[Paper Review] Perturbative QCD factorization of pi gamma* ---> gamma (pi) and B ---> gamma (pi) lepton anti-neutrino

Hsiang-nan Li|arXiv (Cornell University)|Jul 1, 2001

Particle physics theoretical and experimental studies36 references45 citations

TL;DR

This paper establishes perturbative QCD factorization for the processes πγ*→γ and πγ*→π using the Ward identity in covariant gauge, proving cancellation of soft divergences and grouping collinear divergences into a pion wave function defined via a nonlocal matrix element. The gauge invariance and universality of the pion wave function are confirmed, and the framework is extended to exclusive B→γlν̄ and B→πlν̄ decays in the heavy quark limit, where a light-cone B meson wave function is defined in an appropriate frame.

ABSTRACT

We prove the factorization theorem for the processes {pi}{gamma}{sup *}{r_arrow}{gamma} and {pi}{gamma}{sup *}{r_arrow}{pi} to leading twist in the covariant gauge by means of the Ward identity. Soft divergences cancel and collinear divergences are grouped into a pion wave function defined by a nonlocal matrix element. The gauge invariance and universality of the pion wave function are confirmed. The proof is then extended to the exclusive B meson decays B{r_arrow}{gamma}l{bar {nu}} and B{r_arrow}{pi}l{bar {nu}} in the heavy quark limit. It is shown that a light-cone B meson wave function, though absorbing soft dynamics, can be defined in an appropriate frame. Factorization of the B{r_arrow}{pi}l{bar {nu}} decay in k{sub T} space, k{sub T} being parton transverse momenta, is briefly discussed. We comment on the extraction of the leading-twist pion wave function from experimental data.

Motivation & Objective

• To establish a rigorous factorization framework for exclusive processes involving pion and virtual photon transitions in perturbative QCD.
• To resolve the issue of soft and collinear divergences in πγ*→γ and πγ*→π amplitudes through gauge-invariant definitions.
• To extend the factorization formalism to B meson decays B→γlν̄ and B→πlν̄ in the heavy quark limit.
• To define a light-cone B meson wave function that incorporates soft dynamics in a suitable reference frame.
• To provide a theoretical basis for extracting the leading-twist pion wave function from experimental data.

Proposed method

• Utilizes the Ward identity in covariant gauge to prove factorization theorems for πγ*→γ and πγ*→π at leading twist.
• Identifies collinear divergences as being absorbed into a nonlocal matrix element defining the pion wave function.
• Demonstrates cancellation of soft divergences through gauge symmetry, ensuring infrared finiteness.
• Extends the factorization proof to B→γlν̄ and B→πlν̄ decays in the heavy quark effective theory limit.
• Defines a light-cone B meson wave function that captures soft dynamics while preserving gauge invariance in an appropriate frame.
• Discusses factorization in kT space for B→πlν̄ decay, highlighting transverse momentum dependence.

Experimental results

Research questions

• RQ1 How can factorization be rigorously proven for πγ*→γ and πγ*→π processes in perturbative QCD using gauge symmetry?
• RQ2 What is the role of the Ward identity in canceling soft divergences and ensuring gauge invariance of the pion wave function?
• RQ3 Can a light-cone B meson wave function be consistently defined in the heavy quark limit while incorporating soft dynamics?
• RQ4 How does the factorization structure in kT space affect the description of B→πlν̄ decay amplitudes?
• RQ5 What constraints does the theoretical framework impose on extracting the leading-twist pion wave function from experimental data?

Key findings

• Soft divergences cancel in πγ*→γ and πγ*→π processes due to the Ward identity, ensuring gauge-invariant factorization.
• Collinear divergences are systematically grouped into a pion wave function defined by a nonlocal matrix element.
• The pion wave function is shown to be gauge-invariant and universal across processes, confirming its physical relevance.
• The factorization framework is successfully extended to B→γlν̄ and B→πlν̄ decays in the heavy quark limit.
• A light-cone B meson wave function is defined in a suitable frame, absorbing soft dynamics while maintaining gauge invariance.
• The paper provides a theoretical foundation for extracting the leading-twist pion wave function from experimental data on exclusive decays.