particle physics - 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

1. 
   

   The actual masses are accessible in theory, but not from mixing measurements. Cosmological measurements could give us a useable handle on the sum of the masses (though until we settle the hierarchy questions this may not provide a unique answer), or the combination of a much better model of supernovae plus a precision measurement of the differences in arrival times of the light and neutrino wave-fronts from a supernova whose distance is well known could give the masses directly.

   
   


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   First, your information is out of date, $\theta_{13}$ is now the most precisely known of all the mixing angles.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.

   
   

---

¹ Full disclosure, I was a part of Double Chooz.