# What is mass splitting?

1. Jan 20, 2012

### PCSL

Could someone please explain to me what mass splitting is or ideally provide me a link so I could read about it. Also, how is it related to dark matter or Universal Extra Dimensions Theory?

Thanks for any help (I tried google and got nothing).

Last edited: Jan 20, 2012
2. Jan 20, 2012

### Bobbywhy

PCSL, Have you tried a Google search for "mass splitting"? I did and within a few milliseconds I found many many articles, technical papers, etc. concerning this subject.

3. Jan 20, 2012

### PCSL

None explain what it is. The term is used and not defined in all those articles. If I am wrong could you please provide me with an example.

4. Jan 20, 2012

### Bobbywhy

“Neutrino Mass, Mixing, and Flavor Change”

“The evidence that neutrinos change from one flavor to another is compelling [1]. Barring exotic possibilities, neutrino flavor change implies neutrino mass and mixing. Thus, neutrinos almost certainly have nonzero masses and mix.

That neutrinos have masses means that there is a spectrum of three or more neutrino mass eigenstates, ν1, ν2, ν3, . . .. That neutrinos mix means that the neutrino state coupled by the charged current weak interaction to the W boson and a specific charged lepton (such as the electron) is none of the neutrino mass eigenstates, but rather is a mixture of them."

http://arxiv.org/abs/hep-ph/0211134

and here are many scholarly articles about "neutrino mass splitting"

Last edited: Jan 20, 2012
5. Jan 20, 2012

### PCSL

Thank you for trying but I'm still not getting it. Could you post along the lines of mass splitting is ______.

6. Jan 21, 2012

### Chronos

... neutrino mass, mixing and flavor change works for me.

7. Jan 21, 2012

### Bobbywhy

I don’t pretend to know what mass splitting is; it seems to be really complicated. The subject of the below article is mass splitting. Hopefully you will find your answer in this and its references.

“Meson-loop contributions to the rho-omega mass splitting & rho charge radius”

“In a fully-interacting theory, the number of constituents of a hadron is not conserved, and the picture of a hadron as being comprised of three quarks (baryon)
or a quark and antiquark (meson) is na¨ıve. One way to go beyond a picture in which hadrons are simple bound states of valence quarks is to consider their mixing with multiple-hadron states. The success of models which describe
hadrons in terms of only a few degrees of freedom, such as the constituent-quark model, suggests that mixing with multiple-hadron states should represent only a
small correction to the predominant valence quark structure of the hadron.

Some observables may be sensitive to contributions that arise from mixings of hadrons with multiple-hadron states. These observables would provide a means to
probe the structure of hadrons beyond that of the valence quarks. One such observable is the mass splitting between the ρ and ω mesons, which is the subject of this article.”

arXiv:nucl-th/9904079

8. Jan 21, 2012

### Staff: Mentor

I'm with PCSL on this one. Browsing through many of those links doesn't really help me understand.

9. Jan 21, 2012

### PCSL

I can access the link too it is just that it is too technical for me to understand. Thanks for everyone who has replied thus far - I hope someone sees this thread that can help me out.

10. Jan 21, 2012

### Chronos

They are exploring a specific element of the mixing thing. It is highly technical, and not for the faint of heart. They are trying to link p with w masses. Note this article is over ten years old, which is ancient by particle physics standards.

11. Jan 21, 2012

### Staff: Mentor

Something to do with not being able to directly measure certain particle masses, such as quarks?

12. Jan 21, 2012

### PCSL

I've been reading all day trying to figure this out and all I've really learned is that it pertains to not being able to measure certain particle masses (as Drakkith said above). Its amazing how often mass splitting is referenced yet a definition is never given.

13. Jan 22, 2012

### Bobbywhy

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 [Broken]

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

Last edited by a moderator: May 5, 2017