Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.18627

Scheme transformations as the gauge group of DGLAP: sum rules, classification and solution

Tommaso Rainaldi
View original source ↗Read source document ↗Export metadata ↓

Abstract

A parton density depends on the renormalization scheme, and any two schemes are connected by a transformation that preserves the DGLAP form of the evolution. In Mellin space such a transformation acts on the evolution kernels as a gauge transformation, and we take this point of view throughout the discussion. For the unpolarized densities we first ask which transformations also preserve the charge-conjugation and flavor symmetries of the evolution kernels and the momentum and valence number sum rules. The symmetries reduce the transformation to a few blocks, and the sum rules constrain only two Mellin moments, where they leave a single freedom, the split of momentum between the quark singlet and the gluon, and freeze the valence numbers. The resulting classification is complete, because with asymptotic freedom as a boundary condition a change of scheme is determined by its action on the kernels. Inside this group, the transformations that preserve positivity form a semigroup, and the same argument covers the polarized densities. A transformation that fails only the sum rules is not lost either, since a normalization that the sum rules themselves determine repairs it, and we use this to define collinear densities as integrals of transverse-momentum-dependent densities without giving up the sum rules. We then use the same gauge freedom to solve the evolution. Gauging the kernel away reduces DGLAP at any order to a single second-order linear equation plus a quadrature, and it organizes the estimate of missing higher orders in a way that respects the sum rules exactly.

Explore related subjects

hep-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Tommaso Rainaldi. 2026-09-16. Scheme transformations as the gauge group of DGLAP: sum rules, classification and solution. https://arxiv.org/abs/2609.18627

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Stochastic Ultralight Dark Matter Fluctuations in Pulsar Timing Arrays

Metric perturbations induced by ultralight dark matter (ULDM) fields have long been identified as a potential target for pulsar timing array (PTA) observations. Previous works have focused on the coherent oscillation of metric perturbations at the characteristic frequency set by the ULDM mass. In this work, we show that ULDM fields source low-frequency stochastic metric fluctuations and that these low-frequency fluctuations can produce distinctive detectable signals in PTA data. Using the NANOGrav 12.5-year data set and synthetic data sets mimicking present and future PTA capabilities, we show that the current and future PTA observations provide the strongest probe of ULDM density within the solar system for masses in the range of $10^{-18}\;{\rm eV}-10^{-16}\;{\rm eV}$.

hep-ph↗
arXiv2026

On the Origin of QCD Collectivity in High-Multiplicity Jets: A Transport Model Study

The CMS Collaboration has observed an enhancement of elliptic azimuthal anisotropy ($v^{\ast}_2$) in high-multiplicity jets. To investigate its microscopic origin, we employ a hybrid transport model that couples jets generated with \textsc{PYTHIA~8} to partonic and hadronic rescattering. The analysis is performed in the jet frame, where the jet momentum defines the longitudinal axis. We characterize the initial-state geometry using the eccentricity vectors of shower partons and quantify the geometric response by correlating them with the final-state flow vectors of hadrons. By systematically varying the partonic and hadronic interactions, we find that the anisotropy enhancement is dominated by hadronic rescattering in the present model and increases with the initial eccentricity. We further classify jets using the Soft Drop variable $z_gθ_g^β$ and show that this momentum-space substructure variable is sensitive to the initial coordinate-space geometry, although the predicted substructure dependence differs from the current CMS measurement. These results support a geometry--response mechanism for collective behavior inside jets and establish jet substructure as a promising experimental handle on the initial geometry. They also motivate models that treat parton branching and transport interactions concurrently.

hep-ph↗
arXiv2026

Comprehensive effective field theory framework for coherent elastic neutrino-nucleus scattering

Coherent elastic neutrino-nucleus scattering (CE$ν$NS) stands out as a pivotal process for precision tests of the Standard Model electroweak sector, investigations of neutrino properties, and searches for new physics. Recent experimental measurements by COHERENT, CONUS+, and ton-scale xenon detectors--including PandaX-4T and XENONnT--underscore the need for a systematic theoretical framework to bridge high-energy physics scenarios with low-energy observational data. In this work, we develop a comprehensive end-to-end effective field theory (EFT) framework for CE$ν$NS, encompassing the complete energy scale hierarchy spanning the ultraviolet regime down to the nuclear sector. We consider the low-energy EFT (LEFT) operators up to dimension 8, incorporating their QCD renormalization group running effects, and employ the systematic spurion method to achieve matching between these operators and the chiral Lagrangian. A full power counting analysis is performed, extending to nuclear response functions, which evaluates contributions from LEFT operators up to dimension 8 while accounting for the nucleon number enhancement effect intrinsic to CE$ν$NS. Moreover, we match the relevant LEFT operators for CE$ν$NS onto operators up to dimension 8 within the Standard Model EFT. By also providing their complete tree-level ultraviolet completions, this procedure establishes a consistent top-down theoretical workflow. Leveraging a broad suite of CE$ν$NS experimental data, this framework enables a combined analysis to extract constraints on the scales of EFT operators and neutrino non-standard interaction parameters.

hep-ph↗