Induced Operators in QCD

TL;DR

This paper derives induced operators in light-cone QCD that account for unphysical fields, explaining their role in phenomena like pion mass growth and meson splitting, which are not captured by naive approaches.

Contribution

It introduces a derivation of induced operators in light-cone QCD, highlighting their importance in physical predictions like meson mass behavior.

Findings

Induced operators lead to linear pion mass growth with quark mass.

They explain the pi-rho mass splitting at zero quark mass.

Operators are derived from the QCD Lagrangian with some assumptions.

Abstract

Light-cone quantization always involves the solution of differential constraint equations. The solutions to these equations include integration constants (fields independent of $x_-$). These fields are unphysical but when they are consistently removed from the dynamics, additional operators (induced operators), which would not be present if the integration constants were simply set to zero, are included in the dynamics. These induced operators can be taken to act in the usual light-cone subspace, for instance, the space used for DLCQ. Here, I shall give a derivation of two such operators. The operators are derived starting from the QCD Lagrangian but the derivation involves some guesses. The operators will provide for the linear growth of the pion mass squared with the quark bare mass and for the splitting of the pi and the rho at zero quark mass.