### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 259-284 |

Number of pages | 26 |

Journal | Nuclear Physics B |

Volume | 558 |

Issue number | 1-2 |

State | Published - Oct 4 1999 |

Externally published | Yes |

### Fingerprint

### Keywords

- Evolution
- Integrability
- Open spin chain
- Spectrum of eigenvalues
- Three-particle problem
- Twist-three operators

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*558*(1-2), 259-284.

**Integrability and WKB solution of twist-three evolution equations.** / Belitsky, Andrei.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 558, no. 1-2, pp. 259-284.

}

TY - JOUR

T1 - Integrability and WKB solution of twist-three evolution equations

AU - Belitsky, Andrei

PY - 1999/10/4

Y1 - 1999/10/4

N2 - 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.

AB - 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.

KW - Evolution

KW - Integrability

KW - Open spin chain

KW - Spectrum of eigenvalues

KW - Three-particle problem

KW - Twist-three operators

UR - http://www.scopus.com/inward/record.url?scp=0033523570&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033523570&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0033523570

VL - 558

SP - 259

EP - 284

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 1-2

ER -