Constraining GRB 230812B Prompt Emission Parameters with IceCube Neutrino Upper Limits

High energy neutrino detectors such as IceCube and ANTARES have followed up several bright gamma-ray bursts but have not found any associated neutrino signals, instead placing upper limits on the neutrino flux. In this work, we investigate the photo-hadronic interaction model during the prompt phase of GRBs and estimate the resulting neutrino flux. We use various models of the dissipation radius and its connection to the Lorentz factor to constrain the baryon loading parameter. Three emission scenarios, Baryonic Photosphere (BPH), Magnetically Dominated Photosphere (MPH), and Internal Shocks (IS), are analyzed to explore the dissipation radius, Lorentz factor, and baryon loading. For GRB~230812B, we scan the parameter space to identify allowed regions consistent with the neutrino non-detections. Based on the empirical correlation between the Lorentz factor and the isotropic gamma-ray energy, we consider $\Gamma = 187$ and report the dissipation radii in various models: $R_{\rm MPH} = 7.3 \times 10^{11}$ cm, $R_{\rm BPH} = 4.4 \times 10^{12}$ cm, and $R_{\rm IS} = 1.1 \times 10^{14}$ cm. We also estimate the baryon-loading parameter of the jet for these models. Further, we explore GRB parameter space relevant for neutrino detection using the sensitivity curves of the IceCube-Gen2 detector. Our analysis indicates that GRBs at low redshifts ($z \le 0.5$) with Lorentz factors in the range $\Gamma \sim 500$–$1500$ and isotropic energies $E_{\gamma, \rm iso} \sim 3 \times 10^{52}$–$10^{54}$ erg are promising sources of detectable neutrino signals.