PCSL, your question “What is mass splitting?” is a real challenge for me. Although I cannot provide an answer I have tried diligently to find one. Below are fourteen search terms I have tried. As you have said, nobody explains exactly what mass splitting means!
mass splitting in chiral perturbation theory
spin-symmetry breaking
nucleon-delta mass splitting
delta-nucleon mass splitting
Dirac neutrino
Majorana mass terms
neutrino mass eigenstates
Mikheyev-Smirnov-Wolfenstein (MSW) effect
squared-mass splitting
solar mass splitting
atmospheric mass splitting
effective mass splitting
Landau mass splitting of neutron and proton in neutron-rich matter
Dashen’s theorem
Also, I have scanned about fifty papers to no avail. Here are excerpts from three articles that describe how mass splitting is used. These may bring us closer to understanding of your OP question, but NO explanation of exactly what it is:
Assuming that neutrinos do have mass, we have to understand why they are
nevertheless so much lighter than the charged leptons and quarks. The most
popular explanation of this fact is the “see-saw mechanism” [1]. To understand
how this mechanism works, let us recall that, unlike charged particles, neutrinos
may be their own antiparticles. A neutrino which is its own antiparticle consists
of just two states with a common mass: one with spin up and one with spin down.
Such a neutrino is called a Majorana neutrino. By contrast, a neutrino which is
distinct from its antiparticle consists of four states with a common mass: the spinup
and spin-down neutrino, plus the spin-up and spin-down antineutrino. This
collection of four states is called a Dirac neutrino. In the see-saw mechanism, a
four-state Dirac neutrino ND of mass MD gets split by “Majorana mass terms”
into a pair of two-state Majorana neutrinos. One of the latter neutrinos, νM,
has a small mass Mν and is identified as one of the observed light neutrinos.
The other, NM, has a large mass MN reflecting the high mass scale of some new
physics beyond the Standard Model, and has not been observed. The character
of the breakup of ND into νM and NM is such that MνMN ∼= M2D.
Now, it is reasonable to expect that the mass MD of the Dirac particle ND is of the same
order as the typical mass, Mℓ or q, of the charged leptons ℓ and quarks q, since the
latter are Dirac particles as well. Then, MνMN ∼ M2 ℓ or q. With Mℓ or q a typical charged lepton or quark mass and MN very large, this “see-saw relation” explains why Mν is very small. Very importantly, the see-saw mechanism predicts that neutrinos are Majorana particles.
http://arxiv.org/abs/hep-ph/9906244
The results from the Super Kamiokande experiment on the leptons observed in the atmospheric showers of particles stimulated by cosmic rays incident on the top of the atmosphere seem to clearly indicate that the muon neutrino exhibits oscillatory behavior. In particular, the flux of muon neutrinos in the showers is well below the expected flux, while the flux of electron neutrinos is consistent with expectations. Likewise the results for solar neutrinos, e.g., the combined results from SNO and Super-K, suggest that the flux of low energy electron neutrinos from the “known” nuclear physics at the center of the sun is approximately 50% of that expected. This situation is again most easily explained in a scenario where the electron neutrino oscillates into a different flavor with too little energy to interact on the Earth via the charged current (i.e., too little energy to produce the corresponding charged lepton). Both results suggest that at least two of the neutrinos have nonzero masses. As we will see shortly the oscillation process is actually sensitive to the mass splitting between the neutrino mass eigenstates and these two measurements suggest two quite different scales for the two measured oscillation scenarios. The atmospheric air shower data suggest that the muon neutrino oscillation (into something other than the electron neutrino) is characterized by . The solar neutrino data, on the other hand, describe the oscillations of electron neutrinos (into something else) with a implied mass splitting of order.
http://courses.washington.edu/phys55x/Physics%20558_lec12.htm
Effective mass splitting of neutron and proton and isospin emission in heavy-ion collisions
Authors:Zhao-Qing Feng
Within the framework of an isospin and momentum dependent transport model, the emissions of isospin particles (nucleons and light clusters) squeezed out in heavy-ion collisions are investigated as probes of the poorly known symmetry energy at high baryon density. Two different mass splittings of neutrons and protons in nuclear medium as $m_{n}^{\ast}>m_{p}^{\ast}$ and $m_{n}^{\ast}<m_{p}^{\ast}$ are used in the model and their influence on the isospin emission in heavy-ion collisions is discussed thoroughly.
http://arxiv.org/abs/1110.1515
