Fine structure of spectrum of twist-three operators in QCD

TL;DR

The paper analyzes the twist-3 quark–gluon operator spectrum in QCD, exploiting integrability in the large-Nc limit to solve the three-particle evolution problem. By constructing an orthonormal three-point basis in θ-space and identifying a hidden conserved charge Q_T, the authors reduce the problem to a tractable recursion and derive both q_T and energy spectra, including leading and first non-leading (WKB) corrections. They establish bounds on the spectra, present exact lowest trajectories, and connect the results to open spin-chain frameworks, while noting that finite-Nc corrections break integrability and create a mass gap. The work provides a detailed, technically robust route to understanding multiparton correlations and their scale evolution in twist-3 QCD, with implications for phenomenology and integrable systems techniques.

Abstract

We unravel the structure of the spectrum of the anomalous dimensions of the quark-gluon twist-3 operators which are responsible for the multiparton correlations in hadrons and enter as a leading contribution to several physical cross sections. The method of analysis is bases on the recent finding of a non-trivial integral of motion for the corresponding Hamiltonian problem in multicolour limit which results into exact integrability of the three-particle system. Quasiclassical expansion is used for solving the problem. We address the chiral-odd sector as a case of study.

Figures (5)

• Figure 1: The diagrams contributing to the pair-wise quark-anti-quark kernel at one-loop order in the light-cone gauge, $B_+ = 0$. The blobs on the lines stand for the wave function renormalization counterterm.
• Figure 2: Same as in Fig. \ref{['qq-kernel']} but for the quark-gluon kernel. The graph with the crossed fermion propagator corresponds to the contact-type contribution arising from the use of the Heisenberg equation of motion for the quark field.
• Figure 3: The spectrum of the conserved charge $q_T$. Sample trajectories from two sets: for $n = 25$ (counts from above, $n = 0,1,\dots$) and $m = 7$ (counts from below, $m = 1,2,\dots$) are shown by solid curves. Long-dashed lines correspond to the analytical formulae (\ref{['WKBexp']},\ref{['1stWKB']}) with $n = 2,6$. The two exact solutions (\ref{['ExactQT']}) separated from the rest of the spectrum by a finite gap are demonstrated by short-dashed lines.
• Figure 4: Same as in Fig. \ref{['QTcharge']} but for the spectrum of energy eigenstates. The two lowest exact trajectories are calculated from Eqs. (\ref{['ExactE']}).
• Figure 5: The spectrum of eigenvalues of Hamiltonian (\ref{['FiniteNcHamiltonian']}) compared to the range of eigenvalues in the multicolour limit (dashed curves).