M-Theory Exotic Scalar Glueball Decays to Mesons at Finite Coupling

Using the pull-back of the perturbed type IIA metric corresponding to the perturbation of arXiv:hep-th/1306.4339's M-theory uplift of arXiv:hep-th/0902.1540's UV-complete top-down type IIB holographic dual of large-$N$ thermal QCD, at finite coupling, we obtain the interaction Lagrangian corresponding to exotic scalar glueball($G_E$)-$\rho/\pi$-meson interaction, linear in the exotic scalar glueball and up to quartic order in the $\pi$ mesons. In the Lagrangian, the coupling constants are determined as (radial integrals of) arXiv:hep-th/1306.4339's M-theory uplift's metric components and six radial functions appearing in the M-theory metric perturbations. Assuming $M_G>2M_\rho$, we then compute $\rho\rightarrow2\pi, G_E\rightarrow2\pi, 2\rho, \rho+2\pi$ decay widths as well as the direct and indirect (mediated via $\rho$ mesons) $G_E\rightarrow4\pi$ decays. For numerics, we choose $f0[1710]$ and compare with previous calculations. We emphasize that our results can be made to match PDG data (and improvements thereof) exactly by appropriate tuning of some constants of integration appearing in the solution of the M-theory metric perturbations and the $\rho$ and $\pi$ meson radial profile functions - a flexibility that our calculations permits.