[Paper Review] N_f=2 chiral dynamics in the mixed chiral regime

Pilar Hernández, Silvia Necco+2 more|arXiv (Cornell University)|Nov 7, 2012

Quantum chaos and dynamical systems3 citations

TL;DR

This paper presents a next-to-next-to-leading order (NNLO) chiral perturbation theory (ChPT) prediction for the pseudoscalar two-point function in the mixed chiral regime, where valence quarks are in the ε-regime and sea quarks in the p-regime. Using a mixed-action lattice QCD simulation with overlap valence fermions on Nf=2 improved-Wilson sea quarks, the authors compute the residue of the 1/m_v² pole in fixed-topology sectors via zero-mode wave functions, finding good agreement with ChPT at finite volume, though convergence is poor at small L due to large NLO corrections.

ABSTRACT

We present a study of the pseudoscalar propagator in the mixed chiral regime with valence quark masses in the ε-regime and sea quark masses in the p-regime. We first show the NNLO prediction of this observable in the chiral expansion. In sectors of fixed topology, the correlator has a pole in 1/m_v^2 that can be matched to the topological zero-mode contributions to the correlator. We compute the residue of this pole in a N_f=2 mixed-action simulation and compare the results with the prediction in Chiral Perturbation Theory.

Motivation & Objective

• To study the pseudoscalar two-point function in the mixed chiral regime, where valence quarks are in the ε-regime and sea quarks in the p-regime, using chiral perturbation theory (ChPT).
• To compute the residue of the 1/m_v² pole in the correlator at fixed topology, which arises from topological zero-mode contributions in the ε-regime.
• To test the NNLO ChPT prediction against lattice data from a mixed-action simulation with overlap valence fermions on Nf=2 improved-Wilson sea quarks.
• To assess the feasibility and accuracy of extracting low-energy couplings via zero-mode wave functions instead of full all-to-all propagators.

Proposed method

• Use chiral perturbation theory (ChPT) to compute the pseudoscalar two-point function at NNLO in the mixed chiral regime, with valence quark masses in the ε-regime and sea quark masses in the p-regime.
• Derive the analytic form of the 1/m_v² pole residue in fixed-topology sectors, which is proportional to the topological zero-mode wave function contractions.
• Perform a mixed-action lattice simulation with overlap fermions for valence quarks and non-perturbatively O(a)-improved Wilson fermions for sea quarks.
• Extract the residue of the 1/m_v² pole by computing the connected and disconnected contractions of zero-mode wave functions on 24³×48 lattices at β=5.3.
• Fit the time dependence of the residue to the ChPT prediction to extract low-energy couplings.
• Compare the numerical results with the NNLO ChPT prediction, assessing convergence and systematic effects.

Experimental results

Research questions

• RQ1 How does the pseudoscalar two-point function behave in the mixed chiral regime with valence quarks in the ε-regime and sea quarks in the p-regime at NNLO in ChPT?
• RQ2 Can the residue of the 1/m_v² pole in the correlator be reliably extracted from zero-mode wave functions in a mixed-action lattice simulation?
• RQ3 What is the numerical agreement between the lattice computation of the pole residue and the NNLO ChPT prediction?
• RQ4 How does the convergence of the chiral expansion depend on the spatial lattice size L, particularly for small volumes?
• RQ5 Can this method provide a more efficient alternative to full all-to-all propagator computations for matching to ChPT?

Key findings

• The residue of the 1/m_v² pole in the pseudoscalar correlator at fixed topology is successfully extracted from zero-mode wave functions in a mixed-action lattice simulation with Nf=2 sea quarks.
• The extracted values of D_ν / |ν| for ν = 1, 2, 3, 4 show good agreement with the ChPT prediction at the level of statistical uncertainties.
• The time dependence of D_ν / |ν| is well described by the analytic expression derived from ChPT, confirming the theoretical framework.
• Fits to the NNLO ChPT prediction show poor convergence at L ≈ 1.56 fm, with NLO corrections reaching 100% of the LO value for M_ss ≈ 250 MeV.
• The authors conclude that significantly larger volumes (L ≥ 3–4 fm) are required for reliable matching to ChPT, as higher-order corrections remain large at small L.
• The method of using zero-mode wave functions to extract pole residues is robust and efficient, offering a viable alternative to full propagator computations.