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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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Alarcon, J. M., Hiller Blin, A. N., Vicente Vacas, M. J., & Weiss, C. (2017). Peripheral transverse densities of the baryon octet from chiral effective field theory and dispersion analysis. Nucl. Phys. A, 964, 18–54.
Abstract: The baryon electromagnetic form factors are expressed in terms of two-dimensional densities describing the distribution of charge and magnetization in transverse space at fixed light-front time. We calculate the transverse densities of the spin-1/2 flavor-octet baryons at peripheral distances b = O(M-pi(-1)) using methods of relativistic chiral effective field theory (chi EFT) and dispersion analysis. The densities are represented as dispersive integrals over the imaginary parts of the form factors in the timelike region (spectral functions). The isovector spectral functions on the two-pion cut t > 4 M-pi(2) are calculated using relativistic chi EFT including octet and decuplet baryons. The chi EFT calculations are extended into the rho meson mass region using an N / D method that incorporates the pion electromagnetic form factor data. The isoscalar spectral functions are modeled by vector meson poles. We compute the peripheral charge and magnetization densities in the octet baryon states, estimate the uncertainties, and determine the quark flavor decomposition. The approach can be extended to baryon form factors of other operators and the moments of generalized parton distributions.
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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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Chen, Y. H., Yao, D. L., & Zheng, H. Q. (2018). A Study of rho-omega Mixing in Resonance Chiral Theory. Commun. Theor. Phys., 69(1), 50–58.
Abstract: The strong and electromagnetic corrections to rho-omega mixing are calculated using an SU(2) version of resonance chiral theory up to next-to-leading orders in 1/N-C expansion, respectively. Up to our accuracy, the effect of the momentum dependence of rho-omega mixing is incorporated due to the inclusion of loop contributions. We analyze the impact of rho-omega mixing on the pion vector form factor by performing numerical fit to the data extracted from e(+)e(-) -> pi(+)pi(-) and tau -> nu(tau)2 pi, while the decay width of omega -> pi(+)pi(-) is taken into account as a constraint. It is found that the momentum dependence is significant in a good description of the experimental data. In addition, based on the fitted values of the involved parameters, we analyze the decay width of omega -> pi(+)pi(-), which turns out to be highly dominated by the rho-omega mixing effect.
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