Saturday, September 16, 2017

particle physics - Jarlskog Invariant and its mathematical origin


CP violation is present in the weak interactions if



  1. There are no degeneracies in the up-quark/down-quark matrices

  2. The Jarlskog invariant $J=Im(V_{us} V_{cb} V_{ub}^* V_{cs}^*)$ is nonvanishing


Furthermore, all CP violating effects are proportional to $J$.


I am getting stuck on showing how all CP violating effects are proportional to $J$. Also, is the Jarlskog invariant a well-known mathematical property of a unitary matrix? What is it quantifying? I'd like to know this to the extent I can generalize this to larger CKM matrices.


Edit: I did a bad job writing my question. I rewrite it here:



Question:



  1. How do I constructively derive $J=Im(V_{us} V_{cb} V_{ub}^* V_{cs}^*)$, and how do I generalize this to arbitrary $n\times n$ unitary matrices ?

  2. The Jarlskog invariant is invariant under a change of basis. What is the elegant way of showing this?




No comments:

Post a Comment

classical mechanics - Moment of a force about a given axis (Torque) - Scalar or vectorial?

I am studying Statics and saw that: The moment of a force about a given axis (or Torque) is defined by the equation: $M_X = (\vec r \times \...