Pich, A., Rosell, I., & Sanz-Cillero, J. J. (2011). The vector form factor at the next-to-leading order in 1/N-C: chiral couplings L-9(mu) and C-88(mu)-C-90(mu). J. High Energy Phys., 02(2), 109–23pp.
Abstract: Using the Resonance Chiral Theory Lagrangian, we perform a calculation of the vector form factor of the pion at the next-to-leading order (NLO) in the 1/N-C expansion. Imposing the correct QCD short-distance constraints, one fixes the amplitude in terms of the pion decay constant F and resonance masses. Its low momentum expansion determines then the corresponding O(p(4)) and O(p(6)) low-energy chiral couplings at NLO, keeping control of their renormalization scale dependence. At mu(0) = 0.77 GeV, we obtain L-9(mu(0)) = (7.9 +/- 0.4).10(-3) and C-88(mu(0)) – C-90(mu(0)) = (-4.6 +/- 0.4).10(-5).
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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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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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Gomez Dumm, D., Roig, P., Pich, A., & Portoles, J. (2010). tau -> pi pi pi nu(tau) decays and the a(1)(1260) off-shell width revisited. Phys. Lett. B, 685(2-3), 158–164.
Abstract: The tau -> pi pi pi nu(tau) decay is driven by the hadronization of the axial-vector current. Within the resonance chiral theory, and considering the large-N-C expansion, this process has been studied in Ref. [1] (D. Gomez Dumm, A. Pich, J. Portoles, 2004). In the light of later developments we revise here this previous work by including a new off-shell width for the lightest a(1) resonance that provides a good description of the tau -> pi pi pi nu(tau) spectrum and branching ratio. We also consider the role of the rho(1450) resonance in these observables. Thus we bring in an overall description of the tau -> pi pi pi nu(tau) process in excellent agreement with our present experimental knowledge.
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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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Krause, C., Pich, A., Rosell, I., Santos, J., & Sanz-Cillero, J. J. (2019). Colorful imprints of heavy states in the electroweak effective theory. J. High Energy Phys., 05(5), 092–51pp.
Abstract: We analyze heavy states from generic ultraviolet completions of the Standard Model in a model-independent way and investigate their implications on the low-energy couplings of the electroweak effective theory. We build a general effective Lagrangian, implementing the electroweak symmetry breaking SU(2)(L) circle times SU(2)(R) SU(2)(L+R) with a non-linear Nambu-Goldstone realization, which couples the known particles to the heavy states. We generalize the formalism developed in previous works [1, 2] to include colored resonances, both of bosonic and fermionic type. We study bosonic heavy states with J(P) = 0(+/-) and J(P) = 1(+/-), in singlet or triplet SU(2)(L+R) representations and in singlet or octet representations of SU(3)(C) , and fermionic resonances with that are electroweak doublets and QCD triplets or singlets. Integrating out the heavy scales, we determine the complete pattern of low-energy couplings at the lowest non-trivial order. Some specific types of (strongly- and weakly-coupled) ultraviolet completions are discussed to illustrate the generality of our approach and to make contact with current experimental searches.
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Cirigliano, V., Gisbert, H., Pich, A., & Rodriguez-Sanchez, A. (2020). Isospin-violating contributions to epsilon '/epsilon. J. High Energy Phys., 02(2), 032–44pp.
Abstract: The known isospin-breaking contributions to the K -> pi pi amplitudes are reanalyzed, taking into account our current understanding of the quark masses and the relevant non-perturbative inputs. We present a complete numerical reappraisal of the direct CP-violating ratio is an element of(')/is an element of, where these corrections play a quite significant role. We obtain the Standard Model prediction Re (is an element of(')/is an element of) = (14 +/- 5) <bold> </bold>10(-4), which is in very good agreement with the measured ratio. The uncertainty, which has been estimated conservatively, is dominated by our current ignorance about 1/N-C-suppressed contributions to some relevant chiral-perturbation-theory low-energy constants.
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Molina, R., & Ruiz de Elvira, J. (2020). Light- and strange-quark mass dependence of the rho(770) meson revisited. J. High Energy Phys., 11(11), 017–74pp.
Abstract: Recent lattice data on pi pi -scattering phase shifts in the vector-isovector channel, pseudoscalar meson masses and decay constants for strange-quark masses smaller or equal to the physical value allow us to study the strangeness dependence of these observables for the first time. We perform a global analysis on two kind of lattice trajectories depending on whether the sum of quark masses or the strange-quark mass is kept fixed to the physical point. The quark mass dependence of these observables is extracted from unitarized coupled-channel one-loop Chiral Perturbation Theory. This analysis guides new predictions on the rho (770) meson properties over trajectories where the strange-quark mass is lighter than the physical mass, as well as on the SU(3) symmetric line. As a result, the light- and strange-quark mass dependence of the rho (770) meson parameters are discussed and precise values of the Low Energy Constants present in unitarized one-loop Chiral Perturbation Theory are given. Finally, the current discrepancy between two- and three-flavor lattice results for the rho (770) meson is studied.
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Pich, A., & Rodriguez-Sanchez, A. (2021). SU(3) analysis of four-quark operators: K -> pi pi and vacuum matrix elements. J. High Energy Phys., 06(6), 005–43pp.
Abstract: Hadronic matrix elements of local four-quark operators play a central role in non-leptonic kaon decays, while vacuum matrix elements involving the same kind of operators appear in inclusive dispersion relations, such as those relevant in tau -decay analyses. Using an SU(3)(L) circle times SU(3)(R) decomposition of the operators, we derive generic relations between these matrix elements, extending well-known results that link observables in the two different sectors. Two relevant phenomenological applications are presented. First, we determine the electroweak-penguin contribution to the kaon CP-violating ratio epsilon '/epsilon, using the measured hadronic spectral functions in tau decay. Second, we fit our SU(3) dynamical parameters to the most recent lattice data on K -> pi pi matrix elements. The comparison of this numerical fit with results from previous analytical approaches provides an interesting anatomy of the Delta I = 1/2 enhancement, confirming old suggestions about its underlying dynamical origin.
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Feijoo, A., Gazda, D., Magas, V., & Ramos, A. (2021). The (K)over-barN Interaction in Higher Partial Waves. Symmetry-Basel, 13(8), 1434–22pp.
Abstract: We present a chiral (K) over barN interaction model that has been developed and optimized in order to account for the experimental data of inelastic (K) over barN reaction channels that open at higher energies. In particular, we study the effect of the higher partial waves, which originate directly from the chiral Lagrangian, as they could supersede the role of high-spin resonances employed in earlier phenomenological models to describe meson-baryon cross sections in the 2 GeV region. We present a detailed derivation of the partial wave amplitudes that emerge from the chiral SU(3) meson-baryon Lagrangian up to the d-waves and next-to-leading order in the chiral expansion. We implement a nonperturbative unitarization in coupled channels and optimize the model parameters to a large pool of experimental data in the relevant energy range where these new contributions are expected to be important. The obtained results are encouraging. They indicate the ability of the chiral higher partial waves to extend the description of the scattering data to higher energies and to account for structures in the reaction cross-sections that cannot be accommodated by theoretical models limited to the s-waves.
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