Scalar one-loop integrals for QCD
We construct a basis set of infra-red and/or collinearly divergent scalar one-loop integrals and give analytic formulas, for tadpole, bubble, triangle and box integrals, regulating the divergences (ultra-violet, infra-red or collinear) by regularization in D = 4-2 dimensions. For scalar triangle int...
| Main Authors: | , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
2008
|
| _version_ | 1826271240489271296 |
|---|---|
| author | Ellis, R Zanderighi, G |
| author_facet | Ellis, R Zanderighi, G |
| author_sort | Ellis, R |
| collection | OXFORD |
| description | We construct a basis set of infra-red and/or collinearly divergent scalar one-loop integrals and give analytic formulas, for tadpole, bubble, triangle and box integrals, regulating the divergences (ultra-violet, infra-red or collinear) by regularization in D = 4-2 dimensions. For scalar triangle integrals we give results for our basis set containing 6 divergent integrals. For scalar box integrals we give results for our basis set containing 16 divergent integrals. We provide analytic results for the 5 divergent box integrals in the basis set which are missing in the literature. Building on the work of van Oldenborgh, a general, publicly available code has been constructed, which calculates both finite and divergent one-loop integrals. The code returns the coefficients of 1/ 2,1/ 1 and 1/ 0 as complex numbers for an arbitrary tadpole, bubble, triangle or box integral. |
| first_indexed | 2024-03-06T21:53:32Z |
| format | Journal article |
| id | oxford-uuid:4c22d3b8-f024-4a81-b522-d06b230940c8 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T21:53:32Z |
| publishDate | 2008 |
| record_format | dspace |
| spelling | oxford-uuid:4c22d3b8-f024-4a81-b522-d06b230940c82022-03-26T15:47:39ZScalar one-loop integrals for QCDJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:4c22d3b8-f024-4a81-b522-d06b230940c8EnglishSymplectic Elements at Oxford2008Ellis, RZanderighi, GWe construct a basis set of infra-red and/or collinearly divergent scalar one-loop integrals and give analytic formulas, for tadpole, bubble, triangle and box integrals, regulating the divergences (ultra-violet, infra-red or collinear) by regularization in D = 4-2 dimensions. For scalar triangle integrals we give results for our basis set containing 6 divergent integrals. For scalar box integrals we give results for our basis set containing 16 divergent integrals. We provide analytic results for the 5 divergent box integrals in the basis set which are missing in the literature. Building on the work of van Oldenborgh, a general, publicly available code has been constructed, which calculates both finite and divergent one-loop integrals. The code returns the coefficients of 1/ 2,1/ 1 and 1/ 0 as complex numbers for an arbitrary tadpole, bubble, triangle or box integral. |
| spellingShingle | Ellis, R Zanderighi, G Scalar one-loop integrals for QCD |
| title | Scalar one-loop integrals for QCD |
| title_full | Scalar one-loop integrals for QCD |
| title_fullStr | Scalar one-loop integrals for QCD |
| title_full_unstemmed | Scalar one-loop integrals for QCD |
| title_short | Scalar one-loop integrals for QCD |
| title_sort | scalar one loop integrals for qcd |
| work_keys_str_mv | AT ellisr scalaroneloopintegralsforqcd AT zanderighig scalaroneloopintegralsforqcd |