Abstract
Lattice results are available for $\ensuremath{\Delta}S=2$ matrix elements for the first time in full QCD, which improve considerably the status of hadronic uncertainties in $K\mathrm{\text{\ensuremath{-}}}\overline{K}$ mixing with respect to earlier phenomenological studies. Using an average of the ETMC and RBC-UKQCD results, we analyze ${ϵ}_{K}$ in natural supersymmetry (SUSY). This scenario arises as a consistent BSM framework after the latest results from the LHC. The analysis is improved with respect to previous studies including next-to-leading order matching conditions of order ${\ensuremath{\alpha}}_{s}^{3}$. We derive new bounds for SUSY mass insertions in the scenario with a light third generation and study the implications for squark and gluino masses, compared with direct searches at the LHC. Assuming natural values for the flavor-violating SUSY couplings of both chiralities, we find that the sbottom must be heavier than 3 TeV for a gluino mass up to 10 TeV. In this scenario no natural values for squark and gluino masses can satisfy the flavor bounds.
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