Pion in a box

Bietenholz, Wolfgang; Göckeler, M.; Horsley, R.; Nakamura, Y.; Pleiter, D.; Rakow, P. E. L.; Schierholz, G.; Zanotti, J. M.

doi:10.1016/j.physletb.2010.03.063

Cited by 22 publications

(24 citation statements)

References 14 publications

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“…Performing lattice QCD simulations directly in the chiral limit is very challenging, because the standard hybrid Monte Carlo algorithm then no longer works efficiently. Still, partly by extrapolating lattice data from the p-regime into the δ-regime, reasonable agreement with the analytic results has been obtained in [21][22][23].…”

Section: Rotor Spectrum In the B = 0 Vacuum Sectorsupporting

confidence: 70%

Rotor spectra and Berry phases in the chiral limit of QCD on a torus

Власій

Wiese

2018

Phys. Rev. D

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We consider the finite-volume spectra of QCD in the chiral limit of massless up and down quarks and massive strange quarks in the baryon number sectors B ¼ 0 and B ¼ 1 for different values of the isospin. Spontaneous symmetry breaking gives rise to rotor spectra, as the chiral order parameter precesses through the vacuum manifold. Baryons of different isospin influence the motion of the order parameter through nontrivial Berry phases and associated abstract monopole fields. Our investigation provides detailed insights into the dynamics of spontaneous chiral symmetry breaking in QCD on a torus. It also sheds new light on Berry phases in the context of quantum field theory. Interestingly, the Berry gauge field resulting from QCD solves a Yang-Mills-Chern-Simons equation of motion on the vacuum manifold SUð2Þ ¼ S 3 .

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Section: Rotor Spectrum In the B = 0 Vacuum Sectorsupporting

confidence: 70%

Rotor spectra and Berry phases in the chiral limit of QCD on a torus

Власій

Wiese

2018

Phys. Rev. D

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“…The QCDSF collaboration [25][26][27] compared their data for the mass gap from numerical simulations of lattice QCD to (6.1) using values…”

Section: Jhep04(2016)110mentioning

confidence: 99%

Matching effective chiral Lagrangians with dimensional and lattice regularizations

Niedermayer¹,

Weisz²

2016

J. High Energ. Phys.

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Abstract:We compute the free energy in the presence of a chemical potential coupled to a conserved charge in effective O(n) scalar field theory (without explicit symmetry breaking terms) to third order for asymmetric volumes in general d-dimensions, using dimensional (DR) and lattice regularizations. This yields relations between the 4-derivative couplings appearing in the effective actions for the two regularizations, which in turn allows us to translate results, e.g. the mass gap in a finite periodic box in d = 3 + 1 dimensions, from one regularization to the other. Consistency is found with a new direct computation of the mass gap using DR. For the case n = 4, d = 4 the model is the low-energy effective theory of QCD with N f = 2 massless quarks. The results can thus be used to obtain estimates of low energy constants in the effective chiral Lagrangian from measurements of the low energy observables, including the low lying spectrum of N f = 2 QCD in the δ-regime using lattice simulations, as proposed by Peter Hasenfratz, or from the susceptibility corresponding to the chemical potential used.

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“…It is, in particular, remarkable that our one-loop result is closer to the two-loop formula rather than one-loop in the p expansion. In order to understand whether this is a just coincidence or can be explained by the effect of the zero-mode resummation, a further study in the limit of T → ∞, which enters another regime (the δ regime [56][57][58][59][60][61][62]), is needed.…”

Section: Masses and Decay Constantsmentioning

confidence: 99%

Interpolation between theϵandpregimes

2011

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We reconsider chiral perturbation theory in a finite volume and develop a new computational scheme which smoothly interpolates the conventional ǫ and p regimes. The counting rule is kept essentially the same as in the p expansion. The zero-momentum modes of Nambu-Goldstone bosons are, however, treated separately and partly integrated out to all orders as in the ǫ expansion. In this new scheme, the theory remains infra-red finite even in the chiral limit, while the chiral-logarithmic effects are kept present. We calculate the two-point function in the pseudoscalar channel and show that the correlator has a constant contribution in addition to the conventional cosh function of time t. This constant term rapidly disappears in the p regime but it is indispensable for a smooth convergence of the formula to the ǫ regime result. Our calculation is useful to precisely estimate the finite volume effects in lattice QCD simulations on the pion mass M π and kaon mass M K , as well as their decay constants F π and F K .

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Pion in a box

Abstract: The residual mass of the pion in a finite spatial box at vanishing quark masses, the mass gap, is computed with two flavors of dynamical clover fermions. The result is compared with predictions of chiral perturbation theory in the δ regime.

Cited by 22 publications

References 14 publications

Rotor spectra and Berry phases in the chiral limit of QCD on a torus

Rotor spectra and Berry phases in the chiral limit of QCD on a torus

Matching effective chiral Lagrangians with dimensional and lattice regularizations

Interpolation between theϵandpregimes

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