Extracting $F_{\pi }$ from small lattices: unquenched results

Abstract

We calculate the response of the microscopic Dirac spectrum to an imaginary isospin chemical potential for QCD with two dynamical flavors in the chiral limit. This extends our previous calculation from the quenched to the unquenched theory. The resulting spectral correlation function in the $\epsilon$-regime provides here, too, a new and efficient way to measure $F_{\pi }$ on the lattice. We test the method in a hybrid Monte Carlo simulation of the theory with two staggered quarks.

arXiv comment7 pages, 5 figures

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Cited by in corpus (26)

• Phase of the Fermion Determinant at Nonzero Chemical Potential
• Adjoint QCD on ${\mathbb{R}}^3\times S^1$ with twisted fermionic boundary conditions
• Matrix Models and QCD with Chemical Potential
• A new Chiral Two-Matrix Theory for Dirac Spectra with Imaginary Chemical Potential
• Equivalence of QCD in the epsilon-regime and chiral Random Matrix Theory with or without chemical potential
• Parameters of the lowest order chiral Lagrangian from fermion eigenvalues
• Microscopic eigenvalue correlations in QCD with imaginary isospin chemical potential
• Overlap Hypercube Fermions in QCD Simulations Near the Chiral Limit
• QCD with Bosonic Quarks at Nonzero Chemical Potential
• Finite Volume Scaling of Pseudo Nambu-Goldstone Bosons in QCD
• Finite size scaling of meson propagators with isospin chemical potential
• New Ways to Determine Low-Energy Constants with Wilson Fermions
• Staggered chiral random matrix theory
• Finite-volume Correction to the Pion Decay Constant in the Epsilon-Regime
• Determining F_pi from spectral sum rules
• Probing the chiral weak Hamiltonian at finite volumes
• The Sign Problem via Imaginary Chemical Potential
• Chiral Random Matrix Theory and Chiral Perturbation Theory
• Individual Eigenvalue Distributions of Chiral Random Two-Matrix Theory and the Determination of F_pi
• Lessons from Random Matrix Theory for QCD at Finite Density
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• The Fluctuations of the Quark Number and of the Chiral Condensate
• The gradient flow of the Dirac spectrum
• The k-th Smallest Dirac Operator Eigenvalue and the Pion Decay Constant
• Dynamical overlap fermions in the epsilon-regime