Revising the Mass of Light Hybrid Mesons: NLO QCD Sum Rules Point to $\phi (2170)$ as a Prime Candidate

We present a comprehensive next-to-leading order (NLO) QCD sum rule analysis for light hybrid mesons with $J^{PC}=1^{--}$, incorporating condensates up to dimension-8 and NLO corrections to the perturbative, gluon condensate, and four-quark condensate contributions. These corrections are found to be substantial and reveal the necessity of contributions beyond leading order. Employing both Laplace (LSR) and Gaussian (GSR) sum rules, our analysis predicts a mass in the conservative range of $2.1-2.4\text{GeV}$ for the light $1^{--}$ hybrid. These predictions are significantly lower than previous leading-order (LO) estimates (around $2.9\text{GeV}$) and bridge the gap between QCD sum rules and other approaches. Our findings establish the $\phi (2170)$ resonance as a prime candidate for the light vector hybrid meson.