change CKM delta->gamma and add beta-gamma implementation

[peterstangl]

This PR implements the "beta-gamma" parameterization of the CKM matrix based on the update of the ckmutil package in PR https://github.com/DavidMStraub/ckmutil/pull/4.

Both the "beta-gamma" and "tree" CKM parameterizations use the Unitarity Triangle (UT) angle $\gamma$ to determine the CKM phase $\delta$. Since $\delta=\gamma$ is a very accurate approximation, so far $\delta$ was set to $\gamma$ everywhere in flavio and the parameter corresponding to the angle $\gamma$ has been called delta. This is changed by the present PR, which now distinguishes $\gamma$ and $\delta$ and uses the name gamma for the UT angle $\gamma$, while keeping the name delta for the CKM phase $\delta$, which is used in the standard CKM parameterization. This change is motivated by the implementation of the exact relation between $\gamma$ and $\delta$ in the ckmutil package in PR https://github.com/DavidMStraub/ckmutil/pull/4.

[DavidMStraub]

Silly question, why do tests pass if the ckmutil PR is not yet merged?

[peterstangl]

Silly question, why do tests pass if the ckmutil PR is not yet merged?

• The change of delta -> gamma is just renaming the parameter but doesn't need the ckmutil PR
• The new implementation of the beta-gamma scheme is not used as the default one at the moment and there is no test in flavio that explicitly tests this input scheme

[DavidMStraub]

ckmutil 1.1.0 is on PyPI.