
Aguilar, A. C., Brito, N., Ferreira, M. N., Papavassiliou, J., Oliveira, O., & Silva, P. J. (2024). Lattice determination of the BatalinVilkovisky function and the strong running interaction. Phys. Lett. B, 858, 139054–8pp.
Abstract: The BatalinVilkovisky function is a central component in the modern formulation of the background field method and the physical applications derived from it. In the present work we report on novel lattice results for this particular quantity, obtained by capitalizing on its equality with the KugoOjima function in the Landau gauge. The results of the lattice simulation are in very good agreement with the predictions derived from a continuum analysis based on the corresponding SchwingerDyson equations. In addition, we show that an important relation connecting this function with the ghost propagator is fulfilled rather accurately. With the aid of these results, we carry out the first completely latticebased determination of the processindependent strong running interaction, employed in a variety of phenomenological studies.



Aguilar, A. C., De Soto, F., Ferreira, M. N., Papavassiliou, J., PintoGomez, F., RodríguezQuintero, J., et al. (2024). Nonperturbative fourgluon vertex in soft kinematics. Phys. Lett. B, 858, 139065–7pp.
Abstract: We present a nonperturbative study of the form factor associated with the projection of the full fourgluon vertex on its classical tensor, for a set of kinematics with one vanishing and three arbitrary external momenta. The treatment is based on the SchwingerDyson equation governing this vertex, and a largevolume lattice simulation, involving ten thousand gauge field configurations. The key hypothesis employed in both approaches is the “planar degeneracy”, which classifies diverse configurations by means of a single variable, thus enabling their meaningful “averaging”. The results of both approaches show notable agreement, revealing a considerable suppression of the averaged form factor in the infrared. The deviations from the exact planar degeneracy are discussed in detail, and a supplementary variable is used to achieve a more accurate description. The effective charge defined through this special form factor is computed within both approaches, and the results obtained are in excellent agreement.



Aguilar, A. C., De Soto, F., Ferreira, M. N., Papavassiliou, J., & RodriguezQuintero, J. (2021). Infrared facets of the threegluon vertex. Phys. Lett. B, 818, 136352–7pp.
Abstract: We present novel lattice results for the form factors of the quenched threegluon 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 treelevel 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 SchwingerDyson framework, with the aid of special relations obtained from the SlavnovTaylor identities of the theory. The emerging picture of the underlying dynamics is thoroughly corroborated by the lattice results, both qualitatively as well as quantitatively.



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 BetheSalpeter 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 lefthand cut contribution through loops in the crossed t, uchannels. 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 phaseshifts in the scalarisoscalar 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.



Ayala, C., Cvetic, G., & Kogerler, R. (2017). Latticemotivated holomorphic nearly perturbative QCD. J. Phys. G, 44(7), 075001–30pp.
Abstract: Newer lattice results indicate that, in the Landau gauge at low spacelike momenta, the gluon propagator and the ghost dressing function are finite nonzero. This leads to a definition of the QCD running coupling, in a specific scheme, that goes to zero at low spacelike momenta. We construct a running coupling which fulfills these conditions, and at the same time reproduces to a high precision the perturbative behavior at high momenta. The coupling is constructed in such a way that it reflects qualitatively correctly the holomorphic (analytic) behavior of spacelike observables in the complex plane of the squared momenta, as dictated by the general principles of quantum field theories. Further, we require the coupling to reproduce correctly the nonstrange semihadronic decay rate of tau lepton which is the best measured lowmomentum QCD observable with small highertwist effects. Subsequent application of the Borel sum rules to the V + A spectral functions of tau lepton decays, as measured by OPAL Collaboration, determines the values of the gluon condensate and of the V + A sixdimensional condensate, and reproduces the data to a significantly higher precision than the usual (MS) over bar running coupling.



BaezaBallesteros, J., Bijnens, J., Husek, T., RomeroLopez, F., Sharpe, S. R., & Sjo, M. (2023). The isospin3 threeparticle Kmatrix at NLO in ChPT. J. High Energy Phys., 05(5), 187–56pp.
Abstract: The threeparticle Kmatrix, Kdf,K3, is a schemedependent quantity that parametrizes shortrange threeparticle interactions in the relativisticfieldtheory three particle finitevolume formalism. In this work, we compute its value for systems of three pions at maximal isospin through nexttoleading order (NLO) in Chiral Perturbation Theory (ChPT). We compare the values to existing lattice QCD results and find that the agreement between lattice QCD data and ChPT in the first two coefficients of the threshold expansion of Kdf,K3 is significantly improved with respect to leading order once NLO effects are incorporated.



BaezaBallesteros, J., Bijnens, J., Husek, T., RomeroLopez, F., Sharpe, S. R., & Sjo, M. (2024). The threepion Kmatrix at NLO in ChPT. J. High Energy Phys., 03(3), 048–43pp.
Abstract: The threeparticle Kmatrix, Kdf,K3, is a schemedependent quantity that parametrizes shortrange threeparticle interactions in the relativisticfieldtheory threeparticle finitevolume formalism. In this work, we compute its value for systems of three pions in all isospin channels through nexttoleading order in Chiral Perturbation Theory, generalizing previous work done at maximum isospin. We obtain analytic expressions through quadratic order (or cubic order, in the case of zero isospin) in the expansion about the threepion threshold.



BaezaBallesteros, J., Hernandez, P., & RomeroLopez, F. (2022). A lattice study of pi pi scattering at large Nc. J. High Energy Phys., 06(6), 049–39pp.
Abstract: We present the first lattice study of pionpion scattering with varying number of colors, Nc. We use lattice simulations with four degenerate quark flavors, Nf = 4, and Nc= 3 – 6. We focus on two scattering channels that do not involve vacuum diagrams. These correspond to two irreducible representations of the SU(4) flavor group: the fully symmetric one, SS, and the fully antisymmetric one, AA. The former is a repulsive channel equivalent to the isospin2 channel of SU(2). By contrast, the latter is attractive and only exists for Nf >= 4. A representative state is (vertical bar Ds(+) pi(+)> – vertical bar D+ K+ >) /root 2. Using Lfischer's formalism, we extract the nearthreshold scattering amplitude and we match our results to Chiral Perturbation Theory (ChPT) at large Nc. For this, we compute the analytical U(Nf) ChPT prediction for twopion scattering, and use the lattice results to constrain the Nc scaling of the relevant lowenergy couplings.



Baron, R., Boucaud, P., Carbonell, J., Deuzeman, A., Drach, V., Farchioni, F., et al. (2010). Light hadrons from lattice QCD with light (u, d), strange and charm dynamical quarks. J. High Energy Phys., 06(6), 111–31pp.



Baron, R., Boucaud, P., Dimopoulos, P., Frezzotti, R., Palao, D., Rossi, G., et al. (2010). Light meson physics from maximally twisted mass lattice QCD. J. High Energy Phys., 08(8), 097–41pp.
Abstract: We present a comprehensive investigation of light meson physics using maximally twisted mass fermions for Nf = 2 massdegenerate quark flavours. By employing four values of the lattice spacing, spatial lattice extents ranging from 2.0 fm to 2.5 fm and pseudo scalar masses in the range 280 less than or similar to m(PS) less than or similar to 650MeV we control the major systematic effects of our calculation. This enables us to confront our Nf = 2 data with SU(2) chiral perturbation theory and extract low energy constants of the effective chiral Lagrangian and derived quantities, such as the light quark mass.

