User:JWSchmidt/Neutrino
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Purpose of this page
Make a table just for the Neutrino oscillation page.
Neutrino table
I want this table to go to the right of the text about neutrino types that is already on the Neutrino oscillation page.
| Fermion | Symbol | Mass** | |||||
|---|---|---|---|---|---|---|---|
| Generation 1 (electron) | |||||||
| Left Handed Electron neutrino | <math>\nu_e<math> | < 50 eV | |||||
| Left Handed Electron antineutrino | <math>\nu_e^c<math> | < 50 eV | |||||
| Generation 2 (muon) | |||||||
| Left Handed Muon neutrino | <math>\nu_\mu<math> | < 0.5 MeV | |||||
| Left Handed Muon antineutrino | <math>\nu_\mu^c<math> | < 0.5 MeV | |||||
| Generation 3 (tau) | |||||||
| Left Handed Tau neutrino | <math>\nu_\tau<math> | < 70 MeV | |||||
| Left Handed Tau antineutrino | <math>\nu_\tau^c<math> | < 70 MeV | |||||
Currently, the solar neutrino problem is believed to have resulted from an inadequate understanding of the properties of neutrinos. According to the Standard Model of particle physics, there are three different kinds of neutrinos (see table to right):
- electron-neutrinos (which are the ones produced in the sun and the ones detected by the above-mentioned experiments),
- muon-neutrinos and
- tau-neutrinos
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** - Mass is really a coupling between a left handed fermion and a right handed fermion.
- For example, the mass of an electron is really a coupling between a left handed electron and a right handed electron, which is the antiparticle of a left handed positron.
- In the case of neutrinos, there are large mixings in their mass coupling, so it's not accurate to talk about neutrino masses in the flavor basis or to suggest a left handed electron neutrino and a right handed electron neutrino have the same mass as this table seems to suggest.
Complete table
| Fermion | Symbol | Electromagnetic charge | Weak charge (as a representation)* | Weak isospin | Hypercharge | Strong charge (color) (as a representation)* | Mass** |
|---|---|---|---|---|---|---|---|
| Generation 1 | |||||||
| Left Handed Electron | <math>e<math> | -1 | 2 | -1/2 | -1/2 | 1 | 0.511 MeV |
| Left Handed Electron neutrino | <math>\nu_e<math> | 0 | 2 | +1/2 | -1/2 | 1 | < 50 eV |
| Left Handed Positron | <math>e^c<math> | 1 | 1 | 0 | 1 | 1 | 0.511 MeV |
| Left Handed Electron antineutrino | <math>\nu_e^c<math> | 0 | 1 | 0 | 0 | 1 | < 50 eV |
| Left Handed Up quark | <math>u<math> | +2/3 | 2 | +1/2 | +1/6 | 3 | ~5 MeV *** |
| Left Handed Down quark | <math>d<math> | -1/3 | 2 | -1/2 | +1/6 | 3 | ~10 MeV *** |
| Left Handed antiUp antiquark | <math>u^c<math> | -2/3 | 1 | 0 | -2/3 | <math>\bar{3}<math> | ~5 MeV *** |
| Left Handed antiDown antiquark | <math>d^c<math> | +1/3 | 1 | 0 | +1/3 | <math>\bar{3}<math> | ~10 MeV *** |
| Generation 2 | |||||||
| Left Handed Muon | <math>\mu<math> | -1 | 2 | -1/2 | -1/2 | 1 | 105.6 MeV |
| Left Handed Muon neutrino | <math>\nu_\mu<math> | 0 | 2 | +1/2 | -1/2 | 1 | < 0.5 MeV |
| Left Handed antiMuon | <math>\mu^c<math> | 1 | 1 | 0 | 1 | 1 | 105.6 MeV |
| Left Handed Muon antineutrino | <math>\nu_\mu^c<math> | 0 | 1 | 0 | 0 | 1 | < 0.5 MeV |
| Left Handed Charm quark | <math>c<math> | +2/3 | 2 | +1/2 | +1/6 | 3 | ~1.5 GeV |
| Left Handed Strange quark | <math>s<math> | -1/3 | 2 | -1/2 | +1/6 | 3 | ~100 MeV |
| Left Handed antiCharm antiquark | <math>c^c<math> | -2/3 | 1 | 0 | -2/3 | <math>\bar{3}<math> | ~1.5 GeV |
| Left Handed antiStrange antiquark | <math>s^c<math> | +1/3 | 1 | 0 | +1/3 | <math>\bar{3}<math> | ~100 MeV |
| Generation 3 | |||||||
| Left Handed Tau | <math>\tau<math> | -1 | 2 | -1/2 | -1/2 | 1 | 1.784 GeV |
| Left Handed Tau neutrino | <math>\nu_\tau<math> | 0 | 2 | +1/2 | -1/2 | 1 | < 70 MeV |
| Left Handed antiTau | <math>\tau^c<math> | 1 | 1 | 0 | 1 | 1 | 1.784 GeV |
| Left Handed Tau antineutrino | <math>\nu_\tau^c<math> | 0 | 1 | 0 | 0 | 1 | < 70 MeV |
| Left Handed Top quark | <math>t<math> | +2/3 | 2 | +1/2 | +1/6 | 3 | 178 GeV |
| Left Handed Bottom quark | <math>b<math> | -1/3 | 2 | -1/2 | +1/6 | 3 | ~4.7 GeV |
| Left Handed antiTop antiquark | <math>t^c<math> | -2/3 | 1 | 0 | -2/3 | <math>\bar{3}<math> | 178 GeV |
| Left Handed antiBottom antiquark | <math>b^c<math> | +1/3 | 1 | 0 | +1/3 | <math>\bar{3}<math> | ~4.7 GeV |
Fottnotes
* - These are not ordinary Abelian charges which can be added together but labels of Group representations of Lie groups.
** - Mass is really a coupling between a left handed fermion and a right handed fermion. For example, the mass of an electron is really a coupling between a left handed electron and a right handed electron, which is the antiparticle of a left handed positron. Also neutrinos show large mixings in their mass coupling, so it's not accurate to talk about neutrino masses in the flavor basis or to suggest a left handed electron neutrino and a right handed electron neutrino have the same mass as this table seems to suggest.
*** - What is actually measured experimentally are the masses of baryons and hadrons and various cross section rates. Since quarks can't be isolated because of QCD confinement, the quantity here is supposed to be the mass of the quark at the renormalization scale of the QCD phase transition. In order to compute this quantity, physicists have to set up a lattice model and try out various masses for the quarks until the model comes up with a close fit with experimental data. Since the masses of the first generation quarks are significantly below the QCD scale, the uncertainties here are pretty large. In fact, current QCD lattice models seem to suggest a significantly lower mass of these quarks from that of this table.