Exploring scalar contributions with $K^{+}\to {\pi }^{+}{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$

The rare kaon decay $K^{+}\to {\pi }^{+}{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ offers insights into Standard Model (SM) physics and beyond. Driven by vector form factor in the SM, it can also probe non-standard contributions. In this letter we study the scalar contribution, $f_S$. Using differential decay width and Forward-Backward Asymmetry we propose a simultaneous fit to vector and scalar contributions which is necessary for a consistent analysis. Novel bounds on $\mathrm{\mid }{f}_S\mathrm{\mid }$ are presented for the first time through a reinterpretation of the E865, NA48/2, and NA62 experimental results. The analysis results in the most precise bound $f_S<7.9\times {10}^{-6}$ at 90$\mathrm{\%}$ confidence level.