Built on

Z. Ligeti, I. W. Stewart, and F. J. Tackmann, Treating the b quark distribution function with reliable uncertainties
Original
1926
Earlier work this paper cites.
J. C. Collins and D. E. Soper, Parton Distribution and Decay Functions
1982
Earlier work this paper cites.
J. Gatheral, Exponentiation of Eikonal Cross-sections in Nonabelian Gauge Theories
1983
Earlier work this paper cites.
J. Frenkel and J. Taylor, Nonabelian Eikonal Exponentiation
1984
Earlier work this paper cites.
J. C. Collins, D. E. Soper, and G. F. Sterman, Transverse Momentum Distribution in Drell-Yan Pair and W and Z Boson Production
1985
Earlier work this paper cites.
G. P. Korchemsky and A. V. Radyushkin, Renormalization of the Wilson Loops Beyond the Leading Order
1987
Earlier work this paper cites.
D. de Florian and M. Grazzini, Next-to-next-to-leading logarithmic corrections at small transverse momentum in hadronic collisions
2000
Earlier work this paper cites.
C. W. Bauer, S. Fleming, and M. E. Luke, Summing Sudakov logarithms in B → X s γ B\to X_{s}\gamma in effective field theory
2000
Earlier work this paper cites.
S. Catani and M. Grazzini, The soft gluon current at one loop order
2000
Earlier work this paper cites.
D. de Florian and M. Grazzini, The Structure of large logarithmic corrections at small transverse momentum in hadronic collisions
2001
Earlier work this paper cites.
C. W. Bauer, S. Fleming, D. Pirjol, and I. W. Stewart, An Effective field theory for collinear and soft gluons: Heavy to light decays
2001
Earlier work this paper cites.
C. W. Bauer and I. W. Stewart, Invariant operators in collinear effective theory
2001
Earlier work this paper cites.
C. W. Bauer, D. Pirjol, and I. W. Stewart, Soft collinear factorization in effective field theory
2002
Earlier work this paper cites.
M. Beneke, A. P. Chapovsky, M. Diehl, and T. Feldmann, Soft collinear effective theory and heavy to light currents beyond leading power
2002
Earlier work this paper cites.
C. F. Berger, Higher orders in A(alpha(s))/[1-x]+ of nonsinglet partonic splitting functions
2002
Earlier work this paper cites.
C. W. Bauer, D. Pirjol, and I. W. Stewart, Factorization and endpoint singularities in heavy to light decays
2003
Earlier work this paper cites.
S. Moch, J. A. M. Vermaseren, and A. Vogt, The Three loop splitting functions in QCD: The Nonsinglet case
2004
Earlier work this paper cites.
G. Bozzi, S. Catani, D. de Florian, and M. Grazzini, Transverse-momentum resummation and the spectrum of the Higgs boson at the LHC
2006
Earlier work this paper cites.
S. Fleming, A. K. Leibovich, and T. Mehen, Resummation of Large Endpoint Corrections to Color-Octet J / ψ J/\psi Photoproduction
2006
Earlier work this paper cites.
T. Huber and D. Maitre, HypExp: A Mathematica package for expanding hypergeometric functions around integer-valued parameters
2006
Earlier work this paper cites.

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2016

Rapidity renormalized TMD soft and beam functions at two loops

Luebbert, Thomas, Oredsson, Joel, Stahlhofen, Maximilian

Understand

We compute the transverse momentum dependent (TMD) soft function for the production of a color-neutral final state at the LHC within the rapidity renormalization group (RRG) framework to next-to-next-to-leading order (NNLO).

We use this result to extract the universal renormalized TMD beam functions (aka TMDPDFs) in the same scheme and at the same order from known results in another scheme.
We derive recurrence relations for the logarithmic structure of the soft and beam functions, which we use to cross check our calculation.
We also explicitly confirm the non-Abelian exponentiation of the TMD soft function in the RRG framework at two loops.

Built on

Z. Ligeti, I. W. Stewart, and F. J. Tackmann, Treating the b quark distribution function with reliable uncertainties
Original
1926
Earlier work this paper cites.
J. C. Collins and D. E. Soper, Parton Distribution and Decay Functions
1982
Earlier work this paper cites.
J. Gatheral, Exponentiation of Eikonal Cross-sections in Nonabelian Gauge Theories
1983
Earlier work this paper cites.
J. Frenkel and J. Taylor, Nonabelian Eikonal Exponentiation
1984
Earlier work this paper cites.
J. C. Collins, D. E. Soper, and G. F. Sterman, Transverse Momentum Distribution in Drell-Yan Pair and W and Z Boson Production
1985
Earlier work this paper cites.
G. P. Korchemsky and A. V. Radyushkin, Renormalization of the Wilson Loops Beyond the Leading Order
1987
Earlier work this paper cites.
D. de Florian and M. Grazzini, Next-to-next-to-leading logarithmic corrections at small transverse momentum in hadronic collisions
2000
Earlier work this paper cites.
C. W. Bauer, S. Fleming, and M. E. Luke, Summing Sudakov logarithms in B → X s γ B\to X_{s}\gamma in effective field theory
2000
Earlier work this paper cites.
S. Catani and M. Grazzini, The soft gluon current at one loop order
2000
Earlier work this paper cites.
D. de Florian and M. Grazzini, The Structure of large logarithmic corrections at small transverse momentum in hadronic collisions
2001
Earlier work this paper cites.
C. W. Bauer, S. Fleming, D. Pirjol, and I. W. Stewart, An Effective field theory for collinear and soft gluons: Heavy to light decays
2001
Earlier work this paper cites.
C. W. Bauer and I. W. Stewart, Invariant operators in collinear effective theory
2001
Earlier work this paper cites.
C. W. Bauer, D. Pirjol, and I. W. Stewart, Soft collinear factorization in effective field theory
2002
Earlier work this paper cites.
M. Beneke, A. P. Chapovsky, M. Diehl, and T. Feldmann, Soft collinear effective theory and heavy to light currents beyond leading power
2002
Earlier work this paper cites.
C. F. Berger, Higher orders in A(alpha(s))/[1-x]+ of nonsinglet partonic splitting functions
2002
Earlier work this paper cites.
C. W. Bauer, D. Pirjol, and I. W. Stewart, Factorization and endpoint singularities in heavy to light decays
2003
Earlier work this paper cites.
S. Moch, J. A. M. Vermaseren, and A. Vogt, The Three loop splitting functions in QCD: The Nonsinglet case
2004
Earlier work this paper cites.
G. Bozzi, S. Catani, D. de Florian, and M. Grazzini, Transverse-momentum resummation and the spectrum of the Higgs boson at the LHC
2006
Earlier work this paper cites.
S. Fleming, A. K. Leibovich, and T. Mehen, Resummation of Large Endpoint Corrections to Color-Octet J / ψ J/\psi Photoproduction
2006
Earlier work this paper cites.
T. Huber and D. Maitre, HypExp: A Mathematica package for expanding hypergeometric functions around integer-valued parameters
2006
Earlier work this paper cites.