Heavy-flavor mesons in a strong electric field

Very strong electromagnetic field can be generated in peripheral relativistic heavy ion collisions. This work is devoted to exploring the interplay between the effects of a constant external electric field and confining potential on heavy-flavor mesons. As the corresponding vector potential linearly depends on one spatial coordinate for a constant electric field, it might be able to overcome the linear confining potential of QCD and induce deconfinement. To perform analytic calculations and for comparison, one and two dimensional systems are studied together with the realistic three dimensional systems. The one dimensional Schr$\ddot{\text o}$dinger equation can be solved analytically with the help of Airy functions, and deconfinement is indeed realized when the electric field is larger than the string tension. Focus on the confining case, the two and three dimensional Schr$\ddot{\text o}$dinger equations can be solved analytically in large $r$ limit with the help of elliptic cosine/sine functions, and the wave functions are dominated by the region antiparallel to the electric field. When a more realistic potential is applied, a non-monotonic feature is found for $\Upsilon(2S)$ and $\Upsilon(3S)$-like mesons with increasing electric field.