restore the quark-number conservation broken by the cutoff. The resulting renormalized quasi-PDF and matching coefficient can be meaningfully compared with the result obtained in dimensional regularization, and we show how the two are reconciled.
Related
- Typed Transverse Momentum Parton distribution function computations
- Gravitational transverse momentum dependent distributions for the gluons
- Energy-momentum tensor at small x from gravitational transverse-momentum distributions
- Transverse momentum correlations and QED effects in TMD determinations
- Drell-Yan lepton pair production from low to high transverse momentum
BibTeX
@misc{chay2026anatomy,
title = {{Anatomy of the Quasi-PDF with a Transverse-Momentum Cutoff}},
author = {Junegone Chay},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.04182},
eprint = {2607.04182},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.04182},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Anatomy of the Quasi-PDF with a Transverse-Momentum Cutoff
AU - Junegone Chay
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2607.04182
UR - https://arxiv.org/abs/2607.04182
AB - The quasi-PDF is fundamentally different from the light-cone PDF, and large-momentum effective theory relates the two through perturbative matching. This has required considerable effort. One of the difficulties in matching is that no single renormalization scheme has been agreed upon for the quasi-PDF, and the resulting variety of prescriptions can obscure the physics underlying the matching. We study how the choice of scheme affects the renormalized quasi-PDF and the matching coefficient, and how the two are related, aiming to identify a scheme in which this dependence becomes transparent. As a first attempt, we consider the transverse-momentum cutoff scheme. It is not used in practice, since a hard momentum cutoff breaks Lorentz invariance, and it has generally been treated as an illustrative example exhibiting the linear divergence of the spatial Wilson line. A careful study, however, reveals a richer structure than expected. The ultraviolet divergence in this scheme depends not only on the cutoff itself, but also on an independent divergence associated with the momentum fraction of the quasi-PDF. Disentangling these two ultraviolet structures, and following the disentangling through the explicit one-loop calculation, uncovers further structure along the way. Once the ultraviolet contributions are correctly separated and assigned to the renormalization counterterm, a finite ambiguity remains, and we use it to restore the quark-number conservation broken by the cutoff. The resulting renormalized quasi-PDF and matching coefficient can be meaningfully compared with the result obtained in dimensional regularization, and we show how the two are reconciled.
ER -