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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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Lang, N., & Wilson, D. J. (2025). D1 and D2 resonances in coupled-channel scattering amplitudes from lattice QCD. J. High Energy Phys., 07(7), 060–50pp.
Abstract: Isospin-1/2 charmed axial-vector D∗π−D∗η−D∗sK¯ scattering amplitudes are computed, along with interactions in several other I=1/2 JP channels. Using lattice QCD, we work at a light-quark mass corresponding to mπ≈391 MeV, where the lowest three-hadron threshold (Dππ) lies high enough to enable a rigorous treatment of this system considering only two-hadron scattering channels. At this light-quark mass, an axial-vector D1 bound state is observed just below D∗π threshold, that is strongly coupled to D∗π in a relative S-wave and influences a wide energy region up to the D∗η threshold. An axial-vector D′1 resonance is observed in the elastic D∗π energy-region, which is coupled more strongly to D-wave D∗π. A single narrow tensor state is seen in JP=2+ coupled to both Dπ and D∗π. In the region where D∗η and D∗sK¯ are kinematically open, the available energy levels indicate significant S-wave interactions. Upon searching this region for poles, several possibilities exist with large uncertainties. One additional state consistently arises, predominantly coupled to the S-wave D∗π−D∗η−D∗sK¯ amplitudes around the upper energy limit of this analysis.
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