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ScalarC0

ScalarC0[s1,s12,s2,m0,m1,m2]
gives the scalar Passarino-Veltman three-point function for real external invariants , , , and real positive masses , , .

Details and OptionsDetails and Options

  • Mathematical function, suitable for numerical evaluation. For rapid machine precision evaluation, ScalarC0 uses code that is compiled to the Wolfram Virtual Machine (triggered after first numerical evaluation). For arbitrary precision evaluation, ScalarC0 uses Wolfram Language code.
  • ScalarC0[s1,s12,s2,m0,m1,m2] is generated by LoopRefine to maintain compact expressions. Applying C0Expand, or setting option ExplicitC0All to LoopRefine will replace ScalarC0 with its explicit form.
  • The arguments of ScalarC0[s1,s12,s2,m0,m1,m2] correspond to
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    .
  • For vanishing external invariants, ScalarC0 is automatically replaced with its explicit form.
  • ScalarC0[s1,s12,s2,m0,m1,m2] is symmetric with under any of the pair-wise interchanges , , or .
  • ScalarC0[s1,s12,s2,m0,m1,m2] automatically reorganizes its arguments canonically.
  • ScalarC0 evaluates only for real external invariants and masses.
  • The following are equal to ScalarC0[s1,s12,s2,m0,m1,m2] in other packages:
  • FeynCalc/LoopToolsC0[s1,s12,s2,,,]
    Package-X 1.0pvC0[s1,s2,s12,m2,m1,m0]

ExamplesExamplesopen allclose all

Basic Examples  (5)Basic Examples  (5)

Evaluate numerically:

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The precision of the output tracks the precision of the input:

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Evaluate symbolically:

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Make a plot:

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Apply C0Expand to obtain the explicit analytic expression:

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Taylor series:

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