Chiral condensates in massless QCD and the $U(1)_A$ boson mass

Abstract: The $U(1)_A$ boson mass is calculated through the phenomenological characteristics of the vacuum related to spontaneous breaking of chiral symmetry in QCD. The mass is determined by the mixed quark-gluon condensate $\langle \bar q G q \rangle$ that emerges in an appropriate correlation function due to triangle anomaly. For three flavor QCD in chiral limit we find the numerical value for the $U(1)_A$ boson mass to be $M_0=310\pm 50~{\rm MeV}$.