Quarks are elementary particles that carry fractional electric charges. The concept of quarks having fractional charges may seem counterintuitive when we think about the familiar whole number charges of particles like protons (+1) and electrons (-1). However, in the framework of modern particle physics, quarks are considered to be fundamental particles with fractional charges.
Quarks are subject to the strong nuclear force, which is mediated by particles called gluons. This force binds quarks together to form composite particles called hadrons, such as protons and neutrons. Quarks come in six different "flavors": up, down, charm, strange, top, and bottom.
The up quark (u) has a charge of +2/3, while the down quark (d) has a charge of -1/3. This fractional charge arises due to the way quarks interact with the fundamental force carriers, the gluons. The strong nuclear force is described by a theory called quantum chromodynamics (QCD), which is a part of the Standard Model of particle physics.
In QCD, quarks carry a property called "color charge" in addition to their electric charge. The color charge has three possible values: red, green, and blue (note that these colors are just labels and do not correspond to actual visual colors). Quarks can also have an antiquark counterpart with corresponding anticolor charges (anticolors).
The combination of the quark's electric charge and its color charge determines the overall fractional charge. Quarks combine in specific ways to form color-neutral combinations, such as protons and neutrons, which have integral charges.
The fractional charges of quarks are not observed in isolation because quarks are always confined within hadrons due to the strong force. This confinement phenomenon prevents us from directly detecting isolated quarks and only allows us to observe their effects within composite particles.
The fractional charges of quarks and the overall behavior of the strong force are described by mathematical formalisms based on the principles of quantum field theory and the symmetries of the Standard Model. These models have been extensively tested and found to accurately describe the behavior of quarks and other elementary particles in high-energy experiments.