Determine the types of interactions and whether Cabibbo...?

[Poirot]

Homework Statement

By considering the type of particles involved and which quantum numbers are conserved, classify each of the following processes into weak, strong, EM and forbidden interactions. (“Forbidden” means that it can’t be weak, strong nor EM.) For processes which are weak, state which are Cabibbo allowed or suppressed.
(a) p + p → p + n + π⁺(π is a meson containing only u and d quarks/antiquarks.)
(b) π^- + p → p + p +π⁰
(c) K⁺ → π⁰ +e⁺ + ν_e (K is a meson containing an s quark/antiquark plus a u or d quark/antiquark.)
(d) K^- → π⁺ + π^- + e^- +ν_e(anti)

Homework Equations

Quantum numbers:
Charge, Q ≡ 2/3(N_u+N_c+N_t) - 1/3(N_d+N_s+N_b)
Baryon number, B ≡1/3(N_u+N_c+N_t + N_d+N_s+N_b)
Quark Number: N_q = N(q) - N(q(anti))
Lepton Number: L_e = N(e^-) -N(e⁺) + N(ν_e) - N(ν_e(anti)) (and similar for muon and taon)

The Attempt at a Solution

(a) I think this is weak and Cabibbo allowed. I think weak because there is a change in quark species and hence a change in charge so weak must be involved? and Cabibbo allowed as u→d.
(b) I think this is forbidden as Q is not conserved.
(c) I think this is weak and Cabibbo suppressed. Weak because change in species and suppressed as s-bar→u-bar.
(d) I think this is weak and Cabibbo suppressed. I think s→u but I'm really not sure what's actually going on here?

If someone could possibly explain a checklist/guide for determining the types of interactions that would be great. And also any explanation of what's happening in the interactions, for example (a) is there a W- boson coming off one of the quarks (Feynman) to transfer the charge?

Thanks for any help, it would be greatly, greatly appreciated.

 

[mark726]

(a) Yes, this is a weak interaction. The weak interaction is responsible for the conversion of a proton into a neutron, and the emission of a charged pion (π+). This is known as beta decay. The Cabibbo allowed part refers to the fact that the weak interaction is stronger for certain types of quarks (up and down in this case) than for others (strange, charm, bottom, top).

(b) This is a strong interaction, specifically a type of interaction called elastic scattering. This is when two particles collide and exchange energy and momentum, but do not change their identities. In this case, a pion (π-) and a proton (p) collide and exchange energy and momentum, resulting in a proton (p) and a neutral pion (π0).

(c) This is also a weak interaction, specifically a type of interaction called beta decay. In this case, a kaon (K+) decays into a neutral pion (π0), a positron (e+), and a neutrino (νe). This type of decay is Cabibbo suppressed because the kaon contains a strange quark, which is not as favored by the weak interaction as an up or down quark.

(d) This is also a weak interaction, specifically a type of interaction known as beta decay. In this case, a kaon (K-) decays into a charged pion (π+), a negative pion (π-), an electron (e-), and an antineutrino (νe). The s-quark in the kaon is also Cabibbo suppressed, so the weak interaction is not as strong as it would be for an up or down quark.

In general, to determine the type of interaction involved in a process, you need to consider the particles involved and the conservation laws that apply to them. For example, in the case of (a), we know that the proton (p) is made up of two up quarks (u) and one down quark (d). The neutron (n) is made up of one up quark and two down quarks. The pion (π+) is made up of an up quark and an anti-down quark. The weak interaction is responsible for changing the up quark in the proton into a down quark, resulting in a neutron, and emitting a pion. This process conserves both charge (since the proton