A Prediction for the 4-Loop $\beta$ Function

We predict that the four-loop contribution \beta_3 to the QCD \beta function in the MS-bar prescription is given by \beta_3\simeq 23,600(900) - 6,400(200) N_f + 350(70) N_f^2 + 1.5 N_f^3, where N_f is the number of flavours and the coefficient of N_f^3 is an exact result from large-N_f expansion. In...

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Detalles Bibliográficos
Autores principales: Ellis, John R., Karliner, Marek, Samuel, Mark A.
Lenguaje:eng
Publicado: 1996
Materias:
Particle Physics - Phenomenology
Acceso en línea:https://dx.doi.org/10.1016/S0370-2693(97)00342-0
http://cds.cern.ch/record/315973
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author Ellis, John R.
Karliner, Marek
Samuel, Mark A.
author_facet Ellis, John R.
Karliner, Marek
Samuel, Mark A.
author_sort Ellis, John R.
collection CERN
description We predict that the four-loop contribution \beta_3 to the QCD \beta function in the MS-bar prescription is given by \beta_3\simeq 23,600(900) - 6,400(200) N_f + 350(70) N_f^2 + 1.5 N_f^3, where N_f is the number of flavours and the coefficient of N_f^3 is an exact result from large-N_f expansion. In the phenomenologically-interesting case N_f=3, we estimate these QCD predictions, basing them on the demonstrated accuracy of our method in test applications to the O(N) \Phi^4 theory, and on variations in the details of our estimation method, which goes beyond conventional Padé approximants by estimating and correcting for subasymptotic deviations from exact results.
id cern-315973
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 1996
record_format invenio
spelling cern-3159732021-07-15T03:49:12Zdoi:10.1016/S0370-2693(97)00342-0http://cds.cern.ch/record/315973engEllis, John R.Karliner, MarekSamuel, Mark A.A Prediction for the 4-Loop $\beta$ FunctionParticle Physics - PhenomenologyWe predict that the four-loop contribution \beta_3 to the QCD \beta function in the MS-bar prescription is given by \beta_3\simeq 23,600(900) - 6,400(200) N_f + 350(70) N_f^2 + 1.5 N_f^3, where N_f is the number of flavours and the coefficient of N_f^3 is an exact result from large-N_f expansion. In the phenomenologically-interesting case N_f=3, we estimate these QCD predictions, basing them on the demonstrated accuracy of our method in test applications to the O(N) \Phi^4 theory, and on variations in the details of our estimation method, which goes beyond conventional Padé approximants by estimating and correcting for subasymptotic deviations from exact results.We predict that the four-loop contribution \beta_3 to the QCD \beta function in the MS-bar prescription is given by \beta_3\simeq 23,600(900) - 6,400(200) N_f + 350(70) N_f~2 + 1.5 N_f~3, where N_f is the number of flavours and the coefficient of N_f~3 is an exact result from large-N_f expansion. In the phenomenologically-interesting case N_f=3, we estimate \beta_3 = (7.6 \pm 0.1) x 10~3. We discuss our estimates of the errors in these QCD predictions, basing them on the demonstrated accuracy of our method in test applications to the O(N) \Phi~4 theory, and on variations in the details of our estimation method, which goes beyond conventional Pade approximants by estimating and correcting for subasymptotic deviations from exact results.We predict that the four-loop contribution β 3 to the QCD β function in the MS prescription is given by β 3 ⋍ 23600(900) − 6400(200)N f + 350(70)N f 2 + 1.5N f 3 , where N f is the number of flavours and the coefficient of N f 3 is an exact result from large- N f expansion. In the phenomenologically-interesting case N f = 3, we estimate β 3 = (7.6±0.1) × 10 3 . We discuss our estimates of the errors in these QCD predictions, basing them on the demonstrated accuracy of our method in test applications to the O ( N ) Φ 4 theory, and on variations in the details of our estimation method, which goes beyond conventional Padé approximants by estimating and correcting for subasymptotic deviations from exact results.We predict that the four-loop contribution \beta_3 to the QCD \beta function in the MS-bar prescription is given by \beta_3\simeq 23,600(900) - 6,400(200) N_f + 350(70) N_f^2 + 1.5 N_f^3, where N_f is the number of flavours and the coefficient of N_f^3 is an exact result from large-N_f expansion. In the phenomenologically-interesting case N_f=3, we estimate \beta_3 = (7.6 \pm 0.1) x 10^3. We discuss our estimates of the errors in these QCD predictions, basing them on the demonstrated accuracy of our method in test applications to the O(N) \Phi^4 theory, and on variations in the details of our estimation method, which goes beyond conventional Pade approximants by estimating and correcting for subasymptotic deviations from exact results.hep-ph/9612202SLAC-PUB-9826CERN-TH-96-327TAUP-2389-96CERN-TH-96-327TAUP-2389oai:cds.cern.ch:3159731996-11-29
spellingShingle Particle Physics - Phenomenology
Ellis, John R.
Karliner, Marek
Samuel, Mark A.
A Prediction for the 4-Loop $\beta$ Function
title A Prediction for the 4-Loop $\beta$ Function
title_full A Prediction for the 4-Loop $\beta$ Function
title_fullStr A Prediction for the 4-Loop $\beta$ Function
title_full_unstemmed A Prediction for the 4-Loop $\beta$ Function
title_short A Prediction for the 4-Loop $\beta$ Function
title_sort prediction for the 4-loop $\beta$ function
topic Particle Physics - Phenomenology
url https://dx.doi.org/10.1016/S0370-2693(97)00342-0
http://cds.cern.ch/record/315973
work_keys_str_mv AT ellisjohnr apredictionforthe4loopbetafunction
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AT samuelmarka apredictionforthe4loopbetafunction
AT ellisjohnr predictionforthe4loopbetafunction
AT karlinermarek predictionforthe4loopbetafunction
AT samuelmarka predictionforthe4loopbetafunction

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