This concerns an ongoing experiment at

*Daya Bay*, near Hong Kong, set amidst no less than six nuclear reactors. These are arrayed in two clusters near two vertices of a "neutrino detection" triangle. The detector triangle itself is comprised of three separate electron anti-neutrino detectors (about 2 km each from the reactors) and which reside in water baths to unmask any cosmic ray interlopers. Each of the detectors measures the electron anti-neutrino (call it

**) flux from the reactors by recording any light flashes due to**

*-v_e***collisions within its 20 tons of liquid.**

*-v_e*Daya Bay's results proceeded basically in two related phases:

I. Small deficits of

**were previously recorded at short distances from the reactors, and it was further reported that Θ_13, the last of 3 "mixing angles" that characterize neutrino oscillation is non-zero.**

*-v_e*II. Further measurements of Θ_13 disclosed it was not only non-zero but large enough for the Daya experimenters to begin investigating neutrinos as factors in the matter-antimatter asymmetry of the cosmos.

This is big deal stuff, because cosmologists have always been perplexed by the apparent preponderance of matter in relation to antimatter in our universe. (I tried to solve this in a high school science fair project by postulating a

*separate*anti-matter cosmos that operated in the context of 'anti-time' or negative time, i.e. with the time vector negentropic as opposed to entropic)

The survival of so little antimatter in our cosmos requires a violation of what is called "CP symmetry invariance". We don't know WHY there is this asymmetry, but it may have something to do with Fitch and Cronin's (1963-64) discovery of a violation of

*CPT invariance*. (C for charge conjugation, P for parity (spatial reflection) and T for time reversal. Up until their 1960s investigations, it was widely accepted by physicists that nature played no favorites where charge conjugation, parity and time reversal were concerned. The discovery of a fundamental violation (Fitch and Cronin found a tiny fraction: 45 out of 22,700 - K2 mesons, spontaneously disintegrate into

__2 pions__, e.g.

**, (instead of the usual 3) changed all this.**

*π mesons*It was suggested by them that this CPT invariance violation might also - in some way - account for the apparent asymmetry in the distribution of matter with respect to antimatter. Since then experiments have disclosed T-invariance can be subsumed by CP symmetry invariance. Trouble is, the existence of so little antimatter still violates CP invariance. (Weak quark interactions exhibit some CP violation but too small to explain cosmological asymmetry between matter and antimatter).

Given this situation, the large value of the third mixing angle Θ_13 came to the fore. More on this now, and some quantitative details. First, contrary to the old notion that there was only one type ("flavor") of neutrino, we now know there are three: electron, muon and tau neutrinos. In effect, there must be three different corresponding neutrino masses we can call: m1, m2 and m3.

Second we now know that the three "

*flavors*" are really different superpositions (see any of my earlier 2010 blogs on quantum superpositions) of the 3 basic neutrino mass states. Moreover, and to make it more complex, we know that quantum interference between mass states means a neutrino originating in one "flavor" can transmogrify to another over its transit. Experimental confirmation of this (and over large distances) arrives from MeV neutrinos from the Sun and muon neutrinos from the high atmosphere.

Because of the oscillations and quantum interference we need to reckon in a "misalignment" between flavor and the basic neutrino masses. This is done by reference to three independent "mixing angles": Θ_12 , Θ_23 and Θ_13. To a good approximation, oscillation in any one regime is characterized by just one Θ_ij and a corresponding mass difference, defined:

delta m_ij^2 = [m_j^2 - m_i^2]

As an example,

*that a muon neutrino of energy E*

__the probability__*acquires a different flavor*after traversing distance L is:

P = sin^2 Θ_23 sin^2 (L/ lambda23)

where lambda23 is the energy -dependent oscillation length, given by:

4ħ E c / (delta m_32^2)

How well do we know the parameters? Atmospheric neutrino observations yield Θ_23 ~ 45 degrees, while delta m_32^2 = 0.0024 eV^2. Meanwhile, solar neutrino data yield roughly 33 degrees for Θ_12 and delta m_21^2 = 0.00008 eV^2. (Note: ħ is the Planck constant of action divided by 2 π) If then:

delta m_31^2 = [delta m_21^2 + delta m_32^2 ] = 0.00008 eV^2 + 0.0024 eV^2

We know, delta m_31^2 = 0.00248

which is close to delta m_32^2

This was fine as it went, but a further issue that needed to be resolved was whether the oscillation amplitude, e.g. sin^2 (2Θ_13) (for the disappearance of reactor antineutrinos associated with the delta m_31^2, delta m_32^2 approximation) would still be large enough to

__detect__. This was the core experimental quandary facing the Daya Bay collaborators. They were more or less guided (optimistically!) by an earlier independent results that set

*an upper limit*of 0.16 (the Daya Bay

**detector array was designed to measure a smallest value of 0.01)**

*-v_e*In March this year, it was therefore most gratifying when Yifang Wang of the Beijing Institute of High Energy Physics, reported sin^2 (2Θ_13) = 0.092

__+__0.017, corresponding to a Θ_13 = 9 degrees.

Is the "case" closed? Not necessarily! We always must reckon in

*necessaary and sufficient conditions*. The fact is that a non-zero Θ_13 is a

*necessary*but

__not__sufficient condition for CP-violation in neutrino interactions. How to proceed? Well, we know since there are 3 non-zero mixing angles

*the unitary matrix*that describes all the oscillations has an extra degree of freedom.

Note: readers who'd like more familiarity with unitary matrices can check out my earlier blog:

http://brane-space.blogspot.com/2012/01/more-linear-algebra-unitary-and.html

This additional degree of freedom entails an independent phase factor,

exp (i σ)

which dictates the CP -violation. Standard theory can't predict σ so it must be done via experiment. Such an experiment has been proposed and is known as the

*'Long Baseline Neutrino Experiment'*(LBNE) The plan is to direct an intense beam of muon neutrinos from Fermilab at a detector in an underground labo in South Dakota, some hundreds of miles distant.

The problem? Like so many areas of pure and experimental physics -astronomy now, LBNE is encountering funding problems. It appears the Republican House isn't convinced the money spent to solve these open-ended issues is worth it. SO the future of the experiment is in question.

Stay tuned.

-----

*Reference*:

__Physics Today__, May, 2012, p. 13.

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