QCD sum rules for $\mathrm{\Delta }$ isobar in nuclear matter

The self-energies of $\mathrm{\Delta }$ isobar propagating in nuclear matter are calculated using the finite-density QCD sum-rule methods. The calculations show that the Lorentz vector self-energy for the $\mathrm{\Delta }$ is significantly smaller than the nucleon vector self-energy. The magnitude of the $\mathrm{\Delta }$ scalar self-energy is larger than the corresponding value for the nucleon, which suggests a strong attractive net self-energy for the $\mathrm{\Delta }$; however, the prediction for the scalar self-energy is very sensitive to the density dependence of certain in-medium four-quark condensate. Phenomenological implications for the couplings of the $\mathrm{\Delta }$ to the nuclear scalar and vector fields are briefly discussed.