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PVC

PVC[r,n1,n2,s1,s12,s2,m0,m1,m2]
is the Passarino-Veltman coefficient function .

Details and OptionsDetails and Options

  • PVC[r,n1,n2,s1,s12,s2,m0,m1,m2] is the symbolic form of the coefficient function multiplying the symmetrized tensor generated by LoopIntegrate.
  • PVC[r,n1,n2,s1,s12,s2,m0,m1,m2] implicitly depends on the number of spacetime dimensions .
  • PVC[0,0,0,s1,s12,s2,m0,m1,m2] represents the scalar function with full dependence on .
  • PVC[r,n1,n2,s1,s12,s2,m0,m1,m2] is symmetric with respect to the simultaneous interchange , ,
  • PVC does not automatically reorganize its arguments.
  • PVC does not directly evaluate. LoopRefine substitutes PVC with its explicit expression.
  • PVC[r,n1,n2,s1,s12,s2,m0,m1,m2,Weights{w0,w1,w2}] represents the weighted coefficient function .
  • PVC[r,n1,n2,s1,s12,s2,m0,m1,m2,Dimensionsn] represents the coefficient function in spacetime dimensions.
  • The following are equal to PVC[r,n1,n2,s1,s12,s2,m0,m1,m2] in other packages:
  • FeynCalcPaVe[,{s1,s12,s2},{,,}]
    LoopTools (IR finite and , )C0i[cc,s1,s12,s2,,,]

ExamplesExamplesopen allclose all

Basic Examples  (5)Basic Examples  (5)

Apply LoopRefine to substitute the analytic form of PVC:

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Weighted PVC:

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Taylor series expansion around :

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View PVC in TraditionalForm:

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TAdjustmentBox[E, BoxBaselineShift -> 0.5, BoxMargins -> {{-0.3, 0}, {0, 0}}]X code:

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More general cases are given in terms of ScalarC0:

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Set option ExplicitC0All to LoopRefine, or apply C0Expand to obtain an expression in terms of more elementary functions:

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