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32 lines
1.2 KiB
32 lines
1.2 KiB
These are a set of routines performing the reduction of tensor
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integrals to scalar integrals. They are loosely based on the
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paper of van Oldenborgh and Vermaseren
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@article{vanOldenborgh:1989wn,
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author = "van Oldenborgh, G.J. and Vermaseren, J.A.M.",
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title = "{New Algorithms for One Loop Integrals}",
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journal = "Z.Phys.",
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volume = "C46",
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pages = "425-438",
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doi = "10.1007/BF01621031",
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year = "1990",
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reportNumber = "NIKHEF-H/89-17",
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SLACcitation = "%%CITATION = ZEPYA,C46,425;%%",
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}
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In particular on the idea of separating the physical and
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transverse spaces. This allows the reduction to occur by
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relating the Tensor Integrals themselves, rather than the
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form factors as in the Passarino-Veltman method.
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The tensor integrals are functions
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of the the external momenta, p_i not the off-set momenta, q_i.
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The determination of the tensor integrals reduces to
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solving a series of linear equations of the form (say,for n=3)
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where Gram(i,j)=p_i.p_j
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(x1) (b1)
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Gram(i,j) * (x2) = (b2)
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(x3) (b3)
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which are solved by LU decomposition and back substitution.
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