Mass Spectrum, Radii, and Radiative Decay Widths of Toponium

TL;DR

Addresses the spectrum and radiative decays of toponium in a non-relativistic framework. The authors numerically solve the radial Schrödinger equation with a Coulomb-plus-linear potential including spin corrections, using a shooting method with mt = 172.42 GeV to predict masses, RMS radii, and E1/M1 widths. Key findings include a ground-state mass m_ttbar(1S) ≈ 342.867 GeV, RMS radii increasing with n and L, E1 widths up to ~25.32 keV, and M1 widths suppressed by 1/mt^2. The results provide comprehensive predictions for spectra and radiative decays to aid experimental identification of excited ttbar states.

Abstract

In this work, radial Schrodinger equation with a non-relativistic quark potential model (NRQPM) is solved numerically by employing the shooting method. Calculated numerical wave functions (or solutions) are used to compute the masses, root mean square (RMS) radii, $E1$ and $M1$ radiative transitions, and branching ratios of $S, P, D$ and $F$ states of toponium mesons ($t\overline{t}$). Calculated results are compared with recently available theoretical data. This work will be helpful for experimentalists in gaining a deeper understanding of toponium states.

Figures (3)

• Figure 1: S-wave toponium wave functions. $\Upsilon_t$ is represented with solid curve and $\eta_t$ is represented with the dotted curve.
• Figure 2: P-wave toponium wave functions. $\chi_{t2}$, $\chi_{t1}$, $\chi_{t0}$ and $h_{t}$ are represented with black solid line, black dotted line,red solid line and blue solid line curves respectively.
• Figure 3: D-wave toponium wave functions. $\Upsilon_{t3}$, $\Upsilon_{t2}$, $\Upsilon_{t1}$ and $\eta_{t2}$ are represented with solid black line, dotted black line, solid red line and solid blue line curves respectively.