Revisiting the pion leading-twist distribution amplitude within the QCD background field theory

Abstract

We study the pion leading-twist distribution amplitude (DA) within the framework of SVZ sum rules under the background field theory. To improve the accuracy of the sum rules, we expand both the quark propagator and the vertex (z · ↔ D)n of the correlator up to dimension-six operators in the background field theory. The sum rules for the pion DA moments are obtained, in which all condensates up to dimension-six have been taken into consideration. Using the sum rules, we obtain ξ 2 |1 GeV = 0.338 ± 0.032, ξ 4 |1 GeV = 0.211 ± 0.030 and ξ 6 |1 GeV = 0.163 ± 0.030. It is shown that the dimension-six condensates shall provide sizable contributions to the pion DA moments. We show that the first Gegenbauer moment of the pion leading-twist DA is a π 2 |1 GeV = 0.403 ± 0.093, which is consistent with those obtained in the literature within errors but prefers a larger central value as indicated by lattice QCD predictions.

Heavy pseudoscalar leading-twist distribution amplitudes within QCD theory in background fields

“…As a sequential work of Ref. [27], in this paper, we have made a detailed study on the HP leading-twist DAs together with the HP decay constants under the framework of BFT up to dimension-six condensates. Using the sum rules (9), we obtain f η c = 453 ± 4 MeV, f B c = 498 ± 14 MeV and f η b = 811 ± 34 MeV.…”

“…The formulas for relating these matrix elements with the conventional condensates under the D-dimensional space have been given in Appendix B of Ref. [27]. For simplicity, we do not present them here, and the interesting readers may turn to this reference for detailed technology.…”

“…n with full mass dependence up to dimension-six operators [27]. Thus we are facing the opportunity of deriving a more precise sum rule for the HP DA moments and a precise HP DA behavior.…”

“…The quantum fields interact with each other according to the Feynman rule of BFT [24][25][26], for example, the quantum quark-anti-quark pair can be contracted as a propagator, while the remaining background fields shall be kept to form the various vacuum matrix elements. Figure 1 shows the Feynman diagrams for determining the HP decay constant up to dimension-six operators, in which the newly derived quark propagator with up to dimension-six operators has been adopted [27]. In Fig.…”

“…From α s (m Z ) = 0.1184 ± 0.0007 with m Z = (91.1876 ± 0.0021) GeV [35], we predict QCD 270, 257, and 204 MeV for the flavor n f = 3, 4, and 5, respectively. We take the scale-independence dimension-four gluon condensate α s G 2 = (0.038 ± 0.011) GeV 4 [41] and g 3 s f G 3 = (0.013 ± 0.007) GeV 6 [27].…”