Goldstone boson related finite size effects in field theory and critical phenomena with O(N) symmetry

Hasenfratz, P.; Leutwyler, H.

doi:10.1016/0550-3213(90)90603-b

Cited by 344 publications

(559 citation statements)

References 36 publications

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“…where β 1 = 0.140461 is a shape coefficient [47], m 0 and α are the singlet mass and the additional low-energy constant of the singlet kinetic term in the chiral Lagrangian respectively (see ref. [45] for unexplained notation).…”

Section: Jhep04(2007)090mentioning

confidence: 99%

Spontaneous chiral symmetry breaking in QCD: a finite-size scaling study on the lattice

Giusti¹,

Necco²

2007

J. High Energy Phys.

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Spontaneous chiral symmetry breaking in QCD with massless quarks at infinite volume can be seen in a finite box by studying, for instance, the dependence of the chiral condensate from the volume and the quark mass. We perform a feasibility study of this program by computing the quark condensate on the lattice in the quenched approximation of QCD at small quark masses. We carry out simulations in various topological sectors of the theory at several volumes, quark masses and lattice spacings by employing fermions with an exact chiral symmetry, and we focus on observables which are infrared stable and free from mass-dependent ultraviolet divergences. The numerical calculation is carried out with an exact variance-reduction technique, which is designed to be particularly efficient when spontaneous symmetry breaking is at work in generating a few very small low-lying eigenvalues of the Dirac operator. The finite-size scaling behaviour of the condensate in the topological sectors considered agrees, within our statistical accuracy, with the expectations of the chiral effective theory. Close to the chiral limit we observe a detailed agreement with the first Leutwyler-Smilga sum rule. By comparing the mass, the volume and the topology dependence of our results with the predictions of the chiral effective theory, we extract the corresponding low-energy constant.

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Section: Jhep04(2007)090mentioning

confidence: 99%

Spontaneous chiral symmetry breaking in QCD: a finite-size scaling study on the lattice

Giusti¹,

Necco²

2007

J. High Energy Phys.

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“…where c 1 = −2.83729 [47][48][49]. The leading contribution is the well known result for a uniformly charged sphere, while the second term, the leading order (LO) FV correction, is independent of the structure of the charge distribution.…”

Section: Finite-volume Qedmentioning

confidence: 99%

Finite-volume electromagnetic corrections to the masses of mesons, baryons, and nuclei

2014

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Now that Lattice QCD calculations are beginning to include QED, it is important to better understand how hadronic properties are modified by finite-volume QED effects. They are known to exhibit power-law scaling with volume, in contrast to the exponential behavior of finite-volume strong interaction effects. We use non-relativistic effective field theories describing the low-momentum behavior of hadrons to determine the finite-volume QED corrections to the masses of mesons, baryons and nuclei out to O 1/L 4 in a volume expansion, where L is the spatial extent of the cubic volume. This generalizes the previously determined expansion for mesons, and extends it by two orders in 1/L to include contributions from the charge radius, magnetic moment and polarizabilities of the hadron. We make an observation about direct calculations of the muon g − 2 in a finite volume.

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“…For large enough lattices, of course, these finite volume effects will be exponentially small [16,17,33]. There has been a fair amount of work on finite volume corrections to quantities calculated in lattice QCD [14,15,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36], but it is only recently that the properties of baryons, and in particular the nucleon, have been considered [33,34,35,36].…”

Section: Neutron Edm At Finite Volumementioning

confidence: 99%

Extrapolation formulas for neutron EDM calculations in lattice QCD

O’Connell

Savage

2006

Physics Letters B

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Lattice QCD is rapidly progressing toward being able to reliably compute the electric dipole moment of the neutron as a function of the strong CP-violating parameter θ. Present day calculations are performed at unphysical values of the light quark masses, in volumes that are not exceptionally large and at lattice spacings that are not exceptionally small. We use chiral perturbation theory to determine the leading contributions to the neutron electric dipole moment at finite volume, and in partially-quenched calculations. August 20051

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Goldstone boson related finite size effects in field theory and critical phenomena with O(N) symmetry

Cited by 344 publications

References 36 publications

Spontaneous chiral symmetry breaking in QCD: a finite-size scaling study on the lattice

Spontaneous chiral symmetry breaking in QCD: a finite-size scaling study on the lattice

Finite-volume electromagnetic corrections to the masses of mesons, baryons, and nuclei

Extrapolation formulas for neutron EDM calculations in lattice QCD

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