Hansen, M. T., Romero-Lopez, F., & Sharpe, S. R. (2021). Decay amplitudes to three hadrons from finite-volume matrix elements. J. High Energy Phys., 04(4), 113–44pp.
Abstract: We derive relations between finite-volume matrix elements and infinite-volume decay amplitudes, for processes with three spinless, degenerate and either identical or non-identical particles in the final state. This generalizes the Lellouch-Luscher relation for two-particle decays and provides a strategy for extracting three-hadron decay amplitudes using lattice QCD. Unlike for two particles, even in the simplest approximation, one must solve integral equations to obtain the physical decay amplitude, a consequence of the nontrivial finite-state interactions. We first derive the result in a simplified theory with three identical particles, and then present the generalizations needed to study phenomenologically relevant three-pion decays. The specific processes we discuss are the CP-violating K -> 3 pi weak decay, the isospin-breaking eta -> 3 pi QCD transition, and the electromagnetic gamma (*) -> 3 pi amplitudes that enter the calculation of the hadronic vacuum polarization contribution to muonic g – 2.
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Li, X. Q., Yang, Y. D., & Yuan, X. B. (2012). Anomalous tqZ coupling effects in rare B- and K-meson decays. J. High Energy Phys., 03(3), 018–22pp.
Abstract: As a top-factory, the LHC is performing a direct study of top-quark anomalous FCNC couplings, which are, however, correlated closely with the rare B- and K-meson decays. In this paper, we study the effects of anomalous tqZ (with q = u, c) couplings in the rare decays B-s,B-d -> mu(+)mu(-), B -> X-s nu(nu) over bar, B -> K(*)nu(nu) over bar, K+ -> pi(+)nu(nu) over bar, and K-L -> pi(0)nu(nu) over bar. With the up-to-date experimental bounds on the branching ratios of these channels, constraints on the left-handed anomalous couplings X-ct(L), and X-ut(L) are derived, respectively. With these low-energy constraints taken into account, we find that, for real couplings X-ct(L) and X-ut(L), the indirect upper bounds on B(t -> qZ) are much lower than that from the D0 collaboration, but are still compatible with the 5 sigma discovery potential of ATLAS with an integrated luminosity of 10 fb(-1). With refined measurements to be available at the LHCb, the future super-B factories, the NA62 at CERN, and the KOTO at J-PARC, closer correlations between the t -> qZ and the rare B- and K-meson decays are expected in the near future, which will be helpful for the searches of thu e top-quark FCNC decays at the LHC.
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