The question of whether it is possible to split a quark is a complex one. According to our current understanding of the strong nuclear force and the theory of quantum chromodynamics (QCD), quarks are subject to a phenomenon known as color confinement. Color confinement implies that quarks cannot exist as isolated particles in nature; they are always bound together in composite particles such as protons and neutrons.
When attempts are made to separate quarks from one another, the energy required to do so increases. As the quarks move further apart, the energy stored in the strong force field between them also increases. This energy eventually becomes so significant that it becomes more favorable for a new quark-antiquark pair to be created, forming new composite particles rather than allowing the separation of individual quarks.
This phenomenon is often referred to as "hadronization" or "quark confinement." Instead of observing isolated quarks, we observe the formation of color-neutral bound states called hadrons, which include baryons (such as protons and neutrons) and mesons.
Therefore, our current understanding suggests that it is not possible to split a quark and observe it in isolation. The behavior of quarks and the phenomena of color confinement and hadronization are areas of ongoing research in theoretical and experimental physics. Future advancements may provide further insights and potential refinements to our understanding of quark dynamics.