Video Transcript
The Feynman diagram shows a delta
baryon, down, down, down, decaying to a neutron, up, down, down, and a meson. What is the particle X?
The particle X that we’re looking
for is down here in the bottom-right corner of the diagram. Before we go about finding its
identity, though, let’s make sure we understand what this diagram is showing. On the left-hand side of our
diagram corresponding to the initial configuration, we have three down quarks close
together. This is the delta baryon. On the right-hand side of the
diagram, which corresponds to the final configuration, we have two down quarks and
one up quark close together, which is the neutron, and an anti-up quark together
with the mystery particle X, which must form the meson.
In the interior of the diagram, two
of the down quarks don’t undergo any interactions at all. The last down quark, however,
reaches a vertex where it becomes a gluon represented by a cycloid and the mystery
particle X. This gluon then reaches another vertex where it spontaneously decays
into an up quark, which become as part of the neutron, and an anti-up quark, which
become as part of the meson.
All right, now that we’ve
understood what’s being shown in this diagram, let’s start gathering what we know
about the particle X. Firstly, just by looking at the diagram, we know that X is a
particle, not an antiparticle, since the line representing X has an arrow that
points forward in time. Just for contrast, the line
representing the anti-up quark has an arrow that points backwards in time because an
anti-up quark is an antiparticle. The next piece of information we
can gather about X is whether it is a lepton, a quark, or a boson.
From the diagram, we know that X is
part of a meson. And we can recall that a meson is a
composite particle made up of one quark and one antiquark. Since the anti-up is the antiquark
of the meson, X must be the quark. Even without knowing that the
anti-up X pair forms a meson, we could’ve still determined that X is a quark by
conserving baryon number. At this vertex here, a down quark
becomes a gluon and the mystery particle. Since the gluon is a boson, it has
a baryon number of zero. Therefore, to conserve the baryon
number of the down quark, X must also be a quark. All that’s left now is to determine
which quark.
The only other clue we have as to
the identity of X is that it participates in the interaction at this vertex where we
conserved the baryon number. Since the particles at this vertex
are two quarks and one gluon and the gluon is the boson that mediates the strong
force, this vertex must represent a strong interaction. Recall that the strong interaction
affects particles with color charge like quarks and gluons and can only change the
color charge of quarks, not their type. Interactions that change quark type
are weak interactions and are mediated by W and Z bosons.
So, although we don’t know the
color charges of the down quark entering the vertex or the gluon and the particle X
leaving the vertex, we know that whatever type of quark enters the vertex must be
the type of quark that leaves the vertex. Since the quark entering the vertex
is a down quark, the quark leaving the vertex, namely, the particle X, must also be
a down quark.
It’s interesting to note that we
arrived at this answer that X is a down quark not by knowing what the strong
interaction did do to the down quark, but by knowing what it didn’t do. That is to say, by knowing that the
only thing that the strong interaction could have done to this down quark is change
its color charge, we were able to deduce that it did not change the quark type.
