Title: QED correction to neutron beta decay

Abstract: The neutron lifetime is a key precision observable for testing the Standard Model (SM), and a deviation from its predicted value would constitute a clear signal of physics beyond the SM. This talk will briefly review the background of neutron beta decay, with a focus on the Fermi function. Traditional calculations of the Fermi function are typically restricted to high-$Z$ (atomic number) and small-$\beta$ (velocity) regimes. We introduce a new formalism, deriving a Quantum Field Theory (QFT) analog of the Fermi function that is valid for the low-$Z$ and large-$\beta$ region relevant to neutron decay. We will discuss the factorization of this formalism and compute the components of the factorization formula. Furthermore, we will address the resummation and convergence of the associated perturbation theory. Finally, we combine these results to calculate a novel QED correction to the neutron lifetime. We use this updated correction to derive a new, high-precision value for the CKM matrix element $|V_{ud}|$