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Fill in the missing particle. Assume that (a) occurs via the strong interaction while (b) and (c) involve the weak interaction.

$$

\begin{array}{l}{\text { (a) } \mathrm{K}^{+}+\mathrm{p} \rightarrow ?+\mathrm{p}} \\ {\text { (b) } \Omega^{-} \rightarrow ?^{2}+\pi^{-}} \\ {\text { (c) } \mathrm{K}^{+} \rightarrow ?+\mu^{+}+\nu_{\mu}}\end{array}

$$

$(a) \text{K}^+ (b)\Xi^0(c)\pi^0$

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University of Michigan - Ann Arbor

Numerade Educator

University of Washington

McMaster University

in this question beyond identified, the unknown party goes right, which is label s ex in the following treaty reactions. To do that, we are given the hint there the first record undergoes strong direction RST other to actually interact via the weak interaction. So this will help us in identifying what conservation laws will be help. So for strong interaction, all de off the conservation laws must be conserved rest for week direction The strangeness ah value or the strangeness can be violated. But the other conservation laws must you be conserved, Right? So let's start off with the first reaction over here with the strong interaction. So first off, want to find out what is the church off X? Any church we know must be conserved. So on the left we have a charge off plus two on the right. The church is plus one from the proton. And so the xmas half a plus one church. Right. So they were just right over here. Church for unknown is passed one. Next we look at the bear your number to see what I said be really And on the left, we have a K on his own and we have a proton So a bigger number off plus one from the proton Only when you're right We already have a broad on richest plus one Burial number So explosive Be not a burial Right Next we look at the left wants but there's no left turns involved on the 11 side So this no lepton number on the right Amos have no leapt on as well not a leapt on And finally we look at the strangeness for the strangeness The proton has no strangeness but he k on has a strangeness off plus one since we know that this interaction actually must gold True via a strong interaction the strangeness must be conserved The strangers off X must be also plus what so strangeness off plus one So taking into account all this four properties the only Don Baer on with strangeness plus one Any charge off plus one is the positive chaos right which is the same s Oh, in the show Rectal We're here and so this is essentially an elastic scattering process. All right, we're no non off the particles actually undergo nuclear changes Now we move on to t next reaction that is for B. I gotta use a different color for easier. Right? So for B gonna look at a church So the charge on the left is minus one on the right is minus one form the pirate already So x must be neutral looking at the burial number. So this Ah, Omega A sea burial. So bear a number of plus one on the right Pye on its Amy's on. So parent number zero So how X must be a burial, right? To give us a pure number plus one so that you'll be conserved fixed We look at the lepton number so that slowly turns on the left. There should be an eloped on number the right, so not a left on Lastly, the strangeness. So the strangeness for our omega minus particle IHS minus tree you This made up off tree strange quirks on the right. Pye his own doesn't have any strangeness since it has no strange quarks in both. And this tells us that our X must either be minus tree o minus two o minus right And this is because ah, the strangeness value can be either conserved or not conserved in a weak interaction all right. In a four case, it is not possible to have a very on with minus tree if minus tree. Strange to us because a street squawk has charge off minus one toe e. So if you have a barren with ministry Strange Mr Street Strange Cox and the charge would be minus e right. But we want our very want to be neutral. So the only possible strangeness value it can have would be minus two. All right. And so, looking up our table to look for a for your very own with two strange quarks and is neutral this gives us the sigh. Cyberia one zero with a sigh Not right. Was I not particle so excellent your it's sorry. Lastly let us we want or the last reaction Let's reaction Vos killing and the king into X on Don't you quite reef a and t me one with e b one neutrino. So first off you look at a charge chattering lefties past one. When you write, the new one already gives the charge plus one So x must be do show for a charge to be concert Dix looking at the burial number all off them right? The K on it's not a barrier on these are left wants not Barrie Ont. So they left the barrel. Number must be zero. So it is not a bedroom. Now we look at the left on numbers on the left, we have little number off. Zero on the right. The me one plus gives Amy one lepton number off minus one since he said it is an anti you want. And the B one neutrino gives the view one left on number off, plus one. So total is zero as well. And so x martyr zero, right? Left on number. Who? It is not a tone. Finally, we look at the strangeness value. So did strangeness. Uh, que on and see. Strangeness value off plus one. All right. And on the right. So the right to be can I don't have a strangeness off zero last one or plus two linked. But we must also have our judge to be neutral. And, uh, it must not be a very on and not a left on. So looking out for the table off particles, so the possible one of the possible particles would be the pilot reaches no stray cious, and it is neutral, and it satisfy all the various conditions

National University of Singapore