[Paper Review] PQCD Formulations with Heavy Quark Masses and Global Analysis

R. S. Thorne, W. K. Tung|ArXiv.org|Sep 3, 2008

Particle physics theoretical and experimental studies14 references41 citations

TL;DR

This paper provides a comprehensive review of perturbative QCD formulations with heavy quark masses, focusing on the Generalized Mass Variable Flavor Scheme (GM VFNS) as the standard for global global PDF analyses. It clarifies the theoretical foundations, compares implementations by CTEQ and MSTW, identifies flaws in the conventional Zero Mass VFNS, and discusses the implications of intrinsic heavy flavors for LHC phenomenology and PDF fitting accuracy.

ABSTRACT

We critically review heavy quark mass effects in DIS and their impact on global analyses. We lay out all elements of a properly defined general mass variable flavor number scheme (GM VFNS) that are shared by all modern formulations of the problem. We then explain the freedom in choosing specific implementations and spell out, in particular, the current formulations of the CTEQ and MSTW groups. We clarify the approximations in the still widely-used zero mass variable flavor scheme (ZM VFNS), mention the inherent flaws in its conventional implementation, and consider the possibility of mending some of these flaws. We discuss practical issues concerning the use of parton distributions in various physical applications, in view of the different schemes. And we comment on the possible presence of intrinsic heavy flavors.

Motivation & Objective

• To establish a consistent theoretical framework for treating heavy quark masses in perturbative QCD across all energy scales.
• To clarify the differences and commonalities between modern GM VFNS formulations used in global PDF analyses.
• To identify and critique the limitations of the widely used Zero Mass Variable Flavor Scheme (ZM VFNS), especially its conventional implementation.
• To evaluate the phenomenological impact of intrinsic heavy quark components in the nucleon wavefunction on PDF fits and LHC predictions.
• To provide practical guidelines for selecting and using PDFs across different schemes in physical applications.

Proposed method

• Systematically reviews the factorization theorem in PQCD with non-zero quark masses, based on Collins' all-order proof.
• Outlines the structure of the GM VFNS, emphasizing shared components such as the treatment of final-state flavors and phase-space constraints.
• Compares the CTEQ and MSTW implementations of GM VFNS, highlighting differences in prescriptions and scheme variations.
• Analyzes the approximations inherent in the ZM VFNS, particularly the failure to properly account for heavy quark mass effects at low Q².
• Assesses the role of intrinsic charm via global QCD fits, using data from HERA and the LHC to constrain its size and shape.
• Demonstrates that scheme ambiguities due to intrinsic heavy flavors are at the same order as the theoretical uncertainty in leading-twist QCD.

Experimental results

Research questions

• RQ1 What are the key theoretical and practical differences between the Zero Mass VFNS and the Generalized Mass VFNS in global PDF analyses?
• RQ2 How do the CTEQ and MSTW implementations of the GM VFNS differ in their prescriptions and scheme variations?
• RQ3 What are the inherent flaws in the conventional implementation of the ZM VFNS, and can they be corrected?
• RQ4 To what extent can current data constrain the existence and size of intrinsic charm in the nucleon?
• RQ5 How do intrinsic heavy quark components affect the consistency and accuracy of PDF fits and structure function predictions?

Key findings

• The conventional ZM VFNS contains significant approximations that can lead to errors comparable to or larger than experimental uncertainties, especially at low Q².
• The CTEQ and MSTW GM VFNS implementations are self-consistent and produce identical predictions for the same intrinsic charm PDF, despite different technical choices.
• Current data do not tightly constrain the charm distribution, but allow for intrinsic charm contributions up to ~3 times crude model estimates, depending on the x-dependence.
• For the large-x intrinsic charm scenario, data from EMC $F_2^c$ imply contributions somewhat smaller than model estimates.
• The inclusion of intrinsic heavy flavors removes redundancy in coefficient function definitions and leads to scheme ambiguities of order $\mathcal{O}(\Lambda_{QCD}^2/Q^2)$, which is the fundamental limit of accuracy in leading-twist QCD.
• The best possible accuracy in structure function predictions is limited to $\mathcal{O}(\Lambda_{QCD}^2/Q^2)$, and this limit is respected when intrinsic heavy flavors are consistently included in the GM VFNS framework.