Are resonances formed in the scattering of a baryon and a meson?

[crick]

Consider the following reaction of strong interaction (in a scattering process)
$$n+\pi^+\to \Lambda_0+K^+\tag{1}$$

Then the particle $\Lambda_0$ formed decays with weak interaction

$$\Lambda_0\to \pi^+ +p\tag{2}$$

For each decay process I measure the four momenta of $K^+$, $\pi^+$ and $p$ in the final state, I calculate the center-of-mass energy $\sqrt{s}$ of reaction $(1)$. Then I plot the cross section vs $\sqrt{s}$.

Do I get a Breit Wigner resonance curve with central value equal to the sum of masses of $\Lambda_0$ and $K^+$ and width equal to $$\Gamma=\hbar/\tau$$
Where $\tau$ is $\sim 10^{-23}s$, i.e. the characteristic time of strong interaction?

I'm not sure about this because reaction $(1)$ is not a "decay" (while reaction $(2)$ is a decay) and I wonder if the resonances in the cross section are seen also in reactions that are not really a decay.

I suppose that in reaction $(1)$ a kind of "intermediate excited state" is formed and then it decays to the final state, but I'm quite confused about this.

 

[mfb]

You'll get a curve that starts at the sum of the two masses and increases afterwards due to increasing phase space to produce the particles. The timescale of the interaction or the lifetimes of the particles are irrelevant. The excess energy just goes into kinetic energy of the two produced particles.