The properties of hadron screening masses around the deconfinement phase transition at finite baryonic density can be studied by evaluating the Taylor coefficients with respect to the iso-scalar and iso-vector chemical potentials. We simulate 2-flavour lattice QCD with staggered fermions on a 12*12*24*6 lattice with ma = 0.05 and 0.10 and report investigations of nucleon, pseudo-scalar and vector mesons. We present new, strong evidence that in the confining phase, the screening masses at vanishing chemical potential have significant temperature dependence, but the effect of the iso-scalar chemical potential is very small. Above the critical temperature, the second derivative terms of mesons rapidly increase as contrasted to the case of baryon. We also study the responses of the screening masses to an iso-vector chemical potential and discuss some of the issues related to the properties of hadron masses at finite density.

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