Numerical Regularization of Resonances in B -> K* mu+ mu- Decays: An AMDCF-Based Approach with Detector Resolution Modeling

Precision tests of the Standard Model via rare B-meson decays require accurate numerical simulations. However, the presence of Breit-Wigner resonances (J/\psi and \psi(2S)) introduces mathematical singularities that lead to numerical blow-up (floating-point overflow) during Monte Carlo simulations. In this work, we apply the Adaptive Memory-Decay Control Framework (AMDCF) as a dynamic numerical regularizer. By computing the gradient of the decay amplitude, the kernel applies an adaptive damping factor specifically at the resonance peaks, preventing numerical divergence while preserving the physical observables. Crucially, we model the finite detector resolution by smoothing the regularization response with a Gaussian filter, producing a physically realistic and stable response function. The simulation incorporates realistic Wilson coefficients (C_7, C_9, C_{10}), Ball-Zwicky form factors, and the LHCb experimental Veto Regions. The results demonstrate that AMDCF provides a stable, automated, and physically motivated alternative to manual cutoffs in high-energy physics data analysis.