A_1(1260)-meson longitudinal twist-2 distribution amplitude and the Drightarrow a_1(1260)ell ^+nu _ell decay processes

Abstract

In the paper, we investigate the moments langle xi _{2;a_1}^{Vert ;n}rangle of the axial-vector a_1(1260)-meson distribution amplitude by using the QCD sum rules approach under the background field theory. By considering the vacuum condensates up to dimension-six and the perturbative part up to next-to-leading order QCD corrections, its first five moments at an initial scale mu _0=1~{mathrm{GeV}} are langle xi _{2;a_1}^{Vert ;2}rangle |_{mu _0} = 0.223 pm 0.029, langle xi _{2;a_1}^{Vert ;4}rangle |_{mu _0} = 0.098 pm 0.008, langle xi _{2;a_1}^{Vert ;6}rangle |_{mu _0} = 0.056 pm 0.006, langle xi _{2;a_1}^{Vert ;8}rangle |_{mu _0} = 0.039 pm 0.004 and langle xi _{2;a_1}^{Vert ;10}rangle |_{mu _0} = 0.028 pm 0.003, respectively. We then construct a light-cone harmonic oscillator model for a_1(1260)-meson longitudinal twist-2 distribution amplitude phi _{2;a_1}^{Vert }(x,mu ), whose model parameters are fitted by using the least squares method. As an application of phi _{2;a_1}^{Vert }(x,mu ), we calculate the transition form factors (TFFs) of Drightarrow a_1(1260) in large and intermediate momentum transfers by using the QCD light-cone sum rules approach. At the largest recoil point (q^2=0), we obtain A(0) = 0.130_{ - 0.013}^{ + 0.015}, V_1(0) = 1.898_{-0.121}^{+0.128}, V_2(0) = 0.228_{-0.021}^{ + 0.020}, and V_0(0) = 0.217_{ - 0.025}^{ + 0.023}. By applying the extrapolated TFFs to the semi-leptonic decay D^{0(+)} rightarrow a_1^{-(0)}(1260)ell ^+nu _ell , we obtain {mathcal {B}}(D^0rightarrow a_1^-(1260) e^+nu _e) = (5.261_{-0.639}^{+0.745}) times 10^{-5}, {mathcal {B}}(D^+rightarrow a_1^0(1260) e^+nu _e) = (6.673_{-0.811}^{+0.947}) times 10^{-5}, {mathcal {B}}(D^0rightarrow a_1^-(1260) mu ^+ nu _mu )=(4.732_{-0.590}^{+0.685}) times 10^{-5}, {mathcal {B}}(D^+ rightarrow a_1^0(1260) mu ^+ nu _mu )=(6.002_{-0.748}^{+0.796}) times 10^{-5}.