Dynamical Mass Generation of Vector Mesons from QCD Trace Anomaly

TL;DR

This paper derives mass formulas for light-vector mesons in QCD using sum rules related to the trace anomaly, revealing new relations between spectral sums and QCD vacuum fluctuations, and applies the method to axial-vector mesons.

Contribution

It introduces a novel approach using sum rules with half-integer weights that are not obtainable from OPE, providing new insights into meson mass generation from QCD vacuum properties.

Findings

Derived mass formulas linking meson masses to gluon condensate.

Established new sum rules involving spectral sums and vacuum fluctuations.

Applied the method successfully to axial-vector mesons.

Abstract

Mass formulas for the light-vector mesons written in terms of the gluon condensate i.e., the trace anomaly in quantum chromodynamics (QCD), are derived on the basis of finite energy QCD sum rules. We utilize sum rules with $s^n$ and $s^{n+1/2}$ weights, which relate the energy-weighted spectral sums to the vacuum expectation values of certain commutation relations. After evaluating the commutation relations, the sum rules with $s^n$ weights are reduced to the familiar ones obtained from the operator product expansion (OPE). On the other hand, the sum rules with $s^{n+1/2}$ weights cannot be derived from OPE. They give new relations between the spectral sums and QCD vacuum fluctuations. To derive simple mass formula, we adopt the pole + continuum Ansatz for the spectral function, and solve coupled equations given by the sum rules with $s^{0,1}$ weights and the new sum rule with $s^{1/2}$ weight. Application of our approach to the axial-vector meson is also discussed.