ekore.operator_matrix_elements.polarized.space_like package
The polarized, space-like OME.
- ekore.operator_matrix_elements.polarized.space_like.A_singlet(matching_order, n, nf, L)[source]
Compute the tower of the singlet OME.
- ekore.operator_matrix_elements.polarized.space_like.A_non_singlet(matching_order, n, L)[source]
Compute the tower of the non-singlet OME.
Submodules
ekore.operator_matrix_elements.polarized.space_like.as1 module
The NLO OME in the polarized case for the matching conditions in the VFNS.
Heavy quark contribution for intrinsic evolution are not considered for the polarized case.
The matching conditions for the VFNS at \(\mu_F^2 \neq m_H^2\) are provided in [BBlumleinDF+23].
In the paper, the fraction \(\mu_F^2 / m_H^2\) inside the log is inverted, yielding an additional factor of (-1) wherever L has an odd power.
Additionally, a different convention for the anomalous dimensions is used, yielding a factor 2 in the OME’s wherever they are present.
The anomalous dimensions and beta function with the addition ‘hat’ have the form \(\hat\gamma = \gamma^{(nf+1)} - \gamma^{(nf)}\).
- ekore.operator_matrix_elements.polarized.space_like.as1.A_hg(n, L)[source]
Compute the NLO heavy-gluon OME \(A_{Hg}^{S,(1)}\).
Implements 104 of [BBlumleinDF+23].
- ekore.operator_matrix_elements.polarized.space_like.as1.A_gg(L)[source]
Compute the NLO gluon-gluon OME \(A_{gg,H}^{S,(1)}\).
Implements 186 of [BBlumleinDF+23].
- ekore.operator_matrix_elements.polarized.space_like.as1.A_singlet(n, L)[source]
Compute the NLO singlet OME.
\[\begin{split}A^{S,(1)} = \left(\begin{array}{cc} A_{gg,H}^{S,(1)} & 0 & 0\\ 0 & 0 & 0 \\ A_{hg}^{S,(1)} & 0 & 0 \end{array}\right)\end{split}\]- Parameters:
- Returns:
NLO singlet OME \(A^{S,(1)}\)
- Return type:
ekore.operator_matrix_elements.polarized.space_like.as2 module
Contains the NNLO OME in the polarized case for the matching conditions in the VFNS.
The equations are given in [BBlumleinDF+23]. As in the NLO OME, in the paper, an additional factor 2 can be found in front of the anomalous dimensions and factor (-1) for odd powers of L. The anomalous dimensions and beta function with the addition ‘hat’ are defined as in the NLO case.
- ekore.operator_matrix_elements.polarized.space_like.as2.beta_0hat = -0.6666666666666666
This is the lowest order beta function with the addition ‘hat’ defined as above.
- ekore.operator_matrix_elements.polarized.space_like.as2.A_qq_ns(n, cache, L)[source]
Compute NNLO light-light non-singlet OME \(A_{qq,H}^{NS,(2)}\).
Implements 133 of [BBlumleinDF+23].
- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
L (float) – \(\ln(\mu_F^2 / m_h^2)\)
- Returns:
NNLO light-light non-singlet OME \(A_{qq,H}^{NS,(2)}\)
- Return type:
- ekore.operator_matrix_elements.polarized.space_like.as2.A_hq_ps(n, cache, L, nf)[source]
Compute NNLO heavy-light pure-singlet OME \(A_{Hq}^{PS,(2)}\).
Implements 138 of [BBlumleinDF+23].
- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
L (float) – \(\ln(\mu_F^2 / m_h^2)\)
nf (int) – Number of active flavors
- Returns:
NNLO heavy-light pure-singlet OME \(A_{Hq}^{PS,(2)}\)
- Return type:
- ekore.operator_matrix_elements.polarized.space_like.as2.A_hg(n, cache, L)[source]
Compute NNLO heavy-gluon OME \(A_{Hg}^{S,(2)}\).
Implements 111 of [BBlumleinDF+23].
- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
L (float) – \(\ln(\mu_F^2 / m_h^2)\)
- Returns:
NNLO heavy-gluon OME \(A_{Hg}^{S,(2)}\)
- Return type:
- ekore.operator_matrix_elements.polarized.space_like.as2.A_gq(n, cache, L)[source]
Compute NNLO gluon-quark OME \(A_{gq,H}^{S,(2)}\).
Implements 174 of [BBlumleinDF+23].
- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
L (float) – \(\ln(\mu_F^2 / m_h^2)\)
- Returns:
NNLO gluon-quark OME \(A_{gq,H}^{S,(2)}\)
- Return type:
- ekore.operator_matrix_elements.polarized.space_like.as2.A_gg(n, cache, L)[source]
Compute NNLO gluon-gluon OME \(A_{gg,H}^{S,(2)}\).
Implements 187 of [BBlumleinDF+23].
- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
L (float) – \(\ln(\mu_F^2 / m_h^2)\)
- Returns:
NNLO gluon-gluon OME \(A_{gg,H}^{S,(2)}\)
- Return type:
- ekore.operator_matrix_elements.polarized.space_like.as2.A_singlet(n, cache, L, nf)[source]
Compute the NNLO singlet OME.
\[\begin{split}A^{S,(2)} = \left(\begin{array}{cc} A_{gg, H}^{S,(2)} & A_{gq, H}^{S,(2)} & 0 \\ 0 & A_{qq,H}^{NS,(2)} & 0\\ A_{hg}^{S,(2)} & A_{hq}^{PS,(2)} & 0\\ \end{array}\right)\end{split}\]- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
L (float) – \(\ln(\mu_F^2 / m_h^2)\)
nf (int) – Number of active flavors
- Returns:
NNLO singlet OME \(A^{S,(2)}(N)\)
- Return type:
- ekore.operator_matrix_elements.polarized.space_like.as2.A_ns(n, cache, L)[source]
Compute the NNLO non-singlet OME.
\[\begin{split}A^{NS,(2)} = \left(\begin{array}{cc} A_{qq,H}^{NS,(2)} & 0 \\ 0 & 0 \\ \end{array}\right)\end{split}\]- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
L (float) – \(\ln(\mu_F^2 / m_h^2)\)
- Returns:
NNLO non-singlet OME \(A^{NS,(2)}\)
- Return type: