Electromagnetic Splittings and Light Quark Masses in Lattice QCD

Duncan, Anthony; Eichten, E.; Thacker, H.B.

doi:10.1103/physrevlett.76.3894

Cited by 181 publications

(370 citation statements)

References 15 publications

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“…The issues complicating the inclusion of QED in FV calculations with PBCs are well known, the most glaring of which is the inability to preserve Gauss's law [6,15,16], which relates the electric flux penetrating any closed surface to the charge enclosed by the surface, and Ampere's Law, which relates the integral of the magnetic field around a closed loop to the current penetrating the loop. An obvious way to see the problem is to consider the electric field along the axes of the cubic volume (particularly at the surface) associated with a point charge at the center.…”

Section: Finite-volume Qedmentioning

confidence: 99%

“…While naively appearing to be a simple extension of pure LQCD calculations, there are subtleties associated with including QED. In particular, Gauss's law and Ampere's law cannot be satisfied when the electromagnetic gauge field is subject to periodic boundary conditions (PBCs) [14][15][16]. However, a uniform background charge density can be introduced to circumvent this problem and restore these laws.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Finite-volume Qedmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2014

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“…In the absence of QED, hadron self energies contain FV corrections that are exponentially suppressed by the dimensionless parameter m π L, and therefore, neglecting these corrections, the kinematics in the FV are the same as in the continuum. This is no longer the case in the presence of QED as the hadron masses have power-law volume dependencies [42][43][44][45].…”

Section: A Power Counting and Kinematicsmentioning

confidence: 99%

“…In particular, Ampere's law and Gauss's law cannot be satisfied with a QED gauge field subject to periodic boundary conditions (PBCs) [42][43][44][45]. A uniform background charge density can be introduced to circumvent this problem, a procedure which is equivalent to removing the zero modes of the photon.…”

Section: Introductionmentioning

confidence: 99%

Two-particle elastic scattering in a finite volume including QED

2014

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The presence of long-range interactions violates a condition necessary to relate the energy of two particles in a finite volume to their S-matrix elements in the manner of Lüscher. While in infinite volume, QED contributions to low-energy charged particle scattering must be resummed to all orders in perturbation theory (the Coulomb ladder diagrams), in a finite volume the momentum operator is gapped, allowing for a perturbative treatment. The leading QED corrections to the two-particle finite-volume energy quantization condition below the inelastic threshold, as well as approximate formulas for energy eigenvalues, are obtained. In particular, we focus on two spinless hadrons in the A + 1 irreducible representation of the cubic group, and truncate the strong interactions to the s-wave. These results are necessary for the analysis of Lattice QCD+QED calculations of charged-hadron interactions, and can be straightforwardly generalized to other representations of the cubic group, to hadrons with spin, and to include higher partial waves.

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“…[1] where the first lattice calculation of the electromagnetic mass splitting of nucleons and light pseudoscalar mesons has been attempted. The proposed solution consists in quenching a particular set of Fourier modes of the gauge field, in such a way that the global zero-modes decouple from the dynamics.…”

Section: Jhep02(2016)076mentioning

confidence: 99%

Charged hadrons in local finite-volume QED+QCD with C⋆ boundary conditions

Lucini

Patella

Ramos

et al. 2016

J. High Energ. Phys.

177

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In order to calculate QED corrections to hadronic physical quantities by means of lattice simulations, a coherent description of electrically-charged states in finite volume is needed. In the usual periodic setup, Gauss's law and large gauge transformations forbid the propagation of electrically-charged states. A possible solution to this problem, which does not violate the axioms of local quantum field theory, has been proposed by Wiese and Polley, and is based on the use of C boundary conditions. We present a thorough analysis of the properties and symmetries of QED in isolation and QED coupled to QCD, with C boundary conditions. In particular we learn that a certain class of electricallycharged states can be constructed in a fully consistent fashion without relying on gauge fixing and without peculiar complications. This class includes single particle states of most stable hadrons. We also calculate finite-volume corrections to the mass of stable charged particles and show that these are much smaller than in non-local formulations of QED.

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Electromagnetic Splittings and Light Quark Masses in Lattice QCD

Cited by 181 publications

References 15 publications

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

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

Two-particle elastic scattering in a finite volume including QED

Charged hadrons in local finite-volume QED+QCD with C⋆ boundary conditions

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