In reading a theoretical paper on electric dipole moments (well, OK, skimming through it looking for numbers), I ran across several Feynman diagrams with an "X" on one of the particle arrows. The caption contains the presumably-intended-to-be-helpful note "The cross denotes a mass insertion."
I have no idea what that means, and neither does the local person I ask to help me interpret such things. None of the undergrad-level nuclear/ particle texts we looked at contained an explanation, either.
This almost certainly means that it is some subtle technical point that is vastly beyond the level of knowledge that I need for the thing I was working on. Not knowing things bugs me, though, so anybody who does know what it means, and can provide or point to an upper-level-undergrad level explanation, please leave me a comment.
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Unfortunately I have very little time to answer, so this might just confuse things, but the short version is: you can use a massive propagator (like 1/(p slash - m) for a fermion), or you can use a massless propagator with the mass treated as an "insertion" (i.e. a sort of interaction that takes the particle to itself, or its chirality-flipped partner). This can be useful when you're keeping track of, say, the violation of chiral symmetry that comes from the fermion mass: m_e is a small insertion that gives you a rare process of flipping a left-handed electron to a right-handed one, for instance.
http://lmgtfy.com/?q=%22mass+insertion%22
From the top link:
The mass insertion approximation ~MIA! is often used to
simplify expressions involving supersymmetric contributions
to flavor changing neutral current processes from loop diagrams
@1â3#. The simplification is achieved by the replacement
of a sum over all possible internal propagators and the
appropriate mixing at the vertices, with a single ~small! offdiagonal
mass insertion in a basis where all gauge couplings
are diagonal. The resulting expressions are formulated in
terms of parameters which can be estimated in various supersymmetric
models.
This what results when theory is allowed to propagate without constraining empirical observations.
A mass insertion is just a two-particle vertex that comes from using a massless propagator and treating the mass perturbatively. The mass then behaves like any other vertex in the theory, except that it has only two lines, one going in and one coming out.
Obviously, this is useful mainly when the mass can be treated as a small perturbation---when it is small compared with the momenta carried along the propagators. The reason for doing this is that the a Dirac mass insertion flips the helicity of a fermion line. (In massless propagation, of course, helicity is conserved.) So in situations, such as studies of CP violation where keeping track of helicity is important, this can be a useful approximation.