- #1

Aleolomorfo

- 73

- 4

- Homework Statement
- In a bubble chamber experiment on a ##K^-## beam a sample of events of the reaction ##K^- + p \rightarrow \Lambda^0 + \pi^+ + \pi^-## is selected. A resonance is detected both in the ##\Lambda^0\pi^+## and ##\Lambda^0\pi^-## mass distributions. It is called ##\Sigma(1385)##. If the study of the angular distributions establishes that the orbital angular momentum of the ##\Lambda^0\pi##system is ##L=1##, what are the possible spin parity values ##J^p##?

- Relevant Equations
- /

Hello everybody!

Let's begin with the spin. Spin of the ##\Lambda## is ##1/2## and of the pion is ##0##:

$$ \frac{1}{2} \otimes 0 = \frac{1}{2}$$

Since I know from the homework statement that ##L=1##:

$$ \textbf{J} = \textbf{spin} \otimes \textbf{L} = \frac{1}{2} \otimes 1 = \frac{1}{2} \oplus \frac{3}{2} $$

Then the parity of the system:

$$P(\Lambda^0\pi) = P_{\Lambda}P_{\pi}(-1)^L= (+)(-)(-) = +1 $$

So there are two possibilities: ##\frac{1}{2}^+## and ##\frac{3}{2}^+##.

But from PDG ##\Sigma(1385)## is a ##\frac{3}{2}^+## particle. I do not how to reject the other possibility of ##\frac{1}{2}^+##.

Thanks in advance!

Let's begin with the spin. Spin of the ##\Lambda## is ##1/2## and of the pion is ##0##:

$$ \frac{1}{2} \otimes 0 = \frac{1}{2}$$

Since I know from the homework statement that ##L=1##:

$$ \textbf{J} = \textbf{spin} \otimes \textbf{L} = \frac{1}{2} \otimes 1 = \frac{1}{2} \oplus \frac{3}{2} $$

Then the parity of the system:

$$P(\Lambda^0\pi) = P_{\Lambda}P_{\pi}(-1)^L= (+)(-)(-) = +1 $$

So there are two possibilities: ##\frac{1}{2}^+## and ##\frac{3}{2}^+##.

But from PDG ##\Sigma(1385)## is a ##\frac{3}{2}^+## particle. I do not how to reject the other possibility of ##\frac{1}{2}^+##.

Thanks in advance!