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Using a partonic transport model based on the Nambu-Jona-Lasinio model, westudy the effect of scalar and vector mean fields on the elliptic flows ofquarks and antiquarks in relativistic heavy ion collisions in Au+Au collisionsat $\sqrt{s_{\rm NN}}=7.7~$GeV and impact parameter $b=8~{\rm fm}$ that leadsto the production of a baryon-rich matter. Although the scalar mean field,which is attractive for both quarks and antiquarks, reduces both their ellipticflows, the vector mean field, which is repulsive for quarks and attractive forantiquarks, leads to a splitting of their elliptic flows, and this effectincreases with the strength of the vector coupling in the baryon-rich quarkmatter. Converting quarks and antiquarks at hadronization to hadrons via thequark coalescence model, we further study the dependence of the transversemomentum integrated relative elliptic flow differences between protons andantiprotons, lambda and anti-lambdas, and positively and negatively chargedkaons on the strength of the quark vector coupling. These results are thencompared with the experimental data measured by the STAR Collaboration in theBeam Energy Scan program at the Relativistic Heavy Ion Collider.

Partonic mean-field effects on matter and antimatter elliptic flows