[Paper Review] Factorization at Subleading Power and Endpoint Divergences in Soft-Collinear Effective Theory

Ze Long Liu, Bianka Meçaj+2 more|arXiv (Cornell University)|Sep 9, 2020

Particle physics theoretical and experimental studies4 citations

TL;DR

This paper presents the first renormalized factorization theorem at subleading power in soft-collinear effective theory, systematically addressing endpoint divergences in convolution integrals through regularization and rearrangement. It derives evolution equations for the $b$-quark induced Higgs decay $h \to \gamma\gamma$ and resums large logarithms of $M_h/m_b$ at next-to-leading logarithmic order.

ABSTRACT

We derive the first renormalized factorization theorem for a process described at subleading power in soft-collinear effective theory. Endpoint divergences in convolution integrals, which arise generically beyond leading power, are regularized and removed by systematically rearranging the factorization formula. We study in detail the example of the $b$-quark induced $h o\gamma\gamma$ decay of the Higgs boson, for which we derive the evolution equations for all quantities in the factorization theorem and resum large logarithms of the ratio $M_h/m_b$ at next-to-leading logarithmic order.

Motivation & Objective

• To establish a systematic framework for factorization at subleading power in soft-collinear effective theory.
• To address the generic problem of endpoint divergences in convolution integrals that arise beyond leading power.
• To derive evolution equations for all components in the factorization formula for the $b$-quark induced $h \to \gamma\gamma$ decay.
• To resum large logarithms of the ratio $M_h/m_b$ at next-to-leading logarithmic order in this decay process.

Proposed method

• Systematically rearrange the factorization formula to isolate and regularize endpoint divergences in convolution integrals.
• Apply renormalization procedures to remove divergences while preserving the factorization structure at subleading power.
• Construct the factorization formula for $h \to \gamma\gamma$ decay induced by $b$-quarks in soft-collinear effective theory.
• Derive the evolution equations for all hard, soft, and collinear functions in the factorization theorem using renormalization group methods.
• Perform a next-to-leading logarithmic resummation of $\log(M_h/m_b)$ terms in the decay amplitude.
• Use the renormalized factorization formula to compute the resummed cross section with controlled power corrections.

Experimental results

Research questions

• RQ1 How can endpoint divergences in subleading-power convolution integrals be systematically regularized and removed in soft-collinear effective theory?
• RQ2 What is the structure of the factorization theorem for $h \to \gamma\gamma$ decay at subleading power in SCET?
• RQ3 How do the evolution equations for hard, soft, and collinear functions in the factorization formula relate to each other at subleading power?
• RQ4 What is the resummation pattern of large logarithms of $M_h/m_b$ in $h \to \gamma\gamma$ decay at next-to-leading logarithmic order?
• RQ5 Can a consistent renormalized factorization framework be constructed at subleading power for exclusive processes?

Key findings

• The paper establishes the first renormalized factorization theorem at subleading power in soft-collinear effective theory.
• Endpoint divergences in convolution integrals are successfully regularized and removed through systematic rearrangement of the factorization formula.
• Evolution equations are derived for all components—hard, soft, and collinear—of the factorization formula in the $b$-quark induced $h \to \gamma\gamma$ decay.
• Large logarithms of $M_h/m_b$ are resummed at next-to-leading logarithmic order, improving the precision of the decay amplitude.
• The method provides a consistent framework for handling power corrections beyond leading order in exclusive decays within SCET.
• The results lay the foundation for higher-order calculations in subleading-power factorization with controlled divergences and resummation.