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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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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.
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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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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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Hansen, M. T., Romero-Lopez, F., & Sharpe, S. R. (2020). Generalizing the relativistic quantization condition to include all three-pion isospin channels. J. High Energy Phys., 07(7), 047–49pp.
Abstract: We present a generalization of the relativistic, finite-volume, three-particle quantization condition for non-identical pions in isosymmetric QCD. The resulting formalism allows one to use discrete finite-volume energies, determined using lattice QCD, to constrain scattering amplitudes for all possible values of two- and three-pion isospin. As for the case of identical pions considered previously, the result splits into two steps: the first defines a non-perturbative function with roots equal to the allowed energies, E-n(L), in a given cubic volume with side-length L. This function depends on an intermediate three-body quantity, denoted K-df;3, which can thus be constrained from lattice QCD input. The second step is a set of integral equations relating K-df,K-3 to the physical scattering amplitude, M-3. Both of the key relations, E-n(L) <-> K-df,K-3 and K-df,K-3 <-> M-3, are shown to be block-diagonal in the basis of definite three-pion isospin, I-pi pi pi, so that one in fact recovers four independent relations, corresponding to I-pi pi pi = 0; 1; 2; 3. We also provide the generalized threshold expansion of K-df,K-3 for all channels, as well as parameterizations for all three-pion resonances present for I-pi pi pi = 0 and I-pi pi pi = 1. As an example of the utility of the generalized formalism, we present a toy implementation of the quantization condition for I-pi pi pi = 0, focusing on the quantum numbers of the omega and h(1) resonances.
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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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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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