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

• I
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.