•SU(2) result

su2res = endres1 /. n -> 2 // CayleyHamiltonTrick // CommutatorReduce // SUNReduce // UReduce

3/8 < Q _ L '6 Q _ L >^2 (f _ π^(ó  ))^4 + 3/8 < Q _ R '6 Q _ R >^2 (f _ π^(ó  ))^4 + 3/2 < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >^2 (f _ π^(ó  ))^4 + 3/4 < Q _ L '6 Q _ L > < Q _ R '6 Q _ R > (f _ π^(ó  ))^4 - 3/2 < Q _ L '6 Q _ L > < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L > (f _ π^(ó  ))^4 - 3/2 < Q _ R '6 Q _ R > < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L > (f _ π^(ó  ))^4 - 3/4 < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L '6 Q _ L > (f _ π^(ó  ))^2 + 1/4 < ÷s _ μ _ 1(÷„)^† '6 c _ μ _ 1^R Q _ R '6 ÷„ '6 Q _ L > (f _ π^(ó  ))^2 + 1/2 < ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 ÷s _ μ _ 1(÷„) '6 Q _ L > (f _ π^(ó  ))^2 + 1/4 < ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 ÷„ '6 c _ μ _ 1^L Q _ L > (f _ π^(ó  ))^2 - 3/4 < ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 Q _ R '6 ÷s _ μ _ 1(÷„) > (f _ π^(ó  ))^2 + 1/4 < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 c _ μ _ 1^L Q _ L '6 Q _ L > (f _ π^(ó  ))^2 - 1/4 < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L '6 c _ μ _ 1^L Q _ L > (f _ π^(ó  ))^2 + 1/4 < ÷„^† '6 c _ μ _ 1^R Q _ R '6 ÷s _ μ _ 1(÷„) '6 Q _ L > (f _ π^(ó  ))^2 - 1/4 < ÷„^† '6 c _ μ _ 1^R Q _ R '6 Q _ R '6 ÷s _ μ _ 1(÷„) > (f _ π^(ó  ))^2 - 1/4 < ÷„^† '6 χ '6 Q _ L '6 Q _ L > (f _ π^(ó  ))^2 + 1/4 < ÷„^† '6 Q _ R '6 ÷s _ μ _ 1(÷„) '6 c _ μ _ 1^L Q _ L > (f _ π^(ó  ))^2 + 1/4 < ÷„^† '6 Q _ R '6 c _ μ _ 1^R Q _ R '6 ÷s _ μ _ 1(÷„) > (f _ π^(ó  ))^2 + 1/4 < ÷„^† '6 Q _ R '6 χ '6 Q _ L > (f _ π^(ó  ))^2 - 1/4 < ÷„^† '6 Q _ R '6 Q _ R '6 χ > (f _ π^(ó  ))^2 - 1/4 < χ^† '6 ÷„ '6 Q _ L '6 Q _ L > (f _ π^(ó  ))^2 + 1/4 < χ^† '6 Q _ R '6 ÷„ '6 Q _ L > (f _ π^(ó  ))^2 - 1/4 < χ^† '6 Q _ R '6 Q _ R '6 ÷„ > (f _ π^(ó  ))^2 - 1/4 < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L '6 ÷„^† '6 Q _ R '6 ÷„ > (f _ π^(ó  ))^2 + 3/4 < ÷s _ μ _ 1(÷„)^† '6 ÷„ '6 Q _ L '6 ÷„^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L > (f _ π^(ó  ))^2 - 3/4 < ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 ÷„ '6 ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 ÷„ > (f _ π^(ó  ))^2 + 1/4 < ÷„^† '6 Q _ R '6 ÷„ '6 χ^† '6 ÷„ '6 Q _ L > (f _ π^(ó  ))^2 + 1/4 < ÷„ '6 Q _ L '6 ÷„^† '6 χ '6 ÷„^† '6 Q _ R > (f _ π^(ó  ))^2 + 1/4 < Q _ L '6 ÷s _ μ _ 1(÷„)^† '6 ÷„ '6 ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 ÷„ > (f _ π^(ó  ))^2 + 1/6 < ÷s _ μ _ 2(÷„)^† '6 ÷s _ μ _ 1(÷„) >^2 + 3/32 < ÷„^† '6 χ >^2 + 3/32 < χ^† '6 ÷„ >^2 + 1/24 < G _ (μ _ 1 μ _ 2)^L >^2 + 1/24 < G _ (μ _ 1 μ _ 2)^R >^2 + 1/12 < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) > < ÷s _ μ _ 2(÷„)^† '6 ÷s _ μ _ 2(÷„) > + 1/8 < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) > < ÷„^† '6 χ > + 1/8 < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) > < χ^† '6 ÷„ > + 3/16 < ÷„^† '6 χ > < χ^† '6 ÷„ > - 1/12 < G _ (μ _ 1 μ _ 2)^L '6 G _ (μ _ 1 μ _ 2)^L > - 1/12 < G _ (μ _ 1 μ _ 2)^R '6 G _ (μ _ 1 μ _ 2)^R > - 1/12 i < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 2(÷„) '6 G _ (μ _ 1 μ _ 2)^L > + 1/12 i < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 2(÷„) '6 G _ (μ _ 2 μ _ 1)^L > + 1/12 i < ÷s _ μ _ 1(÷„)^† '6 G _ (μ _ 1 μ _ 2)^R '6 ÷s _ μ _ 2(÷„) > - 1/12 i < ÷s _ μ _ 2(÷„)^† '6 G _ (μ _ 1 μ _ 2)^R '6 ÷s _ μ _ 1(÷„) > - 1/4 < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 χ^† '6 ÷s _ μ _ 1(÷„) > - 1/6 < ÷„^† '6 G _ (μ _ 1 μ _ 2)^R '6 ÷„ '6 G _ (μ _ 1 μ _ 2)^L > - 1/4 < ÷„ '6 ÷s _ μ _ 1(÷„)^† '6 χ '6 ÷s _ μ _ 1(÷„)^† > - 2 C^( ) < ÷„^† '6 Q _ R '6 Q _ R '6 ÷„ '6 Q _ L '6 Q _ L > + 2 C^( ) < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L '6 ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L > + 1/12 < G _ (μ _ 1 μ _ 2)^L > < G _ (μ _ 1 μ _ 2)^R > - (2 C^( ) < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L > < ÷„^† '6 Q _ R '6 ÷s _ μ _ 1(÷„) >)/(f _ π^(ó  ))^2 + (C^( ) < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) > < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >)/(f _ π^(ó  ))^2 + (C^( ) < ÷„^† '6 χ > < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >)/(f _ π^(ó  ))^2 + (C^( ) < χ^† '6 ÷„ > < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >)/(f _ π^(ó  ))^2 + (C^( ) < ÷„^† '6 Q _ R '6 χ '6 Q _ L >)/(f _ π^(ó  ))^2 + (C^( ) < χ^† '6 Q _ R '6 ÷„ '6 Q _ L >)/(f _ π^(ó  ))^2 + (C^( ) < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L '6 ÷„^† '6 Q _ R '6 ÷„ >)/(f _ π^(ó  ))^2 + (C^( ) < ÷„^† '6 Q _ R '6 ÷„ '6 χ^† '6 ÷„ '6 Q _ L >)/(f _ π^(ó  ))^2 + (C^( ) < ÷„ '6 Q _ L '6 ÷„^† '6 χ '6 ÷„^† '6 Q _ R >)/(f _ π^(ó  ))^2 - (C^( ) < Q _ L '6 ÷s _ μ _ 1(÷„)^† '6 ÷„ '6 ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 ÷„ >)/(f _ π^(ó  ))^2 - (C^( ) < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L > < Q >)/(f _ π^(ó  ))^2 - (C^( ) < ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 ÷s _ μ _ 1(÷„) > < Q >)/(f _ π^(ó  ))^2 - (C^( ) < ÷„^† '6 χ '6 Q _ L > < Q >)/(f _ π^(ó  ))^2 - (C^( ) < ÷„^† '6 Q _ R '6 χ > < Q >)/(f _ π^(ó  ))^2 - (C^( ) < χ^† '6 ÷„ '6 Q _ L > < Q >)/(f _ π^(ó  ))^2 - (C^( ) < χ^† '6 Q _ R '6 ÷„ > < Q >)/(f _ π^(ó  ))^2 + (8 (C^( ))^2 < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >^2)/(f _ π^(ó  ))^4 + (4 (C^( ))^2 < Q _ L '6 Q _ L > < Q _ R '6 Q _ R >)/(f _ π^(ó  ))^4 + (4 (C^( ))^2 < ÷„^† '6 Q _ R '6 Q _ R '6 ÷„ '6 Q _ L '6 Q _ L >)/(f _ π^(ó  ))^4 + (4 (C^( ))^2 < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L '6 ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >)/(f _ π^(ó  ))^4 - (8 (C^( ))^2 < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L '6 Q _ L > < Q >)/(f _ π^(ó  ))^4 - (8 (C^( ))^2 < ÷„^† '6 Q _ R '6 Q _ R '6 ÷„ '6 Q _ L > < Q >)/(f _ π^(ó  ))^4

su2res1 = Collect[su2res /. su2chicalhamRule // EOMTrick // Expand // UReduce, _UTrace1]

3/8 < Q _ L '6 Q _ L >^2 (f _ π^(ó  ))^4 + 3/8 < Q _ R '6 Q _ R >^2 (f _ π^(ó  ))^4 - 3/2 < Q _ R '6 Q _ R > < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L > (f _ π^(ó  ))^4 - 3/4 < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L '6 Q _ L > (f _ π^(ó  ))^2 + 1/4 < ÷s _ μ _ 1(÷„)^† '6 c _ μ _ 1^R Q _ R '6 ÷„ '6 Q _ L > (f _ π^(ó  ))^2 + 1/2 < ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 ÷s _ μ _ 1(÷„) '6 Q _ L > (f _ π^(ó  ))^2 + 1/4 < ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 ÷„ '6 c _ μ _ 1^L Q _ L > (f _ π^(ó  ))^2 - 3/4 < ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 Q _ R '6 ÷s _ μ _ 1(÷„) > (f _ π^(ó  ))^2 + 1/4 < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 c _ μ _ 1^L Q _ L '6 Q _ L > (f _ π^(ó  ))^2 - 1/4 < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L '6 c _ μ _ 1^L Q _ L > (f _ π^(ó  ))^2 + 1/4 < ÷„^† '6 c _ μ _ 1^R Q _ R '6 ÷s _ μ _ 1(÷„) '6 Q _ L > (f _ π^(ó  ))^2 - 1/4 < ÷„^† '6 c _ μ _ 1^R Q _ R '6 Q _ R '6 ÷s _ μ _ 1(÷„) > (f _ π^(ó  ))^2 - 1/4 < ÷„^† '6 χ '6 Q _ L '6 Q _ L > (f _ π^(ó  ))^2 + 1/4 < ÷„^† '6 Q _ R '6 ÷s _ μ _ 1(÷„) '6 c _ μ _ 1^L Q _ L > (f _ π^(ó  ))^2 + 1/4 < ÷„^† '6 Q _ R '6 c _ μ _ 1^R Q _ R '6 ÷s _ μ _ 1(÷„) > (f _ π^(ó  ))^2 - 1/4 < ÷„^† '6 Q _ R '6 Q _ R '6 χ > (f _ π^(ó  ))^2 - 1/4 < χ^† '6 ÷„ '6 Q _ L '6 Q _ L > (f _ π^(ó  ))^2 - 1/4 < χ^† '6 Q _ R '6 Q _ R '6 ÷„ > (f _ π^(ó  ))^2 + 3/4 < ÷s _ μ _ 1(÷„)^† '6 ÷„ '6 Q _ L '6 ÷„^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L > (f _ π^(ó  ))^2 - 3/4 < ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 ÷„ '6 ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 ÷„ > (f _ π^(ó  ))^2 + 1/4 < ÷„^† '6 Q _ R '6 ÷„ '6 χ^† '6 ÷„ '6 Q _ L > (f _ π^(ó  ))^2 + 1/4 < ÷„ '6 Q _ L '6 ÷„^† '6 χ '6 ÷„^† '6 Q _ R > (f _ π^(ó  ))^2 + 1/6 < ÷s _ μ _ 2(÷„)^† '6 ÷s _ μ _ 1(÷„) >^2 - 1/32 < ÷„^† '6 χ >^2 - 1/32 < χ^† '6 ÷„ >^2 + (3/2 (f _ π^(ó  ))^4 + (8 (C^( ))^2)/(f _ π^(ó  ))^4) < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >^2 + 1/24 < G _ (μ _ 1 μ _ 2)^L >^2 + 1/24 < G _ (μ _ 1 μ _ 2)^R >^2 + {χ^†}/4 + {χ}/4 + 1/2 < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(χ) > + 1/2 < ÷s _ μ _ 1(χ)^† '6 ÷s _ μ _ 1(÷„) > + 1/2 < χ^† '6 χ > - 1/12 < G _ (μ _ 1 μ _ 2)^L '6 G _ (μ _ 1 μ _ 2)^L > - 1/12 < G _ (μ _ 1 μ _ 2)^R '6 G _ (μ _ 1 μ _ 2)^R > - 1/12 i < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 2(÷„) '6 G _ (μ _ 1 μ _ 2)^L > + 1/12 i < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 2(÷„) '6 G _ (μ _ 2 μ _ 1)^L > + 1/12 i < ÷s _ μ _ 1(÷„)^† '6 G _ (μ _ 1 μ _ 2)^R '6 ÷s _ μ _ 2(÷„) > - 1/12 i < ÷s _ μ _ 2(÷„)^† '6 G _ (μ _ 1 μ _ 2)^R '6 ÷s _ μ _ 1(÷„) > - 1/6 < ÷„^† '6 G _ (μ _ 1 μ _ 2)^R '6 ÷„ '6 G _ (μ _ 1 μ _ 2)^L > + < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) > (1/12 < ÷s _ μ _ 2(÷„)^† '6 ÷s _ μ _ 2(÷„) > + (C^( ) < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >)/(f _ π^(ó  ))^2) + < ÷„^† '6 χ > ((C^( ) < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >)/(f _ π^(ó  ))^2 - 1/16 < χ^† '6 ÷„ >) + < Q _ L '6 Q _ L > ((3/4 (f _ π^(ó  ))^4 + (4 (C^( ))^2)/(f _ π^(ó  ))^4) < Q _ R '6 Q _ R > - 3/2 (f _ π^(ó  ))^4 < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >) + (1/4 (f _ π^(ó  ))^2 + (2 C^( ))/(f _ π^(ó  ))^2) < ÷„^† '6 Q _ R '6 χ '6 Q _ L > + (1/4 (f _ π^(ó  ))^2 + (2 C^( ))/(f _ π^(ó  ))^2) < χ^† '6 Q _ R '6 ÷„ '6 Q _ L > + (C^( )/(f _ π^(ó  ))^2 - 1/4 (f _ π^(ó  ))^2) < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L '6 ÷„^† '6 Q _ R '6 ÷„ > + ((4 (C^( ))^2)/(f _ π^(ó  ))^4 - 2 C^( )) < ÷„^† '6 Q _ R '6 Q _ R '6 ÷„ '6 Q _ L '6 Q _ L > + (1/4 (f _ π^(ó  ))^2 - C^( )/(f _ π^(ó  ))^2) < Q _ L '6 ÷s _ μ _ 1(÷„)^† '6 ÷„ '6 ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 ÷„ > + ((4 (C^( ))^2)/(f _ π^(ó  ))^4 + 2 C^( )) < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L '6 ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L > + 1/12 < G _ (μ _ 1 μ _ 2)^L > < G _ (μ _ 1 μ _ 2)^R > + (-(8 < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L '6 Q _ L > (C^( ))^2)/(f _ π^(ó  ))^4 - (8 < ÷„^† '6 Q _ R '6 Q _ R '6 ÷„ '6 Q _ L > (C^( ))^2)/(f _ π^(ó  ))^4 - (< ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 ÷s _ μ _ 1(÷„) > C^( ))/(f _ π^(ó  ))^2 - (< ÷„^† '6 χ '6 Q _ L > C^( ))/(f _ π^(ó  ))^2 - (< ÷„^† '6 Q _ R '6 χ > C^( ))/(f _ π^(ó  ))^2 - (< χ^† '6 ÷„ '6 Q _ L > C^( ))/(f _ π^(ó  ))^2 - (< χ^† '6 Q _ R '6 ÷„ > C^( ))/(f _ π^(ó  ))^2) < Q > - (2 C^( ) < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L > < ÷„^† '6 Q _ R '6 ÷s _ μ _ 1(÷„) >)/(f _ π^(ó  ))^2 + (C^( ) < χ^† '6 ÷„ > < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >)/(f _ π^(ó  ))^2 - (C^( ) < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L > < Q >)/(f _ π^(ó  ))^2

Knecht and Urech's result for general n specialized to n=2:

knechtsu2res2 = Collect[(Expand[knechtres1 /. n -> 2 /. eomRule1] /. su2chicalhamRule /. su2chicalhamRule2 /. su2chicalhamRule1 // CayleyHamiltonTrick // EOMTrick // Expand // UReduce) /. su2qchalhamrule1a /. su2qchalhamrule7 /. su2qchalhamrule8 /. su2qchalhamrule9 /. su2qchalhamrule10 /. su2qchalhamrule3 /. su2qchalhamrule2 /. su2qchalhamrule4 /. UTrace1[UMatrix[(UChiralSpurionRight | UChiralSpurionLeft)[]][x]] -> UTrace1[UMatrix[UChiralSpurion[]][x]] // NMExpand // Expand // UReduce, {a_UTrace1 * b_UTrace1, _UTrace1}]

3/8 < Q _ L '6 Q _ L >^2 (f _ π^(ó  ))^4 + 3/8 < Q _ R '6 Q _ R >^2 (f _ π^(ó  ))^4 - 3/2 < Q _ L '6 Q _ L > < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L > (f _ π^(ó  ))^4 - 3/2 < Q _ R '6 Q _ R > < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L > (f _ π^(ó  ))^4 - 3/4 < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L >^2 (f _ π^(ó  ))^2 - 3/4 < ÷„^† '6 Q _ R '6 ÷s _ μ _ 1(÷„) >^2 (f _ π^(ó  ))^2 - 3/4 < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) > < Q _ L '6 Q _ L > (f _ π^(ó  ))^2 - 1/8 < ÷„^† '6 χ > < Q _ L '6 Q _ L > (f _ π^(ó  ))^2 - 1/8 < χ^† '6 ÷„ > < Q _ L '6 Q _ L > (f _ π^(ó  ))^2 - 3/4 < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) > < Q _ R '6 Q _ R > (f _ π^(ó  ))^2 - 1/8 < ÷„^† '6 χ > < Q _ R '6 Q _ R > (f _ π^(ó  ))^2 - 1/8 < χ^† '6 ÷„ > < Q _ R '6 Q _ R > (f _ π^(ó  ))^2 + 1/4 < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 c _ μ _ 1^L Q _ L '6 Q _ L > (f _ π^(ó  ))^2 - 1/4 < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L '6 c _ μ _ 1^L Q _ L > (f _ π^(ó  ))^2 - 1/4 < ÷„^† '6 c _ μ _ 1^R Q _ R '6 Q _ R '6 ÷s _ μ _ 1(÷„) > (f _ π^(ó  ))^2 + 1/4 < ÷„^† '6 Q _ R '6 c _ μ _ 1^R Q _ R '6 ÷s _ μ _ 1(÷„) > (f _ π^(ó  ))^2 + 1/6 < ÷s _ μ _ 2(÷„)^† '6 ÷s _ μ _ 1(÷„) >^2 - 1/32 < ÷„^† '6 χ >^2 - 1/32 < χ^† '6 ÷„ >^2 + (3/2 (f _ π^(ó  ))^4 + 3 C^( ) + (12 (C^( ))^2)/(f _ π^(ó  ))^4) < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >^2 + 1/6 γ _ (μ _ 1 μ _ 2)^2 < Q >^2 + (3/4 (f _ π^(ó  ))^2 - C^( )/(f _ π^(ó  ))^2) < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) > < Q >^2 + ((3 C^( ))/2 - (2 (C^( ))^2)/(f _ π^(ó  ))^4) < Q _ L '6 Q _ L > < Q >^2 + ((3 C^( ))/2 - (2 (C^( ))^2)/(f _ π^(ó  ))^4) < Q _ R '6 Q _ R > < Q >^2 + (-(12 (C^( ))^2)/(f _ π^(ó  ))^4 - 3 C^( )) < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L > < Q >^2 + {χ^†}/4 + {χ}/4 + 1/2 < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(χ) > + 1/12 < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) > < ÷s _ μ _ 2(÷„)^† '6 ÷s _ μ _ 2(÷„) > + 1/2 < ÷s _ μ _ 1(χ)^† '6 ÷s _ μ _ 1(÷„) > - 1/16 < ÷„^† '6 χ > < χ^† '6 ÷„ > + 1/2 < χ^† '6 χ > - 1/12 < G _ (μ _ 1 μ _ 2)^L '6 G _ (μ _ 1 μ _ 2)^L > - 1/12 < G _ (μ _ 1 μ _ 2)^R '6 G _ (μ _ 1 μ _ 2)^R > + (3/4 (f _ π^(ó  ))^4 - 3 C^( ) + (4 (C^( ))^2)/(f _ π^(ó  ))^4) < Q _ L '6 Q _ L > < Q _ R '6 Q _ R > - 1/6 i < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 2(÷„) '6 G _ (μ _ 1 μ _ 2)^L > + 1/6 i < ÷s _ μ _ 1(÷„)^† '6 G _ (μ _ 1 μ _ 2)^R '6 ÷s _ μ _ 2(÷„) > - 1/6 < ÷„^† '6 G _ (μ _ 1 μ _ 2)^R '6 ÷„ '6 G _ (μ _ 1 μ _ 2)^L > + (1/4 (f _ π^(ó  ))^2 + (2 C^( ))/(f _ π^(ó  ))^2) < ÷„^† '6 χ > < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L > + (1/4 (f _ π^(ó  ))^2 + (2 C^( ))/(f _ π^(ó  ))^2) < χ^† '6 ÷„ > < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L > + (C^( )/(f _ π^(ó  ))^2 - 1/8 (f _ π^(ó  ))^2) < ÷„^† '6 Q _ R '6 χ '6 Q _ L > + (C^( )/(f _ π^(ó  ))^2 - 1/8 (f _ π^(ó  ))^2) < χ^† '6 Q _ R '6 ÷„ '6 Q _ L > + (1/8 (f _ π^(ó  ))^2 - C^( )/(f _ π^(ó  ))^2) < ÷„^† '6 Q _ R '6 ÷„ '6 χ^† '6 ÷„ '6 Q _ L > + (1/8 (f _ π^(ó  ))^2 - C^( )/(f _ π^(ó  ))^2) < ÷„ '6 Q _ L '6 ÷„^† '6 χ '6 ÷„^† '6 Q _ R > - (C^( ) < ÷„^† '6 χ > < Q >^2)/(f _ π^(ó  ))^2 - (C^( ) < χ^† '6 ÷„ > < Q >^2)/(f _ π^(ó  ))^2 - (2 C^( ) < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L > < ÷„^† '6 Q _ R '6 ÷s _ μ _ 1(÷„) >)/(f _ π^(ó  ))^2 + (2 C^( ) < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) > < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >)/(f _ π^(ó  ))^2 + (4 (C^( ))^2 < Q >^4)/(f _ π^(ó  ))^4

knechtterms2 = (List @@ knechtsu2res2 //. a_ * b : (_UTrace1 | _UTrace1^_ | _Det) :> b /; FreeQ[a, UTrace1, Infinity, Heads -> True]) // Sort

{{χ^†}, {χ}, < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(χ) >, < ÷s _ μ _ 2(÷„)^† '6 ÷s _ μ _ 1(÷„) >^2, < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) > < ÷s _ μ _ 2(÷„)^† '6 ÷s _ μ _ 2(÷„) >, < ÷s _ μ _ 1(χ)^† '6 ÷s _ μ _ 1(÷„) >, < ÷„^† '6 χ >^2, < ÷„^† '6 χ > < χ^† '6 ÷„ >, < χ^† '6 ÷„ >^2, < χ^† '6 χ >, < G _ (μ _ 1 μ _ 2)^L '6 G _ (μ _ 1 μ _ 2)^L >, < G _ (μ _ 1 μ _ 2)^R '6 G _ (μ _ 1 μ _ 2)^R >, < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) > < Q _ L '6 Q _ L >, < ÷„^† '6 χ > < Q _ L '6 Q _ L >, < χ^† '6 ÷„ > < Q _ L '6 Q _ L >, < Q _ L '6 Q _ L >^2, < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) > < Q _ R '6 Q _ R >, < ÷„^† '6 χ > < Q _ R '6 Q _ R >, < χ^† '6 ÷„ > < Q _ R '6 Q _ R >, < Q _ L '6 Q _ L > < Q _ R '6 Q _ R >, < Q _ R '6 Q _ R >^2, < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 2(÷„) '6 G _ (μ _ 1 μ _ 2)^L >, < ÷s _ μ _ 1(÷„)^† '6 G _ (μ _ 1 μ _ 2)^R '6 ÷s _ μ _ 2(÷„) >, < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L >^2, < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L > < ÷„^† '6 Q _ R '6 ÷s _ μ _ 1(÷„) >, < ÷„^† '6 Q _ R '6 ÷s _ μ _ 1(÷„) >^2, < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 c _ μ _ 1^L Q _ L '6 Q _ L >, < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L '6 c _ μ _ 1^L Q _ L >, < ÷„^† '6 c _ μ _ 1^R Q _ R '6 Q _ R '6 ÷s _ μ _ 1(÷„) >, < ÷„^† '6 G _ (μ _ 1 μ _ 2)^R '6 ÷„ '6 G _ (μ _ 1 μ _ 2)^L >, < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) > < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >, < ÷„^† '6 χ > < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >, < χ^† '6 ÷„ > < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >, < Q _ L '6 Q _ L > < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >, < Q _ R '6 Q _ R > < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >, < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >^2, < ÷„^† '6 Q _ R '6 c _ μ _ 1^R Q _ R '6 ÷s _ μ _ 1(÷„) >, < ÷„^† '6 Q _ R '6 χ '6 Q _ L >, < χ^† '6 Q _ R '6 ÷„ '6 Q _ L >, < ÷„^† '6 Q _ R '6 ÷„ '6 χ^† '6 ÷„ '6 Q _ L >, < ÷„ '6 Q _ L '6 ÷„^† '6 χ '6 ÷„^† '6 Q _ R >, < Q >^2, < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) > < Q >^2, < ÷„^† '6 χ > < Q >^2, < χ^† '6 ÷„ > < Q >^2, < Q _ L '6 Q _ L > < Q >^2, < Q _ R '6 Q _ R > < Q >^2, < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L > < Q >^2, < Q >^4}

Knecht and Urech's result for n=2:

knechtsu2res1 = (Collect[(knechtsu2res /. {μ -> μ1, ν -> μ2, f -> DecayConstant[Pion], z -> CouplingConstant[ChPTVirtualPhotons2[2]]/DecayConstant[Pion]^4}) // NMExpand // Expand // CycleUTraces, _UTrace1] // UReduce // IndicesCleanup // Expand) /. {GLeft[LorentzIndex[μ2], LorentzIndex[μ1]][x] -> -GLeft[LorentzIndex[μ1], LorentzIndex[μ2]][x], GRight[LorentzIndex[μ2], LorentzIndex[μ1]][x] -> -GRight[LorentzIndex[μ1], LorentzIndex[μ2]][x]} /. NM[Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ2]]], GRight[LorentzIndex[μ1], LorentzIndex[μ2]][x], CovariantFieldDerivative[MM[x], x, LorentzIndex[μ1]]] -> -NM[Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ1]]], GRight[LorentzIndex[μ1], LorentzIndex[μ2]][x], CovariantFieldDerivative[MM[x], x, LorentzIndex[μ2]]] // Expand // Collect[#, {a_UTrace1 * b_UTrace1, _UTrace1}] &

-3/2 < Q _ L '6 Q _ L > < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L > (f _ π^(ó  ))^4 - 3/2 < Q _ R '6 Q _ R > < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L > (f _ π^(ó  ))^4 - 3/4 < ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 ÷„ >^2 (f _ π^(ó  ))^2 - 3/4 < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L >^2 (f _ π^(ó  ))^2 - 3/4 < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) > < Q _ L '6 Q _ L > (f _ π^(ó  ))^2 - 1/8 < ÷„^† '6 χ > < Q _ L '6 Q _ L > (f _ π^(ó  ))^2 - 1/8 < χ^† '6 ÷„ > < Q _ L '6 Q _ L > (f _ π^(ó  ))^2 - 3/4 < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) > < Q _ R '6 Q _ R > (f _ π^(ó  ))^2 - 1/8 < ÷„^† '6 χ > < Q _ R '6 Q _ R > (f _ π^(ó  ))^2 - 1/8 < χ^† '6 ÷„ > < Q _ R '6 Q _ R > (f _ π^(ó  ))^2 + 1/4 < ÷s _ μ _ 1(÷„)^† '6 c _ μ _ 1^R Q _ R '6 Q _ R '6 ÷„ > (f _ π^(ó  ))^2 + 1/4 < ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 ÷„ '6 c _ μ _ 1^L Q _ L > (f _ π^(ó  ))^2 - 1/4 < ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 c _ μ _ 1^R Q _ R '6 ÷„ > (f _ π^(ó  ))^2 + 1/4 < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 c _ μ _ 1^L Q _ L '6 Q _ L > (f _ π^(ó  ))^2 - 1/4 < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L '6 c _ μ _ 1^L Q _ L > (f _ π^(ó  ))^2 + 1/4 < ÷„^† '6 c _ μ _ 1^R Q _ R '6 ÷s _ μ _ 1(÷„) '6 Q _ L > (f _ π^(ó  ))^2 + 1/6 < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 2(÷„) >^2 - 1/32 < ÷„^† '6 χ >^2 - 1/32 < χ^† '6 ÷„ >^2 + (3/8 (f _ π^(ó  ))^4 - (3 C^( ))/4) < Q _ L '6 Q _ L >^2 + (3/8 (f _ π^(ó  ))^4 - (3 C^( ))/4) < Q _ R '6 Q _ R >^2 + (3/2 (f _ π^(ó  ))^4 + 3 C^( ) + (12 (C^( ))^2)/(f _ π^(ó  ))^4) < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >^2 + 1/6 γ _ (μ _ 1 μ _ 2)^2 < Q >^2 + (3/4 (f _ π^(ó  ))^2 - C^( )/(f _ π^(ó  ))^2) < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) > < Q >^2 + ((3 C^( ))/2 - (2 (C^( ))^2)/(f _ π^(ó  ))^4) < Q _ L '6 Q _ L > < Q >^2 + ((3 C^( ))/2 - (2 (C^( ))^2)/(f _ π^(ó  ))^4) < Q _ R '6 Q _ R > < Q >^2 + (-(12 (C^( ))^2)/(f _ π^(ó  ))^4 - 3 C^( )) < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L > < Q >^2 + {χ^†}/2 + {χ}/2 + 1/2 < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(χ) > + 1/12 < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) > < ÷s _ μ _ 2(÷„)^† '6 ÷s _ μ _ 2(÷„) > + 1/2 < ÷s _ μ _ 1(χ)^† '6 ÷s _ μ _ 1(÷„) > - 1/16 < ÷„^† '6 χ > < χ^† '6 ÷„ > + 1/2 < χ^† '6 χ > - 1/12 < G _ (μ _ 1 μ _ 2)^L '6 G _ (μ _ 1 μ _ 2)^L > - 1/12 < G _ (μ _ 1 μ _ 2)^R '6 G _ (μ _ 1 μ _ 2)^R > + (3/4 (f _ π^(ó  ))^4 - (3 C^( ))/2 + (4 (C^( ))^2)/(f _ π^(ó  ))^4) < Q _ L '6 Q _ L > < Q _ R '6 Q _ R > - 1/6 i < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 2(÷„) '6 G _ (μ _ 1 μ _ 2)^L > + 1/6 i < ÷s _ μ _ 1(÷„)^† '6 G _ (μ _ 1 μ _ 2)^R '6 ÷s _ μ _ 2(÷„) > - 1/6 < ÷„^† '6 G _ (μ _ 1 μ _ 2)^R '6 ÷„ '6 G _ (μ _ 1 μ _ 2)^L > + (1/4 (f _ π^(ó  ))^2 + (2 C^( ))/(f _ π^(ó  ))^2) < ÷„^† '6 χ > < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L > + (1/4 (f _ π^(ó  ))^2 + (2 C^( ))/(f _ π^(ó  ))^2) < χ^† '6 ÷„ > < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L > + (C^( )/(f _ π^(ó  ))^2 - 1/8 (f _ π^(ó  ))^2) < ÷„^† '6 Q _ R '6 χ '6 Q _ L > + (C^( )/(f _ π^(ó  ))^2 - 1/8 (f _ π^(ó  ))^2) < χ^† '6 Q _ R '6 ÷„ '6 Q _ L > + (1/8 (f _ π^(ó  ))^2 - C^( )/(f _ π^(ó  ))^2) < ÷„^† '6 Q _ R '6 ÷„ '6 χ^† '6 ÷„ '6 Q _ L > + (1/8 (f _ π^(ó  ))^2 - C^( )/(f _ π^(ó  ))^2) < ÷„ '6 Q _ L '6 ÷„^† '6 χ '6 ÷„^† '6 Q _ R > - (C^( ) < ÷„^† '6 χ > < Q >^2)/(f _ π^(ó  ))^2 - (C^( ) < χ^† '6 ÷„ > < Q >^2)/(f _ π^(ó  ))^2 + (2 C^( ) < ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 ÷„ > < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L >)/(f _ π^(ó  ))^2 + (2 C^( ) < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) > < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >)/(f _ π^(ó  ))^2 + (4 (C^( ))^2 < Q >^4)/(f _ π^(ó  ))^4

knechtterms1 = (List @@ knechtsu2res1 //. a_ * b : (_UTrace1 | _UTrace1^_ | _Det) :> b /; FreeQ[a, UTrace1, Infinity, Heads -> True]) // Sort

{{χ^†}, {χ}, < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 2(÷„) >^2, < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(χ) >, < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) > < ÷s _ μ _ 2(÷„)^† '6 ÷s _ μ _ 2(÷„) >, < ÷s _ μ _ 1(χ)^† '6 ÷s _ μ _ 1(÷„) >, < ÷„^† '6 χ >^2, < ÷„^† '6 χ > < χ^† '6 ÷„ >, < χ^† '6 ÷„ >^2, < χ^† '6 χ >, < G _ (μ _ 1 μ _ 2)^L '6 G _ (μ _ 1 μ _ 2)^L >, < G _ (μ _ 1 μ _ 2)^R '6 G _ (μ _ 1 μ _ 2)^R >, < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) > < Q _ L '6 Q _ L >, < ÷„^† '6 χ > < Q _ L '6 Q _ L >, < χ^† '6 ÷„ > < Q _ L '6 Q _ L >, < Q _ L '6 Q _ L >^2, < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) > < Q _ R '6 Q _ R >, < ÷„^† '6 χ > < Q _ R '6 Q _ R >, < χ^† '6 ÷„ > < Q _ R '6 Q _ R >, < Q _ L '6 Q _ L > < Q _ R '6 Q _ R >, < Q _ R '6 Q _ R >^2, < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 2(÷„) '6 G _ (μ _ 1 μ _ 2)^L >, < ÷s _ μ _ 1(÷„)^† '6 G _ (μ _ 1 μ _ 2)^R '6 ÷s _ μ _ 2(÷„) >, < ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 ÷„ >^2, < ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 ÷„ > < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L >, < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L >^2, < ÷s _ μ _ 1(÷„)^† '6 c _ μ _ 1^R Q _ R '6 Q _ R '6 ÷„ >, < ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 ÷„ '6 c _ μ _ 1^L Q _ L >, < ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 c _ μ _ 1^R Q _ R '6 ÷„ >, < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 c _ μ _ 1^L Q _ L '6 Q _ L >, < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L '6 c _ μ _ 1^L Q _ L >, < ÷„^† '6 c _ μ _ 1^R Q _ R '6 ÷s _ μ _ 1(÷„) '6 Q _ L >, < ÷„^† '6 G _ (μ _ 1 μ _ 2)^R '6 ÷„ '6 G _ (μ _ 1 μ _ 2)^L >, < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) > < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >, < ÷„^† '6 χ > < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >, < χ^† '6 ÷„ > < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >, < Q _ L '6 Q _ L > < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >, < Q _ R '6 Q _ R > < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >, < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >^2, < ÷„^† '6 Q _ R '6 χ '6 Q _ L >, < χ^† '6 Q _ R '6 ÷„ '6 Q _ L >, < ÷„^† '6 Q _ R '6 ÷„ '6 χ^† '6 ÷„ '6 Q _ L >, < ÷„ '6 Q _ L '6 ÷„^† '6 χ '6 ÷„^† '6 Q _ R >, < Q >^2, < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) > < Q >^2, < ÷„^† '6 χ > < Q >^2, < χ^† '6 ÷„ > < Q >^2, < Q _ L '6 Q _ L > < Q >^2, < Q _ R '6 Q _ R > < Q >^2, < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L > < Q >^2, < Q >^4}

Complement[knechtterms2, knechtterms1]

{< ÷s _ μ _ 2(÷„)^† '6 ÷s _ μ _ 1(÷„) >^2, < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L > < ÷„^† '6 Q _ R '6 ÷s _ μ _ 1(÷„) >, < ÷„^† '6 Q _ R '6 ÷s _ μ _ 1(÷„) >^2, < ÷„^† '6 c _ μ _ 1^R Q _ R '6 Q _ R '6 ÷s _ μ _ 1(÷„) >, < ÷„^† '6 Q _ R '6 c _ μ _ 1^R Q _ R '6 ÷s _ μ _ 1(÷„) >}

Complement[knechtterms1, knechtterms2]

{< ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 2(÷„) >^2, < ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 ÷„ >^2, < ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 ÷„ > < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L >, < ÷s _ μ _ 1(÷„)^† '6 c _ μ _ 1^R Q _ R '6 Q _ R '6 ÷„ >, < ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 ÷„ '6 c _ μ _ 1^L Q _ L >, < ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 c _ μ _ 1^R Q _ R '6 ÷„ >, < ÷„^† '6 c _ μ _ 1^R Q _ R '6 ÷s _ μ _ 1(÷„) '6 Q _ L >}

su2diff = Collect[(c knechtsu2res2 - knechtsu2res1 /. _Det -> 0 (* // UReduce // IndicesCleanup *) // Expand) /. {GLeft[LorentzIndex[μ2], LorentzIndex[μ1]][x] -> -GLeft[LorentzIndex[μ1], LorentzIndex[μ2]][x], GRight[LorentzIndex[μ2], LorentzIndex[μ1]][x] -> -GRight[LorentzIndex[μ1], LorentzIndex[μ2]][x]} /. NM[Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ2]]], GRight[LorentzIndex[μ1], LorentzIndex[μ2]][x], CovariantFieldDerivative[MM[x], x, LorentzIndex[μ1]]] -> -NM[Adjoint[CovariantFieldDerivative[MM[x], x, LorentzIndex[μ1]]], GRight[LorentzIndex[μ1], LorentzIndex[μ2]][x], CovariantFieldDerivative[MM[x], x, LorentzIndex[μ2]]] // NMExpand // Expand // CycleUTraces, _UTrace1]

((4 c (C^( ))^2)/(f _ π^(ó  ))^4 - (4 (C^( ))^2)/(f _ π^(ó  ))^4) < Q >^4 + (1/6 c γ _ (μ _ 1 μ _ 2)^2 - 1/6 γ _ (μ _ 1 μ _ 2)^2) < Q >^2 + (-(12 c (C^( ))^2)/(f _ π^(ó  ))^4 + (12 (C^( ))^2)/(f _ π^(ó  ))^4 - 3 c C^( ) + 3 C^( )) < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L > < Q >^2 - 1/6 < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 2(÷„) >^2 + 1/6 c < ÷s _ μ _ 2(÷„)^† '6 ÷s _ μ _ 1(÷„) >^2 + (1/32 - c/32) < ÷„^† '6 χ >^2 + (1/32 - c/32) < χ^† '6 ÷„ >^2 + (3/8 c (f _ π^(ó  ))^4 - 3/8 (f _ π^(ó  ))^4 + (3 C^( ))/4) < Q _ L '6 Q _ L >^2 + (3/8 c (f _ π^(ó  ))^4 - 3/8 (f _ π^(ó  ))^4 + (3 C^( ))/4) < Q _ R '6 Q _ R >^2 + 3/4 (f _ π^(ó  ))^2 < ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 ÷„ >^2 + (3/4 (f _ π^(ó  ))^2 - 3/4 c (f _ π^(ó  ))^2) < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L >^2 - 3/4 c (f _ π^(ó  ))^2 < ÷„^† '6 Q _ R '6 ÷s _ μ _ 1(÷„) >^2 + (3/2 c (f _ π^(ó  ))^4 - 3/2 (f _ π^(ó  ))^4 + 3 c C^( ) - 3 C^( ) + (12 c (C^( ))^2)/(f _ π^(ó  ))^4 - (12 (C^( ))^2)/(f _ π^(ó  ))^4) < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >^2 + (c/2 - 1/2) < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(χ) > + (c/2 - 1/2) < ÷s _ μ _ 1(χ)^† '6 ÷s _ μ _ 1(÷„) > + (c/2 - 1/2) < χ^† '6 χ > + (1/12 - c/12) < G _ (μ _ 1 μ _ 2)^L '6 G _ (μ _ 1 μ _ 2)^L > + (1/12 - c/12) < G _ (μ _ 1 μ _ 2)^R '6 G _ (μ _ 1 μ _ 2)^R > + (i/6 - (i c)/6) < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 2(÷„) '6 G _ (μ _ 1 μ _ 2)^L > + ((i c)/6 - i/6) < ÷s _ μ _ 1(÷„)^† '6 G _ (μ _ 1 μ _ 2)^R '6 ÷s _ μ _ 2(÷„) > - (2 C^( ) < ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 ÷„ > < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L >)/(f _ π^(ó  ))^2 - (2 c C^( ) < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L > < ÷„^† '6 Q _ R '6 ÷s _ μ _ 1(÷„) >)/(f _ π^(ó  ))^2 - 1/4 (f _ π^(ó  ))^2 < ÷s _ μ _ 1(÷„)^† '6 c _ μ _ 1^R Q _ R '6 Q _ R '6 ÷„ > - 1/4 (f _ π^(ó  ))^2 < ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 ÷„ '6 c _ μ _ 1^L Q _ L > + 1/4 (f _ π^(ó  ))^2 < ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 c _ μ _ 1^R Q _ R '6 ÷„ > + (1/4 c (f _ π^(ó  ))^2 - 1/4 (f _ π^(ó  ))^2) < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 c _ μ _ 1^L Q _ L '6 Q _ L > + (1/4 (f _ π^(ó  ))^2 - 1/4 c (f _ π^(ó  ))^2) < ÷„^† '6 ÷s _ μ _ 1(÷„) '6 Q _ L '6 c _ μ _ 1^L Q _ L > - 1/4 (f _ π^(ó  ))^2 < ÷„^† '6 c _ μ _ 1^R Q _ R '6 ÷s _ μ _ 1(÷„) '6 Q _ L > - 1/4 c (f _ π^(ó  ))^2 < ÷„^† '6 c _ μ _ 1^R Q _ R '6 Q _ R '6 ÷s _ μ _ 1(÷„) > + (1/6 - c/6) < ÷„^† '6 G _ (μ _ 1 μ _ 2)^R '6 ÷„ '6 G _ (μ _ 1 μ _ 2)^L > + 1/4 c (f _ π^(ó  ))^2 < ÷„^† '6 Q _ R '6 c _ μ _ 1^R Q _ R '6 ÷s _ μ _ 1(÷„) > + (-1/8 c (f _ π^(ó  ))^2 + 1/8 (f _ π^(ó  ))^2 + (c C^( ))/(f _ π^(ó  ))^2 - C^( )/(f _ π^(ó  ))^2) < ÷„^† '6 Q _ R '6 χ '6 Q _ L > + (-1/8 c (f _ π^(ó  ))^2 + 1/8 (f _ π^(ó  ))^2 + (c C^( ))/(f _ π^(ó  ))^2 - C^( )/(f _ π^(ó  ))^2) < χ^† '6 Q _ R '6 ÷„ '6 Q _ L > + (1/8 c (f _ π^(ó  ))^2 - 1/8 (f _ π^(ó  ))^2 - (c C^( ))/(f _ π^(ó  ))^2 + C^( )/(f _ π^(ó  ))^2) < ÷„^† '6 Q _ R '6 ÷„ '6 χ^† '6 ÷„ '6 Q _ L > + (1/8 c (f _ π^(ó  ))^2 - 1/8 (f _ π^(ó  ))^2 - (c C^( ))/(f _ π^(ó  ))^2 + C^( )/(f _ π^(ó  ))^2) < ÷„ '6 Q _ L '6 ÷„^† '6 χ '6 ÷„^† '6 Q _ R > + < Q _ R '6 Q _ R > ((-(2 c (C^( ))^2)/(f _ π^(ó  ))^4 + (2 (C^( ))^2)/(f _ π^(ó  ))^4 + 3/2 c C^( ) - (3 C^( ))/2) < Q >^2 + (3/2 (f _ π^(ó  ))^4 - 3/2 c (f _ π^(ó  ))^4) < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >) + < Q _ L '6 Q _ L > ((-(2 c (C^( ))^2)/(f _ π^(ó  ))^4 + (2 (C^( ))^2)/(f _ π^(ó  ))^4 + 3/2 c C^( ) - (3 C^( ))/2) < Q >^2 + (3/4 c (f _ π^(ó  ))^4 - 3/4 (f _ π^(ó  ))^4 - 3 c C^( ) + (3 C^( ))/2 + (4 c (C^( ))^2)/(f _ π^(ó  ))^4 - (4 (C^( ))^2)/(f _ π^(ó  ))^4) < Q _ R '6 Q _ R > + (3/2 (f _ π^(ó  ))^4 - 3/2 c (f _ π^(ó  ))^4) < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >) + < χ^† '6 ÷„ > ((C^( )/(f _ π^(ó  ))^2 - (c C^( ))/(f _ π^(ó  ))^2) < Q >^2 + (1/8 (f _ π^(ó  ))^2 - 1/8 c (f _ π^(ó  ))^2) < Q _ L '6 Q _ L > + (1/8 (f _ π^(ó  ))^2 - 1/8 c (f _ π^(ó  ))^2) < Q _ R '6 Q _ R > + (1/4 c (f _ π^(ó  ))^2 - 1/4 (f _ π^(ó  ))^2 + (2 c C^( ))/(f _ π^(ó  ))^2 - (2 C^( ))/(f _ π^(ó  ))^2) < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >) + < ÷„^† '6 χ > ((C^( )/(f _ π^(ó  ))^2 - (c C^( ))/(f _ π^(ó  ))^2) < Q >^2 + (1/16 - c/16) < χ^† '6 ÷„ > + (1/8 (f _ π^(ó  ))^2 - 1/8 c (f _ π^(ó  ))^2) < Q _ L '6 Q _ L > + (1/8 (f _ π^(ó  ))^2 - 1/8 c (f _ π^(ó  ))^2) < Q _ R '6 Q _ R > + (1/4 c (f _ π^(ó  ))^2 - 1/4 (f _ π^(ó  ))^2 + (2 c C^( ))/(f _ π^(ó  ))^2 - (2 C^( ))/(f _ π^(ó  ))^2) < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >) + < ÷s _ μ _ 1(÷„)^† '6 ÷s _ μ _ 1(÷„) > ((3/4 c (f _ π^(ó  ))^2 - 3/4 (f _ π^(ó  ))^2 - (c C^( ))/(f _ π^(ó  ))^2 + C^( )/(f _ π^(ó  ))^2) < Q >^2 + (c/12 - 1/12) < ÷s _ μ _ 2(÷„)^† '6 ÷s _ μ _ 2(÷„) > + (3/4 (f _ π^(ó  ))^2 - 3/4 c (f _ π^(ó  ))^2) < Q _ L '6 Q _ L > + (3/4 (f _ π^(ó  ))^2 - 3/4 c (f _ π^(ó  ))^2) < Q _ R '6 Q _ R > + ((2 c C^( ))/(f _ π^(ó  ))^2 - (2 C^( ))/(f _ π^(ó  ))^2) < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >)

su2diff /. c -> 1 // Expand // UReduce // FullSimplify

1/4 (3 C^( ) (< Q _ L '6 Q _ L > - < Q _ R '6 Q _ R >)^2 - (f _ π^(ó  ))^2 (< ÷s _ μ _ 1(÷„)^† '6 Q _ R '6 ÷„ '6 c _ μ _ 1^L Q _ L > + < ÷„^† '6 c _ μ _ 1^R Q _ R '6 ÷s _ μ _ 1(÷„) '6 Q _ L >))

Converted by Mathematica  (July 10, 2003)