# How can weak interactions not conserve strangeness if the SM always conserves energy?

Weak Interaction and Strangeness transformation

Weak decay iff or if strangeness changes?

Understanding type of force interaction in particle decays

The decay of the strange quark via weak interactions?

As I understand, currently all experimental data support the SM as being the accepted theory. Both weak interactions and strangeness and strange quarks are part of the SM model.

As I understand, energy is always conserved in the SM, and all other forces, EM, gravity and strong all conserve both energy and strangeness.

If the SM is supported by all experimental data, and it always conserves energy, then how is it possible that some weak interactions do not conserve strangeness?

Where does the energy go? How can the energy be conserved by not strangeness?

In our modern understanding, strangeness is conserved during the strong and the electromagnetic interactions, but not during the weak interactions. Consequently, the lightest particles containing a strange quark cannot decay by the strong interaction, and must instead decay via the much slower weak interaction. In most cases these decays change the value of the strangeness by one unit. However, this doesn't necessarily hold in second-order weak reactions, where there are mixes of K0 and K0 mesons. All in all, the amount of strangeness can change in a weak interaction reaction by +1, 0 or -1 (depending on the reaction).

Consequently, the lightest particles containing a strange quark cannot decay by the strong interaction, and must instead decay via the much slower weak interaction.

It is talking about this strangeness conservation braking as if it was only for composite particles, that contain strange quarks. But what about the strange quark itself? Is the strange quark stable, or can the strange quark as elementary particle decay via weak interaction?

Question:

1. If energy is conserved during all weak interactions, then how can strangeness not be conserved? Is strangeness equal to energy asymmetry?

2. Can strangeness not be conserved for (interactions/decay of) non-composite particles?

• The strangeness is not energy, it is just a quantum number. You see particles in the collider, measure their properties, incl. their mass, and their decay chains. I hope a pro will explain it in a more detailed form. My layman view is that something is "extraordinary" with the weak interaction, any time if particles change flavor, it happens due to weak interaction, or annihillation. As if the weak interaction would be like a bridge between the others. – peterh - Reinstate Monica Apr 11 '19 at 21:04
• Your do appreciate quarks cannot be observed in isolation, but get dressed by gluons and quark-antiquark pairs always inside composite hadrons, no? Energy and momentum are conserved in elementary interaction vertices, but these often involve virtual particles violating the energy-momentum on-shell constraints you are used to? – Cosmas Zachos Apr 11 '19 at 21:24
• This sounds a bit unclear. Surely energy isn't the exact same thing as strangeness. What do you think strangeness is? – knzhou Apr 12 '19 at 14:55

Strangness is a quantum number as peterh explained in his comment. Every particle has a strangeness number $$S = -(n_s - n_\overline{s})$$, where $$n_s$$ and $$n_\overline{s}$$ are the number of strange quarks and anti-quarks - the minus sign in the front looks arbitrary, the important thing is that it is the difference between the particles and anti-particles. There are equivalent quantum numbers for other flavours, like Bottomness.
The CKM quark mixing matrix shows how the weak interaction mixes quarks - it arises due to the mass eigenstates not being the same as flavour eigenstates. The charged weak interaction is able to change the flavour of a quark, e.g. beta decay - $$d \rightarrow W^- + u, \Delta S = 0$$. In the same way, you can have a strange quark decaying into an up quark $$s \rightarrow W^- + u, \Delta S = 1$$ or say a top quark decaying into s, $$t \rightarrow W^+ + s, \Delta S = -1$$. The probability of these interactions are proportional to the square of the CKM matrix elements - $$|V_{ij}|^2$$.