Thursday, May 28, 2015

Update to Post on Neutrino Mixing: Visualizing CP violation

In this post, I'll be updating a graph I made last year in a post on the PMNS matrix.
The reason for the update is that there was a recent announcement by the T2K research group of a measurement of anti-muon-neutrinos converting into other anti-neutrino species. I'd like to first show a plot from their recent presentation in which they show the uncertainty in both the 2-3 mixing angle and the 2-3 mass difference.
As can be seen in their figure on Slide 48, the data is entirely consistent with the 2-3 mixing angle being the same for neutrinos as anti-neutrinos. This is a good sign that the mixing angle for anti-neutrinos is the same as for neutrinos; but note that this is also compatible with there being a CP violating phase. In fact, the best fit value for T2K data plus Particle Data Group 2014 data yields a value of the CP violating phase that is close to -90 degrees. What's interesting with these new estimates for the 4 parameters of the PMNS matrix is that (a) the summation of the angles is close to zero (within error) and (b) summation of each of thetas is close to 90 degrees (within error.)



T2K 2015 summary             
Angle (Radians) (Degrees) Sin2(θ) Sin2(2θ)
θ12 0.584 33.5 0.304 0.846
θ13 0.158 9.1 0.0248 0.097
θ23 0.812 46.5 0.527 0.997
δCP -1.55 -88.8
SUM 0.00 0.0

The PMNS corresponding to these values can be visualized using Wolfram Alpha by clicking on the site below:

The 1-sigma uncertainty around the δCP term is approximately -90 +/- 90 degrees. This means that there is a good chance that the value of  δCP is between -180 and 0 degrees, and this also means that there is a really good chance that the exp(i*δCP) is non-real, which means that there can be CP violation due to neutrino mixing.

So, using the data above, I've re-evaluated the eigenvalues and determinant of the PMNS maxtrix. I think that the eigenvalues way of viewing this data is better than listing the 4-parameters because one can visualize how close the eigenvalues are to the unit circle. If the eigenvalues fall on the unit circle, then the PMNS matrix is the neutrino mixing is complete (i.e. the mixing is only into these states.) If eigenvalues all fall outside the unit circle, then there is growth in the total number of neutrinos, and if the eigenvalues all fall within the unit circle, then there is decay in the total number of neutrinos.
As seen below, the eigenvalues fall very close to the unit circle (especially if including uncertainty... which is not shown in the figure below...the size of the markers does not correspond to uncertainty in the value of the eigenvalues.) Using previous data, the eigenvalues fall nearly exactly on the unit circle, whereas using the T2K2015+PDG2014 data, the eigenvalues fall slightly off of the unit circle (though, within 1-sigma uncertainty.) Interestingly, one of the eigenvalues is extremely close to 1+0i. The other two eigenvalues are close to the unit circle, but far away from 1+0i. The other thing to point out is that two eigenvalues far from 1+0i are not mirror images of each other on the unit circle. The fact that they are not mirror images is a sign that there is CP violation in the PMNS matrix. If there were no CP violation, one of these eigenvalues would be the complex conjugate of the other one:  a +/- bi. The other thing to point is that the value of the determinant is using the new data is nearlly entirely Real valued and slightly less than 1  (Det=0.9505+0.001i). This is likely a sign that the values of the 4-parameters were chosen by T2K in a way that is not consistent, but there is also still the possibility that the non-unitary value of the determinant is due to the fact that there is another type of neutrino that mixes with the three main species. (This is just speculation because, as can be seen from the old wiki data, the eigenvalues fall very close to the unit circle when chosen consistently.)


Old Wiki Data
Angle(Radians)
θ120.587
θ130.156
θ230.670
δCP-2.89
SUM-1.48

Tuesday, May 12, 2015

Summary of the Case of ~ 7keV Sterile Neutrinos as Dark Matter

Update 8/15/2017

I just wrote a new post. I still think that dark matter is sterile neutrinos. However, I'm leaning now towards their masses being on the order of 10^10 GeV  (ten to the ten GeV), i.e.
For more information on the predictions of Type I Seesaw models, see this Jan 2017 arxiv manuscript by Stephen F. King. This model appears to be quite predictive as far as being able to predict the angles for neutrino mixing as well as the CP violation term, delta. The CP violation term is very nearly equal to -90 degrees, which means near maximal CP violation.



Original Post
A resonantly-produced-sterile-neutrino-minimal-extension to the SM is entirely consistent with all known particle physics and astrophysics data sets. Such  a SM-extension means that there could only be a small number of adjustments required to the StandardModel of Particle Physics (SM) in order for the SM to explain all astrophysics data sets, i.e. to explain dark matter, dark energy and inflation. What could such a RP-sterile-neutrino-SM-extension model look like:

(1) There are no new particle-classes to be discovered (other than nailing down the mass of the light, active neutrinos and the heavier, sterile neutrinos)

(2) Not counting spin degeneracy: There were likely 24 massless particles before the electro-weak transition. After this transition, some of the particles acquire mass, and the symmetry is broken into:
1 photon, 3 gauge bosons (W+ / W- / Z ) and 8 gluons   (12 Integer spin bosons in total)  
6 quarks, 6 leptons, i.e. electron / neutrinos   (12 Non-integer spin fermions in total)

Note that 24 is the number of symmetry operators in the permutation symmetry group S(4) and the classes within the S(4) symmetry group have sizes 1,3,8 (even permutations) and 6,6 (odd permutations.)  This is likely not a coincidence. Given that there are 4 (known) forces of nature and 4 (known) dimensions of spacetime, the S(4) symmetry group is likely to appear in nature. (See Hagedorn et al. 2006)

(3) Higgs scalar field is the inflaton field required to produce a universe with: (a) near zero curvature (i.e. flat after inflation), (b) Gaussian primordial fluctuations, (c) scalar tilt of ~0.965 for the fluctuations, (d) a near-zero running of the scalar tilt, (e) small, but near zero tensor fluctuations, and (f) no monopoles/knots.

(4) The sum of the rest mass of the squared of the SM bosons is equal to the sum of the rest mass of the squared of the SM fermions, and that the sum of these two is equal to rest mass squared equivalent energy of the Higgs Field. In other words, during the electro-weak transition in which some particles acquire mass via the Higgs mechanism, half of the rest mass squared energy does towards bosons (H, W, Z) and half goes to fermions (e, ve,  u, d, etc...). If this is the case, then there are constraints on the mass of any sterile neutrinos. In order to not effect this "sum of rest mass squared" calculation, the rest mass of any sterile neutrinos must be less than ~10 GeV. A keV sterile neutrino would have no effect on this "sum of rest mass squared" calculation.

So, it is entirely possible that there is no new physics (outside of the neutrino sector), provided that (a) the Higgs scalar field is the inflaton field, (b) sterile neutrinos are the dark matter particles, and (c) light active neutrinos are the cause of what we call dark energy. In the rest of this post, I summarize the case for ~7 keV resonantly-produced, sterile neutrinos as the main dark matter candidate. Note: some of these points, related to (b), can be found in the following papers by de Vega 2014 and Popa et al 2015.

Tuesday, May 5, 2015

Mysterious Cold Spot in the CMB: Still a mystery

Summary: A research group has recently suggested that a supervoid can explain the Cold Spot in the CMB. The problem is that a supervoid (via the ISW effect) can't explain the actual Planck TT data.

There has been a lot of attention over the last decade to a particularly large Cold Spot in the CMB, as seen both by WMAP and Planck (Image from this article.) Though, the Cold Spot is somewhat hard to see in the Planck data without a circle around it because there are so many "large-scale cold spots." The mystery behind the famed Cold Spot in the CMB is that the cold region is surrounded by a relatively hot region, and there is a difference of ~ 70 µK between the core of the cold spot and the surround region. Typical variations between locations these small is only 18 µK.


The two images directly above are from Planck 2015 results. The top of these two figures is the poliarization data, and the bottom of the top is the temperature data. Note that the scale goes from -300 µK to +300 µK.

While this new finding of a massive, supervoid of galaxies in the region near the Cold Spot is interesting, it should and has already been be pointed out that such a supervoid can't explain the ∼ -100 µK cold spot in the CMB via the standard ISW effect. As stated in the article "Can a supervoid explaint he Cold Spot?" by Nadathur et al., a supervoid is always disfavoured as an explanation compared with a random statistical fluctuation on the last scattering surface. There's just not enough of a void to explain the Cold Spot because the temperature would only be ∼  -20µK below the average temperature due to the late-time integrated Sachs-Wolfe effect (ISW.) Nadathur et al. state, "We have further shown that in order to produce ∆T ∼ −150 µK as seen at the Cold Spot location a void would need to be so large and so empty that within the standard ΛCDM framework the probability of its existence is essentially zero." The main argument against the supervoid-only explanation can be seen in the Figure by Seth Nadathur on his blog post regarding the paper he first-authored on this topic.