Transverse Momentum Dependent Soft Function in SCET to NNLO
(2015) FYTM01 20151Theoretical Particle Physics
Department of Astronomy and Theoretical Physics
 Abstract
 We review the factorization theorem for the production of a heavy colorneutral 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 colorneutral 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 nexttonexttoleadingorder (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 nexttonexttoleadinglogprime (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)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/studentpapers/record/7856095
 author
 Oredsson, Joel ^{LU}
 supervisor

 Johan Bijnens ^{LU}
 organization
 course
 FYTM01 20151
 year
 2015
 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 1532
 language
 English
 id
 7856095
 date added to LUP
 20160513 10:08:22
 date last changed
 20160513 10:15:14
@misc{7856095, abstract = {We review the factorization theorem for the production of a heavy colorneutral 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 nexttonexttoleadingorder (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 nexttonexttoleadinglogprime (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}, }