Speaker
Description
Understanding how gluonic dynamics manifests itself in unstable hadrons remains an important challenge in studies of hadron mass generation. We investigate the gluon trace anomaly in the isovector (P)-wave (\pi\pi) channel containing the (\rho) resonance using lattice QCD. A variational basis composed of quark-antiquark (\rho) operators and two-pion operators projected onto the appropriate finite-volume irreducible representations is employed. Solving the generalized eigenvalue problem isolates a tower of interacting finite-volume energy eigenstates. For each optimized state, we calculate a vacuum-subtracted gluonic insertion proportional to (\beta(g)F_{\mu\nu}F_{\mu\nu}/(2g)) and extract the corresponding diagonal matrix element using the summed-ratio method. Away from the resonance region, the matrix elements approximately follow the behavior expected for weakly interacting two-pion states. Near the (\rho) resonance, however, we observe a pronounced peak in the gluon trace-anomaly contribution, correlated with the resonant behavior of the finite-volume spectrum and the changing (\rho)- and (\pi\pi)-operator overlaps. The enhancement indicates that the gluonic response of the interacting two-pion system is significantly stronger in the resonance region than the approximate sum of the individual-pion contributions. Our results demonstrate that gluonic trace operators provide a sensitive probe of resonance formation and establish a framework for studying the gluonic structure of unstable hadrons through finite-volume matrix elements.
