ekore.anomalous_dimensions package
The Altarelli-Parisi splitting kernels.
Normalization is given by
with \(a_s = \frac{\alpha_S(\mu^2)}{4\pi}\). The 3-loop references for the non-singlet [MVV04] and singlet [VMV04] case contain also the lower order results. The results are also determined in Mellin space in terms of the anomalous dimensions (note the additional sign!)
- ekore.anomalous_dimensions.exp_matrix_2D(gamma_S)[source]
Compute the exponential and the eigensystem of the singlet anomalous dimension matrix.
- Parameters:
gamma_S (numpy.ndarray) – singlet anomalous dimension matrix
- Returns:
exp (numpy.ndarray) – exponential of the singlet anomalous dimension matrix \(\gamma_{S}(N)\)
lambda_p (complex) – positive eigenvalue of the singlet anomalous dimension matrix \(\gamma_{S}(N)\)
lambda_m (complex) – negative eigenvalue of the singlet anomalous dimension matrix \(\gamma_{S}(N)\)
e_p (numpy.ndarray) – projector for the positive eigenvalue of the singlet anomalous dimension matrix \(\gamma_{S}(N)\)
e_m (numpy.ndarray) – projector for the negative eigenvalue of the singlet anomalous dimension matrix \(\gamma_{S}(N)\)
- ekore.anomalous_dimensions.exp_matrix(gamma)[source]
Compute the exponential and the eigensystem of a matrix.
- Parameters:
gamma (numpy.ndarray) – input matrix
- Returns:
exp (numpy.ndarray) – exponential of the matrix gamma \(\gamma(N)\)
w (numpy.ndarray) – array of the eigenvalues of the matrix lambda
e (numpy.ndarray) – projectors on the eigenspaces of the matrix gamma \(\gamma(N)\)
Subpackages
- ekore.anomalous_dimensions.polarized package
- ekore.anomalous_dimensions.unpolarized package
- Subpackages
- ekore.anomalous_dimensions.unpolarized.space_like package
gamma_ns()
gamma_singlet()
gamma_ns_qed()
choose_ns_ad_aem1()
choose_ns_ad_as1aem1()
choose_ns_ad_aem2()
gamma_singlet_qed()
gamma_valence_qed()
- Subpackages
- Submodules
- ekore.anomalous_dimensions.unpolarized.space_like.aem1 module
- ekore.anomalous_dimensions.unpolarized.space_like.aem2 module
- ekore.anomalous_dimensions.unpolarized.space_like.as1 module
- ekore.anomalous_dimensions.unpolarized.space_like.as1aem1 module
- ekore.anomalous_dimensions.unpolarized.space_like.as2 module
- ekore.anomalous_dimensions.unpolarized.space_like.as3 module
- ekore.anomalous_dimensions.unpolarized.time_like package
- ekore.anomalous_dimensions.unpolarized.space_like package
- Subpackages