Spectra of Massive and Massless QCD Dirac Operators: A Novel Link

We show that integrable structure of chiral random matrix models incorporating global symmetries of QCD Dirac operators (labeled by the Dyson index $\beta =1,2\mathrm{}$, and $4$) leads to emergence of a connection relation between the spectral statistics of massive and massless Dirac operators. This novel link established for $\beta$-fold degenerate massive fermions is used to explicitly derive (and prove the random matrix universality of) statistics of low-lying spectra of QCD Dirac operators in the presence of $\mathrm{SU}\left(2\right)$ massive fermions in the fundamental representation ( $\beta =1\mathrm{}$) and $\mathrm{SU}(N_c\ge 2)$ massive adjoint fermions ( $\beta =4\mathrm{}$). Comparison with available lattice data for $\mathrm{SU}\left(2\right)$ dynamical staggered fermions reveals a good agreement.