The phenomenon of quarks producing new quarks when they are pulled apart is a consequence of the strong nuclear force and the way it behaves at short distances. This behavior is described by the theory of quantum chromodynamics (QCD), which is a part of the standard model of particle physics.
In QCD, quarks are governed by a property called "color charge." Just as electric charge is associated with the electromagnetic force, color charge is associated with the strong nuclear force. However, unlike electric charge, which comes in positive and negative forms, color charge comes in three types: red, green, and blue (often referred to as colors).
The strong nuclear force is mediated by particles called gluons, which can carry color charge. Quarks interact with gluons by exchanging them, and this interaction becomes stronger as quarks are pulled farther apart. When the energy involved in pulling the quarks apart reaches a certain threshold, it becomes energetically favorable to create new quark-antiquark pairs or additional quarks from the vacuum.
This process is known as quark confinement. It ensures that quarks are always found in combinations that result in color-neutral states, such as mesons (quark-antiquark pairs) or baryons (three quarks). When an attempt is made to separate two quarks, the energy stored in the color field between them becomes large enough to create new quarks and anti-quarks, forming additional hadrons.
Essentially, the strong force acts to prevent the isolation of individual quarks by creating new quarks and binding them together to form color-neutral particles. This behavior is a fundamental aspect of QCD and has been supported by experimental evidence.