The question is really in the title with this one, I just need a little bit of clarity, consider beta-minus decay, which is an interaction governed by the weak nuclear force, $$n\to p^+ +e^- +\bar v_e$$ Here, the corresponding Feymann Diagram is

                                                     enter image description here

which clearly indicates the $W^-$boson as the exchange particle, acting as proof that the interaction occurs due to the weak nuclear force. The question is, if neutron and protons are subject to the strong nuclear force, how can they be involved in weak interactions?

  • $\begingroup$ A particle absolutely can be subject to several forces at once. Protons interact with all four fundamental forces, in fact. $\endgroup$ – Noiralef Nov 2 '17 at 13:09
  • $\begingroup$ It was also called "The Weak Nuclear Force" long before electroweak unification. $\endgroup$ – JEB Nov 2 '17 at 14:20

You have to think about the internal structure of protons and neutrons. Neutrons have two down valence quarks and one up valance quark. Protons have two up valance quarks and one down valance quark. At the fundamental level what happens when a neutron decays into a proton is that a down quark from the neutron changes its flavor into an up quark by emitting a $W^{-}$ boson. Quarks do interact through weak interaction.

Here is the Feynman Diagram for beta$^{-}$ decay.

Feynman Diagram - Beta decay

  • $\begingroup$ You could move the OP's argument one step down: «if [quarks] are subject to the strong nuclear force, how can they be involved in weak interactions?» $\endgroup$ – user154997 Nov 2 '17 at 14:12

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