What quark mass to use in energy conservation? I am looking into energy conservation within decay processes and am getting confused about which mass I need to use for quarks. For example to determine if the reaction:
$$\mu^{-}\rightarrow \nu_\mu+q +\bar q$$
takes place we need:
$$m_\mu \gt 2m_q$$
but what mass/energy should I use for $m_q$? From what I have read the constituent mass seems the most sensible but I am not sure and sources seem to be lacking in this area. Please can someone explain.
 A: The word constituent is a clue:

According to the Feynman diagrams, constituent quarks seem to be 'dressed' current quarks, i.e. current quarks surrounded by a cloud of virtual quarks and gluons. This cloud in the end explains the large constituent-quark masses.
Definition: Constituent quarks are valence quarks for which the correlations for the description of hadrons by means of gluons and sea-quarks are put into effective quark masses of these valence quarks.
The effective quark mass is called constituent quark mass. Hadrons consist of 'glued' constituent quarks. The use of positions for the light constituent quarks is not exactly unproblematic in the description of hadrons.

So it is a quark mass definition useful when considering quarks in the bag of hadrons.
Valence quarks

The quarks that determine the quantum numbers of hadrons are called valence quarks;

.....

Two terms are used in referring to a quark's mass: current quark mass refers to the mass of a quark by itself, while constituent quark mass refers to the current quark mass plus the mass of the gluon particle field surrounding the quark.[71] These masses typically have very different values. Most of a hadron's mass comes from the gluons that bind the constituent quarks together,

The current  quark masses are part of the standard model of particle physics, as written in the particle table and are used in calculations with the Lagrangians .
The reaction you are studying could not have constituent masses because the quarks are not in a bound hadron, thus it has to be the current quark masses written in the particle table.
The smallest constituent mass is  336 MeV (model dependent) . The mass of the muon is 105 MeV.  No choice
The charged pion, the smallest hadron, composed also, as in your reaction, out of a quark and an antiquark, has a mass of 139 MeV, so in actuality your problem is not a description of a physical system, since an 105 MeV muon cannot emit bound quarks of 139 . So even if the energetics work with the current masses the two quarks cannot be a bound pion and since quarks are never free this reaction cannot go by itself. It could go in a quark gluon plasma, even in a secondary interaction with a heavy nucleus.
