Probing Excited $q\bar{q}$ Mesons via QCD Sum Rules

TL;DR

This paper uses advanced QCD sum rule techniques to systematically analyze the masses of excited light $qar{q}$ mesons, achieving results consistent with experimental data.

Contribution

It introduces the use of covariant derivative operators in sum rules to effectively probe excited meson states at NLO.

Findings

Obtained masses of $J^P=2^ u$ nonets matching experimental values.

Identified two distinct $2^{++}$ resonances with a specific current.

Demonstrated the effectiveness of derivative operators in excited hadron studies.

Abstract

We present a systematic study of the masses of light excited $q\bar{q}$ mesons using QCD sum rules at next-to-leading order (NLO). To probe excited states, we construct several interpolating currents with covariant derivatives inserted. The calculation is carried out up to dimension-8 condensates, including NLO perturbative and $m\langle\bar{q}q\rangle$ corrections. Employing Gaussian sum rules, we obtain several $J^P=2^\pm$ nonets with masses that agree well with experiments. Several $J=0,1$ states compatible with experiments are also obtained using both Gaussian and Laplace sum rules. In particular, the $J^{PC}=2^{++}$ current couples to two distinct $2^{++}$ resonances. This work demonstrates the efficacy of operators with covariant derivatives for studying excited hadrons.