Baeza-Ballesteros, J., Bijnens, J., Husek, T., Romero-Lopez, F., Sharpe, S. R., & Sjo, M. (2024). The three-pion K-matrix at NLO in ChPT. J. High Energy Phys., 03(3), 048–43pp.
Abstract: The three-particle K-matrix, K-df,K-3, is a scheme-dependent quantity that parametrizes short-range three-particle interactions in the relativistic-field-theory three-particle finite-volume formalism. In this work, we compute its value for systems of three pions in all isospin channels through next-to-leading 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 three-pion threshold.
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Baeza-Ballesteros, J., Bijnens, J., Husek, T., Romero-Lopez, F., Sharpe, S. R., & Sjo, M. (2023). The isospin-3 three-particle K-matrix at NLO in ChPT. J. High Energy Phys., 05(5), 187–56pp.
Abstract: The three-particle K-matrix, K-df,K-3, is a scheme-dependent quantity that parametrizes short-range three-particle interactions in the relativistic-field-theory three particle finite-volume formalism. In this work, we compute its value for systems of three pions at maximal isospin through next-to-leading 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 K-df,K-3 is significantly improved with respect to leading order once NLO effects are incorporated.
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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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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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Baeza-Ballesteros, J., Hernandez, P., & Romero-Lopez, F. (2022). A lattice study of pi pi scattering at large N-c. J. High Energy Phys., 06(6), 049–39pp.
Abstract: We present the first lattice study of pion-pion scattering with varying number of colors, N-c. We use lattice simulations with four degenerate quark flavors, N-f = 4, and N-c= 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 isospin-2 channel of SU(2). By contrast, the latter is attractive and only exists for N-f >= 4. A representative state is (vertical bar D-s(+) pi(+)> – vertical bar D+ K+ >) /root 2. Using Lfischer's formalism, we extract the near-threshold scattering amplitude and we match our results to Chiral Perturbation Theory (ChPT) at large N-c. For this, we compute the analytical U(N-f) ChPT prediction for two-pion scattering, and use the lattice results to constrain the N-c scaling of the relevant low-energy couplings.
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