7 Mar 2002 | Christian W. Bauer, Dan Pirjol, and Iain W. Stewart
This paper presents the soft-collinear factorization in an effective field theory (SCET), which describes the separation of soft and ultrasoft gluons from collinear particles. The factorization is shown at the level of operators, with exclusive hadronic and inclusive partonic factorization as special cases. The leading order Lagrangian is derived using power counting and gauge invariance. Soft and ultrasoft gluons are treated as background fields to gluons with harder momenta. Two examples are given: the factorization of soft gluons in $ B \rightarrow D\pi $ and the soft-collinear convolution for the $ B \rightarrow X_{s}\gamma $ spectrum.
The paper discusses the use of light cone coordinates and the construction of a soft-collinear effective theory (SCET) to describe the dynamics of hadrons with large energy. Fluctuations with momenta $ p^2 \gtrsim Q^2 $ are integrated out and appear in Wilson coefficients, while fluctuations with $ p^2 \ll Q^2 $ appear in time ordered products of effective theory fields. The effective theory is organized as an expansion in powers of a small parameter $ \lambda $, where $ \lambda = \Lambda_{QCD}/Q $ or $ \lambda = \sqrt{\Lambda_{QCD}/Q} $.
Traditional factorization theorems separate different scales in QCD processes. For inclusive processes, the leading twist cross section is a convolution of a hard scattering kernel, a jet function, and a soft function. For exclusive processes, similar factorization occurs with hard scattering kernels, light-cone hadron wave functions, and soft form factors. The paper discusses the use of the Coleman-Norton theorem and Landau equations to identify infrared divergences and the power counting of infrared divergences.
The paper presents the structure of the effective theory, focusing on interactions involving softer gluons. It discusses the use of Wilson lines in HQET and the construction of the SCET. The effective theory is shown to synthesize the advantages of two approaches: one based on power counting and another based on the method of regions or threshold expansion.
The paper discusses the use of Wilson lines in HQET and the construction of the SCET. It shows how the effective theory can be used to describe the factorization of soft and collinear modes in exclusive decays such as $ B^{-} \rightarrow D^{0}\pi^{-} $ and $ B^{0} \rightarrow D^{+}\pi^{-} $. The paper also discusses the factorization of soft gluons in the inclusive decay $ B \rightarrow X_{s}\gamma $, showing that the photon spectrum can be written as a product of hard, usoft, and collinear factors.
The paper concludes with a discussion of the applications of the effective theory, showing how it can be used to describe the factorization of soft and collinear modes in various processesThis paper presents the soft-collinear factorization in an effective field theory (SCET), which describes the separation of soft and ultrasoft gluons from collinear particles. The factorization is shown at the level of operators, with exclusive hadronic and inclusive partonic factorization as special cases. The leading order Lagrangian is derived using power counting and gauge invariance. Soft and ultrasoft gluons are treated as background fields to gluons with harder momenta. Two examples are given: the factorization of soft gluons in $ B \rightarrow D\pi $ and the soft-collinear convolution for the $ B \rightarrow X_{s}\gamma $ spectrum.
The paper discusses the use of light cone coordinates and the construction of a soft-collinear effective theory (SCET) to describe the dynamics of hadrons with large energy. Fluctuations with momenta $ p^2 \gtrsim Q^2 $ are integrated out and appear in Wilson coefficients, while fluctuations with $ p^2 \ll Q^2 $ appear in time ordered products of effective theory fields. The effective theory is organized as an expansion in powers of a small parameter $ \lambda $, where $ \lambda = \Lambda_{QCD}/Q $ or $ \lambda = \sqrt{\Lambda_{QCD}/Q} $.
Traditional factorization theorems separate different scales in QCD processes. For inclusive processes, the leading twist cross section is a convolution of a hard scattering kernel, a jet function, and a soft function. For exclusive processes, similar factorization occurs with hard scattering kernels, light-cone hadron wave functions, and soft form factors. The paper discusses the use of the Coleman-Norton theorem and Landau equations to identify infrared divergences and the power counting of infrared divergences.
The paper presents the structure of the effective theory, focusing on interactions involving softer gluons. It discusses the use of Wilson lines in HQET and the construction of the SCET. The effective theory is shown to synthesize the advantages of two approaches: one based on power counting and another based on the method of regions or threshold expansion.
The paper discusses the use of Wilson lines in HQET and the construction of the SCET. It shows how the effective theory can be used to describe the factorization of soft and collinear modes in exclusive decays such as $ B^{-} \rightarrow D^{0}\pi^{-} $ and $ B^{0} \rightarrow D^{+}\pi^{-} $. The paper also discusses the factorization of soft gluons in the inclusive decay $ B \rightarrow X_{s}\gamma $, showing that the photon spectrum can be written as a product of hard, usoft, and collinear factors.
The paper concludes with a discussion of the applications of the effective theory, showing how it can be used to describe the factorization of soft and collinear modes in various processes