Integrability and WKB solution of twist-three evolution equations

Details Integrability and WKB solution of twist-three evolution equations Integrability and WKB solution of twist-three evolution equations

1999-03-29

arxiv.org/abs/hep-ph/9903512v2

Nucl.Phys. B558 (1999) 259-284

Physics

High Energy Physics

High Energy Physics - Phenomenology

26 pages, LaTeX, 4 figures; typos fixed

Scientific paper

10.1016/S0550-3213(99)00402-2

We identify an integrable one-dimensional inhomogeneous three-site open spin chain which arises in the problem of diagonalization of twist-three quark-gluon evolution equations in QCD in the chiral-odd sector. Making use of the existence of a non-trivial `hidden' integral of motion the problem of diagonalization of the evolution kernels is reduced to the study of a second order finite-difference equation which is solved in WKB approximation for large conformal spins of the three-particle system. The energies (alias anomalous dimensions) of eigenstates with different scale dependence are found in limiting cases and compared with numerical calculations.

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