•SU(3) intermediate results

Urech's intermediate result for n=3:

del[μ_][x_] := -I/2 USmall[LorentzIndex[μ]][x]

sig := 1/2 UChiPlus[x]

gam[mu_, nu_][x_] := FieldDerivative[UGamma[LorentzIndex[nu]][x], x, {mu}] - FieldDerivative[UGamma[LorentzIndex[mu]][x], x, {nu}] + UCommutator[UGamma[LorentzIndex[mu]][x], UGamma[LorentzIndex[nu]][x]]

urechres = (1/2 UTrace[NM[gam[μ, ν][x], gam[μ, ν][x]]] + UTrace[NM[del[μ][x], del[μ][x]]] UTrace[NM[del[ν][x], del[ν][x]]] + 2 UTrace[NM[del[μ][x], del[ν][x]]]^2 + 3 UTrace[NM[del[μ][x], del[μ][x], del[ν][x], del[ν][x]]] - UTrace[sig] UTrace[NM[del[μ][x], del[μ][x]]] - 3 UTrace[NM[sig, del[μ][x], del[μ][x]]] + 11/36 UTrace[sig]^2 + 5/12 UTrace[NM[sig, sig]] - (f^2 + 2 z) UTrace[NM[del[μ][x], HRight[x]]]^2 - (f^2 - 2 z) UTrace[NM[del[μ][x], HLeft[x]]]^2 - 1/2 (f^2 + 2 z) UTrace[NM[del[μ][x], del[μ][x]]] UTrace[NM[HRight[x], HRight[x]]] - 1/2 (f^2 - 2 z) UTrace[NM[del[μ][x], del[μ][x]]] UTrace[NM[HLeft[x], HLeft[x]]] + 3 (f^2 - z) UTrace[NM[del[μ][x], del[μ][x], HRight[x], HRight[x]]] + 3 (f^2 + z) UTrace[NM[del[μ][x], del[μ][x], HLeft[x], HLeft[x]]] + 1/2 f^2 UTrace[NM[del[μ][x], UCommutator[HRight[x], CovariantNabla[HLeft[x], x, LorentzIndex[μ1]]]]] (* - *) (* Error ? ! ? *) + 1/2 z UTrace[sig] UTrace[NM[HRight[x], HRight[x]] - NM[HLeft[x], HLeft[x]]] + 3/2 z UTrace[NM[sig, HRight[x], HRight[x]]] - 1/2 (f^2 (* Sign error ? ! ? *) + 3 z) UTrace[NM[sig, HLeft[x], HLeft[x]]] - 3/2 (c + 4 z^2) UTrace[NM[HRight[x], HRight[x], HLeft[x], HLeft[x]]] + 9/8 z^2 UTrace[NM[HRight[x], HRight[x]]]^2 + 3/8 (f^4 + 3 z^2) UTrace[NM[HLeft[x], HLeft[x]]]^2 + 1/4 (c + z^2) UTrace[NM[HRight[x], HRight[x]]] UTrace[NM[HLeft[x], HLeft[x]]] + 1/2 (c + z^2) UTrace[NM[HRight[x], HLeft[x]]]^2) /. {μ -> μ1, ν -> μ2, f -> DecayConstant[PhiMeson], z -> CouplingConstant[ChPTVirtualPhotons3[2]]/DecayConstant[PhiMeson]^2, c -> CouplingConstant[ChPTVirtualPhotons3[2]]} ;

urechres1 = (dum * urechres // CycleUTraces // IndicesCleanup) /. dum -> 1 // CycleUTraces // Simplify // IndicesCleanup

3/8 < H _ L '6 H _ L >^2 (f _ ϕ^(ó  ))^4 + 1/4 < H _ L '6 u _ μ _ 1 >^2 (f _ ϕ^(ó  ))^2 + 1/4 < H _ R '6 u _ μ _ 1 >^2 (f _ ϕ^(ó  ))^2 + 1/8 < H _ L '6 H _ L > < u _ μ _ 1 '6 u _ μ _ 1 > (f _ ϕ^(ó  ))^2 + 1/8 < H _ R '6 H _ R > < u _ μ _ 1 '6 u _ μ _ 1 > (f _ ϕ^(ó  ))^2 + 1/4 i < ∇ _ μ _ 1(H _ L) '6 H _ R '6 u _ μ _ 1 > (f _ ϕ^(ó  ))^2 - 1/4 i < ∇ _ μ _ 1(H _ L) '6 u _ μ _ 1 '6 H _ R > (f _ ϕ^(ó  ))^2 - 1/4 < χ _ + '6 H _ L '6 H _ L > (f _ ϕ^(ó  ))^2 - 3/4 < H _ L '6 H _ L '6 u _ μ _ 1 '6 u _ μ _ 1 > (f _ ϕ^(ó  ))^2 - 3/4 < H _ R '6 H _ R '6 u _ μ _ 1 '6 u _ μ _ 1 > (f _ ϕ^(ó  ))^2 + 1/2 C^( ) < H _ L '6 H _ R >^2 + 1/8 < u _ μ _ 1 '6 u _ μ _ 2 >^2 + (11 < χ _ + >^2)/144 + < ∂ _ μ _ 2(Γ _ μ _ 1) '6 ∂ _ μ _ 2(Γ _ μ _ 1) > - < ∂ _ μ _ 2(Γ _ μ _ 1) '6 ∂ _ μ _ 1(Γ _ μ _ 2) > + 1/4 C^( ) < H _ L '6 H _ L > < H _ R '6 H _ R > + 5/48 < χ _ + '6 χ _ + > + 1/16 < u _ μ _ 1 '6 u _ μ _ 1 > < u _ μ _ 2 '6 u _ μ _ 2 > - 2 < ∂ _ μ _ 2(Γ _ μ _ 1) '6 Γ _ μ _ 1 '6 Γ _ μ _ 2 > + 2 < ∂ _ μ _ 2(Γ _ μ _ 1) '6 Γ _ μ _ 2 '6 Γ _ μ _ 1 > + 3/8 < χ _ + '6 u _ μ _ 1 '6 u _ μ _ 1 > - 3/2 C^( ) < H _ L '6 H _ L '6 H _ R '6 H _ R > - < Γ _ μ _ 1 '6 Γ _ μ _ 1 '6 Γ _ μ _ 2 '6 Γ _ μ _ 2 > + < Γ _ μ _ 1 '6 Γ _ μ _ 2 '6 Γ _ μ _ 1 '6 Γ _ μ _ 2 > + 3/16 < u _ μ _ 1 '6 u _ μ _ 1 '6 u _ μ _ 2 '6 u _ μ _ 2 > + 1/8 < u _ μ _ 1 '6 u _ μ _ 1 > < χ _ + > - (C^( ) < H _ L '6 u _ μ _ 1 >^2)/(2 (f _ ϕ^(ó  ))^2) + (C^( ) < H _ R '6 u _ μ _ 1 >^2)/(2 (f _ ϕ^(ó  ))^2) - (C^( ) < H _ L '6 H _ L > < u _ μ _ 1 '6 u _ μ _ 1 >)/(4 (f _ ϕ^(ó  ))^2) + (C^( ) < H _ R '6 H _ R > < u _ μ _ 1 '6 u _ μ _ 1 >)/(4 (f _ ϕ^(ó  ))^2) - (3 C^( ) < χ _ + '6 H _ L '6 H _ L >)/(4 (f _ ϕ^(ó  ))^2) + (3 C^( ) < χ _ + '6 H _ R '6 H _ R >)/(4 (f _ ϕ^(ó  ))^2) - (3 C^( ) < H _ L '6 H _ L '6 u _ μ _ 1 '6 u _ μ _ 1 >)/(4 (f _ ϕ^(ó  ))^2) + (3 C^( ) < H _ R '6 H _ R '6 u _ μ _ 1 '6 u _ μ _ 1 >)/(4 (f _ ϕ^(ó  ))^2) - (C^( ) < H _ L '6 H _ L > < χ _ + >)/(4 (f _ ϕ^(ó  ))^2) + (C^( ) < H _ R '6 H _ R > < χ _ + >)/(4 (f _ ϕ^(ó  ))^2) + (9 (C^( ))^2 < H _ L '6 H _ L >^2)/(8 (f _ ϕ^(ó  ))^4) + ((C^( ))^2 < H _ L '6 H _ R >^2)/(2 (f _ ϕ^(ó  ))^4) + (9 (C^( ))^2 < H _ R '6 H _ R >^2)/(8 (f _ ϕ^(ó  ))^4) + ((C^( ))^2 < H _ L '6 H _ L > < H _ R '6 H _ R >)/(4 (f _ ϕ^(ó  ))^4) - (6 (C^( ))^2 < H _ L '6 H _ L '6 H _ R '6 H _ R >)/(f _ ϕ^(ó  ))^4

urechres1 /. {(HLeft | HRight)[__] -> 0}

1/8 < u _ μ _ 1 '6 u _ μ _ 2 >^2 + (11 < χ _ + >^2)/144 + < ∂ _ μ _ 2(Γ _ μ _ 1) '6 ∂ _ μ _ 2(Γ _ μ _ 1) > - < ∂ _ μ _ 2(Γ _ μ _ 1) '6 ∂ _ μ _ 1(Γ _ μ _ 2) > + 5/48 < χ _ + '6 χ _ + > + 1/16 < u _ μ _ 1 '6 u _ μ _ 1 > < u _ μ _ 2 '6 u _ μ _ 2 > - 2 < ∂ _ μ _ 2(Γ _ μ _ 1) '6 Γ _ μ _ 1 '6 Γ _ μ _ 2 > + 2 < ∂ _ μ _ 2(Γ _ μ _ 1) '6 Γ _ μ _ 2 '6 Γ _ μ _ 1 > + 3/8 < χ _ + '6 u _ μ _ 1 '6 u _ μ _ 1 > - < Γ _ μ _ 1 '6 Γ _ μ _ 1 '6 Γ _ μ _ 2 '6 Γ _ μ _ 2 > + < Γ _ μ _ 1 '6 Γ _ μ _ 2 '6 Γ _ μ _ 1 '6 Γ _ μ _ 2 > + 3/16 < u _ μ _ 1 '6 u _ μ _ 1 '6 u _ μ _ 2 '6 u _ μ _ 2 > + 1/8 < u _ μ _ 1 '6 u _ μ _ 1 > < χ _ + >

sdwsu3Res1 = (dum * sdw2Res1 /. n -> 3 /. UGamma[μ1_] -> UGamma[LorentzIndex[μ1]] // IndicesCleanup // NMExpand // Expand) /. dum -> 1 /. su3calhamruleH /. su3calhamruleUHL /. su3calhamruleUHR /. su3calhamrule4 /. UTrace1[((* In SU (3) Q is traceless *) HRight | HLeft | USmall[_] | UGamma[_])[_] | FieldDerivative[UGamma[_][_], _, _]] -> 0 // UReduce[#, SUNN -> 3, UDimension -> 3] & // CycleUTraces // Simplify ;

sdwsu3Res2 = sdwsu3Res1 /. Power -> NMPower /. Times -> NM /. NM -> nm /. (* Transform back to Minkowski space *) nm[a__] :> (-1)^(Count[nm[a], LorentzIndex[__], Infinity, Heads -> True]/2) * NM[a] /. nm -> NM // CommutatorReduce

1/(144 (f _ ϕ^(ó  ))^4) (54 < H _ L '6 H _ L >^2 (f _ ϕ^(ó  ))^8 - 18 (-2 < H _ L '6 u _ μ _ 1 >^2 - 2 < H _ R '6 u _ μ _ 1 >^2 - < H _ L '6 H _ L > < u _ μ _ 1 '6 u _ μ _ 1 > - < H _ R '6 H _ R > < u _ μ _ 1 '6 u _ μ _ 1 > - 2 i < ∇ _ μ _ 1(H _ L) '6 H _ R '6 u _ μ _ 1 > + 2 i < ∇ _ μ _ 1(H _ L) '6 u _ μ _ 1 '6 H _ R > + 2 < χ _ + '6 H _ L '6 H _ L > + 6 < H _ L '6 H _ L '6 u _ μ _ 1 '6 u _ μ _ 1 > + 6 < H _ R '6 H _ R '6 u _ μ _ 1 '6 u _ μ _ 1 >) (f _ ϕ^(ó  ))^6 + (72 C^( ) < H _ L '6 H _ R >^2 + 18 < u _ μ _ 1 '6 u _ μ _ 2 >^2 + 11 < χ _ + >^2 + 144 < ∂ _ μ _ 2(Γ _ μ _ 1) '6 ∂ _ μ _ 2(Γ _ μ _ 1) > - 144 < ∂ _ μ _ 2(Γ _ μ _ 1) '6 ∂ _ μ _ 1(Γ _ μ _ 2) > + 36 C^( ) < H _ L '6 H _ L > < H _ R '6 H _ R > + 15 < χ _ + '6 χ _ + > + 9 < u _ μ _ 1 '6 u _ μ _ 1 > < u _ μ _ 2 '6 u _ μ _ 2 > - 288 < ∂ _ μ _ 2(Γ _ μ _ 1) '6 Γ _ μ _ 1 '6 Γ _ μ _ 2 > + 288 < ∂ _ μ _ 2(Γ _ μ _ 1) '6 Γ _ μ _ 2 '6 Γ _ μ _ 1 > + 54 < χ _ + '6 u _ μ _ 1 '6 u _ μ _ 1 > - 216 C^( ) < H _ L '6 H _ L '6 H _ R '6 H _ R > - 144 < Γ _ μ _ 1 '6 Γ _ μ _ 1 '6 Γ _ μ _ 2 '6 Γ _ μ _ 2 > + 144 < Γ _ μ _ 1 '6 Γ _ μ _ 2 '6 Γ _ μ _ 1 '6 Γ _ μ _ 2 > + 27 < u _ μ _ 1 '6 u _ μ _ 1 '6 u _ μ _ 2 '6 u _ μ _ 2 > + 18 < u _ μ _ 1 '6 u _ μ _ 1 > < χ _ + >) (f _ ϕ^(ó  ))^4 + 36 C^( ) (-2 < H _ L '6 u _ μ _ 1 >^2 + 2 < H _ R '6 u _ μ _ 1 >^2 - < H _ L '6 H _ L > < u _ μ _ 1 '6 u _ μ _ 1 > + < H _ R '6 H _ R > < u _ μ _ 1 '6 u _ μ _ 1 > - 3 < χ _ + '6 H _ L '6 H _ L > + 3 < χ _ + '6 H _ R '6 H _ R > - 3 < H _ L '6 H _ L '6 u _ μ _ 1 '6 u _ μ _ 1 > + 3 < H _ R '6 H _ R '6 u _ μ _ 1 '6 u _ μ _ 1 > - < H _ L '6 H _ L > < χ _ + > + < H _ R '6 H _ R > < χ _ + >) (f _ ϕ^(ó  ))^2 + 18 (C^( ))^2 (9 < H _ L '6 H _ L >^2 - 4 < H _ R '6 H _ R > < H _ L '6 H _ L > - 8 < H _ L '6 H _ R >^2 + 9 < H _ R '6 H _ R >^2 - 12 < H _ L '6 H _ L '6 H _ R '6 H _ R >))

urechterms = (List @@ (urechres1 // NMExpand // Expand) //. a_ * b : (_UTrace1 | _UTrace1^_ | _Det) :> b /; FreeQ[a, UTrace1, Infinity, Heads -> True]) // Union // Sort

{< ∂ _ μ _ 2(Γ _ μ _ 1) '6 ∂ _ μ _ 2(Γ _ μ _ 1) >, < ∂ _ μ _ 2(Γ _ μ _ 1) '6 ∂ _ μ _ 1(Γ _ μ _ 2) >, < H _ L '6 H _ L >^2, < H _ L '6 H _ R >^2, < H _ L '6 u _ μ _ 1 >^2, < H _ L '6 H _ L > < H _ R '6 H _ R >, < H _ R '6 H _ R >^2, < H _ R '6 u _ μ _ 1 >^2, < χ _ + '6 χ _ + >, < H _ L '6 H _ L > < u _ μ _ 1 '6 u _ μ _ 1 >, < H _ R '6 H _ R > < u _ μ _ 1 '6 u _ μ _ 1 >, < u _ μ _ 1 '6 u _ μ _ 2 >^2, < u _ μ _ 1 '6 u _ μ _ 1 > < u _ μ _ 2 '6 u _ μ _ 2 >, < ∇ _ μ _ 1(H _ L) '6 H _ R '6 u _ μ _ 1 >, < ∇ _ μ _ 1(H _ L) '6 u _ μ _ 1 '6 H _ R >, < ∂ _ μ _ 2(Γ _ μ _ 1) '6 Γ _ μ _ 1 '6 Γ _ μ _ 2 >, < ∂ _ μ _ 2(Γ _ μ _ 1) '6 Γ _ μ _ 2 '6 Γ _ μ _ 1 >, < χ _ + '6 H _ L '6 H _ L >, < χ _ + '6 H _ R '6 H _ R >, < χ _ + '6 u _ μ _ 1 '6 u _ μ _ 1 >, < H _ L '6 H _ L '6 H _ R '6 H _ R >, < H _ L '6 H _ L '6 u _ μ _ 1 '6 u _ μ _ 1 >, < H _ R '6 H _ R '6 u _ μ _ 1 '6 u _ μ _ 1 >, < Γ _ μ _ 1 '6 Γ _ μ _ 1 '6 Γ _ μ _ 2 '6 Γ _ μ _ 2 >, < Γ _ μ _ 1 '6 Γ _ μ _ 2 '6 Γ _ μ _ 1 '6 Γ _ μ _ 2 >, < u _ μ _ 1 '6 u _ μ _ 1 '6 u _ μ _ 2 '6 u _ μ _ 2 >, < H _ L '6 H _ L > < χ _ + >, < H _ R '6 H _ R > < χ _ + >, < u _ μ _ 1 '6 u _ μ _ 1 > < χ _ + >, < χ _ + >^2}

su3terms = (List @@ Expand[sdwsu3Res2] //. a_ * b : (_UTrace1 | _UTrace1^_ | _Det) :> b /; FreeQ[a, UTrace1, Infinity, Heads -> True]) // Union // Sort

{< ∂ _ μ _ 2(Γ _ μ _ 1) '6 ∂ _ μ _ 2(Γ _ μ _ 1) >, < ∂ _ μ _ 2(Γ _ μ _ 1) '6 ∂ _ μ _ 1(Γ _ μ _ 2) >, < H _ L '6 H _ L >^2, < H _ L '6 H _ R >^2, < H _ L '6 u _ μ _ 1 >^2, < H _ L '6 H _ L > < H _ R '6 H _ R >, < H _ R '6 H _ R >^2, < H _ R '6 u _ μ _ 1 >^2, < χ _ + '6 χ _ + >, < H _ L '6 H _ L > < u _ μ _ 1 '6 u _ μ _ 1 >, < H _ R '6 H _ R > < u _ μ _ 1 '6 u _ μ _ 1 >, < u _ μ _ 1 '6 u _ μ _ 2 >^2, < u _ μ _ 1 '6 u _ μ _ 1 > < u _ μ _ 2 '6 u _ μ _ 2 >, < ∇ _ μ _ 1(H _ L) '6 H _ R '6 u _ μ _ 1 >, < ∇ _ μ _ 1(H _ L) '6 u _ μ _ 1 '6 H _ R >, < ∂ _ μ _ 2(Γ _ μ _ 1) '6 Γ _ μ _ 1 '6 Γ _ μ _ 2 >, < ∂ _ μ _ 2(Γ _ μ _ 1) '6 Γ _ μ _ 2 '6 Γ _ μ _ 1 >, < χ _ + '6 H _ L '6 H _ L >, < χ _ + '6 H _ R '6 H _ R >, < χ _ + '6 u _ μ _ 1 '6 u _ μ _ 1 >, < H _ L '6 H _ L '6 H _ R '6 H _ R >, < H _ L '6 H _ L '6 u _ μ _ 1 '6 u _ μ _ 1 >, < H _ R '6 H _ R '6 u _ μ _ 1 '6 u _ μ _ 1 >, < Γ _ μ _ 1 '6 Γ _ μ _ 1 '6 Γ _ μ _ 2 '6 Γ _ μ _ 2 >, < Γ _ μ _ 1 '6 Γ _ μ _ 2 '6 Γ _ μ _ 1 '6 Γ _ μ _ 2 >, < u _ μ _ 1 '6 u _ μ _ 1 '6 u _ μ _ 2 '6 u _ μ _ 2 >, < H _ L '6 H _ L > < χ _ + >, < H _ R '6 H _ R > < χ _ + >, < u _ μ _ 1 '6 u _ μ _ 1 > < χ _ + >, < χ _ + >^2}

Complement[su3terms, urechterms]

{}

Complement[urechterms, su3terms]

{}

test = (Simplify /@ Collect[sdwsu3Res2 - u urechres1 // NMExpand // Expand // CycleUTraces, {a_UTrace1 b_UTrace1, _UTrace1}]) /. {u - 1 -> 0, 1 - u -> 0}

-((u + 2) < H _ L '6 H _ R >^2 (C^( ))^2)/(2 (f _ ϕ^(ó  ))^4) - ((u + 2) < H _ L '6 H _ L > < H _ R '6 H _ R > (C^( ))^2)/(4 (f _ ϕ^(ó  ))^4) + (3 (4 u - 1) < H _ L '6 H _ L '6 H _ R '6 H _ R > (C^( ))^2)/(2 (f _ ϕ^(ó  ))^4)

test /. HRight -> HLeft /. su3calhamrule4 /. UTrace1[HLeft[_]] -> 0 /. u -> 1 // Simplify

0

test (* /. u -> 1 *) /. $Substitutions // NMExpand // Expand // UReduce[#, SUNN -> 3, UDimension -> 3, SMMToMM -> True] &

-(3 u < Q _ L '6 Q _ L >^2 (C^( ))^2)/(4 (f _ ϕ^(ó  ))^4) - (3 < Q _ L '6 Q _ L >^2 (C^( ))^2)/(2 (f _ ϕ^(ó  ))^4) - (3 u < Q _ R '6 Q _ R >^2 (C^( ))^2)/(4 (f _ ϕ^(ó  ))^4) - (3 < Q _ R '6 Q _ R >^2 (C^( ))^2)/(2 (f _ ϕ^(ó  ))^4) + (u < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >^2 (C^( ))^2)/(f _ ϕ^(ó  ))^4 + (2 < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L >^2 (C^( ))^2)/(f _ ϕ^(ó  ))^4 + (u < Q _ L '6 Q _ L > < Q _ R '6 Q _ R > (C^( ))^2)/(2 (f _ ϕ^(ó  ))^4) + (< Q _ L '6 Q _ L > < Q _ R '6 Q _ R > (C^( ))^2)/(f _ ϕ^(ó  ))^4 + (6 u < Q _ L '6 Q _ L '6 Q _ L '6 Q _ L > (C^( ))^2)/(f _ ϕ^(ó  ))^4 - (3 < Q _ L '6 Q _ L '6 Q _ L '6 Q _ L > (C^( ))^2)/(2 (f _ ϕ^(ó  ))^4) + (6 u < Q _ R '6 Q _ R '6 Q _ R '6 Q _ R > (C^( ))^2)/(f _ ϕ^(ó  ))^4 - (3 < Q _ R '6 Q _ R '6 Q _ R '6 Q _ R > (C^( ))^2)/(2 (f _ ϕ^(ó  ))^4) - (12 u < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L '6 ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L > (C^( ))^2)/(f _ ϕ^(ó  ))^4 + (3 < ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L '6 ÷„^† '6 Q _ R '6 ÷„ '6 Q _ L > (C^( ))^2)/(f _ ϕ^(ó  ))^4

% /. UChiralSpurionRight -> UChiralSpurionLeft /. UMatrix[UChi[]][_] -> 0 // NMExpand // Expand

-(u < Q _ L '6 Q _ L >^2 (C^( ))^2)/(f _ ϕ^(ó  ))^4 - (2 < Q _ L '6 Q _ L >^2 (C^( ))^2)/(f _ ϕ^(ó  ))^4 + (u < ÷„^† '6 Q _ L '6 ÷„ '6 Q _ L >^2 (C^( ))^2)/(f _ ϕ^(ó  ))^4 + (2 < ÷„^† '6 Q _ L '6 ÷„ '6 Q _ L >^2 (C^( ))^2)/(f _ ϕ^(ó  ))^4 + (12 u < Q _ L '6 Q _ L '6 Q _ L '6 Q _ L > (C^( ))^2)/(f _ ϕ^(ó  ))^4 - (3 < Q _ L '6 Q _ L '6 Q _ L '6 Q _ L > (C^( ))^2)/(f _ ϕ^(ó  ))^4 - (12 u < ÷„^† '6 Q _ L '6 ÷„ '6 Q _ L '6 ÷„^† '6 Q _ L '6 ÷„ '6 Q _ L > (C^( ))^2)/(f _ ϕ^(ó  ))^4 + (3 < ÷„^† '6 Q _ L '6 ÷„ '6 Q _ L '6 ÷„^† '6 Q _ L '6 ÷„ '6 Q _ L > (C^( ))^2)/(f _ ϕ^(ó  ))^4

Collect[% /. su3calhamrule4 /. UTrace1[UMatrix[UChiralSpurionLeft[]][_]] -> 0 /. su3calhamruleQl // Expand, _UTrace1]

((5 u (C^( ))^2)/(f _ ϕ^(ó  ))^4 - (7 (C^( ))^2)/(2 (f _ ϕ^(ó  ))^4)) < Q _ L '6 Q _ L >^2 + ((u (C^( ))^2)/(f _ ϕ^(ó  ))^4 + (2 (C^( ))^2)/(f _ ϕ^(ó  ))^4) < ÷„^† '6 Q _ L '6 ÷„ '6 Q _ L >^2 + ((3 (C^( ))^2)/(f _ ϕ^(ó  ))^4 - (12 u (C^( ))^2)/(f _ ϕ^(ó  ))^4) < ÷„^† '6 Q _ L '6 ÷„ '6 Q _ L '6 ÷„^† '6 Q _ L '6 ÷„ '6 Q _ L >

Converted by Mathematica  (July 10, 2003)