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Suppose the processes $$ p+\gamma \to n + \bar{l} + \nu_{l}, \quad p+\gamma \to p+\bar{\nu}_{l} + \nu_{l}, $$ where $p$ denotes a proton, $\gamma$ - a photon, $l$, $\nu_{l}$ - a lepton and corresponding neutrino. The $p-\gamma$ energy at their CM frame is of order of $10 \text{ GeV}$.

In order to calculate corresponding cross-sections, can I use the Fermi theory written in terms of the nucleons, or I need to deal with the quarks and corresponding pdf?

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