An improved light-cone harmonic oscillator model for the pionic leading-twist distribution amplitude

Abstract

In this paper, we study the pion leading-twist distribution amplitude φ2;π(x, µ) by improving the traditional light-cone harmonic oscillator model within the reconstruction of the function ϕ2;π(x). In order to constraining the model parameters, we calculate its moments ξ n 2;π |µ in the framework of QCD background field theory sum rule (BFTSR) up to 10 th order. Considering the fact that the sum rule of the 0 th moment ξ 0 2;π|µ cannot be normalized, we suggest a more reasonable sum rule formula for ξ n 2;π |µ. Then, we obtain the values of ξ n 2;π |µ 0 with n = (2, 4, 6, 8, 10) at the initial scale µ0 = 1 GeV. The first two moments are: ξ 2 2;π |µ 0 = 0.271 ± 0.013, ξ 4 2;π |µ 0 = 0.138 ± 0.010; and the corresponding Gegenbauer moments are a 2;π 2 (µ0) = 0.206 ± 0.038, a 2;π 4 (µ0) = 0.047 ± 0.011, respectively. After fitting the moments ξ n 2;π |µ, we obtained the appropriate model parameters by using the least square method. The resultant behavior for twist-2 pion DA is more closely to the AdS/QCD and lattice result, but is narrower than that by Dyson-Schwinger equation. Furthermore, we calculate the pion-photon transition form factors (TFF) and B → π TFF within light-cone sum rule approach, which are conform with experimental and theoretical results.

Pion to photon transition form factors with basis light-front quantization

“…For z 6 , the numerical values are compared with Refs. [39,42,50,87], with our predictions being close to the results evaluated from the QCD instanton vacuum [87]. The inverse moment of the pion DA in the BLFQ-NJL model is in good agreement with Refs.…”

The $D_s$-meson leading-twist distribution amplitude within the QCD sum rules and its application to the $B_s \to D_s$ transition form factor

“…For the gluon condensates, we take α s G 2 = 0.038 ± 0.011 GeV 4 and g 3 s f G 3 = 0.045 GeV 6 [56]. For the remaining vacuum condensates, we adopt ss = κ qq , g s sσT Gs = κ g s qσT Gq , and g s ss 2 = κ 2 g s qq 2 , where κ = 0.74 ± 0.03 [57], qq = −2.417 +0.227 −0.114 × 10 −2 GeV 2 , g s qσT Gq = −1.934 +0.188 −0.103 ×10 −2 GeV 5 and g s qq 2 = 2.082 +0.743 −0.697 × 10 −3 GeV 6 at µ = 2 GeV [50]. The scale evolution equations of those inputs are [50,58,59]…”

“…Following the standard procedures of QCD sum rules [50,51], we obtain the sum rules for the moments of D s -meson leading-twist LCDA, i.e.…”

$η^{(\prime)}$-meson twist-2 distribution amplitude within QCD sum rule approach and its application to the semi-leptonic decay $ D_s^+ \toη^{(\prime)}\ell^+ ν_\ell$

“…Recently, we suggested a new method that the 0th-order moment ξ 0 2;η | µ should be considered to the total results. The reason lies in the accuracy is often up to dimension-six condensates and NLO for the perturbative part instead of the infinite dimension or infinite-order perturbative parts [78]. The final expression for ξ n 2;η | µ can be written as:…”