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The heavy quark effective field theory (HQEFT) provides an effective way todeal with the heavy meson decays. In the paper, we adopt two differentcorrelators to derive the light-cone sum rules of the $B \to \pi$ transitionform factors (TFFs) within the framework of HQEFT. We label those two LCSRresults as LCSR-${\cal U}$ and LCSR-${\cal R}$, which are for conventionalcorrelator and right-handed correlator, respectively. We observe that thecorrelation 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 underdifferent correlators. Moreover, we obtain $|V_{\rm ub}|_{{\rm LCSR}-{\calU}}=(3.45^{+0.28}_{-0.20}\pm{0.13}_{\rm{exp}})\times10^{-3}$ and $|V_{\rmub}|_{{\rm LCSR}-{\cal R}} =(3.38^{+0.22}_{-0.16}\pm{0.12}_{\rm{exp}})\times10^{-3}$. We then obtain $\mathcal{R}_{\pi}|_{{\rmLCSR}-{\cal U}}=0.68^{+0.10}_{-0.09}$ and $\mathcal{R}_{\pi}|_{{\rm LCSR}-{\calR}}=0.65^{+0.13}_{-0.11}$, 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 dominantthe TFF $f^+(q^2)$, which approaches over $\sim97\%$ contribution in the whole$q^2$-region; and the large twist-3 uncertainty for the conventional correlatoris greatly suppressed. One can thus adopt the LCSR-${\cal R}$ prediction totest the properties of the various models for the pion twist-2 distributionamplitudes.

The $B\to \pi \ell\nu_\ell$ semileptonic decay within the LCSR approach under heavy quark effective field theory