# Why is neutron slightly heavier than the proton? [duplicate]

With latest knowledge of QCD, is there any explanation for why the neutron is slightly heavier than the proton? Can it be boiled down to a simple formula?

• Are you asking for a complete and proven rigorous explanation? Or will "the different valence quark combinations interact with the QCD vacuum in different ways, which produces states with different energies, as has been demonstrated using lattice QCD" be sufficient? – probably_someone Dec 27 '18 at 23:05
• "Different valence quark makeups" - proton is uud, neutron is udd. "Interact with the QCD vacuum in different ways" - since the interactions are non-perturbative at these energies, there's not a whole lot more I can say here. – probably_someone Dec 27 '18 at 23:09
• The quark masses account for less than 1% of the nucleon mass. Most of the mass comes from the kinetic energy of the gluons. Calculating that energy is tricky because gluons have color charge, which makes the integrals / Feynmann diagrams messy, unlike in QED, where they converge nicely. So you need a lot of computer time even to calculate an approximate solution. – PM 2Ring Dec 27 '18 at 23:54
• If protons were heavier than neutrons then protons would decay. The universe would be very different if hydrogen were unstable. I guess the only kind of stars would be neutron stars, and complex atoms wouldn't be produced. – PM 2Ring Dec 28 '18 at 0:03
• Possible duplicates: physics.stackexchange.com/q/85/2451 , physics.stackexchange.com/q/264420/2451 and links therein. – Qmechanic Dec 28 '18 at 0:40

• @ Zooby QCd has a property called anti-screening, where the renormalization group flow for the coupling constant increases it with lower energy. We can work well enough with scattering states at high energy because the coupling constant decreases $\sim~g^2/4\pi log(\Lambda/E)$ as I recall. At very low energy coupling becomes large and renormalization schemes for computing these bound states does not work well. This is the reason for lattice QCD. So the oddity is that as the energy or momentum of quarks in a hadron becomes small things go haywire. – Lawrence B. Crowell Dec 28 '18 at 23:26