Improved light-cone harmonic oscillator model for the φ-meson longitudinal leading-twist light-cone distribution amplitude and its effects to D s plus -* φl plus νl

In the present paper, we study the properties of phi-meson longitudinal leading-twist light-cone distribution amplitude phi k 2;phi & eth; x, mu & THORN; by starting from a light-cone harmonic oscillator model for its wave function. To fix the input parameters, we derive the first ten order xi moments of phi k 2;phi & eth; x, mu & THORN; by using the QCD sum rules approach under the background field theory. The curves of phi k 2;phi & eth; x, mu 1 / 4 2 GeV & THORN; tend to be a single-peak behavior, which is consistent with the latest lattice QCD result. To show how the twist-3 light-cone distribution amplitudes (LCDAs) affect the results, we consider two scenarios for the phi-meson chiral twist-3 LCDAs phi perpendicular to 3;phi & eth; x & THORN; and psi perpendicular to 3;phi & eth; x & THORN; , i.e., the ones using the WandzuraWilczek approximation with phi k 2;phi & eth; x, mu & THORN; (S1) and the ones using self-consistent conformal expansion with second-order Gegenbauer moments a 22;phi in this work (S2). As an application, we derive the D & thorn; s-* phi transition form factors (TFFs) by using the QCD light-cone sum rules. The TFFs at large recoil point for those two scenarios are given separately. As for the two TFF ratios gamma V and gamma 2, we obtain gamma & eth; S1 & THORN; V 1 / 4 1 .755 & thorn; 0 .008 -0.005 , gamma & eth; S1 & THORN; 2 1 / 4 0 .852 & thorn; 0 .135 -0.133, gamma & eth; S2 & THORN; V 1 / 4 1 .723 & thorn; 0 .023 -0.021, and gamma & eth; S2 & THORN; 2 1 / 4 0 .785 & thorn; 0 .100 -0.104 . After extrapolating those TFFs to the physically allowable region, we then obtain the transverse, longitudinal, and total decay widths for semileptonic decay D & thorn; s-* phi l & thorn;nu l. Then the branching fractions are B & eth; S1 & THORN; & eth; D & thorn; s-* phi e & thorn; nu e & THORN; 1 / 4 & eth; 2 .347 & thorn; 0 .342 -0.191 & THORN; x 10 - 3 , B & eth; S1 & THORN; & eth; D & thorn; s-* phi mu & thorn; nu mu & THORN; 1 / 4 & eth; 2 .330 & thorn; 0 .341 -0.190 & THORN; x 10 - 3 , B & eth; S2 & THORN; & eth; D & thorn; s-* phi e & thorn; nu e & THORN; 1 / 4 & eth; 2 .367 & thorn; 0 .256 -0.132 & THORN; x 10-3, and B & eth; S2 & THORN; & eth; D & thorn; s-* phi mu & thorn;nu mu & THORN; 1 / 4 & eth; 2 .349 & thorn; 0 .255 -0.132 & THORN; x 10-3, which show good agreement with the data issued by the BESIII, CLEO, and BABAR Collaborations. We finally calculate D & thorn; s-* phi l & thorn;nu l polarization and asymmetry parameters, which can be measured and tested in future experiments.