Correct Definition of the Gluon Fragmentation Function at High Energy Colliders

Abstract

Since the definition of the gluon to hadrons fragmentation amplitude $<H,X|g>$ involves gluon field $Q^{\mu a}(x)$ corresponding to single gluon incoming state $|g>$, the present definition of the gluon fragmentation function at high energy colliders [which involves non-abelian field tensor $F^{\mu \nu a}(x)={\partial }^{\mu }{Q}^{\nu a}(x)-{\partial }^{\nu }{Q}^{\mu a}(x)+g{f}^{abc}{Q}^{\mu b}(x)Q^{\nu c}(x)$ instead of $Q^{\mu a}(x)$ in the initial state] is not consistent with the single gluon incoming state $|g>$. In this paper we derive the correct definition of the gluon fragmentation function at high energy colliders from first principles which is obtained from the single gluon incoming state $|g>$ and is gauge invariant and is consistent with the factorization theorem in QCD.

Comments: 13 pages latex. arXiv admin note: substantial text overlap with arXiv:1506.02651, arXiv:1506.02593, arXiv:1508.01194