Conservation of strangeness and eigenstates

In summary, Povh's book states that the strong force conserves the strangeness of neutral kaons, making them eigenstates of the strong interaction. This is demonstrated by the commutation relation between the strangeness operator and the Hamiltonian. This can also be seen experimentally, as neutral kaons cannot decay via the strong interaction. Therefore, it can be defined that the neutral kaon represents a strong state. Any other basis chosen for the state would result in the same conclusion, as the Hamiltonian can be diagonalized in the strong basis.
  • #1
Xico Sim
43
4
Hi, guys.

In Povh's book, page 198, he says: "The strong force conserves the strangeness S and so the neutral kaons are in an eigenstate of the strong interaction."

I do not see why this must be the case. My atempt to understand it:

$$ŜĤ_s |K_0 \rangle = Ĥ_sŜ |K_0 \rangle$$
So
$$Ŝ(Ĥ_s |K_0 \rangle) = -Ĥ_s |K_0 \rangle $$

Since the ket ##Ĥ_s |K_0 \rangle## has strangeness -1, it belongs to the eigensubspace of ##Ŝ## with eigenvalue -1. I don't know how one conclude, from this, that
$$ Ĥ_s |K_0 \rangle \, \alpha \, |K_0\rangle $$
which is what I want to prove.
 
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  • #2
well, abstractly speaking, can't you write [itex]|K_0>[/itex] state in whichever basis you want? and so the strong interactions' basis... the commutation relation you wrote (and I guess you take as given) will hold in any basis of the state [itex]|K_0>[/itex].
So you can define that the [itex]K_0[/itex] represents a strong state.
 
  • #3
A more experimental approach: neutral kaons cannot decay via the strong interaction (they are the lightest neutral particles with a strange quark and ##K^0 \to K^+ \pi^-## is not possible either), so no matter how you write them as state, they have to be an eigenstate of the strong interaction.
 
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  • #4
ChrisVer said:
So you can define that the [itex]K_0[/itex] represents a strong state.

"So"? i don't see why...
 
  • #5
whether you define the x-axis showing to your left hand, or showing to your right, if there is a left/right symmetry it doesn't really matter.

If we suppose that K0 in your case is not a strong state, you can "rotate" it into being in the strong state K0'...
THis happens by diagonalizing the Hamiltonian in the strong basis by [itex]H \rightarrow H_{\text{str-diag}}=U H U^\dagger [/itex] and so will the states: [itex]|K_0> \rightarrow U |K_0>[/itex] which will be your states written in the strong interaction basis.
The thing is that U is a unitary matrix (since it only changes the basis) and you of course get the same thing..
 
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Related to Conservation of strangeness and eigenstates

1. What is conservation of strangeness and eigenstates?

Conservation of strangeness and eigenstates refers to two fundamental properties of particles: strangeness, which is a measure of their "strange" or unusual behavior, and eigenstates, which are the specific quantum states that particles exist in. These properties are conserved, meaning they remain constant, in certain interactions between particles.

2. How is strangeness measured?

Strangeness is measured as a quantum number, denoted by the letter "S", that is assigned to particles based on their behavior in certain interactions. Particles with strangeness of 0, such as protons and neutrons, behave normally. Those with a strangeness of -1, such as strange quarks, have slightly different behaviors, and those with a strangeness of -2, such as doubly strange particles, have even more unusual behaviors.

3. What are eigenstates?

Eigenstates, also known as "eigenstates of strangeness", are the specific quantum states that particles exist in. These states are characterized by their quantum numbers, including strangeness, and are eigenstates because they are the states that particles naturally "prefer" to be in.

4. How does conservation of strangeness and eigenstates apply to particle interactions?

In particle interactions, such as collisions, certain properties must be conserved. This means that the total amount of these properties before the interaction must be equal to the total amount after the interaction. Strangeness and eigenstates are two properties that are conserved in these interactions. This means that the total strangeness and eigenstates of the particles involved must be the same before and after the interaction.

5. Why is conservation of strangeness and eigenstates important in particle physics?

Conservation of strangeness and eigenstates is important because it allows scientists to understand and predict the behavior of particles in interactions. By studying the conservation of these properties, scientists can uncover new information about the fundamental building blocks of the universe and the forces that govern them.

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