A nucleon in a tiny box

Abstract

We use Chiral Perturbation Theory to compute the nucleon mass-shift due to finite volume and temperature effects. Our results are valid up to next-to-leading order in the "\eps-regime" (mL ~ mβ<< 1) as well as in the "p-regime" (mL ~ mβ>> 1). Based on the two leading orders, we discuss the convergence of the expansion as a function of the lattice size and quark masses. This result can be used to extrapolate lattice results obtained from lattice sizes smaller than the pion cloud, avoiding the numerical simulation of physics under theoretical control. An extraction of the low-energy coefficient c_3 of the chiral Lagrangean from lattice simulations at small volumes and a ``magic'' ratio β=1.22262 L might be possible.

7 figures, numerical examples and discussion changed. Minor misprints corrected. Version accepted by Phys Rev D

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Cited by in corpus (20)

• Chiral Perturbation Theory and Baryon Properties
• Chiral perturbation theory
• Finite-Size Effects in Lattice QCD with Dynamical Wilson Fermions
• Influence of quark boundary conditions on the pion mass in finite volume
• Baryon masses, chiral extrapolations, and all that
• The Delta-resonance in a finite volume
• Modeling Finite-Volume Effects and Chiral Symmetry Breaking in Two-Flavor QCD Thermodynamics
• Baryon Masses and Axial Couplings in the Combined 1/Nc and Chiral Expansions
• Casimir effect for nucleon parity doublets
• Quarks with Twisted Boundary Conditions in the Epsilon Regime
• Finite volume effects in chiral perturbation theory
• External Momentum, Volume Effects, and the Nucleon Magnetic Moment
• Rotor Spectra, Berry Phases, and Monopole Fields: from Antiferromagnets to QCD
• Exponential reduction of finite volume effects with twisted boundary conditions
• Calculation of the axial charge in the epsilon and epsilon' regimes of HBChPT
• Finite-size scaling for the left-current correlator with non-degenerate quark masses
• Probing the chiral weak Hamiltonian at finite volumes
• Finite isospin density probe for conformality
• Heavy Meson Masses in the ε-Regime of HMχPT
• PQChPT with Staggered Sea and Valence Ginsparg-Wilson Quarks: Vector Meson Masses