The paper discusses the factorization of soft and ultrasoft gluons from collinear particles in an effective field theory (EFT). The authors derive the leading-order Lagrangian using power counting and gauge invariance, emphasizing the need for multiple species of gluons. They show that softer gluons appear as background fields to harder gluons. Two examples are provided: the factorization of soft gluons in the decay $B \rightarrow D\pi$ and the soft-collinear convolution for the $B \rightarrow X_s\gamma$ spectrum. The introduction covers the motivation for an EFT, the structure of Wilson lines, and the gauge symmetries in the EFT. The paper then delves into the construction of the EFT Lagrangian, including the collinear, soft, and ultrasoft fields, and their interactions. It explains how soft and ultrasoft gluons decouple from collinear particles at leading order, and provides detailed Feynman rules and examples to illustrate these concepts.The paper discusses the factorization of soft and ultrasoft gluons from collinear particles in an effective field theory (EFT). The authors derive the leading-order Lagrangian using power counting and gauge invariance, emphasizing the need for multiple species of gluons. They show that softer gluons appear as background fields to harder gluons. Two examples are provided: the factorization of soft gluons in the decay $B \rightarrow D\pi$ and the soft-collinear convolution for the $B \rightarrow X_s\gamma$ spectrum. The introduction covers the motivation for an EFT, the structure of Wilson lines, and the gauge symmetries in the EFT. The paper then delves into the construction of the EFT Lagrangian, including the collinear, soft, and ultrasoft fields, and their interactions. It explains how soft and ultrasoft gluons decouple from collinear particles at leading order, and provides detailed Feynman rules and examples to illustrate these concepts.