Nucleon-nucleon scattering lengths in QCD sum rules

Nucleon-nucleon scattering lengths are calculated by QCD sum rules. The calculation is based on the observation that the coefficient of the second-order pole term of the nucleon correlation function in nucleon is proportional to the nucleon-nucleon scattering length at the threshold. By applying Borel sum rules, we express the scattering length in terms of the expectation values of the quark-gluon field operators with respect to the one-nucleon state. The scattering lengths calculated are in qualitative agreement with the experiment. It is shown that in the linear density approximation the nucleon mass shift in nuclear matter is related to the nucleon-nucleon scattering length by δ${\mathit{M}}_{\mathit{N}}$=-(3π/2${\mathit{M}}_{\mathit{N}}$)(${\mathit{a}}_{\mathit{N}\mathit{N}}^1$+${\mathit{a}}_{\mathit{N}\mathit{N}}^3$)ρ.