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Transverse Momentum Dependent Soft Function in SCET to NNLO

Oredsson, Joel LU (2015) FYTM01 20151
Theoretical Particle Physics
Department of Astronomy and Theoretical Physics
Abstract
We review the factorization theorem for the production of a heavy color-neutral final state with a transverse momentum much smaller than its invariant mass in the framework of soft collinear effective field theory (SCET). This phase space region is plagued by large logarithms of widely separated scales, including large logarithms of rapidity ratios, that need to be resummed for sensible results. In this thesis we use a recently developed formalism that introduces a rapidity regulator in addition to dimensional regularization. This results in an additional renormalization scale, which enables one to also resum rapidity logarithms. The factorized cross sections can be written as a product (convolution) of hard, beam and soft functions in... (More)
We review the factorization theorem for the production of a heavy color-neutral final state with a transverse momentum much smaller than its invariant mass in the framework of soft collinear effective field theory (SCET). This phase space region is plagued by large logarithms of widely separated scales, including large logarithms of rapidity ratios, that need to be resummed for sensible results. In this thesis we use a recently developed formalism that introduces a rapidity regulator in addition to dimensional regularization. This results in an additional renormalization scale, which enables one to also resum rapidity logarithms. The factorized cross sections can be written as a product (convolution) of hard, beam and soft functions in position (momentum) space. We compute the soft function to next-to-next-to-leading-order (NNLO) and determine all relevant anomalous dimensions. Based on the known renormalization group structure, we perform an important cross check of the results by deriving an all order formula for the logarithmic structure of the soft and beam functions. This also allows us to obtain the beam functions to NNLO by comparing to known results in another scheme. With our results, one can now compute the transverse momentum distribution of Higgs production to next-to-next-to-leading-log-prime (NNLL$'$) accuracy. A new feature in this formalism is that one can directly perform the complete set of relevant scale variations in order to estimate the uncertainty in the resummed cross section. (Less)
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author
Oredsson, Joel LU
supervisor
organization
course
FYTM01 20151
year
type
H2 - Master's Degree (Two Years)
subject
keywords
renormalization, soft collinear effective field theory, SCET, effective theory, NNLO, Higgs, QCD, precision calculations, loop calculations
report number
LU TP 15-32
language
English
id
7856095
date added to LUP
2016-05-13 10:08:22
date last changed
2016-05-13 10:15:14
@misc{7856095,
  abstract     = {We review the factorization theorem for the production of a heavy color-neutral final state with a transverse momentum much smaller than its invariant mass in the framework of soft collinear effective field theory (SCET). This phase space region is plagued by large logarithms of widely separated scales, including large logarithms of rapidity ratios, that need to be resummed for sensible results. In this thesis we use a recently developed formalism that introduces a rapidity regulator in addition to dimensional regularization. This results in an additional renormalization scale, which enables one to also resum rapidity logarithms. The factorized cross sections can be written as a product (convolution) of hard, beam and soft functions in position (momentum) space. We compute the soft function to next-to-next-to-leading-order (NNLO) and determine all relevant anomalous dimensions. Based on the known renormalization group structure, we perform an important cross check of the results by deriving an all order formula for the logarithmic structure of the soft and beam functions. This also allows us to obtain the beam functions to NNLO by comparing to known results in another scheme. With our results, one can now compute the transverse momentum distribution of Higgs production to next-to-next-to-leading-log-prime (NNLL$'$) accuracy. A new feature in this formalism is that one can directly perform the complete set of relevant scale variations in order to estimate the uncertainty in the resummed cross section.},
  author       = {Oredsson, Joel},
  keyword      = {renormalization,soft collinear effective field theory,SCET,effective theory,NNLO,Higgs,QCD,precision calculations,loop calculations},
  language     = {eng},
  note         = {Student Paper},
  title        = {Transverse Momentum Dependent Soft Function in SCET to NNLO},
  year         = {2015},
}