Analytic calculation of doubly heavy hadron spectral density in coordinate space

A systematic and easy-to-use method is developed to calculate directly the doubly heavy hadron spectral density in the coordinate space. The correlation function is expressed in terms of hypergeometric functions, and the spectral density is obtained through two independent approaches: the simple integral representation method and the epsilon-expansion method, respectively. It is found that the spectral density of doubly heavy hadrons can be analytically expressed through commonly known simple functions. This method can drastically simplify and improve the QCD spectral sum rule calculation of the doubly heavy hadrons. An instructive numerical method is also presented for fast evaluation of the spectral density.