Finite Volume Dependence of the Quark-Antiquark Vacuum Expectation Value

Abstract

A general formula is derived for the finite volume dependence of vacuum expectation values analogous to Luscher's formula for the masses. The result involves no integrals over kinematic quantities and depends only on the matrix element between pions at zero momentum transfer thus presenting a new way to calculate the latter, i.e. pion sigma terms. The full order $p^6$ correction to the vacuum condensate $<\bar{q}q>$ is evaluated and compared with the result from the Luscher formula. Due to the size of the $p^6$ result no conclusion about the accuracy of the Luscher formula can be drawn.

9 pages, conclusions described in much more detail

References in corpus (6)

• Finite volume effects for meson masses and decay constants
• The pion mass in finite volume
• An asymptotic formula for the pion decay constant in a large volume
• Finite volume effects for the pion mass at two loops
• Finite volume effects in chiral perturbation theory
• The role of strange sea quarks in chiral extrapolations on the lattice

Cited by in corpus (17)

• Chiral Perturbation Theory Beyond One Loop
• Technicolor and other QCD-like theories at next-to-next-to-leading order
• Integrating out strange quarks in ChPT
• The Chiral Condensate in a Finite Volume
• Scalar susceptibilities and four-quark condensates in the meson gas within Chiral Perturbation Theory
• $\theta =\pi$ in $SU(N)/{\mathbb{Z}}_N$ gauge theories
• Vector two-point functions in finite volume using partially quenched chiral perturbation theory
• Finite Volume at Two-loops in Chiral Perturbation Theory
• Two-loop Sunset Integrals at Finite Volume
• The expansion by regions in pi K scattering
• CHIRON: a package for ChPT numerical results at two loops
• Pion mass dependence of the $K_{l3}$ semileptonic scalar form factor within finite volume
• Finite Volume for Three-Flavour Partially Quenched Chiral Perturbation Theory through NNLO in the Meson Sector
• Kaon semi-leptonic form factor at zero momentum transfer in finite volume
• Sunset integrals at finite volume
• Finite-size effects and scaling properties of chiral and baryon-number fluctuations
• ChPT loops for the lattice: pion mass and decay constant, HVP at finite volume and $n\bar{n}$-oscillations