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Problem 29 Hard Difficulty

Which of the following processes are allowed by the strong interaction, the electromagnetic interaction, the weak interaction, or no interaction at all?
$$
\text {(a)} \pi^{-}+p \rightarrow 2 \eta^{0} \quad \text { (d) } \Omega^{-} \rightarrow \Xi^{-}+\pi^{0}
$$
$$
\text {(b)} \mathrm{K}^{-}+\mathrm{n} \rightarrow \Lambda^{0}+\pi^{-} \quad \text { (e) } \eta^{0} \rightarrow 2 \gamma
$$
$$
\text {(c)} \mathbf{K} \rightarrow \pi^{-}+\pi^{0}
$$

Answer

(a)
Consider the following reaction:
$\pi^{-}+\mathrm{p} \rightarrow 2 \eta^{0}$
Conservation of charge:
(-1) $+(+1) \rightarrow 2(0)$
$$
0 \rightarrow 0
$$
Conserve baryon number:
$$
1 \rightarrow 0
$$
(b)
Consider the following reaction:
$$
K^{-}+n \rightarrow \Lambda^{0}+\pi^{-}
$$
Conservation of charge:
$$
\begin{array}{l}{\qquad \begin{aligned} & \text { (0) }+(-1) \\ \text { Therefore the charge is conserved } \\ \text { Conserve baryon number: } \\$$$
1 \rightarrow 1
$$$\end{aligned}}\end{array}
$$
Therefore, the baryon number is conserved.
Conserve the strangeness:
$(-1)+(0) \rightarrow(-1)+(0)$
$\quad-1 \rightarrow-1$
All laws are conserved and hence it can via strong interaction.
(c)
Consider the following reaction:
$\mathrm{K}^{-}+\mathrm{n} \rightarrow \Lambda^{0}+\pi^{-}$
Conservation of charge:
$(-1)+(0) \rightarrow(0)+(-1)$
$\quad-1 \rightarrow-1$
Conserve baryon number:
$(0)+(1) \rightarrow(1)+(0)$
1$\rightarrow 1$
Therefore, the baryon number is conserved.
Conservation of strangeness:
$(-1)+(0) \rightarrow(0)+(0)$
$\quad-1 \rightarrow 0$
In this reaction strangeness is not conserved and hence it is occurred via weak interaction.
(d)
Consider the following reaction:
$\mathrm{K}^{-} \rightarrow \pi^{-}+\pi^{0}$
Conservation of charge:
(-1) $\rightarrow(-1)+(0)$
Conserve baryon number:
(0) $\rightarrow(0)+(0)$
0$\rightarrow 0$
Therefore, the baryon number is conserved.
Conservation of strangeness:
$(-1) \rightarrow(0)+(0)$
$-1 \rightarrow 0$
In this reaction strangeness is not conserved and hence it is occurred via weak interaction.
(e)
Consider the following reaction:
$\eta^{0} \rightarrow 2 \gamma$
Conservation of charge:
(0) $\rightarrow 2(0)$
Therefore, the charge is conserved. Since it doesn't involve baryons and strange particles, the
baryon number and the strangeness number are also conserved. It is proceeded via
electromagnetic interaction due to the presence of gamma rays.

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Top Physics 103 Educators
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Cornell University

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Video Transcript

for this particle questions getting at five different reactions. Nuclear reactions? No, What we want to do for all of these reactions is to go through two steps. And the first step is to get what kind of conservation laws it might violate, whether it doesn't even violate any off the conservation laws. And they lost every looking at IHS, the conservation off charge, the conservation off burial or left a number and finally, the cultivation off the strangeness value. After looking at the conservation those you can't make a conclusion about what kindof interaction. Uh uh, What kind of direction mediates the reaction and allows it to Uh huh Carry on. Right? So there are different kinds of indirection. 1st 60 strong interaction usually results any change in T clock content. So if that's ah, large change in, they say from down Cocteau up quirk, etcetera. Most likely it is fired. The strong direction in a week in direction curse usually between the taunts where there's some left on exchange or when the streets just value is not conserved. Usually it is Trudy week direction and finally, actual make direction. You evolves. Four taunts caused the RTM ways so startle 51st equations. First reaction. We checked the conservation laws. So first of all, for charge the neutral or both sacs desperate for the burial number. However, it is not observed. So this two armies owns the pylon and eater are two results. They have serial barrel number, but proton is a barren So left insight has one barrel number. Where's the right hands? That has zero. So it is the barrel number is not conserved. It's by violated So the interaction cannot put seat C s burial place No cut Sift so that state for your sake. Any reaction? We checked the conservation laws. The church? Yes. Make a tiff. Negative one on both sites, The barrel number is one on both sides. The striations value right. Looking at the content castrations value is also conserved. So all the conservation laws are observed now to find out what interaction they were looking at, We can see that equal content. You genius quite a bit. There's some exchange off the quarks going on So most likely 80 strong interaction. We'll be taking please for these particle reaction Unlikely to be weak scenes, strangers value is conserved unlikely to be electromagnetic, since there's no fault wants evolved it. So for the Knicks direction, the church is minus one on both sex for the Baron lepton number zero. The striations value, however, keep he came easily. Okay on has a strange quark in it. So yes. Strangeness off minus one. And but pilot. All right. The pilots do not contain any strange clock. So a serial street value strangeness for the final products. And what this means is death. Striations is not conserved. It's violated until the election can't still occur. But will the viral week in direction? Because it violates street years, so most likely can still occur, but only by a direction. 66 we check again the conservation loss for the next reaction charges minus one off sites barrel number conserved. Right. So one, then, buddy Strangeness. So D omega is made up off tree strange cooks. So that is minus tree, right? The strange, just valuable Hugh is my mystery. A other burial iss strangeness off minus two. That's a too strange quarks and the pipe is on has jewel. So we see that illustrations value is by later again, so most likely can still occur. But only via weekend direction for the last equation, the most simplest one. Alright, charges zero. Both sex is conserved. There are a number zero strangeness. There's no strange clock involved, so zero direction looks likely in actual magnetic because we see a full time right, so it must be actual connected direction.

National University of Singapore
Top Physics 103 Educators
Elyse G.

Cornell University

Christina K.

Rutgers, The State University of New Jersey

Zachary M.

Hope College

Aspen F.

University of Sheffield