### Abstract

Mass formulas for the 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 sn and sn^{+}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 sn weights are reduced to the familiar ones obtained from the operator product expansion (OPE). On the other hand, the sum rules with sn^{+}1^{/}2 weights cannot be derived from OPE. They give new relations between the spectral sums and QCD vacuum fluctuations. To derive a simple mass formula, we adopt the pole+continuum ansatz for the spectral function, and we solve coupled equations given by the sum rules with s0^{,}1 weights and the new sum rule with s1^{/}2 weight. Application of our approach to the axial-vector meson is also discussed.

Original language | English |
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Article number | 036007 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 88 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2013 Aug 20 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)