Thanks to visit codestin.com
Credit goes to github.com

Skip to content

Conversation

@peterstangl
Copy link
Member

@peterstangl peterstangl commented Dec 13, 2023

This PR

  • updates the previous implementation of CKM parameterizations, replacing approximate by exact relations,
  • adds the new $\beta$ - $\gamma$ parameterization, in which all CKM elements are expressed in terms of the CKM elements $V_{us}$ and $V_{cb}$ and the Unitarity Triangle angles $\beta$ and $\gamma$.

The changes to the previous implementation are:

  • The new function gamma_to_delta implements the exact relation between $\delta$ and $\gamma$ but its optional argument delta_expansion_order allows to use the very accurate approximation $\delta=\gamma$ for delta_expansion_order=0 or to include higher-order corrections to this approximation for delta_expansion_order=1 or delta_expansion_order=2.
  • The new functions tree_to_standard and wolfenstein_to_standard, and their inverses standard_to_tree and standard_to_wolfenstein are introduced. They all use exact relations without analytical approximations. In particular, the exact relation between $\bar\rho + i \bar\eta$ and $\rho + i \eta$ has been implemented for the Wolfenstein parameterization and the exact relation between $\delta$ and $\gamma$ is used everywhere (but the new optional argument delta_expansion_order allows to use approximate relations).
  • The old function tree_to_wolfenstein is now a composition of tree_to_standard and standard_to_wolfenstein and its inverse wolfenstein_to_tree is added as a composition of wolfenstein_to_standard and standard_to_tree.
  • The old function ckm_wolfenstein is now a composition of wolfenstein_to_standard and ckm_standard.
  • The old function ckm_tree is now a composition of tree_to_standard and ckm_standard.

The newly implemented $\beta$ - $\gamma$ parameterization consists of:

  • The function beta_gamma_to_delta that implements the exact relation between $\delta$ and $\gamma$ if $\beta$ is known and its optional argument delta_expansion_order allows to use the very accurate approximation $\delta=\gamma$ for delta_expansion_order=0 or to include higher-order corrections to this approximation for delta_expansion_order=1 or delta_expansion_order=2.
  • The new function beta_gamma_to_standard and its inverse standard_to_beta_gamma implement the translations between the $\beta$ - $\gamma$ parameterization and the standard parameterization.
  • The new function ckm_beta_gamma implements the CKM matrix in the $\beta$ - $\gamma$ parameterization in terms of a composition of beta_gamma_to_standard and ckm_standard.

The unittests have been updated and extended.

@DavidMStraub
Copy link
Collaborator

Ready to merge?

@peterstangl
Copy link
Member Author

Yes, this PR should be ready to merge! Thank you :)

@DavidMStraub DavidMStraub merged commit 7beed57 into flav-io:master Dec 14, 2023
@peterstangl peterstangl deleted the ckm_para branch December 14, 2023 19:16
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment

Labels

None yet

Projects

None yet

Development

Successfully merging this pull request may close these issues.

2 participants