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Problem 48 Hard Difficulty

The reaction $\pi^{-}+\mathrm{p} \rightarrow \mathrm{K}^{0}+\Lambda^{0}$ occurs with high probability, whereas the reaction $\pi^{-}+\mathrm{p} \rightarrow \mathrm{K}^{0}+\mathrm{n}$ never occurs. Analyze these reactions at the quark level. Show that the first reaction conserves the total number of each type of quark and the second reaction does not.

Answer

Consider the reaction:
$\pi^{-}+\mathrm{p} \rightarrow \mathrm{K}^{0}+\mathrm{n}$
Express the above equation in terms of quark composition:
$\overline{\mathrm{u} d}+$ uud $\rightarrow \mathrm{d} \overline{\mathrm{s}}+$ udd
Write the net quarks in the above equation and use the condition that the particle and
antiparticles get canceled.
u $+2 \mathrm{d} \rightarrow \mathrm{u}+3 \mathrm{d}+\overline{\mathrm{s}}$
Therefore, the quarks number is not conserved on both sides of the equation and hence it is not
possible reaction.

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Top Physics 103 Educators
Elyse G.

Cornell University

Christina K.

Rutgers, The State University of New Jersey

Farnaz M.

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Meghan M.

McMaster University

Video Transcript

police Christian were given to different reactions And given that the first direction actually a curse, you know, much higher probability while the second reaction never curse. Right? And you want to understand why by looking at the clock content before and after every reaction. So let us look at the first reaction first and in a nice domestic cook. Corsetti, once flight pilots IHS ante up, Don't proton areas up. Don't cloak, right On the other hand, for the K on it is known a strange club and district and inlanders not, is up, down Strange, right? And so, looking at the quote content, you can see that 40 up cook and he don't cook parents where the different changes You see that assuming the ante up and anti ah, at the up club actually cancels each other out. They see in it quirk content off a single up quark and two down quarks on the right side to be assuming that he strange and anti strange cancel each other out. The net 10 is went up and two down. Right, So they are the same. The last really second reaction. You start off with the same Rick tins we have tea. Que on again, but not really heavy neutron. The neutron is up. Down. Don't. So, first off the net quite content is up. Down, down on the left. Not the right. We have tree Don't cooks one up cook and one anti street. So first off, the strange, strange nurses not conserved already. Khowst three f one anti strange Over here about that snow, nor strange quarks over here on the left hand side. And another thing instead, the number off up number of down Cox is different. Yes, higher than two. So don't Cox, which is on the left. I saw it doesn't conserve the net number off each type off work and so it's possible it why it doesn't occur as much as the first reaction.

National University of Singapore
Top Physics 103 Educators
Elyse G.

Cornell University

Christina K.

Rutgers, The State University of New Jersey

Farnaz M.

Other Schools

Meghan M.

McMaster University