•Expansion of \!\(H\_\(\* StyleBox[\"R\",\nFontSlant->\"Plain\"]\)\)

do = 1

1

DiscardTerms[NM[Adjoint[uExpRight[x, ExpansionOrder -> do]], UMatrix[UChiralSpurionRight[]][x], uExpRight[x, ExpansionOrder -> do]] + NM[uExpLeftAdj[x, ExpansionOrder -> do], UMatrix[UChiralSpurionLeft[]][x], Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] // NMExpand // Expand, Retain -> {Particle[UPerturbation] -> do}]

(i (öÆ^† '6 Q _ R '6 öÆ '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(2^(1/2) f) - (i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 Q _ R '6 öÆ))/(2^(1/2) f) + (i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 Q _ L '6 öÆ^†))/(2^(1/2) f) - (i (öÆ '6 Q _ L '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(2^(1/2) f)

-I/Sqrt[2]/DecayConstant[PhiMeson] UCommutator[xi[x], HLeft[x]] /. $Substitutions // NMExpand // Expand

(i (öÆ^† '6 Q _ R '6 öÆ '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(2^(1/2) f) - (i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 Q _ R '6 öÆ))/(2^(1/2) f) + (i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 Q _ L '6 öÆ^†))/(2^(1/2) f) - (i (öÆ '6 Q _ L '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(2^(1/2) f)

% - %%

0

do = 2

2

DiscardTerms[NM[Adjoint[uExpRight[x, ExpansionOrder -> do]], UMatrix[UChiralSpurionRight[]][x], uExpRight[x, ExpansionOrder -> do]] + NM[uExpLeftAdj[x, ExpansionOrder -> do], UMatrix[UChiralSpurionLeft[]][x], Adjoint[uExpLeftAdj[x, ExpansionOrder -> do]]] // NMExpand // Expand, Retain -> {Particle[UPerturbation] -> do}]

-(öÆ^† '6 Q _ R '6 öÆ '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(4 f^2) + (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 Q _ R '6 öÆ '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(2 f^2) - (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 Q _ R '6 öÆ)/(4 f^2) - (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 Q _ L '6 öÆ^†)/(4 f^2) + (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 Q _ L '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(2 f^2) - (öÆ '6 Q _ L '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(4 f^2)

-1/4/DecayConstant[PhiMeson]^2 UCommutator[xi[x], UCommutator[xi[x], HRight[x]]] /. $Substitutions // NMExpand // Expand

-(öÆ^† '6 Q _ R '6 öÆ '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(4 f^2) + (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 Q _ R '6 öÆ '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(2 f^2) - (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 Q _ R '6 öÆ)/(4 f^2) - (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 Q _ L '6 öÆ^†)/(4 f^2) + (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 Q _ L '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(2 f^2) - (öÆ '6 Q _ L '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(4 f^2)

% - %%

0

Coeff[HRight][0][x_] = HRight[x]

H _ R

Coeff[HRight][1][x_] = -I/Sqrt[2]/DecayConstant[PhiMeson] UCommutator[xi[x], HLeft[x]]

-(i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 H _ L - H _ L '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(2^(1/2) f)

Coeff[HRight][2][x_] = -1/4/DecayConstant[PhiMeson]^2 UCommutator[xi[x], UCommutator[xi[x], HRight[x]]]

-(Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 H _ R - H _ R '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]) - (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 H _ R - H _ R '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]) '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(4 f^2)

Converted by Mathematica  (July 10, 2003)