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Aguilar, A. C., Binosi, D., & Papavassiliou, J. (2010). QCD effective charges from lattice data. J. High Energy Phys., 07(7), 002–24pp.
Abstract: We use recent lattice data on the gluon and ghost propagators, as well as the Kugo-Ojima function, in order to extract the non-perturbative behavior of two particular definitions of the QCD effective charge, one based on the pinch technique construction, and one obtained from the standard ghost-gluon vertex. The construction relies crucially on the definition of two dimensionful quantities, which are invariant under the renormalization group, and are built out of very particular combinations of the aforementioned Green's functions. The main non-perturbative feature of both effective charges, encoded in the infrared finiteness of the gluon propagator and ghost dressing function used in their definition, is the freezing at a common finite (non-vanishing) value, in agreement with a plethora of theoretical and phenomenological expectations. We discuss the sizable discrepancy between the freezing values obtained from the present lattice analysis and the corresponding estimates derived from several phenomenological studies, and attribute its origin to the difference in the gauges employed. A particular toy calculation suggests that the modifications induced to the non-perturbative gluon propagator by the gauge choice may indeed account for the observed deviation of the freezing values.
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Blanton, T. D., Hanlon, A. D., Ben Horz, Morningstar, C., Romero-Lopez, F., & Sharpe, S. R. (2021). Interactions of two and three mesons including higher partial waves from lattice QCD. J. High Energy Phys., 10(10), 023–59pp.
Abstract: We study two- and three-meson systems composed either of pions or kaons at maximal isospin using Monte Carlo simulations of lattice QCD. Utilizing the stochastic LapH method, we are able to determine hundreds of two- and three-particle energy levels, in nine different momentum frames, with high precision. We fit these levels using the relativistic finite-volume formalism based on a generic effective field theory in order to determine the parameters of the two- and three-particle K-matrices. We find that the statistical precision of our spectra is sufficient to probe not only the dominant s-wave interactions, but also those in d waves. In particular, we determine for the first time a term in the three-particle K-matrix that contains two-particle d waves. We use three N-f = 2 + 1 CLS ensembles with pion masses of 200, 280, and 340 MeV. This allows us to study the chiral dependence of the scattering observables, and compare to the expectations of chiral perturbation theory.
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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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Bernardoni, F., Hernandez, P., & Necco, S. (2010). Heavy-light mesons in the epsilon-regime. J. High Energy Phys., 01(1), 070–30pp.
Abstract: We study the finite-size scaling of heavy-light mesons in the static limit. We compute two-point functions of chiral current densities as well as pseudoscalar densities in the epsilon-regime of heavy meson Chiral Perturbation Theory (HMChPT). As expected, finite volume dependence turns out to be significant in this regime and can be predicted in the effective theory in terms of the infinite-volume low-energy couplings. These results might be relevant for extraction of heavy-meson properties from lattice simulations.
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Coppola, M., Gomez Dumm, D., Noguera, S., & Scoccola, N. N. (2020). Magnetic field driven enhancement of the weak decay width of charged pions. J. High Energy Phys., 09(9), 058–19pp.
Abstract: We study the effect of a uniform magnetic field B on the decays pi- > l- nu_l bar, where l(-)=e(-), μ(-), carrying out a general analysis that includes four pi (-) decay constants. Taking the values of these constants from a chiral effective Nambu-Jona-Lasinio (NJL) model, it is seen that the total decay rate gets strongly increased with respect to the B = 0 case, with an enhancement factor ranging from similar to 10 for eB = 0.1 GeV2 up to similar to 10(3) for eB = 1 GeV2. The ratio between electronic and muonic decays gets also enhanced, reaching a value of about 1 : 2 for eB = 1 GeV2. In addition, we find that for large B the angular distribution of outgoing antineutrinos shows a significant suppression in the direction of the magnetic field.
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