GRB 250424A: A Case Study of Energy Injection with Multiwavelength Observations

We present a comprehensive multiwavelength analysis of the long-duration gamma-ray burst (GRB) 250424A. Our dataset spans from the prompt gamma-ray emission to late-time optical monitoring, including spectra obtained with the Keck 10\,m telescope. We find that the afterglow light curves display a prominent, simultaneous shallow decay phase in both X-ray and optical bands, followed by an achromatic transition to a standard decay regime. The broadband spectral energy distributions are well-modeled by a single power-law function, indicating a common synchrotron origin for the emission across frequencies. We interpret the afterglow evolution within the framework of a relativistic forward shock refreshed by continuous energy injection. This scenario successfully reproduces the observed temporal and spectral behavior, yielding an isotropic equivalent kinetic energy of $E_{\rm K,iso} \approx 5.5 \times 10^{52}$ erg and an injection index of $q\approx 0.34$ in a constant-density circumburst environment. The shallow decay phase is consistent with sustained energy injection lasting $\sim$ 9 ks. Despite the relatively low redshift, late-time optical observations reveal no distinct supernova component; however, our derived upper limits do not strictly rule out the presence of a typical GRB-associated supernova.