From 8601f5ac57d055233528e43c3b98da032a49e971 Mon Sep 17 00:00:00 2001
From: t7phy <t7phy.in@gmail.com>
Date: Mon, 10 Apr 2023 13:12:00 +0200
Subject: [PATCH 01/22] tl ome as1

---
 doc/source/refs.bib                           | 13 ++++
 .../unpolarized/time_like/as1.py              |  2 +-
 .../unpolarized/time_like/as1.py              | 76 +++++++++++++++++++
 3 files changed, 90 insertions(+), 1 deletion(-)
 create mode 100644 src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py

diff --git a/doc/source/refs.bib b/doc/source/refs.bib
index 5c720a857..c26c631c0 100644
--- a/doc/source/refs.bib
+++ b/doc/source/refs.bib
@@ -894,3 +894,16 @@ @article{Almasy:2011eq
     pages = "133--152",
     year = "2012"
 }
+
+@article{Cacciari:2005ry,
+    author = "Cacciari, Matteo and Nason, Paolo and Oleari, Carlo",
+    title = "{Crossing heavy-flavor thresholds in fragmentation functions}",
+    eprint = "hep-ph/0504192",
+    archivePrefix = "arXiv",
+    reportNumber = "BICOCCA-FT-05-8, LPTHE-05-09",
+    doi = "10.1088/1126-6708/2005/10/034",
+    journal = "JHEP",
+    volume = "10",
+    pages = "034",
+    year = "2005"
+}
diff --git a/src/ekore/anomalous_dimensions/unpolarized/time_like/as1.py b/src/ekore/anomalous_dimensions/unpolarized/time_like/as1.py
index 43d33bbee..a71bc0a6c 100644
--- a/src/ekore/anomalous_dimensions/unpolarized/time_like/as1.py
+++ b/src/ekore/anomalous_dimensions/unpolarized/time_like/as1.py
@@ -1,4 +1,4 @@
-"""The unpolarized |LO| Altarelli-Parisi splitting kernels."""
+"""The unpolarized time-like |LO| Altarelli-Parisi splitting kernels."""
 
 import numba as nb
 import numpy as np
diff --git a/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py b/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
new file mode 100644
index 000000000..f721ddb51
--- /dev/null
+++ b/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
@@ -0,0 +1,76 @@
+"""The unpolarized |NLO| matching conditions."""
+
+import numba as nb
+import numpy as np
+
+from eko.constants import CF
+
+
+@nb.njit(cache=True)
+def A_hg(N, L):
+    r"""Compute the |NLO| heavy-gluon |OME|.
+
+    Implements :eqref:`27` from :cite:`Cacciari:2005ry`
+
+    Parameters
+    ----------
+    N : complex
+        Mellin moment
+    L : float
+        :math:`\ln(\mu_F^2 / m_h^2)
+
+    Returns
+    -------
+    A_hg : complex
+        |NLO| heavy-gluon |OME|
+        :math:`A_{Hg}^{S,(1)}
+
+    """
+    result = (
+        2
+        * CF
+        * (
+            (2 + N + N**2) / (N * (N**2 - 1)) * (L - 1)
+            + 4 / (N - 1) ** 2
+            - 4 / N**2
+            + 2 / (N + 1) ** 2
+        )
+    )
+    return result
+
+
+@nb.njit(cache=True)
+def A_singlet(N, L):
+    r"""Compute the |NLO| singlet |OME|.
+
+    Parameters
+    ----------
+    N : complex
+        Mellin moment
+    L : float
+        :math:`\ln(\mu_F^2 / m_h^2)
+
+    Returns
+    -------
+    A_singlet : numpy.ndarray
+        |NLO| singlet |OME|
+        :math:`A^{S,(1)}`
+
+    """
+    result = np.array([[0, 0, 0], [0, 0, 0], [A_hg(N, L), 0, 0]], np.complex_)
+    return result
+
+
+@nb.njit(cache=True)
+def A_ns():
+    r"""Compute the |NLO| non-singlet |OME|.
+
+    Returns
+    -------
+    A_ns : numpy.ndarray
+        |NLO| non-singlet |OME|
+        :math:`A^{S,(1)}
+
+    """
+    result = np.array([[0, 0], [0, 0]], np.complex_)
+    return result

From e1e781e554124ad2ec7ca0ca16ef31b1ac54c65f Mon Sep 17 00:00:00 2001
From: t7phy <t7phy.in@gmail.com>
Date: Mon, 10 Apr 2023 13:14:13 +0200
Subject: [PATCH 02/22] fix title

---
 src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py b/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
index f721ddb51..0fdac5c72 100644
--- a/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
+++ b/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
@@ -1,4 +1,4 @@
-"""The unpolarized |NLO| matching conditions."""
+"""The unpolarized time-like |NLO| matching conditions."""
 
 import numba as nb
 import numpy as np

From 0e17578bebbab449c966ae4ba468555629234537 Mon Sep 17 00:00:00 2001
From: t7phy <t7phy.in@gmail.com>
Date: Mon, 10 Apr 2023 13:43:19 +0200
Subject: [PATCH 03/22] tl ome init

---
 .../operator_matrix_element.py                |  4 +-
 .../unpolarized/time_like/__init__.py         | 57 +++++++++++++++++--
 .../unpolarized/time_like/as1.py              |  8 +--
 3 files changed, 57 insertions(+), 12 deletions(-)

diff --git a/src/eko/evolution_operator/operator_matrix_element.py b/src/eko/evolution_operator/operator_matrix_element.py
index 95e4ddff9..7ab021da9 100644
--- a/src/eko/evolution_operator/operator_matrix_element.py
+++ b/src/eko/evolution_operator/operator_matrix_element.py
@@ -167,7 +167,7 @@ def quad_ker(
                 A = ome_ps.A_singlet(order, ker_base.n, sx, nf, L, is_msbar, sx_ns)
         else:
             if is_time_like:
-                A = ome_ut.A_singlet(order, ker_base.n, sx, nf, L, is_msbar, sx_ns)
+                A = ome_ut.A_singlet(order, ker_base.n, L)
             else:
                 A = ome_us.A_singlet(order, ker_base.n, sx, nf, L, is_msbar, sx_ns)
     else:
@@ -179,7 +179,7 @@ def quad_ker(
                 A = ome_ps.A_non_singlet(order, ker_base.n, sx, nf, L)
         else:
             if is_time_like:
-                A = ome_ut.A_non_singlet(order, ker_base.n, sx, nf, L)
+                A = ome_ut.A_non_singlet(order, ker_base.n, L)
             else:
                 A = ome_us.A_non_singlet(order, ker_base.n, sx, nf, L)
 
diff --git a/src/ekore/operator_matrix_elements/unpolarized/time_like/__init__.py b/src/ekore/operator_matrix_elements/unpolarized/time_like/__init__.py
index bb20ff58b..bcde46b45 100644
--- a/src/ekore/operator_matrix_elements/unpolarized/time_like/__init__.py
+++ b/src/ekore/operator_matrix_elements/unpolarized/time_like/__init__.py
@@ -1,15 +1,60 @@
 r"""The polarized, time-like |OME|."""
 
 import numba as nb
+import numpy as np
+
+from . import as1
 
 
 @nb.njit(cache=True)
-def A_non_singlet(_matching_order, _n, _sx, _nf, _L):
-    """Compute the non-singlet |OME|."""
-    raise NotImplementedError("Time-like is not yet implemented")
+def A_non_singlet(matching_order, N, L):
+    r"""Compute the non-singlet |OME|.
+
+    Parameters
+    ----------
+    matching_order : tuple(int, int)
+        perturbative matching order
+    N : complex
+        Mellin moment
+    L : float
+        :math:`\ln(\mu_F^2 / m_h^2)`
+
+    Returns
+    -------
+    A_non_singlet : numpy.ndarray
+        non-singlet |OME|
+
+    """
+    A_ns = np.zeros((matching_order[0], 2, 2), np.complex_)
+    if matching_order[0] > 1:
+        raise Exception("Time-like matching conditions are only known upto NLO")
+    else:
+        A_ns[0] = as1.A_ns()
+    return A_ns
 
 
 @nb.njit(cache=True)
-def A_singlet(_matching_order, _n, _sx, _nf, _L, _is_msbar, _sx_ns=None):
-    """Compute the singlet |OME|."""
-    raise NotImplementedError("Time-like is not yet implemented")
+def A_singlet(matching_order, N, L):
+    r"""Compute the singlet |OME|.
+
+    Parameters
+    ----------
+    matching_order : tuple(int, int)
+        perturbative matching order
+    N : complex
+        Mellin moment
+    L : float
+        :math:`\ln(\mu_F^2 / m_h^2)`
+
+    Returns
+    -------
+    A_singlet : numpy.ndarray
+        singlet |OME|
+
+    """
+    A_singlet = np.zeros((matching_order[0], 3, 3), np.complex_)
+    if matching_order[0] > 1:
+        raise Exception("Time-like matching conditions are only known upto NLO")
+    else:
+        A_singlet[0] = as1.A_singlet(N, L)
+    return A_singlet
diff --git a/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py b/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
index 0fdac5c72..b5237a551 100644
--- a/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
+++ b/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
@@ -17,13 +17,13 @@ def A_hg(N, L):
     N : complex
         Mellin moment
     L : float
-        :math:`\ln(\mu_F^2 / m_h^2)
+        :math:`\ln(\mu_F^2 / m_h^2)`
 
     Returns
     -------
     A_hg : complex
         |NLO| heavy-gluon |OME|
-        :math:`A_{Hg}^{S,(1)}
+        :math:`A_{hg}^{S,(1)}`
 
     """
     result = (
@@ -48,7 +48,7 @@ def A_singlet(N, L):
     N : complex
         Mellin moment
     L : float
-        :math:`\ln(\mu_F^2 / m_h^2)
+        :math:`\ln(\mu_F^2 / m_h^2)`
 
     Returns
     -------
@@ -69,7 +69,7 @@ def A_ns():
     -------
     A_ns : numpy.ndarray
         |NLO| non-singlet |OME|
-        :math:`A^{S,(1)}
+        :math:`A^{S,(1)}`
 
     """
     result = np.array([[0, 0], [0, 0]], np.complex_)

From 833801b409d8bababfd14a7382e8c7d65a35d20d Mon Sep 17 00:00:00 2001
From: t7phy <t7phy.in@gmail.com>
Date: Mon, 10 Apr 2023 15:03:42 +0200
Subject: [PATCH 04/22] fix test_ome

---
 tests/eko/evolution_operator/test_ome.py | 117 ++++++++++++-----------
 1 file changed, 59 insertions(+), 58 deletions(-)

diff --git a/tests/eko/evolution_operator/test_ome.py b/tests/eko/evolution_operator/test_ome.py
index 2c0fdf644..af30072ee 100644
--- a/tests/eko/evolution_operator/test_ome.py
+++ b/tests/eko/evolution_operator/test_ome.py
@@ -81,7 +81,7 @@ def test_build_ome_nlo():
 
 
 def test_quad_ker_errors():
-    for p, t in [(True, False), (False, True), (True, True)]:
+    for p, t in [(True, False), (True, True)]:
         for mode0, mode1 in [
             (21, br.matching_hplus_pid),
             (200, br.matching_hminus_pid),
@@ -128,63 +128,64 @@ def test_quad_ker(monkeypatch):
         lambda *args: np.array([zeros, zeros, zeros]),
     )
     for is_log in [True, False]:
-        res_ns = quad_ker(
-            u=0,
-            order=(3, 0),
-            mode0=200,
-            mode1=200,
-            is_log=is_log,
-            logx=0.123,
-            areas=np.zeros(3),
-            backward_method=None,
-            a_s=0.0,
-            nf=3,
-            L=0.0,
-            sv_mode=sv.Modes.expanded,
-            Lsv=0.0,
-            is_msbar=False,
-            is_polarized=False,
-            is_time_like=False,
-        )
-        np.testing.assert_allclose(res_ns, 1.0)
-        res_s = quad_ker(
-            u=0,
-            order=(3, 0),
-            mode0=100,
-            mode1=100,
-            is_log=is_log,
-            logx=0.123,
-            areas=np.zeros(3),
-            backward_method=None,
-            a_s=0.0,
-            nf=3,
-            L=0.0,
-            sv_mode=sv.Modes.expanded,
-            Lsv=0.0,
-            is_msbar=False,
-            is_polarized=False,
-            is_time_like=False,
-        )
-        np.testing.assert_allclose(res_s, 1.0)
-        res_s = quad_ker(
-            u=0,
-            order=(3, 0),
-            mode0=100,
-            mode1=21,
-            is_log=is_log,
-            logx=0.0,
-            areas=np.zeros(3),
-            backward_method=None,
-            a_s=0.0,
-            nf=3,
-            L=0.0,
-            sv_mode=sv.Modes.expanded,
-            Lsv=0.0,
-            is_msbar=False,
-            is_polarized=False,
-            is_time_like=False,
-        )
-        np.testing.assert_allclose(res_s, 0.0)
+        for p, t in [(False, False), (False, True)]:
+            res_ns = quad_ker(
+                u=0,
+                order=(3, 0),
+                mode0=200,
+                mode1=200,
+                is_log=is_log,
+                logx=0.123,
+                areas=np.zeros(3),
+                backward_method=None,
+                a_s=0.0,
+                nf=3,
+                L=0.0,
+                sv_mode=sv.Modes.expanded,
+                Lsv=0.0,
+                is_msbar=False,
+                is_polarized=p,
+                is_time_like=t,
+            )
+            np.testing.assert_allclose(res_ns, 1.0)
+            res_s = quad_ker(
+                u=0,
+                order=(3, 0),
+                mode0=100,
+                mode1=100,
+                is_log=is_log,
+                logx=0.123,
+                areas=np.zeros(3),
+                backward_method=None,
+                a_s=0.0,
+                nf=3,
+                L=0.0,
+                sv_mode=sv.Modes.expanded,
+                Lsv=0.0,
+                is_msbar=False,
+                is_polarized=p,
+                is_time_like=t,
+            )
+            np.testing.assert_allclose(res_s, 1.0)
+            res_s = quad_ker(
+                u=0,
+                order=(3, 0),
+                mode0=100,
+                mode1=21,
+                is_log=is_log,
+                logx=0.0,
+                areas=np.zeros(3),
+                backward_method=None,
+                a_s=0.0,
+                nf=3,
+                L=0.0,
+                sv_mode=sv.Modes.expanded,
+                Lsv=0.0,
+                is_msbar=False,
+                is_polarized=p,
+                is_time_like=t,
+            )
+            np.testing.assert_allclose(res_s, 0.0)
 
     # test expanded intrisic inverse kernels
     labels = [(200, 200), *br.singlet_labels]

From a343085f18ccce536d2a31e7c5c782b20792d0ed Mon Sep 17 00:00:00 2001
From: t7phy <t7phy.in@gmail.com>
Date: Mon, 10 Apr 2023 15:17:59 +0200
Subject: [PATCH 05/22] fix test_ome order

---
 tests/eko/evolution_operator/test_ome.py | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/tests/eko/evolution_operator/test_ome.py b/tests/eko/evolution_operator/test_ome.py
index af30072ee..e2e6d7b8b 100644
--- a/tests/eko/evolution_operator/test_ome.py
+++ b/tests/eko/evolution_operator/test_ome.py
@@ -128,10 +128,10 @@ def test_quad_ker(monkeypatch):
         lambda *args: np.array([zeros, zeros, zeros]),
     )
     for is_log in [True, False]:
-        for p, t in [(False, False), (False, True)]:
+        for order, p, t in [((3, 0), False, False), ((2, 0), False, True)]:
             res_ns = quad_ker(
                 u=0,
-                order=(3, 0),
+                order=order,
                 mode0=200,
                 mode1=200,
                 is_log=is_log,
@@ -150,7 +150,7 @@ def test_quad_ker(monkeypatch):
             np.testing.assert_allclose(res_ns, 1.0)
             res_s = quad_ker(
                 u=0,
-                order=(3, 0),
+                order=order,
                 mode0=100,
                 mode1=100,
                 is_log=is_log,
@@ -169,7 +169,7 @@ def test_quad_ker(monkeypatch):
             np.testing.assert_allclose(res_s, 1.0)
             res_s = quad_ker(
                 u=0,
-                order=(3, 0),
+                order=order,
                 mode0=100,
                 mode1=21,
                 is_log=is_log,

From 4cc95b6a7ab7218df87f21d67fb08e5b1bd653e3 Mon Sep 17 00:00:00 2001
From: t7phy <t7phy.in@gmail.com>
Date: Mon, 10 Apr 2023 15:32:41 +0200
Subject: [PATCH 06/22] fix typo

---
 tests/eko/evolution_operator/test_ome.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/tests/eko/evolution_operator/test_ome.py b/tests/eko/evolution_operator/test_ome.py
index e2e6d7b8b..5d8c2e23b 100644
--- a/tests/eko/evolution_operator/test_ome.py
+++ b/tests/eko/evolution_operator/test_ome.py
@@ -128,7 +128,7 @@ def test_quad_ker(monkeypatch):
         lambda *args: np.array([zeros, zeros, zeros]),
     )
     for is_log in [True, False]:
-        for order, p, t in [((3, 0), False, False), ((2, 0), False, True)]:
+        for order, p, t in [((3, 0), False, False), ((1, 0), False, True)]:
             res_ns = quad_ker(
                 u=0,
                 order=order,

From 79690809e1f2b76658f9a874130de47f77ae73ff Mon Sep 17 00:00:00 2001
From: t7phy <t7phy.in@gmail.com>
Date: Mon, 10 Apr 2023 17:19:19 +0200
Subject: [PATCH 07/22] add test_init

---
 .../unpolarized/time_like/__init__.py                |  4 ++--
 .../unpolarized/time_like/as1.py                     |  5 +++--
 .../unpolarized/time_like/test_init.py               | 12 ++++--------
 3 files changed, 9 insertions(+), 12 deletions(-)

diff --git a/src/ekore/operator_matrix_elements/unpolarized/time_like/__init__.py b/src/ekore/operator_matrix_elements/unpolarized/time_like/__init__.py
index bcde46b45..269ba7c0f 100644
--- a/src/ekore/operator_matrix_elements/unpolarized/time_like/__init__.py
+++ b/src/ekore/operator_matrix_elements/unpolarized/time_like/__init__.py
@@ -52,9 +52,9 @@ def A_singlet(matching_order, N, L):
         singlet |OME|
 
     """
-    A_singlet = np.zeros((matching_order[0], 3, 3), np.complex_)
     if matching_order[0] > 1:
         raise Exception("Time-like matching conditions are only known upto NLO")
     else:
-        A_singlet[0] = as1.A_singlet(N, L)
+        A_singlet = np.zeros((matching_order[0], 3, 3), np.complex_)
+    #        A_singlet[0] = as1.A_singlet(N, L)
     return A_singlet
diff --git a/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py b/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
index b5237a551..0bf702cb1 100644
--- a/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
+++ b/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
@@ -3,7 +3,8 @@
 import numba as nb
 import numpy as np
 
-from eko.constants import CF
+# from eko.constants import CF
+CF = 4 / 3
 
 
 @nb.njit(cache=True)
@@ -57,7 +58,7 @@ def A_singlet(N, L):
         :math:`A^{S,(1)}`
 
     """
-    result = np.array([[0, 0, 0], [0, 0, 0], [A_hg(N, L), 0, 0]], np.complex_)
+    result = np.array([[0 + 0j, 0, 0], [0 + 0j, 0, 0], [A_hg(N, L), 0, 0]], np.complex_)
     return result
 
 
diff --git a/tests/ekore/operator_matrix_elements/unpolarized/time_like/test_init.py b/tests/ekore/operator_matrix_elements/unpolarized/time_like/test_init.py
index b10e3ecf3..eedc47ed2 100644
--- a/tests/ekore/operator_matrix_elements/unpolarized/time_like/test_init.py
+++ b/tests/ekore/operator_matrix_elements/unpolarized/time_like/test_init.py
@@ -1,10 +1,6 @@
-import pytest
+import ekore.operator_matrix_elements.unpolarized.time_like as ome
 
-import ekore.operator_matrix_elements.unpolarized.time_like as ome_ut
 
-
-def test_init():
-    with pytest.raises(NotImplementedError):
-        ome_ut.A_non_singlet((1, 0), 1.0, [], 4, 0.0)
-    with pytest.raises(NotImplementedError):
-        ome_ut.A_singlet((1, 0), 1.0, [], 4, 0.0, False)
+def test_shapes():
+    assert ome.A_singlet((1, 0), complex(0, 1), 0).shape == (1, 3, 3)
+    assert ome.A_non_singlet((1, 0), complex(0, 1), 0).shape == (1, 2, 2)

From 9fff9e70e4c5562dc031a18c880065a17d7b68e8 Mon Sep 17 00:00:00 2001
From: t7phy <t7phy.in@gmail.com>
Date: Mon, 10 Apr 2023 17:58:49 +0200
Subject: [PATCH 08/22] test_as1 added

---
 .../unpolarized/time_like/test_as1.py         | 19 +++++++++++++++++++
 .../unpolarized/time_like/test_init.py        |  2 ++
 2 files changed, 21 insertions(+)
 create mode 100644 tests/ekore/operator_matrix_elements/unpolarized/time_like/test_as1.py

diff --git a/tests/ekore/operator_matrix_elements/unpolarized/time_like/test_as1.py b/tests/ekore/operator_matrix_elements/unpolarized/time_like/test_as1.py
new file mode 100644
index 000000000..971110588
--- /dev/null
+++ b/tests/ekore/operator_matrix_elements/unpolarized/time_like/test_as1.py
@@ -0,0 +1,19 @@
+r"""Test NLO |OME|."""
+
+import numpy as np
+
+import ekore.operator_matrix_elements.unpolarized.time_like.as1 as ome_as1
+
+
+def test_A_hg():
+    res = [
+        complex(-752 / 75, 112 / 25),
+        complex(-3268 / 4225, -24872 / 12675),
+        complex(437984 / 950625, -4829264 / 2851875),
+    ]
+    for i, N, L in [
+        (0, complex(1, 1), 1),
+        (1, complex(2, 2), 2),
+        (2, complex(3, 3), 3),
+    ]:
+        np.testing.assert_almost_equal(ome_as1.A_hg(N, L), res[i])
diff --git a/tests/ekore/operator_matrix_elements/unpolarized/time_like/test_init.py b/tests/ekore/operator_matrix_elements/unpolarized/time_like/test_init.py
index eedc47ed2..051274596 100644
--- a/tests/ekore/operator_matrix_elements/unpolarized/time_like/test_init.py
+++ b/tests/ekore/operator_matrix_elements/unpolarized/time_like/test_init.py
@@ -1,3 +1,5 @@
+r"""Test |OME|."""
+
 import ekore.operator_matrix_elements.unpolarized.time_like as ome
 
 

From 5c4966b72c63a8b829158a0f0bf1ca30e2b2b2c4 Mon Sep 17 00:00:00 2001
From: t7phy <t7phy.in@gmail.com>
Date: Mon, 10 Apr 2023 18:04:31 +0200
Subject: [PATCH 09/22] modify docs

---
 doc/source/theory/TimeLike.rst | 3 +++
 1 file changed, 3 insertions(+)

diff --git a/doc/source/theory/TimeLike.rst b/doc/source/theory/TimeLike.rst
index 7397e0c73..1a2084a98 100644
--- a/doc/source/theory/TimeLike.rst
+++ b/doc/source/theory/TimeLike.rst
@@ -19,6 +19,9 @@ The relevant setting in the operator card is thus called ``time_like = True``.
 We implement the time-like |DGLAP| anomalous dimensions up to |NNLO| in :class:`~ekore.anomalous_dimensions.unpolarized.time_like`.
 The implementation for the |LO| and |NLO| splitting functions is based on :cite:`Mitov:2006wy, Gluck:1992zx` and the implementation for
 the |NNLO| splitting functions is based on :cite:`Mitov:2006ic, Moch:2007tx, Almasy:2011eq`.
+We also implement the time-like matching conditions up to |NLO| in :class:`~ekore.operator_matrix_elements.unpolarized.time_like` which
+are based on :cite:`Cacciari:2005ry`. The time-like matching conditions for |NNLO| are not known.
+
 Supplying new anomalous dimensions and new matching conditions is the only change required for the eko program (e.g. the
 solution strategies are unaffected).
 

From 7854ad8731f4ec9a0cd196ce89b6089e175152c0 Mon Sep 17 00:00:00 2001
From: t7phy <t7phy.in@gmail.com>
Date: Mon, 10 Apr 2023 23:31:42 +0200
Subject: [PATCH 10/22] few corrections

---
 benchmarks/FF_LHAPDF_bench.py                                 | 2 +-
 doc/source/theory/TimeLike.rst                                | 1 -
 .../unpolarized/time_like/__init__.py                         | 4 ++--
 3 files changed, 3 insertions(+), 4 deletions(-)

diff --git a/benchmarks/FF_LHAPDF_bench.py b/benchmarks/FF_LHAPDF_bench.py
index c9c9816a6..9bcdb2e2b 100644
--- a/benchmarks/FF_LHAPDF_bench.py
+++ b/benchmarks/FF_LHAPDF_bench.py
@@ -104,7 +104,7 @@ def benchmark_lo(self, ff_index, Q0=10, mugrid=(100,)):
 
         self.run([theory_card], [operator_card], [FF_sets_lo[ff_index]])
 
-    def benchmark_nlo(self, ff_index, Q0=10, mugrid=(100,)):
+    def benchmark_nlo(self, ff_index, Q0=10, mugrid=(1.65,)):
         theory_card = {
             **base_theory,
             "PTO": 1,
diff --git a/doc/source/theory/TimeLike.rst b/doc/source/theory/TimeLike.rst
index 1a2084a98..6287bf57a 100644
--- a/doc/source/theory/TimeLike.rst
+++ b/doc/source/theory/TimeLike.rst
@@ -21,7 +21,6 @@ The implementation for the |LO| and |NLO| splitting functions is based on :cite:
 the |NNLO| splitting functions is based on :cite:`Mitov:2006ic, Moch:2007tx, Almasy:2011eq`.
 We also implement the time-like matching conditions up to |NLO| in :class:`~ekore.operator_matrix_elements.unpolarized.time_like` which
 are based on :cite:`Cacciari:2005ry`. The time-like matching conditions for |NNLO| are not known.
-
 Supplying new anomalous dimensions and new matching conditions is the only change required for the eko program (e.g. the
 solution strategies are unaffected).
 
diff --git a/src/ekore/operator_matrix_elements/unpolarized/time_like/__init__.py b/src/ekore/operator_matrix_elements/unpolarized/time_like/__init__.py
index 269ba7c0f..20e2609eb 100644
--- a/src/ekore/operator_matrix_elements/unpolarized/time_like/__init__.py
+++ b/src/ekore/operator_matrix_elements/unpolarized/time_like/__init__.py
@@ -25,10 +25,10 @@ def A_non_singlet(matching_order, N, L):
         non-singlet |OME|
 
     """
-    A_ns = np.zeros((matching_order[0], 2, 2), np.complex_)
     if matching_order[0] > 1:
         raise Exception("Time-like matching conditions are only known upto NLO")
     else:
+        A_ns = np.zeros((matching_order[0], 2, 2), np.complex_)
         A_ns[0] = as1.A_ns()
     return A_ns
 
@@ -56,5 +56,5 @@ def A_singlet(matching_order, N, L):
         raise Exception("Time-like matching conditions are only known upto NLO")
     else:
         A_singlet = np.zeros((matching_order[0], 3, 3), np.complex_)
-    #        A_singlet[0] = as1.A_singlet(N, L)
+        A_singlet[0] = as1.A_singlet(N, L)
     return A_singlet

From 0f53e86bc2617ce0acb88aa3a95bed3e1617aaae Mon Sep 17 00:00:00 2001
From: t7phy <t7phy.in@gmail.com>
Date: Tue, 11 Apr 2023 14:48:04 +0200
Subject: [PATCH 11/22] commas and full stops

---
 .../anomalous_dimensions/unpolarized/time_like/__init__.py    | 2 +-
 src/ekore/anomalous_dimensions/unpolarized/time_like/as1.py   | 2 +-
 src/ekore/anomalous_dimensions/unpolarized/time_like/as2.py   | 2 +-
 src/ekore/anomalous_dimensions/unpolarized/time_like/as3.py   | 2 +-
 .../unpolarized/time_like/__init__.py                         | 2 +-
 .../operator_matrix_elements/unpolarized/time_like/as1.py     | 4 ++--
 6 files changed, 7 insertions(+), 7 deletions(-)

diff --git a/src/ekore/anomalous_dimensions/unpolarized/time_like/__init__.py b/src/ekore/anomalous_dimensions/unpolarized/time_like/__init__.py
index 293f62a0c..59b69e478 100644
--- a/src/ekore/anomalous_dimensions/unpolarized/time_like/__init__.py
+++ b/src/ekore/anomalous_dimensions/unpolarized/time_like/__init__.py
@@ -1,4 +1,4 @@
-"""The unpolarized time-like Altarelli-Parisi splitting kernels."""
+"""The unpolarized, time-like Altarelli-Parisi splitting kernels."""
 
 import numba as nb
 import numpy as np
diff --git a/src/ekore/anomalous_dimensions/unpolarized/time_like/as1.py b/src/ekore/anomalous_dimensions/unpolarized/time_like/as1.py
index a71bc0a6c..44913ba05 100644
--- a/src/ekore/anomalous_dimensions/unpolarized/time_like/as1.py
+++ b/src/ekore/anomalous_dimensions/unpolarized/time_like/as1.py
@@ -1,4 +1,4 @@
-"""The unpolarized time-like |LO| Altarelli-Parisi splitting kernels."""
+"""The unpolarized, time-like |LO| Altarelli-Parisi splitting kernels."""
 
 import numba as nb
 import numpy as np
diff --git a/src/ekore/anomalous_dimensions/unpolarized/time_like/as2.py b/src/ekore/anomalous_dimensions/unpolarized/time_like/as2.py
index 8afd836b8..68c3955b1 100644
--- a/src/ekore/anomalous_dimensions/unpolarized/time_like/as2.py
+++ b/src/ekore/anomalous_dimensions/unpolarized/time_like/as2.py
@@ -1,4 +1,4 @@
-"""The unpolarized time-like |NLO| Altarelli-Parisi splitting kernels."""
+"""The unpolarized, time-like |NLO| Altarelli-Parisi splitting kernels."""
 
 import numba as nb
 import numpy as np
diff --git a/src/ekore/anomalous_dimensions/unpolarized/time_like/as3.py b/src/ekore/anomalous_dimensions/unpolarized/time_like/as3.py
index 4e16cb556..fdd8a8daf 100644
--- a/src/ekore/anomalous_dimensions/unpolarized/time_like/as3.py
+++ b/src/ekore/anomalous_dimensions/unpolarized/time_like/as3.py
@@ -1,4 +1,4 @@
-"""The unpolarized time-like |NNLO| Altarelli-Parisi splitting kernels."""
+"""The unpolarized, time-like |NNLO| Altarelli-Parisi splitting kernels."""
 
 import numba as nb
 import numpy as np
diff --git a/src/ekore/operator_matrix_elements/unpolarized/time_like/__init__.py b/src/ekore/operator_matrix_elements/unpolarized/time_like/__init__.py
index 20e2609eb..ca75297e3 100644
--- a/src/ekore/operator_matrix_elements/unpolarized/time_like/__init__.py
+++ b/src/ekore/operator_matrix_elements/unpolarized/time_like/__init__.py
@@ -1,4 +1,4 @@
-r"""The polarized, time-like |OME|."""
+r"""The unpolarized, time-like |OME|."""
 
 import numba as nb
 import numpy as np
diff --git a/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py b/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
index 0bf702cb1..81f03542f 100644
--- a/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
+++ b/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
@@ -1,4 +1,4 @@
-"""The unpolarized time-like |NLO| matching conditions."""
+"""The unpolarized, time-like |NLO| matching conditions."""
 
 import numba as nb
 import numpy as np
@@ -11,7 +11,7 @@
 def A_hg(N, L):
     r"""Compute the |NLO| heavy-gluon |OME|.
 
-    Implements :eqref:`27` from :cite:`Cacciari:2005ry`
+    Implements :eqref:`27` from :cite:`Cacciari:2005ry`.
 
     Parameters
     ----------

From c58185744fc515c4855760abf4001254187fbd71 Mon Sep 17 00:00:00 2001
From: t7phy <t7phy.in@gmail.com>
Date: Tue, 11 Apr 2023 15:26:58 +0200
Subject: [PATCH 12/22] A_gg added

---
 .../unpolarized/time_like/as1.py              | 24 ++++++++++++++++++-
 1 file changed, 23 insertions(+), 1 deletion(-)

diff --git a/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py b/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
index 81f03542f..0b328a01f 100644
--- a/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
+++ b/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
@@ -40,6 +40,26 @@ def A_hg(N, L):
     return result
 
 
+@nb.njit(cache=True)
+def A_gg(L):
+    r"""Compute the |NLO| gluon-gluon |OME|.
+
+    They are defined as the Mellin transform of :eqref:`B.6` from :cite:`Buza_1998`.
+
+    Parameters
+    ----------
+    L : float
+        :math:`\ln(\mu_F^2 / m_h^2)`
+
+    Returns
+    -------
+    A_gg : complex
+        |NLO| gluon-gluon |OME| :math:`A_{gg,H}^{S,(1)}`
+
+    """
+    return -2.0 / 3.0 * L
+
+
 @nb.njit(cache=True)
 def A_singlet(N, L):
     r"""Compute the |NLO| singlet |OME|.
@@ -58,7 +78,9 @@ def A_singlet(N, L):
         :math:`A^{S,(1)}`
 
     """
-    result = np.array([[0 + 0j, 0, 0], [0 + 0j, 0, 0], [A_hg(N, L), 0, 0]], np.complex_)
+    result = np.array(
+        [[A_gg(L), 0, 0], [0 + 0j, 0, 0], [A_hg(N, L), 0, 0]], np.complex_
+    )
     return result
 
 

From d9089d12868725c6830f2eb292315770867efa8c Mon Sep 17 00:00:00 2001
From: t7phy <t7phy.in@gmail.com>
Date: Tue, 11 Apr 2023 15:29:51 +0200
Subject: [PATCH 13/22] use CF from eko

---
 .../operator_matrix_elements/unpolarized/time_like/as1.py      | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py b/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
index 0b328a01f..066e57a41 100644
--- a/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
+++ b/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
@@ -3,8 +3,7 @@
 import numba as nb
 import numpy as np
 
-# from eko.constants import CF
-CF = 4 / 3
+from eko.constants import CF
 
 
 @nb.njit(cache=True)

From b2d79a8e315f8e98c0670a462da572d98f249b40 Mon Sep 17 00:00:00 2001
From: t7phy <t7phy.in@gmail.com>
Date: Tue, 11 Apr 2023 15:32:39 +0200
Subject: [PATCH 14/22] source of values in tests

---
 .../operator_matrix_elements/unpolarized/time_like/test_as1.py  | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/tests/ekore/operator_matrix_elements/unpolarized/time_like/test_as1.py b/tests/ekore/operator_matrix_elements/unpolarized/time_like/test_as1.py
index 971110588..c5c224e82 100644
--- a/tests/ekore/operator_matrix_elements/unpolarized/time_like/test_as1.py
+++ b/tests/ekore/operator_matrix_elements/unpolarized/time_like/test_as1.py
@@ -1,4 +1,4 @@
-r"""Test NLO |OME|."""
+"""Testing values obtained from Mathematica."""
 
 import numpy as np
 

From 7937aa183cf181c8063487cdfa4c87e31460296b Mon Sep 17 00:00:00 2001
From: t7phy <t7phy.in@gmail.com>
Date: Tue, 11 Apr 2023 15:39:42 +0200
Subject: [PATCH 15/22] add 0j

---
 src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py b/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
index 066e57a41..bc9aacdbc 100644
--- a/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
+++ b/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
@@ -78,7 +78,7 @@ def A_singlet(N, L):
 
     """
     result = np.array(
-        [[A_gg(L), 0, 0], [0 + 0j, 0, 0], [A_hg(N, L), 0, 0]], np.complex_
+        [[A_gg(L), 0 + 0j, 0], [0 + 0j, 0, 0], [A_hg(N, L), 0, 0]], np.complex_
     )
     return result
 

From e4d5c33f0286314160a3d8bff22461aca12c3e78 Mon Sep 17 00:00:00 2001
From: t7phy <t7phy.in@gmail.com>
Date: Tue, 11 Apr 2023 15:59:22 +0200
Subject: [PATCH 16/22] simplify init

---
 .../unpolarized/time_like/__init__.py                  | 10 ++++------
 1 file changed, 4 insertions(+), 6 deletions(-)

diff --git a/src/ekore/operator_matrix_elements/unpolarized/time_like/__init__.py b/src/ekore/operator_matrix_elements/unpolarized/time_like/__init__.py
index ca75297e3..6eecc372c 100644
--- a/src/ekore/operator_matrix_elements/unpolarized/time_like/__init__.py
+++ b/src/ekore/operator_matrix_elements/unpolarized/time_like/__init__.py
@@ -27,9 +27,8 @@ def A_non_singlet(matching_order, N, L):
     """
     if matching_order[0] > 1:
         raise Exception("Time-like matching conditions are only known upto NLO")
-    else:
-        A_ns = np.zeros((matching_order[0], 2, 2), np.complex_)
-        A_ns[0] = as1.A_ns()
+    A_ns = np.zeros((matching_order[0], 2, 2), np.complex_)
+    A_ns[0] = as1.A_ns()
     return A_ns
 
 
@@ -54,7 +53,6 @@ def A_singlet(matching_order, N, L):
     """
     if matching_order[0] > 1:
         raise Exception("Time-like matching conditions are only known upto NLO")
-    else:
-        A_singlet = np.zeros((matching_order[0], 3, 3), np.complex_)
-        A_singlet[0] = as1.A_singlet(N, L)
+    A_singlet = np.zeros((matching_order[0], 3, 3), np.complex_)
+    A_singlet[0] = as1.A_singlet(N, L)
     return A_singlet

From e879f4b00712b439a8bb9be5167bc329c5e0e418 Mon Sep 17 00:00:00 2001
From: t7phy <t7phy.in@gmail.com>
Date: Tue, 11 Apr 2023 16:45:25 +0200
Subject: [PATCH 17/22] change cite

---
 src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py b/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
index bc9aacdbc..e52127349 100644
--- a/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
+++ b/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
@@ -43,7 +43,7 @@ def A_hg(N, L):
 def A_gg(L):
     r"""Compute the |NLO| gluon-gluon |OME|.
 
-    They are defined as the Mellin transform of :eqref:`B.6` from :cite:`Buza_1998`.
+    Implements the Mellin transform of :eqref:`24` from :cite:`Cacciari:2005ry`.
 
     Parameters
     ----------

From 1d5232fdd267cda15a10db8cb732feb345902ff0 Mon Sep 17 00:00:00 2001
From: t7phy <t7phy.in@gmail.com>
Date: Tue, 11 Apr 2023 16:50:40 +0200
Subject: [PATCH 18/22] test A_gg

---
 .../unpolarized/time_like/test_as1.py                       | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/tests/ekore/operator_matrix_elements/unpolarized/time_like/test_as1.py b/tests/ekore/operator_matrix_elements/unpolarized/time_like/test_as1.py
index c5c224e82..ca9c7e4a3 100644
--- a/tests/ekore/operator_matrix_elements/unpolarized/time_like/test_as1.py
+++ b/tests/ekore/operator_matrix_elements/unpolarized/time_like/test_as1.py
@@ -17,3 +17,9 @@ def test_A_hg():
         (2, complex(3, 3), 3),
     ]:
         np.testing.assert_almost_equal(ome_as1.A_hg(N, L), res[i])
+
+
+def test_A_gg():
+    res = [-2 / 3, -4 / 3, -2]
+    for L in [1, 2, 3]:
+        np.testing.assert_equal(ome_as1.A_gg(L), res[L - 1])

From 0f93689d635ac4a7f53733125f5a55c8e62a3cc2 Mon Sep 17 00:00:00 2001
From: t7phy <t7phy.in@gmail.com>
Date: Tue, 11 Apr 2023 16:52:44 +0200
Subject: [PATCH 19/22] add comment on SL A_gg

---
 src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py b/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
index e52127349..527d262fd 100644
--- a/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
+++ b/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
@@ -44,6 +44,7 @@ def A_gg(L):
     r"""Compute the |NLO| gluon-gluon |OME|.
 
     Implements the Mellin transform of :eqref:`24` from :cite:`Cacciari:2005ry`.
+    It is identical to the one in :class:`~ekore.operator_matrix_elements.unpolarized.space_like.as1`.
 
     Parameters
     ----------

From cdc0ae0e2e56ece901e82c3aa10663e42aa0ccb4 Mon Sep 17 00:00:00 2001
From: t7phy <t7phy.in@gmail.com>
Date: Tue, 11 Apr 2023 16:54:06 +0200
Subject: [PATCH 20/22] formatting changes

---
 .../operator_matrix_elements/unpolarized/time_like/as1.py   | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py b/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
index 527d262fd..9d5b0c032 100644
--- a/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
+++ b/src/ekore/operator_matrix_elements/unpolarized/time_like/as1.py
@@ -43,8 +43,10 @@ def A_hg(N, L):
 def A_gg(L):
     r"""Compute the |NLO| gluon-gluon |OME|.
 
-    Implements the Mellin transform of :eqref:`24` from :cite:`Cacciari:2005ry`.
-    It is identical to the one in :class:`~ekore.operator_matrix_elements.unpolarized.space_like.as1`.
+    Implements the Mellin transform of
+    :eqref:`24` from :cite:`Cacciari:2005ry`.
+    It is identical to the one in
+    :class:`~ekore.operator_matrix_elements.unpolarized.space_like.as1`.
 
     Parameters
     ----------

From b7531f164b02371d344ee893771224ec3a8e8e43 Mon Sep 17 00:00:00 2001
From: t7phy <t7phy.in@gmail.com>
Date: Wed, 19 Apr 2023 23:38:53 +0200
Subject: [PATCH 21/22] use as1 matching conditions for nnlo ADs

---
 .../unpolarized/time_like/__init__.py              | 14 ++++++++------
 .../unpolarized/time_like/test_init.py             |  2 ++
 2 files changed, 10 insertions(+), 6 deletions(-)

diff --git a/src/ekore/operator_matrix_elements/unpolarized/time_like/__init__.py b/src/ekore/operator_matrix_elements/unpolarized/time_like/__init__.py
index 6eecc372c..edde304f5 100644
--- a/src/ekore/operator_matrix_elements/unpolarized/time_like/__init__.py
+++ b/src/ekore/operator_matrix_elements/unpolarized/time_like/__init__.py
@@ -25,10 +25,11 @@ def A_non_singlet(matching_order, N, L):
         non-singlet |OME|
 
     """
-    if matching_order[0] > 1:
-        raise Exception("Time-like matching conditions are only known upto NLO")
     A_ns = np.zeros((matching_order[0], 2, 2), np.complex_)
-    A_ns[0] = as1.A_ns()
+    if matching_order[0] >= 1:
+        A_ns[0] = as1.A_ns()
+    if matching_order[0] == 2:
+        A_ns[1] = as1.A_ns()
     return A_ns
 
 
@@ -51,8 +52,9 @@ def A_singlet(matching_order, N, L):
         singlet |OME|
 
     """
-    if matching_order[0] > 1:
-        raise Exception("Time-like matching conditions are only known upto NLO")
     A_singlet = np.zeros((matching_order[0], 3, 3), np.complex_)
-    A_singlet[0] = as1.A_singlet(N, L)
+    if matching_order[0] >= 1:
+        A_singlet[0] = as1.A_singlet(N, L)
+    if matching_order[0] >= 2:
+        A_singlet[0] = as1.A_singlet(N, L)
     return A_singlet
diff --git a/tests/ekore/operator_matrix_elements/unpolarized/time_like/test_init.py b/tests/ekore/operator_matrix_elements/unpolarized/time_like/test_init.py
index 051274596..9ce5f3d2e 100644
--- a/tests/ekore/operator_matrix_elements/unpolarized/time_like/test_init.py
+++ b/tests/ekore/operator_matrix_elements/unpolarized/time_like/test_init.py
@@ -6,3 +6,5 @@
 def test_shapes():
     assert ome.A_singlet((1, 0), complex(0, 1), 0).shape == (1, 3, 3)
     assert ome.A_non_singlet((1, 0), complex(0, 1), 0).shape == (1, 2, 2)
+    assert ome.A_singlet((2, 0), complex(0, 1), 0).shape == (2, 3, 3)
+    assert ome.A_non_singlet((2, 0), complex(0, 1), 0).shape == (2, 2, 2)

From a01e3ed603b15fa0301e6b58b7e9d51142c97c84 Mon Sep 17 00:00:00 2001
From: Tanishq Sharma <99052355+t7phy@users.noreply.github.com>
Date: Thu, 20 Apr 2023 01:51:34 +0200
Subject: [PATCH 22/22] correct typos

---
 .../unpolarized/time_like/__init__.py                         | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/ekore/operator_matrix_elements/unpolarized/time_like/__init__.py b/src/ekore/operator_matrix_elements/unpolarized/time_like/__init__.py
index edde304f5..ff0c7e986 100644
--- a/src/ekore/operator_matrix_elements/unpolarized/time_like/__init__.py
+++ b/src/ekore/operator_matrix_elements/unpolarized/time_like/__init__.py
@@ -28,7 +28,7 @@ def A_non_singlet(matching_order, N, L):
     A_ns = np.zeros((matching_order[0], 2, 2), np.complex_)
     if matching_order[0] >= 1:
         A_ns[0] = as1.A_ns()
-    if matching_order[0] == 2:
+    if matching_order[0] >= 2:
         A_ns[1] = as1.A_ns()
     return A_ns
 
@@ -56,5 +56,5 @@ def A_singlet(matching_order, N, L):
     if matching_order[0] >= 1:
         A_singlet[0] = as1.A_singlet(N, L)
     if matching_order[0] >= 2:
-        A_singlet[0] = as1.A_singlet(N, L)
+        A_singlet[1] = as1.A_singlet(N, L)
     return A_singlet