[Paper Review] Chiral Properties of Quenched and Full QCD

R. D. Young, Derek B. Leinweber+2 more|ArXiv.org|Nov 22, 2001

Particle physics theoretical and experimental studies1 references3 citations

TL;DR

This paper proposes a chiral extrapolation method for baryon masses in quenched and full QCD that incorporates leading and next-to-leading non-analytic (LNA/NLNA) meson loop contributions from chiral perturbation theory. It shows that the primary difference between quenched and full QCD baryon masses arises from these loop corrections, with the $Δ$ mass in quenched QCD being 300–400 MeV higher than in full QCD due to enhanced chiral loops, while the nucleon mass remains nearly linear in the quark mass.

ABSTRACT

We extend a technique for the chiral extrapolation of hadron masses calculated with dynamical fermions to those generated by quenched simulations. The method ensures the correct leading and next-to-leading non-analytic behaviour for either QCD or quenched QCD in the chiral limit, as well as the correct large quark mass behaviour. We find that the primary difference between quenched and dynamical baryon masses can be described by the meson loops which give rise to the different leading and next-to-leading non-analytic behaviour.

Motivation & Objective

• To develop a chiral extrapolation method that correctly captures the LNA and NLNA behaviour of baryon masses in both quenched and full QCD.
• To investigate whether the quenched approximation can be systematically corrected using chiral loop structures known from quenched chiral perturbation theory (Q$χ$PT).
• To determine if the pion cloud source scale $Λ$ is similar in quenched and full QCD, enabling a unified extrapolation framework.
• To quantify the impact of quenching on the $Δ$–$N$ mass splitting and baryon mass curvature in the chiral limit.

Proposed method

• The method uses a functional form $M_B = \alpha_B + \beta_B m_\pi^2 + \Sigma_B(m_\pi, \Lambda)$, where $\Sigma_B$ includes LNA and NLNA contributions from pion loops.
• The self-energy contributions $\sigma_{BB'}^\pi$ are computed via a discrete sum over lattice pion momenta, incorporating finite volume and lattice spacing artifacts.
• The chiral loops are derived from effective field theory, with $\Sigma_B$ representing $B \to B'\pi \to B$ processes for nucleon and $\Delta$ baryons.
• The dipole mass scale $\Lambda = 0.8$ GeV is used as a common regulator for both quenched and full QCD, based on phenomenological consistency.
• Fits are performed to lattice data from Bernard et al. (2001av), using improved Kogut-Susskind fermions and the Sommer scale for physical scale setting.
• The method ensures consistency with both chiral perturbation theory (low mass limit) and heavy quark effective theory (high mass limit).

Experimental results

Research questions

• RQ1 How do the chiral extrapolation behaviours of baryon masses differ between quenched and full QCD?
• RQ2 To what extent can the quenched approximation be corrected using chiral loop structures from quenched chiral perturbation theory?
• RQ3 Is the pion cloud source scale $\Lambda$ similar in quenched and full QCD, allowing a common extrapolation framework?
• RQ4 Why does the $\Delta$ mass exhibit upward curvature in the quenched chiral limit while the nucleon mass remains nearly linear?
• RQ5 What is the quantitative contribution of meson loops to the $\Delta$–$N$ mass splitting in quenched versus full QCD?

Key findings

• The best-fit parameters $\alpha_N$, $\beta_N$, $\alpha_\Delta$, and $\beta_\Delta$ for quenched and full QCD agree within errors, indicating similar quark mass dependence of the pion cloud source.
• The $\Delta$ mass in quenched QCD is expected to be 300–400 MeV higher than in full QCD due to enhanced chiral loop contributions.
• The $\Delta$–$N$ mass splitting increases to approximately 400 MeV in the quenched approximation, compared to ~100 MeV in full QCD.
• The nucleon mass shows nearly linear quark mass dependence in quenched QCD, while the $\Delta$ mass exhibits significant upward curvature.
• The dominant difference between quenched and full QCD baryon masses arises from one-loop meson graphs, particularly those contributing to LNA and NLNA terms.
• The method successfully reproduces both chiral and heavy quark limits, lending confidence to its use in extrapolating lattice data.