[Paper Review] Light and heavy quark masses, Flavour breaking of chiral condensates, Meson weak leptonic decay constants in QCD

Stéphan Narison|arXiv (Cornell University)|Feb 21, 2002

Quantum Chromodynamics and Particle Interactions3 references21 citations

TL;DR

This paper presents a comprehensive review of determinations of light and heavy quark masses, chiral condensates, and meson weak leptonic decay constants using QCD spectral sum rules (QSSR). It reports precise values such as $\overline{m}_s(2\,\text{GeV}) = 117.4 \pm 23.4\,\text{MeV}$, $f_{B_s} \approx 230\,\text{MeV}$, and a flavor-breaking ratio $\langle\bar{s}s\rangle/\langle\bar{u}u\rangle = 0.66 \pm 0.10$, demonstrating strong consistency with lattice QCD and experimental data.

ABSTRACT

We review the present status for the determinations of the light and heavy quark masses, the light quark chiral condensate and the decay constants of light and heavy-light (pseudo)scalar mesons from QCD spectral sum rules (QSSR). Bounds on the light quark running masses at 2 GeV are found to be: 6 MeV/=0.66\pm 0.10. The last section is dedicated to the QSSR determinations of f_{D_{(s)}} and f_{B_{(s)}}.

Motivation & Objective

• To update and consolidate determinations of light and heavy quark masses using QCD spectral sum rules (QSSR), addressing challenges from quark confinement.
• To assess the flavor-breaking structure of the chiral condensate via global fits of pseudoscalar and scalar meson systems.
• To improve predictions for weak leptonic decay constants of light and heavy-light mesons, including $f_{D_{(s)}}$ and $f_{B_{(s)}}$, using QSSR and HQET constraints.
• To test the self-consistency of QSSR by comparing results with lattice QCD and experimental measurements, particularly for $f_B$ and $f_{B_s}$.
• To validate the QCD running behavior of quark masses by comparing $\overline{m}_b(M_Z)$ with LEP data, confirming renormalization group predictions.

Proposed method

• Uses QCD spectral sum rules (QSSR) to extract quark masses and decay constants from hadronic spectral functions, incorporating perturbative and nonperturbative contributions.
• Applies renormalization group equations (RGEs) to evolve running masses from $2\,\text{GeV}$ to $M_Z$, enabling comparison with LEP data.
• Performs global fits of QSSR predictions across multiple channels (pseudoscalar, scalar, vector) to extract consistent values for $f_{B_s}$, $f_{B}$, and $f_D$.
• Incorporates heavy quark effective theory (HQET) constraints and sum rule duality to estimate $1/M_b$ and $1/M_b^2$ corrections to $f_B$.
• Uses the optical theorem and moment sum rules to relate spectral functions to decay widths, enabling extraction of $f_{B_s}$ and $f_B$.
• Compares results with lattice QCD and experimental data (e.g., LEP three-jet events) to validate the QSSR approach.

Experimental results

Research questions

• RQ1 What are the most precise QSSR-based determinations of the running light and strange quark masses at $2\,\text{GeV}$?
• RQ2 How do QSSR predictions for $f_{B_s}$ and $f_B$ compare with lattice QCD and experimental measurements?
• RQ3 To what extent does the QSSR approach self-consistently describe flavor breaking in the chiral condensate?
• RQ4 How well do QSSR predictions for heavy quark masses and their ratios agree with experimental data from LEP?
• RQ5 What are the $1/M_b$ and $1/M_b^2$ corrections to $f_B$, and how do they compare with HQET expectations?

Key findings

• The running strange quark mass is determined as $\overline{m}_s(2\,\text{GeV}) = 117.4 \pm 23.4\,\text{MeV}$, consistent with ChPT and lattice results.
• The ratio $m_s/(m_u + m_d) = 24.2$ from pseudoscalar sum rules agrees with the ChPT value of $24.4 \pm 1.5$, confirming consistency of the QSSR approach.
• The $b$-quark mass at $M_Z$ is found to be $\overline{m}_b(M_Z) = 2.83 \pm 0.04\,\text{GeV}$, in excellent agreement with the LEP average of $2.82 \pm 0.63\,\text{GeV}$.
• The flavor-breaking ratio of normal-ordered chiral condensates is determined as $\langle\bar{s}s\rangle/\langle\bar{u}u\rangle = 0.66 \pm 0.10$ from a global fit of light and $B_s$ mesons.
• The weak decay constant of the $B_s$ meson is predicted as $f_{B_s} \approx 230\,\text{MeV}$, consistent with lattice QCD and phenomenological expectations.
• The coefficient of the $1/M_b$ correction to $f_B$ is estimated as $A \approx 0.98\,\text{GeV}$, in good agreement with HQET and lattice calculations.