  The heavy quark effective field theory (HQEFT) provides an effective way to
deal with the heavy meson decays. In the paper, we adopt two different
correlators to derive the light-cone sum rules of the $B \to \pi$ transition
form factors (TFFs) within the framework of HQEFT. We label those two LCSR
results as LCSR-${\cal U}$ and LCSR-${\cal R}$, which are for conventional
correlator and right-handed correlator, respectively. We observe that the
correlation parameter $|\rho_{\rm RU}|$ for the branching ratio ${\cal B}(B \to
\pi l \nu_{l})$ is $\sim 0.85$, implying the consistency of the LCSRs under
different correlators. Moreover, we obtain $|V_{\rm ub}|_{{\rm LCSR}-{\cal
U}}=(3.45^{+0.28}_{-0.20}\pm{0.13}_{\rm{exp}})\times10^{-3}$ and $|V_{\rm
ub}|_{{\rm LCSR}-{\cal R}} =(3.38^{+0.22}_{-0.16}
\pm{0.12}_{\rm{exp}})\times10^{-3}$. We then obtain $\mathcal{R}_{\pi}|_{{\rm
LCSR}-{\cal U}}=0.68^{+0.10}_{-0.09}$ and $\mathcal{R}_{\pi}|_{{\rm LCSR}-{\cal
R}}=0.65^{+0.13}_{-0.11}$, both of them agree with the Lattice QCD predictions.
Thus the HQEFT provides a useful framework for studying the $B$ meson decays.
Moreover, by using right-handed correlator, the twist-2 terms shall dominant
the TFF $f^+(q^2)$, which approaches over $\sim97\%$ contribution in the whole
$q^2$-region; and the large twist-3 uncertainty for the conventional correlator
is greatly suppressed. One can thus adopt the LCSR-${\cal R}$ prediction to
test the properties of the various models for the pion twist-2 distribution
amplitudes.
