Video Transcript
The following equation shows a D
meson decaying into a kaon and two pions. What is the total charm before this
interaction takes place? What is the total charm after this
interaction takes place?
The equation we see shows us a D
meson, made up of a charm quark and an up antiquark, decaying into a positively
charged kaon, made of an up quark and a strange antiquark, a positively charged
pion, made of an up quark and a down antiquark, and then lastly a neutral pion, made
of an up quark and an up antiquark. It’s important to know what quarks
make up each of these particles because that will help us answer these questions
about the total charm in the interaction.
We can recall that this property
called charm is determined by the number of charm quarks and charm antiquarks a
particle may possess. Every charm quark contributes a
charm of positive one, while every charm antiquark contributes a charm of negative
one. Any quarks that are not of this
type do not contribute to the charm of the particle overall.
Knowing this, we can figure out the
answer to the first part of our question by computing the charm of our D meson. This is the only particle that
exists before the interaction. And we see that it’s made up of one
charm quark, that contributes a charm of positive one to the meson, and one up
antiquark. This particle makes no contribution
to the overall charm. The overall charm of the D Meson,
then, is positive one. This is the total charm in this
equation before the interaction takes place.
The second part of our question
asks about the total charm after the interaction has taken place. At this point, the D meson has
decayed into the kaon and the two pions. So now, we want to calculate the
total charm for these three particles combined. We’ll do this by adding together
the charm of each individual particle. First, we consider the kaon. The quarks that make it up are the
up quark and the strange antiquark. Neither of these impacts the charm
of the particle overall, which means that its charm is zero.
Considering next our positive pion,
we see this is made of an up quark and a down antiquark. These also have no impact on
charm. So therefore, the charm of this
particle is zero too, and so is the charm of our neutral pion because this also is
not made up of any charm quarks or charm antiquarks. The way we figure out the total
charm after the interaction has taken place is by adding together the charm of what
we could call the products. Zero plus zero plus zero is
zero. So, that is the total charm after
the interaction. And note that in this interaction,
charm is not conserved. It started out as one and ended up
as zero.
