Quarkonium spectra with magnetically-induced anisotropic confinement

Abstract

Strong magnetic fields modify the force that confines quarks inside hadrons and make it direction-dependent. Using quark-antiquark potentials obtained from lattice simulations as inputs to a quark potential model, we investigate how the anisotropic confinement affects the mass spectrum of quarkonium. In the strong-field regime, we find downward mass shifts induced by a softening of the confining potential along the field direction. In particular, the mass shifts of radially excited states are more significant than that of the ground state. For the longitudinal spin eigenstates, the excited-state spectrum strongly depends on the magnetic-field strength, in contrast to the spectrum with conventional isotropic confinement, which is insensitive to the field strength. This provides a clean probe of magnetically induced confinement anisotropy that can be confirmed in future lattice simulations.

Figures (4)

• Figure 1: Schematics of magnetic-field-induced anisotropy effects in quarkonia in the weak- and strong-field regimes: (a) anisotropic confinement potential, (b) harmonic-oscillator potential arising from Landau quantization of quarks, and (c) the sum of both contributions. The conventional isotropic (i.e., linear and Coulomb) potential is also plotted for comparison.
• Figure 2: Magnetic-field-induced anisotropy of the string tension, extracted from our fits and compared with available lattice-QCD results Bonati:2016kxjDElia:2021tfb, where we put the four data points at the finest lattice spacing $a = 0.0989$ fm in Ref. Bonati:2016kxj and the two data at $eB=4,9$ GeV$^2$ in Ref. DElia:2021tfb.
• Figure 3: Charmonium mass spectrum as a function of the magnetic-field strength $eB$ under anisotropic confinement. The left and right panels correspond to longitudinal ($S_z=0$) and transverse ($S_z=\pm1$) charmonia, respectively. Dotted lines are the numerical results with the isotropic potentials.
• Figure 4: Root-mean-square longitudinal and transverse radii, $\sqrt{\langle z^{2}\rangle}$ and $\sqrt{\langle r_\perp^{2}\rangle}$, as functions of the magnetic field $eB$, for anisotropic confinement. Dotted lines are the numerical results with the isotropic potentials.