High Energy Physics - Lattice

We revisit the lattice QCD description of the doubly charmed tetraquark $T_{cc}^+$ using a finite-volume scattering formalism that incorporates one-pion exchange nonperturbatively, thereby making the nearest left-hand cut explicit while respecting unitarity and analyticity. We simultaneously determine the $D D^\star \pi$ coupling and the isoscalar $DD^\star$ scattering amplitude by reanalyzing the previously computed finite-volume $DD^\star$ spectrum below the $D^\star D^\star$ threshold, on lattices with pion mass $m_\pi\approx391~{\rm MeV}$. We find that the inclusion of pion exchange changes the $T_{cc}^+$ from a real-valued to a complex-valued pole in the second sheet of the $J^P=1^+$, $DD^\star$ amplitude below threshold. We further predict that the $T_{cc}^+$ pole will move closer to the real-energy axis as the pion mass approaches its physical value.

The recently announced NA62 measurement of the $K^{+}\to\pi^{+}\nu\bar{\nu}$ branching ratio, based on 2016--2024 data, is fully consistent with its very accurate Standard Model (SM) prediction. While it is not excluded that the final result based on 2016--2026 data will deviate from the SM prediction, the question arises whether a similar fate awaits the $K_{L}\to\pi^{0}\nu\bar{\nu}$ decay. This decay is currently being searched for by the KOTO experiment, with the present upper bound roughly two orders of magnitude above its very precise SM prediction. The proposed KOTO II experiment aims to provide the first discovery of the $K_{L}\to\pi^{0}\nu\bar{\nu}$ decay and measure its branching ratio. Building on the findings of several previous papers we demonstrate that in the presence of suitably chosen large new complex phases and of a small amount of new right-handed $\bar s d$ couplings, in addition to the left-handed ones, the $K_{L}\to\pi^{0}\nu\bar{\nu}$ branching ratio can still be enhanced by one order of magnitude with respect to the SM prediction while keeping both $K^{+}\to\pi^{+}\nu\bar{\nu}$ and $\varepsilon_K$ SM-like. Simultaneously the decays $K_S\to\mu^+\mu^-$, studied by LHCb, and $K_L\to\pi^0\ell^+\ell^-$, searched for by KOTO II, can be strongly enhanced and the anomaly in the ratio $\varepsilon^{\prime}/\varepsilon$, as claimed by Dual QCD, removed. We illustrate this with an example of a specific $Z^\prime$ scenario.