Masses, Decay Constants and Electromagnetic Form-factors with Twisted Boundary Conditions

Abstract

Using Chiral Perturbation Theory at one-loop we analyze the consequences of twisted boundary conditions. We point out that due to the broken Lorentz and reflection symmetry a number of unexpected terms show up in the expressions. We explicitly discuss the pseudo-scalar octet masses, axial-vector and pseudo-scalar decay constants and electromagnetic form-factors. We show how the Ward identities are satisfied using the momentum dependent masses and the non-zero vacuum-expectation-values values for the electromagnetic (vector) currents. Explicit expressions at one-loop are provided and an appendix discusses the needed one-loop twisted finite volume integrals.

arXiv comment23 pages, Main changes: New references [6,16] with overlap in results and conclusions added, and a new section describing the interpretation of our results and the relation with earlier results in detail. Other changes: figures changed to be more readable and minor misprints corrected

References in corpus (9)

• Twisted Boundary Conditions in Lattice Simulations
• Aharonov-Bohm effect and nucleon-nucleon phase shifts on the lattice
• QCD Isospin Breaking in Meson Masses, Decay Constants and Quark Mass Ratios
• On the discretization of physical momenta in lattice QCD
• Pion and Kaon Electromagnetic Form Factors
• Two-point Functions at Two Loops in Three Flavour Chiral Perturbation Theory
• A Numerical Study of Partially Twisted Boundary Conditions
• Flavor Twisted Boundary Conditions, Pion Momentum, and the Pion Electromagnetic Form Factor
• Two-loop Sunset Integrals at Finite Volume

Cited by in corpus (9)

• The size of the pion from full lattice QCD with physical $u$, $d$, $s$ and $c$ quarks
• Light meson electromagnetic form factors from three-flavor lattice QCD with exact chiral symmetry
• Vector two-point functions in finite volume using partially quenched chiral perturbation theory
• Exponential reduction of finite volume effects with twisted boundary conditions
• Finite Volume Effects on the Extraction of Form Factors at Zero Momentum
• Chiral Perturbation Theory for Neutron-antineutron Oscillations
• Twisted finite-volume corrections to $K_{l3}$ decays with partially-quenched and rooted-staggered quarks
• Pseudoscalar mesons in a finite cubic volume with twisted boundary conditions
• ChPT loops for the lattice: pion mass and decay constant, HVP at finite volume and $n\bar{n}$-oscillations