A theoretical preprint reports that quark and gluon orbital-angular-momentum (OAM) distributions and helicity distributions share the same small-x intercept. In practical terms, the calculation gives both sectors the same fitted power as x becomes small. The study asks how to formulate and solve this evolution in the large-Nc&Nf limit. The document is an arXiv version-one preprint presenting a model calculation within that framework.
The term intercept refers here to the power extracted from the small-x behavior of the calculated amplitudes. The paper reports a common intercept for OAM and helicity distributions rather than separate leading powers. Its framework uses the double-logarithmic approximation, derives evolution equations for moment amplitudes and solves them numerically together with helicity evolution. The shared power is therefore a result of the stated evolution setup.
The number changes with flavor count
The common pattern does not mean the fitted coefficient is independent of the model's flavor setting. The numerical calculation uses Nf = 2, 3, 4, 5 and 6, with unit initial conditions for the moment-amplitude evolution. For those cases, the I3 intercept coefficients are 3.539(6), 3.473(6), 3.399(6), 3.315(6) and 3.214(6), respectively. The sequence declines as Nf increases, with the parenthetical figures giving the reported numerical uncertainties.
To estimate the intercepts, the authors regress logarithmic amplitudes over the high-eta interval from 0.75 eta_max to eta_max for each discretization step. In the model comparison, the quadratic fit, called model 3, is selected by minimum AIC, the model-selection score used in the analysis. Model 4 has a higher AIC and insignificant parameters.
Ratios settle near constants, with caveats
The paper also fits the OAM-to-helicity ratios, comparing each OAM distribution with its helicity counterpart. At Q2 = 10 GeV2, Nc = 3 and Nf = 3, the quark fit gives Aq = -1.01061(5) and Bq = -0.042(2). The fitted form describes the quark ratio as approaching a negative constant with a small logarithmic correction.
The gluon fit approaches a more negative constant, with the logarithmic correction having the opposite sign. At Q2 = 10 GeV2, Nc = 3 and Nf = 3, it gives AG = -1.94346(1) and BG = 0.0772(6). In the model's asymptotic description, the gluon OAM-to-helicity ratio therefore approaches a more negative constant with a small positive logarithmic correction.
Changing the flavor count affects these ratio fits differently. Across Nf values from 2 through 6, Aq and Bq are numerically consistent, while AG varies by 0.3 percent and BG increases by roughly 20 percent. The quoted flavor dependence is thus modest for the quark coefficients and AG, but more visible in BG.
A revised operator changes the calculation
The result rests on a revised operator treatment. The quark OAM operator expression is revised, and both quark and gluon OAM are related to impact-parameter moments of polarized dipole amplitudes. The F+- operator contribution brings in a new IE moment amplitude. That new IE amplitude couples the helicity and moment sectors through evolution, so the calculation treats them as a coupled system.
The same F+- contribution carries into the paper's elastic-dijet calculation. It reports non-vanishing corrections to the azimuthal harmonics, or angular components, of the longitudinal double-spin asymmetry. Those corrections come from the previously omitted F+- contribution in the modeled dijet observable.
The boundary of the claim
The strongest caution concerns the ratios. They remain strongly dependent on initial conditions down to x approximately 10^-7. The authors warn that saturation may make the linear DLA inapplicable at such small x and describe the extracted asymptotic ratios as mainly academic. The shared intercept and quoted coefficients should therefore be read as outputs of the stated evolution model, with the ratio results carrying particular sensitivity to how the calculation is started.
Paper data and sources
Original title: Orbital angular momentum at small $x$ in the large $N_c\&N_f$ limit
Authors: G. Zardo Becker, Yuri V. Kovchegov, Ming Li et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-25
DOI: Not available
Original paper · Full text