Jet observables and energy-momentum tensor
P. S. Cherzor, N. A. Sveshnikov
TL;DR
The paper clarifies and extends the Sveshnikov–Tkachov theorem to non-scalar fields, massless particles, and gauge theories by deriving explicit operator representations of the jet-observable proxy $\varepsilon(\mathbf{n})$ in terms of asymptotic field operators and the energy-momentum tensor. It carefully treats massless light-cone subtleties and employs stationary-phase analysis and Gupta–Bleuler quantization to ensure a gauge-invariant, bound-state–independent connection between jet observables and $T_{\mu\nu}$. The results provide explicit forms for massive scalar, spinor, and vector fields, and correct massless limits with proper regulator prescriptions, reinforcing the theoretical robustness of jet observable descriptions in high-energy QCD. The work also discusses extending these results to general gauges and axiomatic proofs, with implications for precision QCD calculations and KLN-type theorems for jet observables.
Abstract
We clarify and extend the theorem of Sveshnikov and Tkachov [hep-ph/9512370], which gives an explicit connection between jet observables and energy-momentum tensor. We check the relation between jet observables and energy-momentum tensor for non-scalar (spinor and vector) field, give a correct treatment of the light-cone singularity for massless particles, and extend the theorem to the massless case. We also discuss the issue of gauge invariance.