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Title: Bootstrapping the QCD Soft Anomalous Dimension

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Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
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Resource Type:
Program Document
Country of Publication:
United States

Citation Formats

None. Bootstrapping the QCD Soft Anomalous Dimension. United States: N. p., 2017. Web.
None. Bootstrapping the QCD Soft Anomalous Dimension. United States.
None. Fri . "Bootstrapping the QCD Soft Anomalous Dimension". United States. doi:.
title = {Bootstrapping the QCD Soft Anomalous Dimension},
author = {None},
abstractNote = {},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Fri Jun 30 00:00:00 EDT 2017},
month = {Fri Jun 30 00:00:00 EDT 2017}

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  • We examine the anomalous dimension matrix appropriate for the phase space restricted B{yields}X{sub u}l{nu} and B{yields}X{sub s}{gamma} decay spectra to subleading nonperturbative order. The time ordered products of the HQET Lagrangian with the leading order shape function operator are calculated, as are the anomalous dimensions of subleading operators. We establish the renormalizability and closure of a subset of the nonlocal operator basis, a requirement for the establishment of factorization theorems at this order. Operator mixing is found between the operators which occur to subleading order, requiring the subleading operator basis be extended. We comment on the requirement for new shapemore » functions to be introduced to characterize the matrix elements of these new operators, and the phenomenological consequences for extractions of V{sub ub}.« less
  • Cited by 19
  • The resummation of soft gluon exchange for QCD hard scattering requires a matrix of anomalous dimensions. We compute this matrix directly for arbitrary 2 {yields} n massless processes for the first time at two loops. Using color generator notation, we show that it is proportional to the one-loop matrix. This result reproduces all pole terms in dimensional regularization of the explicit calculations of massless 2 {yields} 2 amplitudes in the literature, and it predicts all poles at next-to-leading order in any 2 {yields} n process that has been computed at next-to-leading order. The proportionality of the one- and two-loop matricesmore » makes possible the resummation in closed form of the next-to-next-to-leading logarithms and poles in dimensional regularization for the 2 {yields} n processes.« less
  • We extend the resummation of dimensionally-regulated amplitudes to next-to-next-to-leading poles. This requires the calculation of two-loop anomalous dimension matrices for color mixing through soft gluon exchange. Remarkably, we find that they are proportional to the corresponding one-loop matrices. Using the color generator notation, we reproduce the two-loop single-pole quantities H{sup (2)} introduced by Catani for quark and gluon elastic scattering. Our results also make possible threshold and a variety of other resummations at next-to-next-to leading logarithm. All of these considerations apply to 2 {yields} n processes with massless external lines.