The concept of mass in particle physics is complex and arises from a combination of factors. In the case of protons, which are composite particles, their mass can be attributed to the masses of their constituent quarks, as well as the binding energy resulting from the strong nuclear force.
Protons are made up of three valence quarks: two up quarks (each with a charge of +2/3) and one down quark (with a charge of -1/3). These quarks are bound together by the exchange of gluons, which are the carriers of the strong nuclear force. The strong force is responsible for holding quarks together inside the proton.
Quarks themselves have intrinsic mass, meaning they possess mass even when they are not bound within a particle. The up quark is the lightest among the six known quarks, while the down quark is slightly heavier. The masses of the quarks contribute to the overall mass of the proton. However, the masses of the three quarks alone do not account for the entire mass of the proton.
The majority of the mass of a proton actually arises from the strong nuclear force and the dynamics of the quarks within. According to quantum chromodynamics (QCD), the theory describing the strong interaction, the strong force creates a complex environment inside the proton. The exchange of gluons between the quarks generates a "sea" of virtual quark-antiquark pairs that continually pop in and out of existence. These virtual particles contribute to the overall mass of the proton.
Additionally, the strong force itself contributes to the proton's mass through its binding energy. According to Einstein's mass-energy equivalence (E = mc²), the binding energy of the quarks within the proton manifests as mass.
Therefore, the mass of a proton is the combined result of the masses of its constituent quarks, the binding energy of the strong force, and the contributions from the virtual particles that exist due to the dynamics of the strong interaction. It is worth noting that the precise calculation of the mass of the proton is a challenging task in quantum chromodynamics, and it involves complex computations using numerical techniques such as lattice QCD.