[Paper Review] Soft-Collinear Factorization and Sudakov Resummation of Heavy Meson Decay Amplitudes with Effective Field Theories

Björn Lange|ArXiv.org|Sep 23, 2004

Particle physics theoretical and experimental studies93 references3 citations

TL;DR

This paper develops a soft-collinear effective field theory (SCET) framework to resum large logarithms in heavy meson decays, particularly in B → πlν and B → ρlν transitions. By factorizing the amplitude into hard, jet, and soft functions and solving their renormalization-group equations, the authors show that Sudakov suppression is absent for universal form factors, with spin-symmetric soft overlaps dominating over hard-scattering contributions.

ABSTRACT

In this thesis we present an introduction to Soft-Collinear Effective Theory, which can be used to prove (or disprove) factorization theorems to all orders in the strong coupling constant for some B decays into light and energetic particles. Specifically, the factorizable amplitudes for inclusive B->X_u l nu and exclusive B->gamma l nu are calculated in renormalization-group improved perturbation theory to first non-trivial order. Form factors encoding the exclusive decay amplitudes for B->P l nu and B->V l nu (P=light pseudoscalar meson, V=light vector meson) are studied and proved to be dominated by the non-factorizable Feynman mechanism.

Motivation & Objective

• To systematically resum large logarithms in exclusive B meson decays using effective field theories.
• To address the challenge of non-factorizable contributions in form factors beyond leading power in ΛQCD/mb.
• To clarify the role of soft-collinear interactions in exclusive decay amplitudes where standard factorization fails.
• To provide a framework for improving theoretical precision in flavor physics and New Physics searches.
• To extend QCD factorization to processes with multiple energy scales, particularly in the large recoil limit.

Proposed method

• Employing Soft-Collinear Effective Theory (SCET) to separate physics at different energy scales: soft, collinear, and hard modes.
• Implementing a two-step matching procedure: QCD → SCET I → SCET II, enabling factorization of the hard-scattering amplitude.
• Deriving and solving renormalization-group equations (RGEs) for the hard and jet functions to achieve Sudakov resummation.
• Identifying a non-factorizable soft contribution via a long-distance operator O5 that mixes into short-distance operators.
• Using the anomalous dimension of O5 as an eigenvalue to control the short-distance dependence on large recoil energy.
• Demonstrating that the soft overlap matrix element is endpoint-finite and unsuppressed, dominating over hard-scattering terms.

Experimental results

Research questions

• RQ1 How can large logarithms in exclusive B meson decays be systematically resummed using effective field theories?
• RQ2 To what extent do non-factorizable soft contributions affect the form factors in B → P, V decays?
• RQ3 Why is there no Sudakov suppression for universal form factors in the large recoil limit?
• RQ4 What is the role of the soft-collinear sector in the factorization of decay amplitudes?
• RQ5 How does the anomalous dimension of the soft operator O5 influence the behavior of form factors at high recoil?

Key findings

• Sudakov resummation via RGEs in SCET enhances the decay amplitude rather than suppressing it, contrary to naive expectations.
• The soft-collinear sector does not decouple, leading to a non-factorizable contribution from the operator O5.
• The matrix element of O5 is endpoint-finite and unsuppressed, dominating over factorizable hard-scattering contributions.
• The anomalous dimension of O5 matches that of heavy-to-collinear current operators, enabling control over short-distance dynamics.
• Spin-symmetric soft overlaps are the dominant contribution to form factors in the large recoil limit, not hard-scattering terms.
• The framework provides a consistent power and coupling expansion for exclusive decays, with implications for precision flavor physics and New Physics searches.