Effects of an induced electric field on the pi(-)/pi(+) ratio in heavy-ion collisions

Using an isospin- and momentum-dependent transport model, we examine the effects of an electric field induced by a variable magnetic field on the pi(-)/pi(+) ratio in central to peripheral heavy-ion collisions at beam energies of 400 and 1500 MeV/nucleon. It is shown that while the induced electric field does not affect the total multiplicities of both pi(-) and pi(+) mesons at both the lower beam energy of 400 MeV/nucleon and the higher beam energy of 1500 MeV/nucleon, it reduces (enhances) the emission of pi(-)(pi(+)) mesons in midrapidity, but enhances (reduces) the emission of pi(-)(pi(+)) mesons in forward and backward rapidities especially for the more peripheral collisions at the lower beam energy because of the rapidly transient variable magnetic field at more peripheral collisions and the longer reaction duration time at the lower beam energy. These findings indicate that the total pi(-)/pi(+) ratio is still a precisely reliable probe of symmetry energy at both the lower and the higher beam energies, but one should consider the induced electric field when using the differential pi(-)/pi(+) ratio to probe the symmetry energy especially for the lower beam energy and more peripheral collisions. Finally, the relative suppression factor based on the ratio of pi(-)/pi(+) in different rapidities is proposed to be an effective probe of the induced electric field generated in heavy-ion collisions due to its maximizing effects of induced electric fields on the differential pi(-)/pi(+) ratio but minimizing effects of some uncertainty factors in heavy-ion collisions.