[Paper Review] Pion vector and scalar form factors with dynamical overlap quarks

Jlqcd, Twqcd Collaborations+12 more|arXiv (Cornell University)|Oct 15, 2008

Quantum Chromodynamics and Particle Interactions1 references8 citations

TL;DR

This study presents the first lattice QCD calculation of the pion scalar form factor including disconnected quark contractions using dynamical overlap fermions on a 16³×32 lattice at a=0.1184 fm. Employing all-to-all quark propagators and two-loop chiral perturbation theory, it obtains consistent results with experiment for the vector and scalar radii, with ⟨r²⟩_V = 0.404(22)(22) fm² and ⟨r²⟩_S = 0.578(69)(46) fm², and determines LECs such as l̄₄ = 4.06(44)(99).

ABSTRACT

We calculate the pion vector and scalar form factors in two-flavor QCD. Gauge configurations are generated with dynamical overlap quarks on a 16^3 x 32 lattice at a lattice spacing of 0.12 fm with sea quark masses down to a sixth of the physical strange quark mass. Contributions of disconnected diagrams to the scalar form factor is calculated employing the all-to-all quark propagators. We present a detailed comparison of the vector and scalar radii with chiral perturbation theory to two loops.

Motivation & Objective

• To compute the pion vector and scalar form factors in two-flavor QCD using dynamical overlap fermions.
• To include disconnected quark contractions for the scalar form factor via all-to-all quark propagators.
• To test two-loop chiral perturbation theory against lattice data in the chiral regime.
• To extract low-energy constants (LECs) of chiral Lagrangians from non-perturbative lattice results.
• To assess systematic uncertainties from fixed topology and quenched strange quarks in the simulation setup.

Proposed method

• Gauge configurations are generated using the overlap quark action on a 16³×32 lattice at a=0.1184 fm with sea quark masses down to 1/6 of the physical strange quark mass.
• All-to-all quark propagators are computed by exactly contracting the 100 lowest eigenmodes of the overlap operator and stochastically estimating the remaining modes via Z₂ noise vectors.
• Meson fields are constructed from these propagators using local and exponential smearing functions to improve signal-to-noise ratios.
• Connected, disconnected, and vacuum expectation value (vev) contributions to three-point functions are computed for vector and scalar currents.
• Simultaneous chiral extrapolations of ⟨r²⟩_V, ⟨r²⟩_S, and c_V are performed using two-loop chiral perturbation theory with four free parameters.
• Systematic errors are estimated by varying inputs for l̄₂ and l̄₃, restricting fit data, and testing alternative parametrizations of F_S(q²).

Experimental results

Research questions

• RQ1 How do the pion vector and scalar form factors behave in two-flavor QCD with dynamical overlap fermions at small quark masses?
• RQ2 To what extent do two-loop chiral perturbation theory formulae describe the lattice data for the form factors and their radii?
• RQ3 What is the impact of disconnected quark contractions on the scalar form factor, and can they be reliably computed on the lattice?
• RQ4 How do the extracted low-energy constants l̄₄, l̄₆, and l̄₁,₂ compare with phenomenological estimates and experimental data?
• RQ5 What are the systematic uncertainties in the chiral extrapolation due to fixed topology and quenched strange quarks?

Key findings

• The vector charge radius is determined as ⟨r²⟩_V = 0.404(22)(22) fm², consistent with experimental values.
• The scalar charge radius is found to be ⟨r²⟩_S = 0.578(69)(46) fm², with significant uncertainty due to disconnected contractions.
• The vector channel parameter c_V = 3.11(14)(86) GeV⁻⁴ is consistent with experimental data and two-loop ChPT.
• The low-energy constant l̄₄ = 4.06(44)(99) is in agreement with previous lattice and phenomenological estimates.
• The LEC l̄₆ = 11.8(0.7)(1.3) is slightly smaller than the phenomenological value of 16.0(0.9), indicating a possible tension in the form factor description.
• The O(p⁶) LECs r_V,1ʳ and r_V,2ʳ are extracted with large uncertainties (50–100%), suggesting the need for higher statistics or improved methods.