Problem: Prove that the reaction $p+p\rightarrow p+K^+$ is impossible, where $p=\text{proton}$, $K^+=\text{kaon}$.
(Side question: Is there a specific name for a positive Kaon, just like a "positive electron" is called a positron?)
I did this by considering the baryon number on both sides: Since the proton is a baryon we have B=1, and since kaon is a meson we have $B=0$. So the Baryon numbers are 1+1=1+0 or 2=1, a contradiction. Therefore the interaction is impossible.
However, I was also wondering if we could do this by considering strangeness. The kaon has a strangeness of +1 and protons have strangeness of 0, so strangeness isn't conserved in the reaction. However, in order to prove this cannot happen we need to show that the interaction happened via the strong interaction, otherwise if it was by the weak interaction strangeness alone doesn't suffice to prove it is impossible because weak interactions change quark type (i.e. [stiff with no strange quarks] –> [stuff with a strange quark in it] is still a possibility).
So my question is: Is this interaction a strong interaction? If so, how do you prove it, and in general how do you find out if an interaction is strong or weak just by looking at the reaction equation.
Best Answer
You're right that the reaction fails to conserve baryon number.
The change in strangeness is a strike against the reaction, but not a fatal one; after all, the strange $K$ mesons decay into various mixtures of zero-strangeness mesons, charged leptons, and neutrinos. The thing to notice is that only the charged weak current, mediated by the $W$ boson, changes particle flavor. To generate a kaon without involving any leptons would require either one of the "hyperons" (heavy baryons) to carry away the strangeness, or flavor-changing neutral currents.