Transverse momentum resummation in soft-collinear effective theory

TL;DR

This paper develops a universal SCET-based framework for transverse momentum resummation, explicitly connecting it to the Collins-Soper-Sterman pQCD formalism at NLLO. By performing QCD-to-SCET matching, decoupling usoft and collinear sectors, and factorizing the cross section in impact-parameter space, the authors derive a CSS-like resummed expression with universal A,B,C coefficients and a process-dependent hard factor. They demonstrate the method for Higgs production via gluon fusion and extend it to Drell-Yan and joint resummation, arguing that SCET provides a natural, unified EFT approach to soft/collinear emissions. The work clarifies the separation of universal and process-specific contributions and suggests a straightforward path to higher-order refinements within the EFT framework.

Abstract

We present a universal formalism for transverse momentum resummation in the view of soft-collinear effective theory (SCET), and establish the relation between our SCET formula and the well known Collins-Soper-Sterman's pQCD formula at the next-to-leading logarithmic order (NLLO). We also briefly discuss the reformulation of joint resummation in SCET.

Figures (6)

• Figure 1: Graphical representation for quark current matching.
• Figure 2: Factorization of on-shell form factor (a) and off-shell form factor (b) in SCET. In (b), the soft Wilson lines are terminated and the external quarks are amputated, therefore, (b) can be taken as a sub-diagram of (a). Both diagrams are depicted under the gauge $\bar{n} \cdot A_{n}=n \cdot A_{\bar{n}} = 0$.
• Figure 3: Graphical representation for gluon current matching.
• Figure 4: General structure of SCET cross section for Higgs-boson production under the gauge $n\cdot A_{\bar{n}}=\bar{n}\cdot A_n=0$
• Figure 5: Feynman rules for $n$-direction collinear particles in Feynman gauge $\alpha=1$bsr. Here the direction of gluon momentum in the Wilson line is along the collinear particle. The rules for soft fields and collinear gluon are the same as that for QCD, and $n\leftrightarrow\bar{n}$ for $\bar{n}$-direction collinear particles.