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Albaladejo, M., Oller, J. A., Oset, E., Rios, G., & Roca, L. (2012). Finite volume treatment of pi pi scattering and limits to phase shifts extraction from lattice QCD. J. High Energy Phys., 08(8), 071–22pp.
Abstract: We study theoretically the effects of finite volume for pi pi scattering in order to extract physical observables for infinite volume from lattice QCD. We compare three different approaches for pi pi scattering (lowest order Bethe-Salpeter approach, N/D and inverse amplitude methods) with the aim of studying the effects of the finite size of the box in the potential of the different theories, specially the left-hand cut contribution through loops in the crossed t, u-channels. We quantify the error made by neglecting these effects in usual extractions of physical observables from lattice ()CD spectrum. We conclude that for pi pi phase-shifts in the scalar-isoscalar channel up to 800 MeV this effect is negligible for box sizes bigger than 2,5m(pi)(-1) and of the order of 5% at around 1.5 – 2m(pi)(-1). For isospin 2 the finite size effects can reach up to 10% for that energy. We also quantify the error made when using the standard Luscher method to extract physical observables from lattice QCD, which is widely used in the literature but is an approximation of the one used in the present work.
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Zhou, B., Sun, Z. F., Liu, X., & Zhu, S. L. (2017). Chiral corrections to the 1(-+) exotic meson mass. Chin. Phys. C, 41(4), 043101–12pp.
Abstract: We first construct the effective chiral Lagrangians for the 1(-+) exotic mesons. With the infrared regularization scheme, we derive the one-loop infrared singular chiral corrections to the pi(1) (1600) mass explicitly. We investigate the variation of the different chiral corrections with the pion mass under two schemes. Hopefully, the explicit non-analytical chiral structures will be helpful for the chiral extrapolation of lattice data from the dynamical lattice QCD simulation of either the exotic light hybrid meson or the tetraquark state.
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