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

The rare kaon decay $K^+ \to \pi^+\ell^+\ell^-$ 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 $|f_S|$ 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$\%$ confidence level.