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As I understand in the deep inelastic scattering process, a collision of electron beams and protons occurs, resulting in a scattered electron. However, when the proton absorbs the virtual photon emitted by the electron, it gains more energy and mass by generating sea quarks and gluons.

But this energy can't just disappear.

Therefore I just want to ask:

i) What happens to the proton after inelastic scattering?

ii) Would it remain to still have the sea quarks and sea gluons?

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There is no proton after inelastic scattering. If there were, it would be elastic scattering.

The struck parton is ejected and hadronizes on the way out. Of course, the now destroyed proton could reform into a proton with the ejected parton turning into pions.

If you strike a strange sea quark, you going to get kaons and a strange baryon. By detecting the ejected kaon, you can tag the $s$-quark and learn about the sea distribution.

But really, anything that doesn't violate conservation laws can happen: it's involved both experimentally and theoretically.

TJNAF is designed to study these interactions, which, when you detect some part of the final hadronic state are called "semi-inclusive deep inelastic scattering".

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