# What is the meaning behind the neutrino oscillation parameter?

As far as I can tell, there are 6 parameters that describe how a neutrino oscillates: 2 mass squared differences, 3 mixing angles and another parameter I don't understand at all (delta). Thus I have three questions:

1. I understand that the 2 mass differences is enough information for the three masses, but we cant yet measure the actual mass. Is this limit due to current technology or is the mass squared difference the most fundamental information about the mass we could possibly acquire?

2. What exactly do the mixing angles physically represent? Are they all of the same importance, and if so why has the theta-13 angle been studied so relatively little? I have also read that a non-zero theta-13 angle hints towards an asymmetry between matter and anti-matter. How so, and why the 13 angle in particular over the other angles?

3. What is the delta parameter? I know that current technology does not have the capacity to measure it, but the next generation (hopefully) will. What does this parameter represent and what implications would measuring it have?

• Answer to 1): The particles are a mix of mass eigenstates, and therefore HAVE no well-defined mass. – Danu Apr 16 '14 at 21:02
• @Danu: the flavor basis and the mass basis are both valid and equivalent descriptions of the system. The flavor states do not have a well defined mass, but just as importantly the mass states do not have well defined flavor. – dmckee Apr 17 '14 at 2:23
• @Danu: "The particles are a mix of mass eigenstates, and therefore HAVE no well-defined mass." -- True for weak processes in which a charged lepton of definite mass/flavor takes part (is produced), i.e. either $e^-$, $e^+$, $\mu^-$, $\mu^+$, $\tau^-$, or $\tau^+$. But some higher order Penguin decays, such as (the extremely rare) $B^- \rightarrow \nu \overline{\nu} D^{*-}$ may proceed by "just the right mixture" of (virtual) weak processes, producing "just the right mixture" of weak $\nu$ eigenstates to have well-defined mass. – user12262 Apr 17 '14 at 4:58
• @dmckee: "The flavor states do not have a well defined mass [...]" -- This use of the term "flavor state" (as if it were distinct from "mass state") when referring to neutrinos is inconsistent with the use of the term "flavor state" as it is used when referring to quarks, or to charged leptons (where it is synonymous to "mass state"). In order to use terminology consistently, it may be better to say instead that (in all cases) "The weak (eigen-)states do not have a well defined mass ...". – user12262 Apr 17 '14 at 5:04
• @dmckee I was, of course, assuming that OP was talking about the flavor/weak (eigen-)states, which is how they usually appear in tables etc.; user12262: interesting, I was not aware! – Danu Apr 17 '14 at 7:23

2. First, your information is out of date, $\theta_{13}$ is now the most precisely known of all the mixing angles. Go Daya Bay, Reno and Double Chooz!1 Now, what they represent is a bit abstract. Hmmm...they are angles but in an obscure mathematical space. Taken together they fully specify the flavor content of the mass states or the mass content of the flavor states. If that doesn't have any meaning to you, you need to study quantum mechanics to get the full story. In the mean time, you can think of them as parameters in a complicated trigonometric expression that explains how strongly the flavors mix in terms of distance between production and detection and the energy of the neutrino.
3. Finally $\delta_{CP}$. If, $\theta_{13}$ is non-zero (it is) and $\delta_{CP}$ is neither zero nor $\pi$, then it is possible for neutrino mixing to fail to observe the symmetry called "CP". CP symmetry is the assertion that the laws of physics look the same if you both (a) change all the matter particles in the system to anti-matter and (b) reflect the system through a point. CP is good in most systems (in all the systems you will encounter in everyday life), but it is already known to be violate in some flavor-violating quark decays. The thing is that we think CP violation might explain why the universe we see today is all matter when we believe is started out half matter and half anti-matter. Only the know sources of CP violation don't seem to be enough, so finding another source would make a large class of cosmological theorists very happy.