Editing Proton (section)

== Quarks and the mass of a proton ==
In [[quantum chromodynamics]], the modern theory of the nuclear force, most of the mass of protons and [[neutron]]s is explained by [[special relativity]]. The mass of a proton is about 80–100 times greater than the sum of the rest masses of its three valence [[quark]]s, while the [[gluon]]s have zero rest mass. The extra energy of the [[quark]]s and [[gluon]]s in a proton, as compared to the rest energy of the quarks alone in the [[QCD vacuum]], accounts for almost 99% of the proton's mass. The rest mass of a proton is, thus, the [[invariant mass]] of the system of moving quarks and gluons that make up the particle, and, in such systems, even the energy of massless particles confined to a system is [[Mass–energy equivalence#Composite systems|still measured]] as part of the rest mass of the system.

Two terms are used in referring to the mass of the quarks that make up protons: ''[[current quark]] mass'' refers to the mass of a quark by itself, while ''[[constituent quark]] mass'' refers to the current quark mass plus the mass of the [[gluon]] [[quantum field theory|particle field]] surrounding the quark.<ref name="Waston2004" />{{rp|285–286}}<ref name="Smith2003" />{{rp|150–151}} These masses typically have very different values. The kinetic energy of the quarks that is a consequence of confinement is a contribution (see ''[[Mass in special relativity]]''). Using [[lattice QCD]] calculations, the contributions to the mass of the proton are the quark condensate (~9%, comprising the up and down quarks and a sea of virtual strange quarks), the quark kinetic energy (~32%), the gluon kinetic energy (~37%), and the anomalous gluonic contribution (~23%, comprising contributions from condensates of all quark flavors).<ref>{{cite magazine|author=André Walker-Loud|title=Dissecting the Mass of the Proton|magazine=Physics|date=19 November 2018|volume=11|page=118|doi=10.1103/Physics.11.118|bibcode=2018PhyOJ..11..118W|url=https://physics.aps.org/articles/v11/118|access-date=2021-06-04|doi-access=free|archive-date=2021-06-05|archive-url=https://web.archive.org/web/20210605002635/https://physics.aps.org/articles/v11/118|url-status=live}}</ref>

The constituent quark model wavefunction for the proton is
<math display="block">\mathrm{|p_\uparrow\rangle = \tfrac{1}{\sqrt {18}} \left(2| u_\uparrow d_\downarrow u_\uparrow \rangle + 2| u_\uparrow  u_\uparrow d_\downarrow \rangle + 2| d_\downarrow u_\uparrow   u_\uparrow \rangle - | u_\uparrow u_\downarrow d_\uparrow\rangle  -| u_\uparrow d_\uparrow u_\downarrow\rangle  - | u_\downarrow d_\uparrow u_\uparrow\rangle
- | d_\uparrow u_\downarrow u_\uparrow\rangle  - |d_\uparrow  u_\uparrow u_\downarrow\rangle-| u_\downarrow u_\uparrow d_\uparrow\rangle\right)}.</math>

The internal dynamics of protons are complicated, because they are determined by the quarks' exchanging gluons, and interacting with various vacuum condensates. [[Lattice QCD]] provides a way of calculating the mass of a proton directly from the theory to any accuracy, in principle. The most recent calculations<ref name="SMAnswers" /><ref name="Fodor2008" /> claim that the mass is determined to better than 4% accuracy, even to 1% accuracy (see Figure S5 in Dürr ''et al.''<ref name="Fodor2008" />). These claims are still controversial, because the calculations cannot yet be done with quarks as light as they are in the real world. This means that the predictions are found by a process of [[extrapolation]], which can introduce systematic errors.<ref name="Perdrisat2007" /> It is hard to tell whether these errors are controlled properly, because the quantities that are compared to experiment are the masses of the [[hadron]]s, which are known in advance.

These recent calculations are performed by massive supercomputers, and, as noted by Boffi and Pasquini: "a detailed description of the nucleon structure is still missing because ... long-distance behavior requires a nonperturbative and/or numerical treatment&nbsp;..."<ref name="Boffi2007" />
More conceptual approaches to the structure of protons are: the [[skyrmion|topological soliton]] approach originally due to [[Tony Skyrme]] and the more accurate [[AdS/QCD|AdS/QCD approach]] that extends it to include a [[string theory]] of gluons,<ref name="Erlich2008" /> various QCD-inspired models like the [[bag model]] and the [[constituent quark]] model, which were popular in the 1980s, and the [[SVZ sum rules]], which allow for rough approximate mass calculations.<ref name="Calangelo2000" /> These methods do not have the same accuracy as the more brute-force lattice QCD methods, at least not yet.