ekore.anomalous_dimensions.unpolarized.space_like.as4 package
The N3LO Altarelli-Parisi splitting kernels.
For further documentation see N3LO anomalous dimensions
- ekore.anomalous_dimensions.unpolarized.space_like.as4.gamma_singlet(N, nf, cache, variation)[source]
Compute the N3LO singlet anomalous dimension matrix.
\[\begin{split}\gamma_S^{(3)} = \left(\begin{array}{cc} \gamma_{qq}^{(3)} & \gamma_{qg}^{(3)}\\ \gamma_{gq}^{(3)} & \gamma_{gg}^{(3)} \end{array}\right)\end{split}\]- Parameters:
N (complex) – Mellin moment
nf (int) – Number of active flavors
cache (numpy.ndarray) – Harmonic sum cache
variation (tuple) – N3LO anomalous dimension variation
(gg, gq, qg, qq)
- Returns:
N3LO singlet anomalous dimension matrix \(\gamma_{S}^{(3)}(N)\)
- Return type:
- ekore.anomalous_dimensions.unpolarized.space_like.as4.gamma_singlet_qed(N, nf, cache, variation)[source]
Compute the leading-order singlet anomalous dimension matrix for the unified evolution basis.
\[\begin{split}\\gamma_S^{(3,0)} = \\left(\begin{array}{cccc} \\gamma_{gg}^{(3,0)} & 0 & \\gamma_{gq}^{(3,0)} & 0\\ 0 & 0 & 0 & 0 \\ \\gamma_{qg}^{(3,0)} & 0 & \\gamma_{qq}^{(3,0)} & 0 \\ 0 & 0 & 0 & \\gamma_{qq}^{(3,0)} \\ \\end{array}\right)\end{split}\]- Parameters:
N (complex) – Mellin moment
nf (int) – Number of active flavors
cache (numpy.ndarray) – Harmonic sum cache
- Returns:
Leading-order singlet anomalous dimension matrix \(\\gamma_{S}^{(3,0)}(N)\)
- Return type:
- ekore.anomalous_dimensions.unpolarized.space_like.as4.gamma_valence_qed(N, nf, cache)[source]
Compute the leading-order valence anomalous dimension matrix for the unified evolution basis.
\[\begin{split}\\gamma_V^{(3,0)} = \\left(\begin{array}{cc} \\gamma_{nsV}^{(3,0)} & 0\\ 0 & \\gamma_{ns-}^{(3,0)} \\end{array}\right)\end{split}\]- Parameters:
N (complex) – Mellin moment
nf (int) – Number of active flavors
cache (numpy.ndarray) – Harmonic sum cache
- Returns:
Leading-order singlet anomalous dimension matrix \(\\gamma_{V}^{(3,0)}(N)\)
- Return type:
Subpackages
- ekore.anomalous_dimensions.unpolarized.space_like.as4.fhmruvv package
gamma_singlet()gamma_singlet_qed()gamma_valence_qed()- Submodules
- ekore.anomalous_dimensions.unpolarized.space_like.as4.fhmruvv.ggg module
- ekore.anomalous_dimensions.unpolarized.space_like.as4.fhmruvv.ggq module
- ekore.anomalous_dimensions.unpolarized.space_like.as4.fhmruvv.gnsm module
- ekore.anomalous_dimensions.unpolarized.space_like.as4.fhmruvv.gnsp module
- ekore.anomalous_dimensions.unpolarized.space_like.as4.fhmruvv.gnsv module
- ekore.anomalous_dimensions.unpolarized.space_like.as4.fhmruvv.gps module
- ekore.anomalous_dimensions.unpolarized.space_like.as4.fhmruvv.gqg module
Submodules
ekore.anomalous_dimensions.unpolarized.space_like.as4.ggg module
The unpolarized, space-like anomalous dimension \(\gamma_{gg}^{(3)}\).
- ekore.anomalous_dimensions.unpolarized.space_like.as4.ggg.gamma_gg_nf3(n, cache)[source]
Return the part proportional to \(nf^3\) of \(\gamma_{gg}^{(3)}\).
The expression is copied exact from 3.14 of [DVR+17].
- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
- Returns:
N3LO non-singlet anomalous dimension \(\gamma_{gg}^{(3)}|_{nf^3}\)
- Return type:
- ekore.anomalous_dimensions.unpolarized.space_like.as4.ggg.gamma_gg_nf1(n, cache, variation)[source]
Return the part proportional to \(nf^1\) of \(\gamma_{gg}^{(3)}\).
- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
variation (int) – N3LO anomalous dimension variation
- Returns:
N3LO non-singlet anomalous dimension \(\gamma_{gg}^{(3)}|_{nf^1}\)
- Return type:
- ekore.anomalous_dimensions.unpolarized.space_like.as4.ggg.gamma_gg_nf2(n, cache, variation)[source]
Return the part proportional to \(nf^2\) of \(\gamma_{gg}^{(3)}\).
- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
variation (int) – N3LO anomalous dimension variation
- Returns:
N3LO non-singlet anomalous dimension \(\gamma_{gg}^{(3)}|_{nf^2}\)
- Return type:
- ekore.anomalous_dimensions.unpolarized.space_like.as4.ggg.gamma_gg_nf0(n, cache, variation)[source]
Return the part proportional to \(nf^0\) of \(\gamma_{gg}^{(3)}\).
- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
variation (int) – N3LO anomalous dimension variation
- Returns:
N3LO non-singlet anomalous dimension \(\gamma_{gg}^{(3)}|_{nf^0}\)
- Return type:
- ekore.anomalous_dimensions.unpolarized.space_like.as4.ggg.gamma_gg(n, nf, cache, variation)[source]
Compute the N3LO gluon-gluon singlet anomalous dimension.
- Parameters:
n (complex) – Mellin moment
nf (int) – Number of active flavors
cache (numpy.ndarray) – Harmonic sum cache
variation (int) – N3LO anomalous dimension variation
- Returns:
N3LO gluon-gluon singlet anomalous dimension \(\gamma_{gg}^{(3)}(N)\)
- Return type:
ekore.anomalous_dimensions.unpolarized.space_like.as4.ggq module
The unpolarized, space-like anomalous dimension \(\gamma_{gq}^{(3)}\).
- ekore.anomalous_dimensions.unpolarized.space_like.as4.ggq.gamma_gq_nf3(n, cache)[source]
Return the part proportional to \(nf^3\) of \(\gamma_{gq}^{(3)}\).
The expression is copied exact from 3.13 of [DVR+17].
- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
- Returns:
N3LO non-singlet anomalous dimension \(\gamma_{gq}^{(3)}|_{nf^3}\)
- Return type:
- ekore.anomalous_dimensions.unpolarized.space_like.as4.ggq.gamma_gq_nf0(n, cache, variation)[source]
Return the part proportional to \(nf^0\) of \(\gamma_{gq}^{(3)}\).
- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
variation (int) – N3LO anomalous dimension variation
- Returns:
N3LO non-singlet anomalous dimension \(\gamma_{gq}^{(3)}|_{nf^0}\)
- Return type:
- ekore.anomalous_dimensions.unpolarized.space_like.as4.ggq.gamma_gq_nf1(n, cache, variation)[source]
Return the part proportional to \(nf^1\) of \(\gamma_{gq}^{(3)}\).
- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
variation (int) – N3LO anomalous dimension variation
- Returns:
N3LO non-singlet anomalous dimension \(\gamma_{gq}^{(3)}|_{nf^1}\)
- Return type:
- ekore.anomalous_dimensions.unpolarized.space_like.as4.ggq.gamma_gq_nf2(n, cache, variation)[source]
Return the part proportional to \(nf^2\) of \(\gamma_{gq}^{(3)}\).
This therm is parametrized using the analytic result from [FHM+24] with an higher number of moments (30).
- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
variation (int) – N3LO anomalous dimension variation
- Returns:
N3LO non-singlet anomalous dimension \(\gamma_{gq}^{(3)}|_{nf^2}\)
- Return type:
- ekore.anomalous_dimensions.unpolarized.space_like.as4.ggq.gamma_gq(n, nf, cache, variation)[source]
Compute the N3LO gluon-quark singlet anomalous dimension.
- Parameters:
n (complex) – Mellin moment
nf (int) – Number of active flavors
cache (numpy.ndarray) – Harmonic sum cache
variation (int) – N3LO anomalous dimension variation
- Returns:
N3LO gluon-quark singlet anomalous dimension \(\gamma_{gq}^{(3)}(N)\)
- Return type:
ekore.anomalous_dimensions.unpolarized.space_like.as4.gnsm module
The unpolarized, space-like anomalous dimension \(\gamma_{ns,-}^{(3)}\).
- ekore.anomalous_dimensions.unpolarized.space_like.as4.gnsm.gamma_ns_nf3(n, cache)[source]
Return the common part proportional to \(nf^3\).
Holds for \(\gamma_{ns,+}^{(3)},\gamma_{ns,-}^{(3)},\gamma_{ns,v}^{(3)}\). The expression is copied exact from 3.6 of [DVR+17].
- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
- Returns:
N3LO non-singlet anomalous dimension \(\gamma_{ns}^{(3)}|_{nf^3}\)
- Return type:
- ekore.anomalous_dimensions.unpolarized.space_like.as4.gnsm.gamma_nsm_nf2(n, cache)[source]
Return the parametrized valence-like non-singlet part proportional to \(nf^2\).
From [MRU+17] ancillary files.
- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
- Returns:
N3LO valence-like non-singlet anomalous dimension \(\gamma_{ns,-}^{(3)}|_{nf^2}\)
- Return type:
- ekore.anomalous_dimensions.unpolarized.space_like.as4.gnsm.gamma_nsm_nf1(n, cache)[source]
Return the parametrized valence-like non-singlet part proportional to \(nf^1\).
- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
- Returns:
N3LO valence-like non-singlet anomalous dimension \(\gamma_{ns,-}^{(3)}|_{nf^1}\)
- Return type:
- ekore.anomalous_dimensions.unpolarized.space_like.as4.gnsm.gamma_nsm_nf0(n, cache)[source]
Return the parametrized valence-like non-singlet part proportional to \(nf^0\).
- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
- Returns:
N3LO valence-like non-singlet anomalous dimension \(\gamma_{ns,-}^{(3)}|_{nf^0}\)
- Return type:
- ekore.anomalous_dimensions.unpolarized.space_like.as4.gnsm.gamma_nsm(n, nf, cache)[source]
Compute the N3LO valence-like non-singlet anomalous dimension.
- Parameters:
n (complex) – Mellin moment
nf (int) – Number of active flavors
cache (numpy.ndarray) – Harmonic sum cache
- Returns:
N3LO valence-like non-singlet anomalous dimension \(\gamma_{ns,-}^{(3)}(N)\)
- Return type:
ekore.anomalous_dimensions.unpolarized.space_like.as4.gnsp module
The unpolarized, space-like anomalous dimension \(\gamma_{ns,+}^{(3)}\).
- ekore.anomalous_dimensions.unpolarized.space_like.as4.gnsp.gamma_nsp_nf2(n, cache)[source]
Return the parametrized singlet-like non-singlet part proportional to \(nf^2\).
From [MRU+17] ancillary files.
- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
- Returns:
N3LO singlet-like non-singlet anomalous dimension \(\gamma_{ns,+}^{(3)}|_{nf^2}\)
- Return type:
- ekore.anomalous_dimensions.unpolarized.space_like.as4.gnsp.gamma_nsp_nf1(n, cache)[source]
Return the parametrized singlet-like non-singlet part proportional to \(nf^1\).
- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
- Returns:
N3LO singlet-like non-singlet anomalous dimension \(\gamma_{ns,+}^{(3)}|_{nf^1}\)
- Return type:
- ekore.anomalous_dimensions.unpolarized.space_like.as4.gnsp.gamma_nsp_nf0(n, cache)[source]
Return the parametrized singlet-like non-singlet part proportional to \(nf^0\).
- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
- Returns:
N3LO singlet-like non-singlet anomalous dimension \(\gamma_{ns,+}^{(3)}|_{nf^0}\)
- Return type:
- ekore.anomalous_dimensions.unpolarized.space_like.as4.gnsp.gamma_nsp(n, nf, cache)[source]
Compute the N3LO singlet-like non-singlet anomalous dimension.
- Parameters:
n (complex) – Mellin moment
nf (int) – Number of active flavors
cache (numpy.ndarray) – Harmonic sum cache
- Returns:
N3LO singlet-like non-singlet anomalous dimension \(\gamma_{ns,+}^{(3)}(N)\)
- Return type:
ekore.anomalous_dimensions.unpolarized.space_like.as4.gnsv module
The unpolarized, space-like anomalous dimension \(\gamma_{ns,v}^{(3)}\).
- ekore.anomalous_dimensions.unpolarized.space_like.as4.gnsv.gamma_nss_nf2(n, cache)[source]
Return the sea non-singlet part proportional to \(nf^2\).
Implements 3.5 of [DVR+17].
- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
- Returns:
N3LO sea non-singlet anomalous dimension \(\gamma_{ns,s}^{(3)}|_{nf^2}\)
- Return type:
- ekore.anomalous_dimensions.unpolarized.space_like.as4.gnsv.gamma_nss_nf1(n, cache)[source]
Return the sea non-singlet part proportional to \(nf^1\).
The expression is the average of the Mellin transform of 4.19 and 4.20 of [MRU+17].
- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
- Returns:
N3LO sea non-singlet anomalous dimension \(\gamma_{ns,s}^{(3)}|_{nf^1}\)
- Return type:
- ekore.anomalous_dimensions.unpolarized.space_like.as4.gnsv.gamma_nsv(n, nf, cache)[source]
Compute the N3LO valence non-singlet anomalous dimension.
- Parameters:
n (complex) – Mellin moment
nf (int) – Number of active flavors
cache (numpy.ndarray) – Harmonic sum cache
- Returns:
N3LO valence non-singlet anomalous dimension \(\gamma_{ns,v}^{(3)}(N)\)
- Return type:
ekore.anomalous_dimensions.unpolarized.space_like.as4.gps module
The unpolarized, space-like anomalous dimension \(\gamma_{ps}^{(3)}\).
- ekore.anomalous_dimensions.unpolarized.space_like.as4.gps.gamma_ps_nf3(n, cache)[source]
Return the part proportional to \(nf^3\) of \(\gamma_{ps}^{(3)}\).
The expression is copied exact from 3.10 of [DVR+17].
- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
- Returns:
N3LO non-singlet anomalous dimension \(\gamma_{ps}^{(3)}|_{nf^3}\)
- Return type:
- ekore.anomalous_dimensions.unpolarized.space_like.as4.gps.gamma_ps_nf1(n, cache, variation)[source]
Return the part proportional to \(nf^1\) of \(\gamma_{ps}^{(3)}\).
- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
variation (int) – N3LO anomalous dimension variation
- Returns:
N3LO non-singlet anomalous dimension \(\gamma_{ps}^{(3)}|_{nf^1}\)
- Return type:
- ekore.anomalous_dimensions.unpolarized.space_like.as4.gps.gamma_ps_nf2(n, cache)[source]
Return the part proportional to \(nf^2\) of \(\gamma_{ps}^{(3)}\).
This therm is parametrized using the analytic result from [GvMSY24] with an higher number of moments (30).
- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
- Returns:
N3LO non-singlet anomalous dimension \(\gamma_{ps}^{(3)}|_{nf^2}\)
- Return type:
- ekore.anomalous_dimensions.unpolarized.space_like.as4.gps.gamma_ps(n, nf, cache, variation)[source]
Compute the N3LO pure singlet quark-quark anomalous dimension.
- Parameters:
n (complex) – Mellin moment
nf (int) – Number of active flavors
cache (numpy.ndarray) – Harmonic sum cache
variation (int) – N3LO anomalous dimension variation
- Returns:
N3LO pure singlet quark-quark anomalous dimension \(\gamma_{ps}^{(3)}(N)\)
- Return type:
ekore.anomalous_dimensions.unpolarized.space_like.as4.gqg module
The unpolarized, space-like anomalous dimension \(\gamma_{qg}^{(3)}\).
- ekore.anomalous_dimensions.unpolarized.space_like.as4.gqg.gamma_qg_nf3(n, cache)[source]
Return the part proportional to \(nf^3\) of \(\gamma_{qg}^{(3)}\).
The expression is copied exact from 3.12 of [DVR+17].
- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
- Returns:
N3LO non-singlet anomalous dimension \(\gamma_{qg}^{(3)}|_{nf^3}\)
- Return type:
- ekore.anomalous_dimensions.unpolarized.space_like.as4.gqg.gamma_qg_nf1(n, cache, variation)[source]
Return the part proportional to \(nf^1\) of \(\gamma_{qg}^{(3)}\).
- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
variation (int) – N3LO anomalous dimension variation
- Returns:
N3LO non-singlet anomalous dimension \(\gamma_{qg}^{(3)}|_{nf^1}\)
- Return type:
- ekore.anomalous_dimensions.unpolarized.space_like.as4.gqg.gamma_qg_nf2(n, cache, variation)[source]
Return the part proportional to \(nf^2\) of \(\gamma_{qg}^{(3)}\).
- Parameters:
n (complex) – Mellin moment
cache (numpy.ndarray) – Harmonic sum cache
variation (int) – N3LO anomalous dimension variation
- Returns:
N3LO non-singlet anomalous dimension \(\gamma_{qg}^{(3)}|_{nf^2}\)
- Return type:
- ekore.anomalous_dimensions.unpolarized.space_like.as4.gqg.gamma_qg(n, nf, cache, variation)[source]
Compute the N3LO quark-gluon singlet anomalous dimension.
- Parameters:
n (complex) – Mellin moment
nf (int) – Number of active flavors
cache (numpy.ndarray) – Harmonic sum cache
variation (int) – N3LO anomalous dimension variation
- Returns:
N3LO quark-gluon singlet anomalous dimension \(\gamma_{qg}^{(3)}(N)\)
- Return type: