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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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Ferreira, M. N., & Papavassiliou, J. (2023). Gauge Sector Dynamics in QCD. Particles, 6(1), 312–363.
Abstract: The dynamics of the QCD gauge sector give rise to non-perturbative phenomena that are crucial for the internal consistency of the theory; most notably, they account for the generation of a gluon mass through the action of the Schwinger mechanism, the taming of the Landau pole, the ensuing stabilization of the gauge coupling, and the infrared suppression of the three-gluon vertex. In the present work, we review some key advances in the ongoing investigation of this sector within the framework of the continuum Schwinger function methods, supplemented by results obtained from lattice simulations.
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Bernardoni, F., Blossier, B., Bulava, J., Della Morte, M., Fritzsch, P., Garron, N., et al. (2014). The b-quark mass from non-perturbative N-f=2 Heavy Quark Effective Theory at O(1/m(h)). Phys. Lett. B, 730, 171–177.
Abstract: We report our final estimate of the b-quark mass from N-f = 2 lattice QCD simulations using Heavy Quark Effective Theory non-perturbatively matched to QCD at O(1/m(h)). Treating systematic and statistical errors in a conservative manner, we obtain (m) over bar ((MS) over bar)(b) (2 GeV) = 4.88(15) GeV after an extrapolation to the physical point.
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Bernardoni, F., Blossier, B., Bulava, J., Della Morte, M., Fritzsch, P., Garron, N., et al. (2014). Decay constants of B-mesons from non-perturbative HQET with two light dynamical quarks. Phys. Lett. B, 735, 349–356.
Abstract: We present a computation of B-meson decay constants from lattice QCD simulations within the framework of Heavy Quark Effective Theory for the b-quark. The next-to-leading order corrections in the HQET expansion are included non-perturbatively. Based on N-f = 2 gauge field ensembles, covering three lattice spacings a approximate to (0.08-0.05) fm and pion masses down to 190 MeV, a variational method for extracting hadronic matrix elements is used to keep systematic errors under control. In addition we perform a careful autocorrelation analysis in the extrapolation to the continuum and to the physical pion mass limits. Our final results read f(B) = 186(13) MeV, f(Bs) = 224(14) MeV and f(Bs)/f(B) = 1.203(65). A comparison with other results in the literature does not reveal a dependence on the number of dynamical quarks, and effects from truncating HQET appear to be negligible.
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Ren, X. L., Alvarez-Ruso, L., Geng, L. S., Ledwig, T., Meng, J., & Vicente Vacas, M. J. (2017). Consistency between SU(3) and SU(2) covariant baryon chiral perturbation theory for the nucleon mass. Phys. Lett. B, 766, 325–333.
Abstract: Treating the strange quark mass as a heavy scale compared to the light quark mass, we perform a matching of the nucleon mass in the SU(3) sector to the two-flavor case in covariant baryon chiral perturbation theory. The validity of the 19low-energy constants appearing in the octet baryon masses up to next-to-next-to-next-to-leading order[1] is supported by comparing the effective parameters (the combinations of the 19couplings) with the corresponding low-energy constants in the SU(2) sector[2]. In addition, it is shown that the dependence of the effective parameters and the pion-nucleon sigma term on the strange quark mass is relatively weak around its physical value, thus providing support to the assumption made in Ref.[2] that the SU(2) baryon chiral perturbation theory can be applied to study n(f) = 2 + 1lattice QCD simulations as long as the strange quark mass is close to its physical value.
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Aguilar, A. C., De Soto, F., Ferreira, M. N., Papavassiliou, J., & Rodriguez-Quintero, J. (2021). Infrared facets of the three-gluon vertex. Phys. Lett. B, 818, 136352–7pp.
Abstract: We present novel lattice results for the form factors of the quenched three-gluon vertex of QCD, in two special kinematic configurations that depend on a single momentum scale. We consider three form factors, two associated with a classical tensor structure and one without tree-level counterpart, exhibiting markedly different infrared behaviors. Specifically, while the former display the typical suppression driven by a negative logarithmic singularity at the origin, the latter saturates at a small negative constant. These exceptional features are analyzed within the Schwinger-Dyson framework, with the aid of special relations obtained from the Slavnov-Taylor identities of the theory. The emerging picture of the underlying dynamics is thoroughly corroborated by the lattice results, both qualitatively as well as quantitatively.
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Pinto-Gomez, F., De Soto, F., Ferreira, M. N., Papavassiliou, J., & Rodriguez-Quintero, J. (2023). Lattice three-gluon vertex in extended kinematics: Planar degeneracy. Phys. Lett. B, 838, 137737–8pp.
Abstract: We present novel results for the three-gluon vertex, obtained from an extensive quenched lattice simulation in the Landau gauge. The simulation evaluates the transversely projected vertex, spanned on a special tensorial basis, whose form factors are naturally parametrized in terms of individually Bosesymmetric variables. Quite interestingly, when evaluated in these kinematics, the corresponding form factors depend almost exclusively on a single kinematic variable, formed by the sum of the squares of the three incoming four-momenta, q, r, and p. Thus, all configurations lying on a given plane in the coordinate system (q2, r2, p2) share, to a high degree of accuracy, the same form factors, a property that we denominate planar degeneracy. We have confirmed the validity of this property through an exhaustive study of the set of configurations satisfying the condition q2 = r2, within the range [0, 5 GeV]. This drastic simplification allows for a remarkably compact description of the main bulk of the data, which is particularly suitable for future numerical applications. A semi-perturbative analysis reproduces the lattice findings rather accurately, once the inclusion of a gluon mass has cured all spurious divergences.
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