Add colorcorrelation sum test

feynamp/form/color.py

@@ -153,7 +153,7 @@ def get_full_color_correlation_matrix(fds, legs, model, s2):
         vec += [get_color_vector(fds[0], legs[i], model)]
         ids += [color_vector_to_id(vec[i])]
         mom += [get_leg_momentum(legs[i])]
-        ops += [color_vector_to_operator(vec[i])]
+        ops += [("(-1)*" if swap[i] else "") + str(color_vector_to_operator(vec[i]))]
         ind += [color_vector_to_index(vec[i])]
         ind1 += [str(ind[i]) + legs[i].id]
         ind2 += [str(ind[i]) + get_dummy_index(underscore=False, questionmark=False)]
@@ -180,8 +180,9 @@ def get_full_color_correlation_matrix(fds, legs, model, s2):
                     right += f"\ncolorcorrelation({mom[i]},{mom[j]})*{ops[i]}({i1},{i2},{dummy})*{ops[j]}({j1},{j2},{dummy}){deltas[:-1]}+"
                     # right += f"\n{ops[i]}({i1},{i2},{dummy})*{ops[j]}({j1},{j2},{dummy}){deltas[:-1]}+"
                     # right += f"\ncolorcorrelation({mom[i]},{mom[j]})*d_({i1},{i2})*d_({j1},{j2}){deltas[:-1]}+"
+    # The minus sign below is from https://arxiv.org/pdf/1002.2581 Eq. 2.6
     ret = f"""
-    id {left[:-1]} = {right[:-1]};
+    id {left[:-1]} = -({right[:-1]});
     """
     print(ret)
     return ret

feynamp/leg.py

@@ -18,9 +18,17 @@ def get_leg_momentum(leg):
     return mom
 
 
+def color_vector_to_casimir(color_vector: str) -> str:
+    if color_vector == "VA":
+        return "Ca"
+    if color_vector == "VC":
+        return "Cf"
+    return None
+
+
 def color_vector_to_operator(color_vector):
     if color_vector == "VA":
-        return "f"
+        return "complex(0,1)*f"
     if color_vector == "VC":
         return "T"
     return None

feynamp/test/colorcorrelation.py

@@ -0,0 +1,52 @@
+from typing import List
+
+from feynml.leg import Leg
+
+from feynamp import sympy
+from feynamp.leg import color_vector_to_casimir, get_color_vector, get_leg_momentum
+
+
+def assert_colorcorrelation(sympy_expr, fd, legs: List[Leg], model):
+    """
+    sympy_expr: sympy expression of cc/born
+    """
+    for j in range(len(legs)):
+        vec = get_color_vector(fd, legs[j], model)
+        if vec is not None:
+            casimir = color_vector_to_casimir(vec)
+            sum = sympy_expr
+            for i in range(len(legs)):
+                momi = get_leg_momentum(legs[i])
+                momj = get_leg_momentum(legs[j])
+                # colorcorrelation is symmetric, and we only have sorted vertices
+                sum = sum.replace(
+                    sympy.parse_expr(
+                        f"colorcorrelation({momi},{momj})".replace("Mom_", "")
+                    ),
+                    1,
+                )
+                sum = sum.replace(
+                    sympy.parse_expr(
+                        f"colorcorrelation({momj},{momi})".replace("Mom_", "")
+                    ),
+                    1,
+                )
+            # TODO can be optimized
+            for k in range(len(legs)):
+                for l in range(len(legs)):
+                    momi = get_leg_momentum(legs[k])
+                    momj = get_leg_momentum(legs[l])
+                    sum = sum.replace(
+                        sympy.parse_expr(
+                            f"colorcorrelation({momi},{momj})".replace("Mom_", "")
+                        ),
+                        0,
+                    )
+                    sum = sum.replace(
+                        sympy.parse_expr(
+                            f"colorcorrelation({momj},{momi})".replace("Mom_", "")
+                        ),
+                        0,
+                    )
+            # replace all remaining colorcorrelation(mom,mom) with 0
+            assert sum.equals(sympy.parse_expr(casimir))

tests/form/qcd/2_to_2/colorcorrelation/test_colorcorrelation_ee_qq.py

@@ -10,6 +10,7 @@
 from xsdata.formats.dataclass.parsers import XmlParser
 
 from feynamp.form import compute_squared
+from feynamp.test.colorcorrelation import assert_colorcorrelation
 
 logger = logging.getLogger("feynamp")
 logger.setLevel(logging.DEBUG)
@@ -35,3 +36,5 @@ def test_colorcorrelation_ee_qq():
     born = compute_squared(fds, fm, colorcorrelated=False)
     cc = compute_squared(fds, fm, colorcorrelated=True)
     assert (cc / born).simplify().equals(sympy.parse_expr("Cf*colorcorrelation(p3,p4)"))
+
+    assert_colorcorrelation(cc / born, fds[0], fds[0].legs, fm)

tests/form/qcd/2_to_2/colorcorrelation/test_colorcorrelation_qq_qq.py

@@ -10,6 +10,7 @@
 from xsdata.formats.dataclass.parsers import XmlParser
 
 from feynamp.form import compute_squared
+from feynamp.test.colorcorrelation import assert_colorcorrelation
 
 logger = logging.getLogger("feynamp")
 logger.setLevel(logging.DEBUG)
@@ -40,6 +41,8 @@ def test_colorcorrelation_qq_photon_qq():
         .equals("Cf*(colorcorrelation(p1, p2) + colorcorrelation(p3, p4))")
     )
 
+    assert_colorcorrelation(cc / born, fds[0], fds[0].legs, fm)
+
 
 def test_colorcorrelation_qq_gluon_qq():
     fm = load_ufo_model("ufo_sm")
@@ -65,7 +68,9 @@ def test_colorcorrelation_qq_gluon_qq():
         .simplify()
         .equals(
             sympy.parse_expr(
-                "Cf*colorcorrelation(p1, p2) + Cf*colorcorrelation(p3, p4) - Nc*colorcorrelation(p1, p2)/2 + Nc*colorcorrelation(p1, p3)/4 - Nc*colorcorrelation(p1, p4)/4 - Nc*colorcorrelation(p2, p3)/4 + Nc*colorcorrelation(p2, p4)/4 - Nc*colorcorrelation(p3, p4)/2 + Nc**2*colorcorrelation(p1, p3)/(8*Cf) + Nc**2*colorcorrelation(p1, p4)/(8*Cf) + Nc**2*colorcorrelation(p2, p3)/(8*Cf) + Nc**2*colorcorrelation(p2, p4)/(8*Cf) - 5*colorcorrelation(p1, p3)/(8*Cf) - 5*colorcorrelation(p1, p4)/(8*Cf) - 5*colorcorrelation(p2, p3)/(8*Cf) - 5*colorcorrelation(p2, p4)/(8*Cf) + colorcorrelation(p1, p3)/(2*Cf*Nc**2) + colorcorrelation(p1, p4)/(2*Cf*Nc**2) + colorcorrelation(p2, p3)/(2*Cf*Nc**2) + colorcorrelation(p2, p4)/(2*Cf*Nc**2)"
+                "Cf*colorcorrelation(p1, p2) + Cf*colorcorrelation(p3, p4) - Nc*colorcorrelation(p1, p2)/2 + Nc*colorcorrelation(p1, p3)/4 + Nc*colorcorrelation(p1, p4)/4 + Nc*colorcorrelation(p2, p3)/4 + Nc*colorcorrelation(p2, p4)/4 - Nc*colorcorrelation(p3, p4)/2 + Nc**2*colorcorrelation(p1, p3)/(8*Cf) - Nc**2*colorcorrelation(p1, p4)/(8*Cf) - Nc**2*colorcorrelation(p2, p3)/(8*Cf) + Nc**2*colorcorrelation(p2, p4)/(8*Cf) - 5*colorcorrelation(p1, p3)/(8*Cf) + 5*colorcorrelation(p1, p4)/(8*Cf) + 5*colorcorrelation(p2, p3)/(8*Cf) - 5*colorcorrelation(p2, p4)/(8*Cf) + colorcorrelation(p1, p3)/(2*Cf*Nc**2) - colorcorrelation(p1, p4)/(2*Cf*Nc**2) - colorcorrelation(p2, p3)/(2*Cf*Nc**2) + colorcorrelation(p2, p4)/(2*Cf*Nc**2)"
             )
         )
     )
+
+    assert_colorcorrelation(cc / born, fds[0], fds[0].legs, fm)