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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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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., HernAndez, P., & Romero-Lopez, F. (2025). The ππ scattering amplitude at large Nc. J. High Energy Phys., 08(8), 110–65pp.
Abstract: We study the scaling of meson-meson scattering amplitudes with the number of colors, N-c. We use lattice calculations in a theory with N-f= 4 degenerate flavors, with N-c= 3-6a nd pion mass M-pi approximate to 560 MeV. We focus on three different scattering channels, two of which have the same quantum numbers as some tetraquark candidates recently found at LHCb: the T-cs0(0)(2900),T-c s0(++)(2900),T-c s0(0)(2900) and T-cs1(0)(2900)states. Finite-volume energies are extracted using a large set of operators, containing two-particle operators with the form of two pions or two vector mesons, and local tetraquark operators. The resulting energy spectra is used to constrain the infinite-volume scattering amplitude by means of Luscher'squantization condition. We consider polynomial parametrizations of the phase shift, as well as one-loop chiral perturbation theory (ChPT) predictions. We find that our lattice results follow the expected N-c scaling and are sensitive to sub leading Nc corrections. In addition, we constrain the scaling of different combinations of low-energy constants from matching to large N-c ChPT. The results for the channel corresponding to a(pi D-+(s)+-K+D+)state show evide Nce of a virtual bound state with energy Evirtual= 1.63(10)M pi for N-c= 3, while this pole disappears atN(c)>3. This may be connected to the exotic states found in experiment
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Gomez Nicola, A., Molina, R., & Sanchez, J. A. (2026). Pion scattering in finite volume within the Inverse Amplitude Method. J. High Energy Phys., 06(6), 057–50pp.
Abstract: We study the effect of a finite volume for pion-pion scattering within Chiral Perturbation Theory (ChPT) and the Inverse Amplitude Method (IAM) in a L3 box (rest frame). Our full ChPT calculation takes into account the discretization not only in the s-channel loops but also in the t, u- channels and tadpole contributions. Hence, not only the unitarity right-hand cut but also the continuum contributions to the left-hand cut are calculated in the finite volume. A proper extension of the standard Veltman-Passarino identities is needed, as well as a suitable projection on the internal space spanned by the irreducible representations (irreps) of the octahedral group, based on either a finite set of cubic harmonics or the matrices which represent the irreps properly. From the ChPT we construct the IAM in the internal space, which provides the full volume dependence of the interacting energy levels of two pions scattering in the finite volume. Our results for various sets of low-energy constants show sizable corrections with respect to previous analyses in the literature for m pi L less than or similar to 2, being compatible with energy levels lattice data. We expect that our analysis and results will help to optimize the process of determining energy levels and phase-shifts with higher accuracy.
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