CP violation is present in the weak interactions if
- There are no degeneracies in the up-quark/down-quark matrices
- 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:
- 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 ?
- The Jarlskog invariant is invariant under a change of basis. What is the elegant way of showing this?
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