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Bertone, V., Carrasco, N., Ciuchini, M., Dimopoulos, P., Frezzotti, R., Gimenez, V., et al. (2013). Kaon mixing beyond the SM from N-f=2 tmQCD and model independent constraints from the UTA. J. High Energy Phys., 03(3), 089–53pp.
Abstract: We present the first unquenched, continuum limit, lattice QCD results for the matrix elements of the operators describing neutral kaon oscillations in extensions of the Standard Model. Owing to the accuracy of our calculation on Delta S = 2 weak Hamiltonian matrix elements, we are able to provide a refined Unitarity Triangle analysis improving the bounds coming from model independent constraints on New Physics. In our non-perturbative computation we use a combination of N-f = 2 maximally twisted sea quarks and Osterwalder-Seiler valence quarks in order to achieve both O(a)-improvement and continuum-like renormalization properties for the relevant four-fermion operators. The calculation of the renormalization constants has been performed non-perturbatively in the RI-MOM scheme. Based on simulations at four values of the lattice spacing and a number of quark masses we have extrapolated/interpolated our results to the continuum limit and physical light/strange quark masses.
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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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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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Ayala, C., Cvetic, G., & Kogerler, R. (2017). Lattice-motivated 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 non-zero. 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 low-momentum QCD observable with small higher-twist 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 six-dimensional condensate, and reproduces the data to a significantly higher precision than the usual (MS) over bar running coupling.
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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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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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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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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 N-f = 2 mass-degenerate 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 N-f = 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.
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Bernard, V., & Passemar, E. (2010). Chiral extrapolation of the strangeness changing scalar K pi form factor. J. High Energy Phys., 04(4), 001–18pp.
Abstract: We perform a chiral extrapolation of lattice data on the scalar K pi form factor and the ratio of the kaon and pion decay constants within Chiral Perturbation Theory to two loops. We determine the value of the scalar form factor at zero momentum transfer, at the Callan-Treiman point and at its soft kaon analog as well as its slope. Results are in good agreement with their determination from experiment using the standard couplings of quarks to the W boson. The slope is however rather large. A study of the convergence of the chiral expansion is also performed.
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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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