The following equation shows a Xi
baryon decaying into a lambda baryon and a pion, which is an interaction that does
not conserve strangeness. What is the total strangeness
before the interaction takes place? What is the total strangeness after
the interaction takes place?
Looking at our equation, we see
this particle here, called a Xi baryon, decaying into a lambda baryon and a
pion. Along with the symbol for each of
these particles, in parentheses, we’re told what quarks make up each one. So, for example, for our pion, this
is made up of an up antiquark and a down quark.
Our question is focused on the
strangeness of this interaction. And we can recall that this has to
do with how many strange quarks and strange antiquarks are present. Specifically, every strange quark
in a particle has a strangeness of negative one, while every strange antiquark has a
strangeness of positive one. This means, for example, that if we
had a strange quark all by itself, then the strangeness of that particle would be
The first part of our question asks
about the total strangeness before the interaction takes place. In other words, what is the
strangeness of the Xi baryon before it decays into the lambda baryon and the
pion? We see that this particle is made
up of a down quark and two strange quarks. The down quark doesn’t contribute
anything to strangeness. Only strange quarks and strange
antiquarks can. But each one of the strange quarks,
according to our rule, will contribute negative one to the overall strangeness of
the particle. So if we call 𝑆 sub b the total
strangeness before our interaction takes place, that’s equal to zero, that’s the
contribution of the down quark in the Xi baryon, minus one minus one. Those are the contributions of the
two strange quarks. So that equals negative two. And that’s our answer to the first
part of our question.
Part two asks us, what is the total
strangeness after the interaction takes place? Now, if strangeness was conserved
in this equation, then our answer here would be the same as our answer earlier. But our problem statement tells us
that, in this case, strangeness is not conserved. So let’s take a look at the product
side of this interaction.
First, we have our lambda
baryon. And we see this is made of an up
quark, a down quark, and a strange quark. Both the up and the down quark
don’t contribute anything to the strangeness of this particle overall, while the
strange quark, according to our rule, contributes a strangeness of negative one. We can say then that the overall
strangeness of our lambda baryon is negative one.
And next, we look at the pion,
which we see is made up of an up antiquark and a down quark. Since neither of these is a strange
quark or a strange antiquark, they contribute nothing to the strangeness of the
pion. And so we can say that the
strangeness of the pion overall is zero. This means that the total
strangeness of this interaction after the interaction takes place is negative one
plus zero or just negative one. And we see now that indeed
strangeness is not conserved in this interaction. Before the interaction, it was
negative two. And after, it’s negative one.