ekore.anomalous_dimensions.unpolarized.space_like.as4.fhmruvv package
The FHMRUVV N3LO Altarelli-Parisi splitting kernels approximations.
Authors follow Pegasus convention and so there is an additional global minus sign with respect to our conventions.
- ekore.anomalous_dimensions.unpolarized.space_like.as4.fhmruvv.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.fhmruvv.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
variation (tuple) – N3LO anomalous dimension variation
(gg, gq, qg, qq)
- Returns:
Leading-order singlet anomalous dimension matrix \(\\gamma_{S}^{(3,0)}(N)\)
- Return type:
- ekore.anomalous_dimensions.unpolarized.space_like.as4.fhmruvv.gamma_valence_qed(N, nf, cache, variation)[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
variation (tuple) – N3LO anomalous dimension variation
(nsm, nsv)
- Returns:
Leading-order singlet anomalous dimension matrix \(\\gamma_{V}^{(3,0)}(N)\)
- Return type:
Submodules
ekore.anomalous_dimensions.unpolarized.space_like.as4.fhmruvv.ggg module
The unpolarized, space-like anomalous dimension \(\gamma_{gg}^{(3)}\).
- ekore.anomalous_dimensions.unpolarized.space_like.as4.fhmruvv.ggg.gamma_gg(n, nf, cache, variation)[source]
Compute the N3LO gluon-gluon singlet anomalous dimension.
The routine is taken from [MRU+24].
- 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.fhmruvv.ggq module
The unpolarized, space-like anomalous dimension \(\gamma_{gq}^{(3)}\).
- ekore.anomalous_dimensions.unpolarized.space_like.as4.fhmruvv.ggq.gamma_gq(n, nf, cache, variation)[source]
Compute the N3LO gluon-quark singlet anomalous dimension.
The routine is taken from [MRU+24].
- 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.fhmruvv.gnsm module
The unpolarized, space-like anomalous dimension \(\gamma_{ns,-}^{(3)}\).
- ekore.anomalous_dimensions.unpolarized.space_like.as4.fhmruvv.gnsm.gamma_nsm(n, nf, cache, variation)[source]
Compute the N3LO valence-like non-singlet anomalous dimension.
The routine is taken from [MRU+17].
The \(nf^{0,1}\) leading large-nc contributions and the \(nf^2\) part are high-accuracy (0.1% or better) parametrizations of the exact results. The \(nf^3\) expression is exact up to numerical truncations.
The remaining \(nf^{0,1}\) terms are approximations based on the first eight odd moments together with small-x and large-x constraints. The two sets spanning the error estimate are called via IMOD = 1 and IMOD = 2. Any other value of IMOD invokes their average.
- 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 valence-like non-singlet anomalous dimension \(\gamma_{ns,-}^{(3)}(N)\)
- Return type:
ekore.anomalous_dimensions.unpolarized.space_like.as4.fhmruvv.gnsp module
The unpolarized, space-like anomalous dimension \(\gamma_{ns,+}^{(3)}\).
- ekore.anomalous_dimensions.unpolarized.space_like.as4.fhmruvv.gnsp.gamma_nsp(n, nf, cache, variation)[source]
Compute the N3LO singlet-like non-singlet anomalous dimension.
The routine is taken from [MRU+17].
The \(nf^{0,1}\) leading large-nc contributions and the \(nf^2\) part are high-accuracy (0.1% or better) parametrizations of the exact results. The \(nf^3\) expression is exact up to numerical truncations.
The remaining \(nf^{0,1}\) terms are approximations based on the first eight even moments together with small-x and large-x constraints. The two sets spanning the error estimate are called via IMOD = 1 and IMOD = 2. Any other value of IMOD invokes their average.
- 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 singlet-like non-singlet anomalous dimension \(\gamma_{ns,+}^{(3)}(N)\)
- Return type:
ekore.anomalous_dimensions.unpolarized.space_like.as4.fhmruvv.gnsv module
The unpolarized, space-like anomalous dimension \(\gamma_{ns,v}^{(3)}\).
- ekore.anomalous_dimensions.unpolarized.space_like.as4.fhmruvv.gnsv.gamma_nss(n, nf, cache, variation)[source]
Compute the N3LO sea non-single anomalous dimension.
The routine is taken from [MRU+17].
The \(nf^2\) part is a high-accuracy (0.1% or better) parametrization of the exact expression obtained in [DVR+17], see xpns3m.f
The \(nf^1\) part is an approximation based on the first 9 odd moments. The two sets spanning the error estimate are called via IMOD = 1 and IMOD = 2. Any other value of IMOD invokes their average.
- 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 sea non-singlet anomalous dimension \(\gamma_{ns,s}^{(3)}\)
- Return type:
- ekore.anomalous_dimensions.unpolarized.space_like.as4.fhmruvv.gnsv.gamma_nsv(n, nf, cache, variation)[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
variation (int) – N3LO anomalous dimension variation
- Returns:
N3LO valence non-singlet anomalous dimension \(\gamma_{ns,v}^{(3)}(N)\)
- Return type:
ekore.anomalous_dimensions.unpolarized.space_like.as4.fhmruvv.gps module
The unpolarized, space-like anomalous dimension \(\gamma_{ps}^{(3)}\).
- ekore.anomalous_dimensions.unpolarized.space_like.as4.fhmruvv.gps.gamma_ps(n, nf, cache, variation)[source]
Compute the N3LO pure singlet quark-quark anomalous dimension.
The routine is taken from [FHMV23b].
- 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.fhmruvv.gqg module
The unpolarized, space-like anomalous dimension \(\gamma_{qg}^{(3)}\).
- ekore.anomalous_dimensions.unpolarized.space_like.as4.fhmruvv.gqg.gamma_qg(n, nf, cache, variation)[source]
Compute the N3LO quark-gluon singlet anomalous dimension.
The routine is taken from [FHMV23a].
- 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: