Initial momentum anisotropies in the kT-factorization of the CGC I: Gradient Expansion
Abstract
We revisit single-inclusive gluon production in the dilute--dilute limit of the Color Glass Condensate and show that k⊥-factorization is only the zeroth order of a systematic gradient expansion in the transverse positions of the two colliding sources, organized in powers of 1/(QsR), with Qs the saturation scale and R the size over which the sources vary. Collecting terms order by order builds a ladder of scalar and tensor structures from the local distributions and their transverse derivatives, yielding an extended k⊥-factorized formula that retains the spatial dependence of the sources and, through kinetic moments of the spectrum, the energy-momentum tensor. Repeating the expansion from a real-time computation of the classical Glasma fields in the future light cone reproduces the momentum-space result in the eikonal limit, but additionally retains coherent interference between amplitude and conjugate. This adds terms to the ladder (flow responses, chromo-electric--magnetic interference, and a longitudinal energy flux) further suppressed by powers of the large outgoing momentum |pp|≫ Qs. The hierarchy thus reveals momentum-space anisotropies present in the initial state before any hydrodynamic evolution, which leading k⊥-factorization misses by construction. Since each order is a local operator on the same unintegrated distributions, these corrections can be added directly to existing saturation-based initial-state models, giving a dynamically generated initial momentum anisotropy and a more faithful early-time energy-momentum tensor without abandoning the tractable factorized form. Set by gradients of the transverse density profiles, they grow towards more dilute, fluctuation-dominated systems, e.g. light-ion collisions. Phenomenological consequences will be developed in a companion paper.
Related
- Native transverse-momentum evolution and matching for TMD factorization and extraction
- Parton Distribution Functions from Large Momentum Expansion of Current-Current Correlators
- Analyzing momentum distributions in light nuclei with the operator product expansion
- Heavy-quark expansion at leading power for local QCD operators in gradient flow
- Analytical Series Expansion for Efficient Gradient Evaluation in Multi-Qubit Optimal Control
BibTeX
@misc{garciamontero2026initial,
title = {{Initial momentum anisotropies in the kT-factorization of the CGC I: Gradient Expansion}},
author = {Oscar Garcia-Montero},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07847},
eprint = {2609.07847},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07847},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Initial momentum anisotropies in the kT-factorization of the CGC I: Gradient Expansion
AU - Oscar Garcia-Montero
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07847
UR - https://arxiv.org/abs/2609.07847
AB - We revisit single-inclusive gluon production in the dilute--dilute limit of the Color Glass Condensate and show that k_⊥-factorization is only the zeroth order of a systematic gradient expansion in the transverse positions of the two colliding sources, organized in powers of 1/(Q_sR), with Q_s the saturation scale and R the size over which the sources vary. Collecting terms order by order builds a ladder of scalar and tensor structures from the local distributions and their transverse derivatives, yielding an extended k_⊥-factorized formula that retains the spatial dependence of the sources and, through kinetic moments of the spectrum, the energy-momentum tensor. Repeating the expansion from a real-time computation of the classical Glasma fields in the future light cone reproduces the momentum-space result in the eikonal limit, but additionally retains coherent interference between amplitude and conjugate. This adds terms to the ladder (flow responses, chromo-electric--magnetic interference, and a longitudinal energy flux) further suppressed by powers of the large outgoing momentum |pp|≫ Q_s. The hierarchy thus reveals momentum-space anisotropies present in the initial state before any hydrodynamic evolution, which leading k_⊥-factorization misses by construction. Since each order is a local operator on the same unintegrated distributions, these corrections can be added directly to existing saturation-based initial-state models, giving a dynamically generated initial momentum anisotropy and a more faithful early-time energy-momentum tensor without abandoning the tractable factorized form. Set by gradients of the transverse density profiles, they grow towards more dilute, fluctuation-dominated systems, e.g. light-ion collisions. Phenomenological consequences will be developed in a companion paper.
ER -