Isospin issue

[martin-ueding]

For some reason the isospin part is too simple, it does not exhibit the sufficient symmetry under particle exchange.

[martin-ueding]

To flesh this out a bit: The isospin contraction is done like so:

wc = WickContract[\[Pi]\[Pi]I1Bar[s1, s2, s3, s4, c1, c2, so[1], 
     so[2]] ** \[Pi]\[Pi]I1[s5, s6, s7, s8, c5, c6, si[1], si[2]]];
qc = QuarkContract[wc];

We obtain the following contraction:

trace[Gamma^5.DE[{"up", "up"}, {si[1], so[2]}].Gamma^5.DE[{"dn", 
      "dn"}, {so[2], si[1]}]] trace[
   Gamma^5.DE[{"up", "up"}, {so[1], si[2]}].Gamma^5.DE[{"dn", 
      "dn"}, {si[2], so[1]}]] + 
 trace[Gamma^5.DE[{"up", "up"}, {si[1], si[2]}].Gamma^5.DE[{"dn", 
      "dn"}, {si[2], si[1]}]] trace[
   Gamma^5.DE[{"up", "up"}, {so[1], so[2]}].Gamma^5.DE[{"dn", 
      "dn"}, {so[2], so[1]}]] - 
 trace[Gamma^5.DE[{"dn", "dn"}, {so[2], si[1]}].Gamma^5.DE[{"up", 
     "up"}, {so[1], so[2]}].Gamma^5.DE[{"dn", "dn"}, {si[2], 
     so[1]}].Gamma^5.DE[{"up", "up"}, {si[1], si[2]}]] - 
 trace[Gamma^5.DE[{"up", "up"}, {so[1], si[2]}].Gamma^5.DE[{"dn", 
     "dn"}, {so[2], so[1]}].Gamma^5.DE[{"up", "up"}, {si[1], 
     so[2]}].Gamma^5.DE[{"dn", "dn"}, {si[2], si[1]}]]

Properly converted into dataset name templates this is

-"C4cB_uuuu_p`pso2`.d000.g5_p`psi1`.d000.g5_p`psi2`.d000.g5_p`pso1`.d000.g5" +
"C4cD_uuuu_p`pso1`.d000.g5_p`psi2`.d000.g5_p`pso2`.d000.g5_p`psi1`.d000.g5" +
"C4cV_uuuu_p`pso2`.d000.g5_p`pso1`.d000.g5_p`psi2`.d000.g5_p`psi1`.d000.g5" -
 Conjugate["C4cB_uuuu_p`pso2`.d000.g5_p`psi1`.d000.g5_p`psi2`.d000.g5_p`pso1`.d000.g5"]

It seems as there are just too few terms here, in order to actually have the particle exchange symmetries that we want.

[martin-ueding]

Hah! Mathematica only has implicit line continuation after a binary operator (like R and Python). Therefore the second summand in the pion operator got silently dropped.