In the Standard Model (SM) of particle physics, the mesons comprise two of quarks and anti-quarks and the baryons comprise three of quarks and anti-quarks, while the quarks and anti-quarks carry fractional charge ± 1 / 3 e or ± 2 / 3 e , e being the magnitude of the electron charge $^{[1]}$. The successes of SM in the fields of the spectroscopy and the high energy inter- action of the hadrons have motivated a lot of experimental searches for fractional charge, isolatable, lepton-like particles. There has been a large number of experiments searching for free fractional charge particles using a variety of methods and no evidence up to date has been found to confirm their existence. There are three kinds of experiments used to search for fractional charge particles, which are based on the collision products of accelera- tor beams [3 − $^{6]}$, cosmic rays$^{[7]}$, and bulk matters[8] respectively. No observation of fractional charge particles results in the confinement concept that the quarks are permanently confined within the hadrons. The questions are whether there is a small fraction of quarks transi- tioning to the unconfinement phase from the confinement phase and whether there are new sensitive methods to search for them. It is noted that dE/dx ionization energy loss measurements are used to identify charged particle species for e $^{+}$e − [3 , 4] (or proton anti-proton [5] or heavy ions $^{[6]}$) collisions in accelerator based experiments. The energy loss fluctuation is described by Landau’s theory $^{[9]}$. One wonders if the theory is still valid for quarks, which take part in both the electroweak interaction and the strong interaction and is sensitive enough to distinguish the quarks from the five stable particles such as the electron, muon ,pion, kaon and proton if there is a small fraction of quarks which are unconfined. However it is no doubt that the conservation law of momentum and energy (four-momentum) applies to all kinds of interactions, which can be used to search for fractional charge particles in combination with the Lorentz force law for low energy accelerator experiments. The prerequisite for this kind of search is that a detector is required to possess large coverage, good particle identification, precise momentum resolution of charged tracks and energy resolution of neutral tracks and collect large data samples. For instance, recently upgraded CLEOc [10] and BESIII [11] detectors can search for fractional charge particles based on the laws. The center masses energy of the e $^{+}$e − collisions in CLEOc and BESIII cover the energy range of the charmonium production. Therefore fractional charge particles in the mass range of 0 to 2 GeV can be conceived to appear in the products of the collisions if they are physical reality. The momentum measurement of a track with charge qe produced in an e $^{+}$e − event is 2