Can an electron be produced inside a proton?

Question

We know that inside a proton there is a sea of quarks, antiquarks and gluons. This happens as the valence quarks emit gluons which then split into a quark-antiquark pairs. These pairs become gluons which are absorbed back into valence quarks.

My guestion is, can electron-positron pairs be produced inside a proton? A valence or a sea quark or antiquark would emit a photon, which then splits into a electron-positron pair. The pair would then annihilate back to photon and be absorbed into quark/antiquark.

Is there something preventing this from happening?

If this is the case, wouldn't it then be reasonable to study the PDF equivalent for electron distribution inside a proton?

Answer 1

Yes, the proton structure includes electrons and positrons, but their contribution is negligible because electromagnetism is so much weaker than the strong interaction that produces the proton's quark-gluon sea. The contribution from photons is, however, a hundred times greater than the $e^+e^-$ contribution and is – according to "How Bright is the Proton? A Precise Determination of the Photon Parton Distribution Function" – too large to be ignored in current parameterizations of the proton's Parton Distribution Functions (PDF).

According to Figure 20 of "The photon content of the proton", the fraction of a proton's momentum carried by photons increases logarithmically with the energy scale being probed, from about $0.3\%$ at $10$ GeV to $0.6\%$ at $10$ TeV. These values are consistent with naive expectations based on the lowest order processes involved.

For momenta high enough for the parton masses to be negligible, we roughly expect the contributions of different particles to the proton's structure to be:

• gluons: $\sim \alpha_S \sim 1$
• quark-antiquark pairs: $\sim (\alpha_S)^2 \sim 1$
• photons: $\sim \alpha_{QED} \approx 1/137 \sim 10^{-2}$
• electron-positron pairs: $\sim (\alpha_{QED})^2 \sim 10^{-4}$

I am not aware of any attempt to precisely determine the electron-positron content of the proton, but the analogous electron-positron content of the electron is more tractable and has been calculated. If my quick and dirty numerical integrations of the PDFs in Figure 5 (below) of "The partonic structure of the electron at the next-to-leading logarithmic accuracy in QED" are correct, at an energy scale of $100$ GeV, photons carry a few percent of an electron's momentum and positrons carry about $0.02\%$.

Answer 2

Simply put, if you are thinking of "being in the proton" as simply having a ghostly appearance in the form of loop diagrams with processes like $\gamma\to e^\pm$, sure nothing prevents such a thing. But you'll never really get real asymptotic states of electrons unless it's a beta plus decay where protons can convert into neutrons (well technically they emit positrons but you get the gist).