# A Comparative Study of f$_{B}$ within QCD Sum Rules with Two Typical Correlators up to Next-to-Leading Order 

Xing-Gang Wu $^{a}$, Yao Yu, Gu Chen and Hua-Yong Han 

Department of Physics, Chongqing University, Chongqing 400044, P.R. China 

(Dated: December 4, 2018) 

## Abstract 

The B -meson decay constant f$_{B}$ is an important component for studying the B -meson decays, which can be studied through QCD sum rules. We make a detailed discussion on f$_{B}$ from two sum rules up to next-to-leading order, 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. The sum rules II involves less non-perturbative condensates as that of sum rules I, and in principle, 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 I and II prefer smaller pole b -quark mass, m$_{b}$ = 4 . 68 ± 0 . 07 GeV. By varying all the input parameters within their reasonable regions and by adding all the uncertainties in quadrature, we obtain f$_{B}$ = 172 +23 − 25 MeV for sum rules I and f$_{B}$ = 214 +26 − 34 MeV for sum rules II. 

PACS numbers: 11.55.Hx, 12.38.-t, 13.20.He, 12.38.Lg 

Key words: QCD sum rules, Decay Constant, Correlator 

