Collinear functions for QCD resummations
Abstract The singular behaviour of QCD squared amplitudes in the collinear limit is factorized and controlled by splitting kernels with a process-independent structure. We use these kernels to define collinear functions that can be used in QCD resummation formulae of hard-scattering observables. Dif...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-03-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP03(2023)200 |
| _version_ | 1797795925983232000 |
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| author | Stefano Catani Prasanna K. Dhani |
| author_facet | Stefano Catani Prasanna K. Dhani |
| author_sort | Stefano Catani |
| collection | DOAJ |
| description | Abstract The singular behaviour of QCD squared amplitudes in the collinear limit is factorized and controlled by splitting kernels with a process-independent structure. We use these kernels to define collinear functions that can be used in QCD resummation formulae of hard-scattering observables. Different collinear functions are obtained by integrating the splitting kernels over different phase-space regions that depend on the hard-scattering observables of interest. The collinear functions depend on an auxiliary vector n μ that can be either light-like (n 2 = 0) or time-like (n 2 > 0). In the case of transverse-momentum dependent (TMD) collinear functions, we show that the use of a time-like auxiliary vector avoids the rapidity divergences, which are instead present if n 2 = 0. The perturbative computation of the collinear functions lead to infrared (IR) divergences that can be properly factorized with respect to IR finite functions that embody the logarithmically-enhanced collinear contributions to hard-scattering cross sections. We evaluate various collinear functions and their n μ dependence at O $$ \mathcal{O} $$ (α S). We compute the azimuthal-correlation component of the TMD collinear functions at O α S 2 $$ \mathcal{O}\left({\alpha}_{\textrm{S}}^2\right) $$ , and we present the results of the O α S 2 $$ \mathcal{O}\left({\alpha}_{\textrm{S}}^2\right) $$ contribution of linearly-polarized gluons to transverse-momentum resummation formulae. Beyond O α S 2 $$ \mathcal{O}\left({\alpha}_{\textrm{S}}^2\right) $$ the collinear functions of initial-state colliding partons are process dependent, as a consequence of the violation of strict collinear factorization of QCD squared amplitudes. |
| first_indexed | 2024-03-13T03:25:24Z |
| format | Article |
| id | doaj.art-9e36b6971c29466d954ccbb769ff6ded |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-13T03:25:24Z |
| publishDate | 2023-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-9e36b6971c29466d954ccbb769ff6ded2023-06-25T11:06:45ZengSpringerOpenJournal of High Energy Physics1029-84792023-03-012023315610.1007/JHEP03(2023)200Collinear functions for QCD resummationsStefano Catani0Prasanna K. Dhani1INFN, Sezione di Firenze and Dipartimento di Fisica e Astronomia, Università di FirenzeINFN, Sezione di GenovaAbstract The singular behaviour of QCD squared amplitudes in the collinear limit is factorized and controlled by splitting kernels with a process-independent structure. We use these kernels to define collinear functions that can be used in QCD resummation formulae of hard-scattering observables. Different collinear functions are obtained by integrating the splitting kernels over different phase-space regions that depend on the hard-scattering observables of interest. The collinear functions depend on an auxiliary vector n μ that can be either light-like (n 2 = 0) or time-like (n 2 > 0). In the case of transverse-momentum dependent (TMD) collinear functions, we show that the use of a time-like auxiliary vector avoids the rapidity divergences, which are instead present if n 2 = 0. The perturbative computation of the collinear functions lead to infrared (IR) divergences that can be properly factorized with respect to IR finite functions that embody the logarithmically-enhanced collinear contributions to hard-scattering cross sections. We evaluate various collinear functions and their n μ dependence at O $$ \mathcal{O} $$ (α S). We compute the azimuthal-correlation component of the TMD collinear functions at O α S 2 $$ \mathcal{O}\left({\alpha}_{\textrm{S}}^2\right) $$ , and we present the results of the O α S 2 $$ \mathcal{O}\left({\alpha}_{\textrm{S}}^2\right) $$ contribution of linearly-polarized gluons to transverse-momentum resummation formulae. Beyond O α S 2 $$ \mathcal{O}\left({\alpha}_{\textrm{S}}^2\right) $$ the collinear functions of initial-state colliding partons are process dependent, as a consequence of the violation of strict collinear factorization of QCD squared amplitudes.https://doi.org/10.1007/JHEP03(2023)200FactorizationRenormalization GroupHigher-Order Perturbative CalculationsResummation |
| spellingShingle | Stefano Catani Prasanna K. Dhani Collinear functions for QCD resummations Journal of High Energy Physics Factorization Renormalization Group Higher-Order Perturbative Calculations Resummation |
| title | Collinear functions for QCD resummations |
| title_full | Collinear functions for QCD resummations |
| title_fullStr | Collinear functions for QCD resummations |
| title_full_unstemmed | Collinear functions for QCD resummations |
| title_short | Collinear functions for QCD resummations |
| title_sort | collinear functions for qcd resummations |
| topic | Factorization Renormalization Group Higher-Order Perturbative Calculations Resummation |
| url | https://doi.org/10.1007/JHEP03(2023)200 |
| work_keys_str_mv | AT stefanocatani collinearfunctionsforqcdresummations AT prasannakdhani collinearfunctionsforqcdresummations |