The concept of splitting a quark is not directly applicable within the framework of quantum chromodynamics (QCD) and the understanding of the strong force. Quarks are considered to be elementary particles and are subject to a phenomenon known as color confinement.
Color confinement means that quarks cannot exist in isolation; they are always bound together to form composite particles such as protons, neutrons, and mesons. When quarks are separated from each other, the energy stored in the strong force field between them increases. As this energy reaches a certain threshold, new quark-antiquark pairs are created from the vacuum, resulting in the formation of new hadrons.
This phenomenon prevents the direct splitting or isolation of a single quark. Instead, the strong force maintains the bound state of quarks within hadrons, and any attempt to separate them only leads to the creation of additional quark-antiquark pairs and the formation of new hadrons.
However, it's worth noting that within the framework of QCD, there are rare and hypothetical phenomena known as "quark deconfinement" or "quark liberation" that are thought to occur under extreme conditions of temperature and density, such as in the early universe shortly after the Big Bang or in the cores of neutron stars. In these extreme conditions, it is postulated that quarks may exist in a deconfined state, forming a quark-gluon plasma (QGP) where quarks and gluons are free to move over large distances. However, under normal conditions, quarks remain confined within composite particles.