A matrix formulation for small-x singlet evolution

We propose a matrix evolution equation in (x,kt)-space for flavour singlet, unintegrated quark and gluon densities, which generalizes DGLAP and BFKL equations in the relevant limits. The matrix evolution kernel is constructed so as to satisfy renormalization group constraints in both the ordered and...

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Autores principales: Ciafaloni, M., Colferai, D., Salam, G.P., Stasto, A.M.
Lenguaje:eng
Publicado: 2007
Materias:
Acceso en línea:https://dx.doi.org/10.1088/1126-6708/2007/08/046
http://cds.cern.ch/record/1046190
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author Ciafaloni, M.
Colferai, D.
Salam, G.P.
Stasto, A.M.
author_facet Ciafaloni, M.
Colferai, D.
Salam, G.P.
Stasto, A.M.
author_sort Ciafaloni, M.
collection CERN
description We propose a matrix evolution equation in (x,kt)-space for flavour singlet, unintegrated quark and gluon densities, which generalizes DGLAP and BFKL equations in the relevant limits. The matrix evolution kernel is constructed so as to satisfy renormalization group constraints in both the ordered and antiordered regions of exchanged momenta kt, and incorporates the known NLO anomalous dimensions in the MSbar scheme as well as the NLx BFKL kernel. We provide a hard Pomeron exponent and effective eigenvalue functions that include the n_f-dependence, and give also the matrix of resummed DGLAP splitting functions. The results connect smoothly with those of the single-channel approach. The novel P_{qa} splitting functions show resummation effects delayed down to x=0.0001, while both P_{ga} entries show a shallow dip around x=0.001, similarly to the gluon-gluon single-channel results. We remark that the matrix formulation poses further constraints on the consistency of a BFKL framework with the MSbar scheme, which are satisfied at NLO, but marginally violated by small n_f/N_c^2-suppressed terms at NNLO.
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spelling cern-10461902023-03-14T19:50:43Zdoi:10.1088/1126-6708/2007/08/046http://cds.cern.ch/record/1046190engCiafaloni, M.Colferai, D.Salam, G.P.Stasto, A.M.A matrix formulation for small-x singlet evolutionParticle Physics - PhenomenologyWe propose a matrix evolution equation in (x,kt)-space for flavour singlet, unintegrated quark and gluon densities, which generalizes DGLAP and BFKL equations in the relevant limits. The matrix evolution kernel is constructed so as to satisfy renormalization group constraints in both the ordered and antiordered regions of exchanged momenta kt, and incorporates the known NLO anomalous dimensions in the MSbar scheme as well as the NLx BFKL kernel. We provide a hard Pomeron exponent and effective eigenvalue functions that include the n_f-dependence, and give also the matrix of resummed DGLAP splitting functions. The results connect smoothly with those of the single-channel approach. The novel P_{qa} splitting functions show resummation effects delayed down to x=0.0001, while both P_{ga} entries show a shallow dip around x=0.001, similarly to the gluon-gluon single-channel results. We remark that the matrix formulation poses further constraints on the consistency of a BFKL framework with the MSbar scheme, which are satisfied at NLO, but marginally violated by small n_f/N_c^2-suppressed terms at NNLO.We propose a matrix evolution equation in (x,kt)-space for flavour singlet, unintegrated quark and gluon densities, which generalizes DGLAP and BFKL equations in the relevant limits. The matrix evolution kernel is constructed so as to satisfy renormalization group constraints in both the ordered and antiordered regions of exchanged momenta kt, and incorporates the known NLO anomalous dimensions in the MSbar scheme as well as the NLx BFKL kernel. We provide a hard Pomeron exponent and effective eigenvalue functions that include the n_f-dependence, and give also the matrix of resummed DGLAP splitting functions. The results connect smoothly with those of the single-channel approach. The novel P_{qa} splitting functions show resummation effects delayed down to x=0.0001, while both P_{ga} entries show a shallow dip around x=0.001, similarly to the gluon-gluon single-channel results. We remark that the matrix formulation poses further constraints on the consistency of a BFKL framework with the MSbar scheme, which are satisfied at NLO, but marginally violated by small n_f/N_c^2-suppressed terms at NNLO.arXiv:0707.1453CERN-PH-TH-2007-104DFF-436-07-07CERN-PH-TH-2007-104DFF 436-07-07oai:cds.cern.ch:10461902007-07-11
spellingShingle Particle Physics - Phenomenology
Ciafaloni, M.
Colferai, D.
Salam, G.P.
Stasto, A.M.
A matrix formulation for small-x singlet evolution
title A matrix formulation for small-x singlet evolution
title_full A matrix formulation for small-x singlet evolution
title_fullStr A matrix formulation for small-x singlet evolution
title_full_unstemmed A matrix formulation for small-x singlet evolution
title_short A matrix formulation for small-x singlet evolution
title_sort matrix formulation for small-x singlet evolution
topic Particle Physics - Phenomenology
url https://dx.doi.org/10.1088/1126-6708/2007/08/046
http://cds.cern.ch/record/1046190
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