The D∗Dπ and B∗Bπ couplings from light-cone sum rules
Alexander Khodjamirian, Blaženka Melić, Yu-Ming Wang, Yan-Bing Wei
Abstract
A bstract We revisit the calculation of the strong couplings D ∗ Dπ and B ∗ Bπ from the QCD light-cone sum rules using the pion light-cone distribution amplitudes. The accuracy of the correlation function, calculated from the operator product expansion near the light-cone, is upgraded by taking into account the gluon radiative corrections to the twist-3 terms. The double spectral density of the correlation function, including the twist-2, 3 terms at $$ \mathcal{O}\left({\alpha}_s\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msub> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:mfenced> </mml:math> and the twist-4 LO terms, is presented in an analytical form for the first time. This form allows us to use various versions of the quark-hadron duality regions in the double dispersion relation underlying the sum rules. We predict $$ {g}_{D^{\ast } D\pi}={14.1}_{-1.2}^{+1.3} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>g</mml:mi> <mml:mrow> <mml:msup> <mml:mi>D</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> <mml:mi>Dπ</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mn>14.1</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1.2</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>1.3</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> and $$ {g}_{B^{\ast } B\pi}={30.0}_{-2.4}^{+2.6} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>g</mml:mi> <mml:mrow> <mml:msup> <mml:mi>B</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> <mml:mi>Bπ</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mn>30.0</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2.4</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>2.6</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> when the decay constants of heavy mesons entering the light-cone sum rule are taken from lattice QCD results. We compare our results with the experimental value for the charmed meson coupling and with the lattice QCD calculations.