Leptons as Hadrons

Updated April 2022

In "Colors as quaternions" quarks are presented as spin 1/2 particles with the quaternion units i, j, k, -i, -j, -k as colors. The conjecture is proposed that there should exist spin 1/2 particles of color 1 and -1 and that these very well could be the leptons. If we accept the conjecture, does the electron have color 1 or -1? (Quaternion units 1 and -1, is meant here.) I am unable to make calculations, but I can estimate some results.

Electrons as Baryons

1) Suppose the electron color is -1. The electron then is an antiparticle. The electron is dragged into the nucleus, the wave function of the electron in the nucleus is not entirely zero. It is normalized at zero in the nucleus, but the original wave function has some value there. The electron can react easily with one of the colors of the quarks there:

i * -1 = -i

j * -1 = -j

k * -1 = -k

The electron and the quark merge via the strong nuclear force to one quark of opposite color and spin 1 or 0. A half spin can be carried off by an anti electron neutrino via the weak nuclear force. The electric charge becoms +2/3 -1 = -1/3 (merging with u-quark) or -1/3 -1 = -4/3 (merge with d-quark).

However, the anticolor of that single quark can by no means be combined with the two colors of the remaining quarks in the same baryon. It will lead to a colored end state of the baryon and that is forbidden.

So for the quark there is no other way than to re-emit the electron again long before the electromagnetic force or the weak nuclear force can perform any action. So no, any electron will not be absorbed by any quark in the nucleus, which fits in with every-day observation. Compare the black gluon at fig 3.9 at page 3 of QCD.

(Maybe problems can arise when within the same duration of 10^-23 sec 2 electrons are absorbed by one quark, 2 other electrons by the second quark and 2 electrons absorbed by the last quark of one single baryon.)

So, except for cases like 6 absorbed electrons, the elecron very well might have color -1 and be an antiparticle.

2) The positron. When the electron has color -1 then the positron has color 1. The positron is a particle. When in the nucleus absorption of the positron by a quark is inevitable. The colors become:

i * 1 = i

j * 1 = j

k * 1 = k

and this gives zero net color end states. A half spin can be carried away by an electron neutrino via the weak nuclear force.

When the d-quark absorbs the positron, the electric charge becomes -1/3 +1 = +2/3, a neutron (udd) changes in a proton (uud), or a proton (uud) changes in a delta++ (uuu) but the last possibility will cost a lot of energy. When the u-quark absorbs the positron one gets electric charge +2/3 +1 = +5/3 and together with two d-quarks in a neutron this yields still a unitary electric charge. It seems not forbidden. Although in a proton u +5/3 electric charge together with another u +2/3 and one d -1/3 yields a proton with double electric charge, and that seems forbidden. Still I hesitate to restrict to only u +2/3 and d -1/3 from the very first moment, there may be a mechanism - yet unknown - of electric charge redistribution at work.

I suppose the repulsion between the electrically positive nucleus and the also positive positron makes the contribution of the wavefunction in the nucleus very small. Most likely the positron will annihilate with an electron long before being observed in the nucleus.

3) What if the electron has color 1? Things would immediately go awfully wrong. Each of the three quark can absorb the color 1 easy, the neutrino carries away a spin 1/2.

When the u-quark absorbs the -1 electric charge, one gets +2/3 -1 = -1/3, a proton converts in a neutron, or a neutron converts to the delta-minus (ddd) which cost more energy. When the d-quark in a proton absorbs the -1 electric charge, one gets -1/3 -1 = -4/3 and together with two u-quarks this still yields a unitary electric charge (zero, that is). It seems not forbidden. When the d-quark in a neutron absorbs the -1 electric charge, this yields one d with -4/3 and one d with -1/3. This also seems not forbidden, but the introduction of different d-quarks makes situation more complicated. well, let's suppose there allways is some mechanism of electric charge redistribution at work to maintain u-quarks at +2/3 and d-quarks at -1/3.

As final result virtually all electrons would be absorbed by the nuclei within a second and that has no resemblance with observation. No, the electron cannot have color 1.

1), 2) and 3) are in nice agreement with the considerations in "The baryon number and lepton number of a black hole" at page 5 of the storyline EXPANSION OF THE UNIVERSE.

Neutrinos as Baryons

The standard model says that, except for gravitation, neutrinos can only couple to the W+, W- or Z0 particle. Neutrinos do not couple to any of the other particles, including themselves. Also according to the standard model, there only are spin +1/2 neutrino's and spin -1/2 antineutrinos. In earlier times, when one still thought the neutrinos were massless, the neutrinos were supposed to propagate at light speed. The picture then is strange but not immediately leading to contradiction. But since the neutrinos turn out to have some mass, things are different.

Suppose, for one W-particle W1 the neutrino n1 has spin +1/2 and a velocity of, let's say, half light speed. In principle n1 and W1 can couple. Then, in the frame of reference of W1, there is a second W-particle W2 that moves in the same direction as n1 but with a larger velocity, e.g. 0.9 c. In the frame of W2 n1 now moves in the opposite direction and thus has spin -1/2 and thus cannot couple to W2. So for every neutrino when there are W-particles that can couple to it, there can be found other W-particles that cannot, depending on their relative motion. This must be the picture then. The point of view that spin -1/2 neutrinos and spin +1/2 antineutrinos don't exist, leads to a different world view of W1 an W2 (not agreeing on the existing of n1) and therefore must be abandoned in the standard model.

Now for TONE. In TONE also the neutrinos would have color 1 or -1, see the text below table (4.3.6) in chapter 4 Quaternion Gravitation. A meson can be converted by W+ or W- or Z0 to an electron (lepton number 1) and an anti electron neutrino (lepton number -1). From the previous paragraph we know the electron is an antiparticle with color -1. Then the anti electron neutrino must be a particle and have color 1.

About names, personally I would favor to replace in the neutrino name anti electron neutrino by positron neutrino. Positrons have color +1 in TONE, and so has the positron neutrino.

This means that in TONE neutrinos can react with each other by the strong nuclear force. They don't glue but they can couple to each other, they can merge by the strong nuclear force to a spin 1 particle of color 1 x 1 = 1. Subsequently an extra spin of 1/2 is carried away by... a neutrino. So after all the number of neutrinos doesn't change.

A spin 1 particle of color 1 x 1 = 1, isn't that a white glueball? Well, the two neutrinos have some mass, so the merger has mass too. Does the white gluon has mass? TONE assumes not. Then the neutrino merger is not a white gluon.

Neutrinos do not really merge with any quark either. Regard in the nucleus a neutron that converts into a proton by one of its d-quarks emitting an electron and a spin -1/2 anti electron neutrino, now to be called a spin -1/2 positron neutrino. The electron has color -1 and is an antiparticle. The positron neutrino is a particle and has color 1. This, as far as color is concerned, makes the positron neutrino extremely vulnerable for absorption by any quark via the strong nuclear force, compare 2) in Electrons as baryons above. But then again, where to leave the extra spin -1/2? There is not enough energy to get rid of it by emission of an electron or heavier fermion. There is no other way than to re-emit the positron neutrino again. So yes, the positron neutrino reacts extremely easily with the quarks in the nucleus, but no, they don't stay there.

Well, that is, two simultaneous neutrinos can do the job: within one and the same 10^-23 sec two positron neutrinos happen to coincide near a quark in a proton or neutron. The two neutrinos then merge by the strong nuclear force to a spin 1 particle of color 1 x 1 = 1 that is immediately absorbed by the quark. The quark then emits the extra spin 1 by one photon. It seems possible, but doesn't sound as an easy process.

What if an u-quark in a proton emits a positron and a spin +1 electron neutrino? As argued the positron is the particle so the electron neutrino is an antiparticle and has color -1. Color -1 has no change to be absorbed by a quark, compare 1) in Electrons as baryons. Electron neutrinos don't react with the quarks in the nucleus.

So positron neutrinos (they have color 1) are observed and electron neutrinos (color -1) are not.

A new type of radiation: Neutrinophotons

In TONE is argued the gluon consists of a quark and an antiquark, massless coinciding. Also is argued the photon consists of an electron and a positron massless coinciding. Then the row can be pursued by a neutrino and an antineutrino massless coinciding to a spin 0 or spin 1 particle. A kind of photon, but not originating from electric charges and thus without internal electric or magnetic fields. This particle needs a new name. My proposal would be neutrinophoton.

The neutrinophoton would be able to decay again, but now to a muon neutrino plus anti muon neutrino, or tau neutrino plus anti tau neutrino. The neutrinophoton can convert between neutrino types, is my conjecture.

Is there a difference between a photon made of an electron and a positron, and a photon made of a muon and an antimuon? Should there be a difference between merging electron neutrinos and antineutrinos, and merging muon neutrinos and antineutrinos, or merging tau neutrinos and antineutrinos? Since mass is the only difference between the generations, and since the particle and antiparticle coincide massless, I suppose there is no difference observable.

The leptonic Higgs field

At page 5 of NET FORCE IN QED is taken a field of spin 0 photons as lepton Higgs field. At this page (page 4 of QG) the electron is proposed as possessing color black, quaternion value -1, a colorless color but nevertheless a kind of color. Why shouldn't then the electron and the other leptons gain their mass just as quarks are supposed to do, by absorbing a color-anticolor gluon pair from the vacuum? Maybe energy considerations prevail here. Maybe a color-anticolor pair of gluons take a lot of energy, yielding high mass, as is suitable for quarks. The electron as black color, the positron as white and the spin 0 photon as massless coinciding of these two offers the possibility to absorb only one spin 0 photon from the vacuum, instead of two gluons. I guess this yields a much lower mass as is desired for the electron.

If so then maybe the mass of the muon is formed when at each Higgs field absorption two photons are absorbed. However I don't immediately see a reason why this should happen all the time during the lifetime of the muon. The tauon then might absorb three spin 0 photons at each Higgs field absorption, as long as it lives. And at four spin 0 photon Higgs field absorptions the threshold mass of the lightest quark would have been crossed. From then on mass absorption can be done by the gluon pair absorptions as is used for quarks. Four spin 0 photons would have more energy than one vacuum spin 1 gluon pair. This is the conjecture, although I cannot offer a calculation to sustain this.

Mark the energy of the absorbed vacuum particles is converted to mass, that energy is not available for practical use.

The neutrino Higgs field

Maybe there is a separate neutrino Higgs field too, made of neutrinophotons where the neutrino's absorb their mass from. This depends on whether there is a measurable difference between ordinary photons with electromagnetic fields in it and neutrinophotons without such fields.