Spectroscopy of $$\varvec{(\eta _b(nS),\,\Upsilon (nS))}$$ States and Exotic $$\varvec{Z_b(10610)}$$, $$\varvec{Y_b(10860)}$$, $$\varvec{Y_b(10890)}$$ Bottomonium-Like Resonances: Hyperfine Spin Splittings, and Radiative Decays

Abstract We investigate the mass spectrum, dynamical properties, and radiative transitions of bottomonium S -wave states within a theoretical framework that incorporates non-compact extra spatial dimensions. A modified non-relativistic Cornell potential, augmented by a harmonic oscillator confinement term and a non-perturbative spin–spin interaction is adopted as the interquark potential. The N -dimensional radial Schrödinger equation is solved numerically using a hybrid strategy that combines the matrix Numerov method with a shooting technique, yielding accurate eigenvalues and wave functions for all S -wave states from $$n=1$$ n = 1 to $$n=7$$ n = 7 . From these solutions we compute the masses of $$b\bar{b}$$ b b ¯ states, hyperfine splittings, pseudoscalar and vector decay constants, leptonic, two-photon and two-gluon decay widths, spin-averaged mass spectra, and magnetic dipole ( M 1) radiative transition widths. The influence of the spatial dimensionality number N is studied systematically: the bottomonium mass increases with N , while decay constants and decay widths are suppressed by the weaker confinement in higher-dimensional spaces. Our predictions are in good agreement with experimental data from the Particle Data Group (PDG 2024) and compare favourably with several state-of-the-art theoretical models. The possible assignments of the exotic resonances $$Y_b(10{,}890)$$ Y b ( 10 , 890 ) , $$Y_b(10{,}860)$$ Y b ( 10 , 860 ) , and $$Z_b(10{,}610)$$ Z b ( 10 , 610 ) to specific S -wave bottomonium states are examined. We find that $$Y_b(10{,}890)$$ Y b ( 10 , 890 ) is very likely associated with the $$5^3S_1\equiv \Upsilon (5S)$$ 5 3 S 1 ≡ Υ ( 5 S ) state, whereas the mass of $$Y_b(10{,}860)$$ Y b ( 10 , 860 )