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ScalarD0IR13

ScalarD0IR13[s2,s3,s4,s12,s23,m2,m3]
gives the finite part of Ellis-Zanderighi collinear singular box 13, for real , , , , and positive and .

Details and OptionsDetails and Options

  • Mathematical function, suitable for numerical evaluation. For rapid machine precision evaluation, ScalarD0IR13 uses code that is compiled to the Wolfram Virtual Machine (triggered after first numerical evaluation). For arbitrary precision evaluation, ScalarD0IR13 uses Wolfram Language code.
  • ScalarD0IR13[s2,s3,s4,s12,s23,m2,m3] is generated by LoopRefine to maintain compact expressions. Applying D0Expand will replace ScalarD0IR13 with its explicit form.
  • Below all thresholds, ScalarD0IR13[s2,s3,s4,s12,s23,m2,m3] satisfies the dispersion relation:
        ,
    where
    ,
    .
  • ScalarD0IR13[s2,s3,s4,s12,s23,m2,m3] is symmetric with respect to the pair-wise interchange .

ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

Generate ScalarD0IR13 by reduction of a Passarino-Veltman D function:

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Apply D0Expand to obtain an analytic expression in terms of logarithms:

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Evaluate numerically:

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

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