Faster than light neutrinos, A possible solution

I've been a few weeks late to comment on CERN's OPERA experiment's paradigm breaking result, that neutrinos travel faster than light (nature), (orignal paper). Initial skeptism has not lead to any resolution of the result via mis-measurement. The excess is in speed measured is small, three thousandth of a percent, the muon neutrinos, crossing the 732 kilometers from the CERN lab where there created to the OPERA neutrino detector in Italy, some 60 nanoseconds earlier than the light would have done. OPERA quote a 6 sigma statistical significance and the results do match with earlier measurement at the MINOS experement at Fermilab. The quoted speed at OPERA is (v − c)/c = [+2.48 ± 0.28(stat) ± 0.3(syst)] × 10−5.

Standard Special Relativity does allow for particles that travel faster than light, know as tachyons, they obey the standard equations of relativity except they have negative squared mass, another words imaginary mass in the sense of complex numbers. Allowing Tachyons however cause quantum field theory to be unstable, describing a vacuum that would decay. More over the OPERA results do not fit standard tachyons, the tachyon mass of the neutrino would be i*120MeV in gross contrast to the measured neutrino mass, and also tachyons travel slower with increasing energy, nearer the speed of light from above at infinite energy, and traveling infinity fast when the have zero energy. OPERA in fact notice a constant speed for neutrinos across a doubling of energy from 17 to 35 Gev. While vacuum stability might be saved by the handedness (chirality) of neutrinos, empty space emitting a back to back pair of an neutrino and an anti-neutrino would violate spin conservation by one unit, due to the neutrino being left handed while the anti-neutrino is right handed. Thus a field theory of tachyonic chiral neutrino might be stable while it would be unstable for normal particles. However such a theory still would not fit the OPERA results.

Moreover neutrinos in empty space do not apear to be superluminal. When the supernova SN1987A exploded in the large Magellanic could the neutrinos where detect to arrive some 3 hours before the light. This might seem superluminally however the light is delayed by traveling though the stars core. If the neutrinos traveled at the OPERA speed, they would have arrived some 4.5 years earlier.

In order to achieve a resolution of the OPERA result compatible with both quantum field theory and the light speed measurement of the supernova neutrinos. It is necessary to find a theory where the speed of propagation of neutrinos is faster than light only in the presence of a matter field. In fact quantum field theory can vary the speed of light depending on the energy density of the QED vacuum, a result found in 1994 by Latorre, Pascual and Tarrach. Given a vacuum energy density of ρ. The speed of light is modified to.

$$ v = 1 - {44/135} α^2 {ρ/m_e^4} $$

In unit where c=hbar =1.

In keeping with our axial force, the same formula should carry over to the speed of axi-photons and the maximum speed of neutrinos (approached as the neutrino speed became very much greater than there rest mass time c squared). The electron mass in the formula would replaced with the mass of the lightest neutrino, and alpha with the axial coupling constant, which we predicted was some 60 times smaller the than alpha in QED.

$$ α_ν =~ {1/137} * {1/60} =~ 0.121*10^{-4}$$

The mass of the lightness neutrino is unknown, but we estimated to be 0.14 milli-electron volts in order to produced dark energy. This would lead to a negative energy density of

$$ ρ = -2*10^{-12} (eV)^4 = -2 (meV)^4 $$

Interestingly this is in the same region as the observed figure of dark energy density in cosmology about 3 (meV)^4, however dark energy is still a positive energy density, only the pressure need be negative, representing a self attracting fluid. The standard speed of supernova neutrinos further would imply that the these is no dark energy in the local region of our galaxy, stellar radiation must blow the region clear of any dark energy. Since no expansion of trapped galactic cluster is observed this is very compatible with cosmology.

In ordinary situations the QED and QAD vacuum energy would be both zero for empty space, and for matter depend quite separately upon the electron density and columb potential and the neutrino density and axial potential. We have already shown that ordinary matter would contain a background sea of neutrinos necessary to cancel the axial charges of the nuclei of atoms, and this background sea would be bound to nuclei with some energy density. From the above we have
around 1 nano eV per cubic nanometer. A binding energy this small, requires a light bosonic particle carrying the axial force, with an rest mass not much larger than the neutrino.

In our paper we have shown that, Neutrino scattering on the the background sea, is strongly suppressed at high energies, falling as $(m_v/E)^2$. The neutrino speed would approach approach the modified speed as $1-(m_v/E)^2$, Thus in the earth between CERN and OPERA, the measured speed would be the modified speed of axi-photons, given the axial binding energy density. An experiment demonstrating the axial force nature of the superluminal speed of neutrino could be produced, by vary the composition of material the neutrinos travel through. The excess speed would vary as bind energy density, which would vary as the atomic number density of the matter passed.

Evidence for dark radiation

I've just read this paper which looks deeply at the cosmic background radiation, and up dates our estimate for number of light (low mass) particles around the time of the big bang. The data clearly shows the equivalent of 4 neutrino species. This provides evidence for at least one unknown low mass particle, perhaps an additional low mass right handed neutrino, or any light scalar or vector super-symmetric neutrino as speculated about below. To be clear a axi-photon would not show up in the radiation count from CMB, because the axi-photon rapidly interacts with neutrinos to pair produce further neutrinos, as show in my paper. For temperatures belows a few MeV, almost no axi-photons would be present in the radiation count.

Tevatron finds top/anti-top asymmetry sign of axi-gluons?

Fermilabs Tevatron particle accelerator has found a mysterious asymmetry in high energy collisions that produce pairs of top and anti-top quark. It seems that the at high energies there is a preference for which direction the top quark quark is produced travelling towards. The standard model predicts no or little such asymmetry, if the result continues to be confirmed, new physics and possibly new particle will be required to explain it. The measurement has a been around for over a year, having already grown from a 2.6 sigma signal a year ago to a 4 sigma signal in June 2011. Physicists normally like to have a 5 sigma signal to confirm a result, unfortunately the Tevatron is at the end of its life, and since the LHC collides proton against protons, and not protons against anti-protons, it will be difficult to get more data to confirm the result.

This hasn't stopped a large crop of papers looking to explain the result with new physics as summarised in ArXiv:1107.0841. A recent model I was particular fascinated by is one where the asymmetry is caused by an axigluon, as described most recently by Tavares and Schmaltz. Gluons are the gauge boson holding quarks together and normally act vectorially, identically to left and right handed particles, however a axigluon that acts exactly oppositely on left and right handed particles is also possible. To explain the top anti-top forward backward asymmetry an octet of axigluons with mass of around 450 GeV is introduced. They then also required doubling the number of quark, adding vector like pairs of quarks, that then decay rapidly by axigluon exchange. Their model contains exactly the extra quarks, I introduced to cancel the anomalies in adding a neutrino interacting axi-photon to the standard model, and in fact looks similar to the E6 model I described below. A axigluon explanation of the top and anti-top asymmetry, would be then very supporting of axial force theory, which is perhaps why I've biasedly am attracted to it. The LHC should however soon be able to confirm or disprove such an axigluon model. So time will tell.

Symmetry Breaking, Groups E8 and E6

Reviewing articles at ArVix its come to my attention, that most popular super-symmetry and String phenomenologist aren't choosing the right models of symmetry breaking, ignoring classic papers, and proofs, just so they can use too easy but wrong models to fit Higgs bosons into a grand unified theory of the universe. In particle physics a phenomenologist is a physicist that tries to make the bridge between mathematical elegant models produced by theorists, and the experimental results. Because theories like super-symmetry and super-gravity are so remote from practical energy scales and can produce so many different result depend upon how our universe has broken these symmetries, phenomenology is very difficult subject, but it is perhaps the most important, it is where theory lives or dies depending on weather it describe a universe looking like our universe.

The most popular models start with string theory or supergravity which only allows certain mathematical groups to produce self consistent theories. In particular group E8 * E8, is often the starting point. This leads to two copies of matter in the universe so presumably mirror matter should be a favourite model of the missing matter in the universe. In fact mirror matter is only relatively vary investigated though it still looks very consistent with the DAMA and Cogent observations. E8 is particularly nice because choosing it automatically gives the three generations of quarks and leptons share the same forces, as observed, and describe by the standard model. E8 also is the biggest finite lie alegebra (248 roots), and self adjoint, meaning it contains both the groups needed to represent particles and forces in the same represention. That makes is automatically super-symmetric, you get 248 spin-1 force carriers and 248 spin-1/2 particles, see Steven L. Adlers classic paper: . What you don't get is any scalar bosons, so your Higgs particles have to be composites condensing out of the particles that are attracted to themselves with such strength that the lowest energy state of the vacuum contains a sea of these particles. Breaking E8 to three generations of a smaller group E6.

Now E6 has 27 particles its fundamental representation, and when you ask how it breaks symmetry by vacuum condensing, the computation been done and its either $E6 -> F4 * U(1) $ but with every force carrier picking up a mass (clearly not our universe), or $E6 -> SU(2) * SU(6), 27 -> 15 + 12$. The vacuum condensation is complicated enough that it was to be done in simulation by a computer, but the result stands. And do phenomenologists use it? no they don't, again and again they break E6, to SO(10)*U(1), and them have Higgs bosons, (doublets) in the group. Somehow they of they own choice have added scalar multiplets to the models that isn't suppose to have scalars in it, and further, have choosen SO(10) just because its a favourite GUT model, (not one that works, as it predicts faster proton decay than could be real without it have been measured by now. In fact SO(10) is a left-right symmetry theory, while E8 is left-right symmetric and E6 is chiral (chooses a particular direction), so when phenomenologists use E6->SO(10), have broken parity, unbroken it, and rebroken it at second time along there trail. This seem to happen because they of course start with a popular model and see what happens down the trail to low-energy, forgetting what made the popular model, popular in the first place.

To my mind, and using a axial-force, E8, contains U(2) left , U(2) right which will eventually break to U(1)_em, U(1)_axial, SU(2)_left weak force, SU(2)_right, breaking at the same time as 3 seperate generations of particles has formed., then E6 has SU(3) color, U(1)_axial, U(1)_em and SU(2)_left weak force in its SU(6), leaving a SU(2) grouping splitting E6 into the 15 known particles of the standard model grouped into left handed and right handed E6 multiples, and 12 extra quarks grouped into particle and anti-particles multiplets. All the anomalies of U(1)_em and U(1)_axial cancel in this representation, which I wouldn't have found, if I wasn't so keen on having a U(1) axial force. The extra vector-like quarks (i've called terra quarks, borrowing the name from different model by Gamor), then need to gain extra mass, and may form a left-right symmetry breaking condensate reacting with the generation permuting right handed neutrinos that appear when breaking E8 to E6. We have a rather complex vacuum condensate, which will need computational analysis, instead of a standard model Higgs, so phenomological prediction won't be easy from this model, but it does follow the spirit of E8 down to low energy, and doesn't introduce ad hoc scalars, but compute scalar condensates them from first principles. I'm blogging to try and promote this model to someone with the time to compute it.

Neutron Scattering and Fifth Forces

I regularly read ArXiv for reports on the experimental limits on Fifth Forces. But this on I missed up to now. Neutron Scattering is regularly performed on every material under the sun, and in neutron scattering, scientist clearly see point like scattering from the strong force of a nucleus, giving very clear scattering from a collation of femtoscopic points. What scatterers don't see is any scattering from long range $1/r^2$ type columb forces. This clearly limits strongly any fifth force felt by neutrons. Unfortunately the one paper producing limits on fifth forces from neutron scattering is the R. Barbieri and T.E.O. 1975, and they start there calculation from a parameterised best fit to scattering from a Russian experiment done in 1966. Another words, the experiment hasn't been done with a good level of statistical checking. However thinking about its very clear that a massless force with strength 100-1000 time weaker than the electromagnetic force is clearly and obviously excluded by neutron scattering experiments, it would stand out like a sore thumb.

Where does this level fifth forces in general, and in particular our axial force. First B-L forces which act between all known particles are clearly excluded, saying goodbye to B-L chameleon force. In describing our axial force we could not see any way to pin down the particular charges on a proton or neutron, and w guessed at +1/2 for a proton and -1/2 for a neutron as that would be symmetrical and prevent proton decay. However we cannot rule out a charge on 0 on a neutron and 1 on a proton. Thus our axial force remains viable with these charges, we still have requirement that some light charged scalar or vector fields (mass around a few eV) exists to prevent Fermi energy from becoming too great. With both light scalars and neutrinos as light charged fermions under a fifth force, chameleon like behaviour should screen any axial force down to the nanometer scale, guaranteeing that it would not have been observed in existing experiments.

Vectrinos, the Solar Corona, and the Neutrino Sea

In my previous post, I discuss the Fermi Energy needed to allow enough neutrinos to
live inside ordinary substances, in order to balance out the effects of an axial force. Its clear, the values are just to high to be practically possible. This doesn't yet rule out the axial force, provided a scalar or vector particle with mass in the region 10meV to 1eV, exists, such a particle, would not be subject to Fermi repulsion, and could be present in whatever quantities needed to balance out the axial charges on nucleons. Scalar or Vector neutrino (normally scalar, but I find theories with fundamental scalars unattractive), are present in super-symmetric theories with unknown masses. So a super-symmetric theory might allow an axial force.

Such a particle would also help with another problem the axial force faces, Radiation
from the Sun and Stars. The hot gases in star is in thermodynamic equilibrium and as such we expect all degrees of freedom to have equal energy. Thus we would expect the Sun to radiate an equal amount of photons and axi-photons. The axi-photons would be absorbed in the Earth atmosphere, and we'd observe a Sun burning half as brightly as expected. Astronomers current calculations describe the brightness of the Sun up to a few percent either way, so a Sun radiating equal amounts of axi-photons is not credible.

Let us investigate a super-symmetric vector (spin-1) analog of a neutrino, also with +1 or -1 axial charge, with a mass in the 1 eV region ( 1eV ~13000 Kelvin). We'll call it a Vectrino. Vectrinos are more interesting to us, than sneutrinos because, an
axi-photon can easierly pair produce Vectrinos, spin 1 -> spin 1 + spin 1. Remember this is in three dimension of spin, the extra spin on the RHS of the equation, can occur if the Vectrino, anti-Vectrino pair is emitted near 45 degrees to the incoming axi-photon. The Vectrinos can further scatter producing more axi-photons. The result is that Vectrinos lead to a region, absorbing all the axi-photon and other axial energy converting it in to a region as dense in Vectrinos as pressure will allow. It will act as an opaque thermal conduction barrier, allow only standard light through.
This wouldn't happen with scalar neutrinos, where the spin 1 -> spin 0 + spin 0, is impossible, and pair production is strongly suppressed.

Our Vectrino dense region would occur in the suns chromosphere, absorbing up coming energy in a region containing little hydrogen. At the top of the chromosphere high temperature protons, attracted by the axially negative region, would supply the pressure necessary to keep the Vectrinos compressed and in place. Light would cross the region normally and find a lot few protons in the corona to be shared between. Thus we have a new explanation of solar coronal heating, which has needed one of a while, see this paper.

Our original paper, used right handed neutrinos with a mass of a around 30eV, to preform the same trick of stabilising matter against Fermi pressure, and heating the
solar corona. However I do not now believe such massive particles could exists without there decay energy, showing up, in for instance the boiling of water. Scalar or Vector particles on the other hand, would cap the Fermi energy at just below there mass. The balance of Fermi-energy, axial binding energy, and scalar mass energy, would be hidden in lab experiments.

We have saved the axial force, at the expense of adding a usually new particle. The particle belong to super-symmetry, but an unusually form of super-symmetry, and the axial force was already unknown to physics. Scientifically, our belief in the axial force must reduce accordingly. It would help if one experiment or observation definitively needed an axial force, but without that the axial force is reduced to the realm of possible but not likely or needed.

The Axial Force and the neutrino sea.

Regularly readers will know that my blog is many about the possibility of a fifth force, which acts primary between neutrinos. The strength of the force is unknown, but
can be comparatively large and still not noticeable by traditionally experimental because it doesn't interact with electrons at all. The simplest case a long force is a fully conversed charges with a massless force carrier, the axi-photon. I have not yet
investigate the case of massive force carrier, but the massive case would show up to easierly in accelerator experiments for masses ranges 137 MeV (more massive than a Pion) to 100 GeV.

If neutrinos carry this conversed charge so much protons and or neutrons, specifically the charge on the Neutron must equal the charge on a proton plus the charge on a neutrino, so that beta decay can occur. Further since both protons and neutrons can flip the spins easierly. The axial charge on a spin up nucleon is the same as that on a spin down nucleon. This is the opposite to neutrinos where by definition a right handed neutrino or anti-neutrino has the opposite axial charge to the left handed neutrino.

In any material with a axial net charge its nuclei, the axial force will collect a sea of neutrinos in order to the cancel out it the net axial charge. Since neutrinos are light this will effective screen out the axial force, and make it very difficult to observe, hence why the axial force has not yet been observed. However neutrinos are fermions can as such there is a limit to how many can be placed in a given volume of material. I make a terrible error, in my first paper. I used the wrong formule of the Fermi Energy of the neutrino sea, I used the non-relativistic, when formule when most of the neutrinos are clearly travelling near the speed of light.
The correct formula is.

$$E_F = {\h c}/{2} ({3 ρ}/{π} )^{1/3} $$

Thats the Energy of the most energetic neutrino assuming a neutrino number density of ρ The total Energy is just

$$E_T = {3/4}N E_F = {3/4} {ρ}V E_F $$

We don't need to know the strength of the axial force to calculate the Fermi Energy due to neutrinos (we assume 3 kinds as so far known). If the force isn't strong enough to bind neutrinos of the maximum (fermi) energy to the substance, then the substance will be left with an overall charge. This might lead to a detectable long range forces between substances, which might well have been observed already.

In fact the Fermi energy for most substance is rather large, assuming the axial charge is -1/2 on a proton and +1/2 on a neutron. We have.

Material	Neutrino Density $cm^{-3}$	Fermi Energy
Day Air	$1 * 10^{13} $	1.9 eV
Water	$3.34 * 10^{22} $	1.3 KeV
Uranium-238	$3.5 * 10^{24}$	4.68 KeV
Bismith	$1.78 * 10^{24} $	3.5 KeV
NaCl (Salt)	$2.7 * 10^{22} $	1.27 KeV
Pyrex Glass	$ 1.16 *10^{21} $	0.4 KeV
Palladium	$4.89* 10^{23} $	3.3 KeV
Copper	$ 2.34* 10^{23} $	2.6 KeV
Zinc	$ 1.76 * 10^{23} $	2.4 KeV
Barium Chloride	$ 2.9*10^{23} $	2.24 KeV

The total energies are thus just to high to be practicle, some 2.7 Mega Joules in one cubic centimeter of tap water.

In order to save the axial force we need to add either several sterlie neutrinos in the 1eV to 1KeV ranges, or more add scalar sneutrinos in the mass range 0.1 eV to 100eV. Scalar neutrinos would not generate any Fermi Energy at all, and would allow any density of matter. Similar arguments apply for any long ranges force that need to cancelled inside matter. For instance a chameleonic B-L (baryon number minus Lepton number) force,
again needs a light charged scalar particle in order to solve the problem of Fermi-Energy.