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ScalarD0

ScalarD0[s1,s2,s3,s4,s12,s23,m0,m1,m2,m3]
gives the scalar Passarino-Veltman four-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, ScalarD0 uses code that is compiled to the Wolfram Virtual Machine (triggered after first numerical evaluation). For arbitrary precision evaluation, ScalarD0 uses Wolfram Language code.
  • ScalarD0[s1,s2,s3,s4,s12,s23,m0,m1,m2,m3] is generated by LoopRefine to maintain compact expressions. Applying D0Expand will replace ScalarD0 with an analytic expression if it is known.
  • The arguments of ScalarD0[s1,s2,s3,s4,s12,s23,m0,m1,m2,m3] correspond to
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    .
  • For vanishing external invariants, ScalarD0 is automatically replaced with its explicit form.
  • ScalarD0[s1,s2,s3,s4,s12,s23,m0,m1,m2,m3] is symmetric under combinations of the following transformations: »
    1. cyclic,
    2. order reversal,
    3. transposition,
    4. transposition,
  • ScalarD0[s1,s2,s3,s4,s12,s23,m0,m1,m2,m3] automatically sorts its arguments based on the set of possible orderings generated by the cyclic and order reversal transformations only.
  • ScalarD0 evaluates only for real external invariants and masses.
  • The following are equal to ScalarD0[s1,s2,s3,s4,s12,s23,m0,m1,m2,m3] in other packages:
  • FeynCalc/LoopToolsD0[s1,s2,s3,s4,s12,s23,,,,]

ExamplesExamplesopen allclose all

Basic Examples  (4)Basic Examples  (4)

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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Taylor series:

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