Integrability and WKB solution of twist - three evolution equations
Mar, 1999Citations per year
Abstract:
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.Note:
- 26 pages, LaTeX, 4 figures; typos fixed
- 11.10.Gh
- 11.15.Kc
- 11.30.Na
- 12.38.Cy
- Twist-three operators
- Evolution
- Three-particle problem
- Integrability
- Open spin chain
- Spectrum of eigenvalues
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