•Expansion of
Converted by
Mathematica
(July 10, 2003)
![\!\(H\_\(\* StyleBox[\"R\",\nFontSlant->\"Plain\"]\)\)](../HTMLFiles/index_63.gif){kind=small}
![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}]](../HTMLFiles/index_66.gif)
![(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)](../HTMLFiles/index_67.gif)
![-I/Sqrt[2]/DecayConstant[PhiMeson] UCommutator[xi[x], HLeft[x]] /. $Substitutions // NMExpand // Expand](../HTMLFiles/index_68.gif){kind=small}
![(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)](../HTMLFiles/index_69.gif)
![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}]](../HTMLFiles/index_74.gif)
![-(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)](../HTMLFiles/index_75.gif)
![-1/4/DecayConstant[PhiMeson]^2 UCommutator[xi[x], UCommutator[xi[x], HRight[x]]] /. $Substitutions // NMExpand // Expand](../HTMLFiles/index_76.gif){kind=small}
![-(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)](../HTMLFiles/index_77.gif)
![Coeff[HRight][0][x_] = HRight[x]](../HTMLFiles/index_80.gif){kind=small}
![Coeff[HRight][1][x_] = -I/Sqrt[2]/DecayConstant[PhiMeson] UCommutator[xi[x], HLeft[x]]](../HTMLFiles/index_82.gif){kind=small}
![-(i (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 H _ L - H _ L '6 Overscript[ξ^( ), ->] · Overscript[σ, ->]))/(2^(1/2) f)](../HTMLFiles/index_83.gif)
![Coeff[HRight][2][x_] = -1/4/DecayConstant[PhiMeson]^2 UCommutator[xi[x], UCommutator[xi[x], HRight[x]]]](../HTMLFiles/index_84.gif){kind=small}
![-(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)](../HTMLFiles/index_85.gif){kind=small}
![Coeff[HRight][do_ ? ((# > 2) &)][x_] := Coeff[HRight][do][x] = (Message[UPerturb :: nocoeff, do] ; 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}] // UReduce) ;](../HTMLFiles/index_86.gif)
![Coeff[HRight][4][x]](../HTMLFiles/index_87.gif){kind=small}
![(öÆ^† '6 Q _ R '6 öÆ '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(96 f^4) - (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 Q _ R '6 öÆ '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(24 f^4) + (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 Q _ R '6 öÆ '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(16 f^4) - (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 Q _ R '6 öÆ '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(24 f^4) + (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ^† '6 Q _ R '6 öÆ)/(96 f^4) + (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 Q _ L '6 öÆ^†)/(96 f^4) - (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 Q _ L '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(24 f^4) + (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 Q _ L '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(16 f^4) - (Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 öÆ '6 Q _ L '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(24 f^4) + (öÆ '6 Q _ L '6 öÆ^† '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->] '6 Overscript[ξ^( ), ->] · Overscript[σ, ->])/(96 f^4)](../HTMLFiles/index_89.gif)