Biphoton bound state right above e-p pair birth threshold

A biphoton state of matter that is an instant interplay between electromagnetic energy and electron–positron pairs is reported. The biphoton ladder diagram right above the e-p pair birth threshold is summed up. Only one ladder diagram is most relevant, and the obtained propagator has a diffusion pole, with the diffusion coefficient expressed as D ∼ α⁻²h/m ∼ 2 × 10⁴ cm²/s, where α is the fine-structure constant and m is the electron mass. This is a realization of an object with oscillation of energy between an electromagnetic field and an e-p pair. This continuous oscillation holds energy localized in space, expanding relatively slowly following the diffusion equation. The above diffusion coefficient, dependent only on fundamental constants, can describe an observable macroscopic object, for example, ball lightning.