Evidence for Quark Confinement in the Proton

The strong interaction is the fundamental force that holds quarks and the gluon force carriers together to form protons and neutrons and also binds the atomic nucleus. The theory governing quark-gluon interactions is quantum chromodynamics (QCD). A wide variety of experimental data teaches us that quarks and gluons cannot be observed in isolation, a phenomenon known as confinement that is unique to QCD. But no one has used QCD to mathematically prove confinement. Here, we show how to define and measure the force on quarks in the proton using available experimental data. Direct evidence for confinement is obtained because the force is found to be attractive and constant for a wide range of quark positions. This work guides future experimental efforts at future electron-ion colliders aimed at obtaining a rigorous quantitative understanding of confinement and the origin of nuclear mass.