A Comparative Study of $f_B$ within QCD Sum Rules with Two Typical Correlators up to Next-to-Leading Order

The B-decay constant $f_B$ is an important component for studying $B$-meson decays, which can be studied through QCD sum rules. We make a detailed discussion on $f_B$ from two sum rules, i.e. sum rules I and II, which are derived from the conventional correlator and the correlator with chiral currents respectively. It is found that these two sum rules are consistent with each other. However, the sum rules II has less uncertainty sources than that of sum rules I, and then it can be more accurate if we know the dimension-four gluon condensate well. It is found that $f_B$ decreases with the increment of $m_b$, and to compare with the Belle experimental data on $f_B$, both sum rules prefer smaller pole $b$-quark mass, $m_b=4.68\pm0.07$ GeV. By varying all the input parameters in their reasonable region and adding all the uncertainties together in quadrature, we obtain $f_B=172^{+23}_{-25}$ MeV for sum rules I and $f_B=214_{-34}^{+26}$ MeV for sum rules II.