Study The Distribution Amplitude Of Pion Leading-twist Under The QCD Sum Rules

A first half of this paper introduces three models of pion distribution amplitude.The calculation of the pion distribution amplitude use the large momentum effective field theory(LaMET)Lattice-QCD approach,which allows us to extract lightcone parton from a Euclidean lattice.The mass corrections needed to extract the pion distribution amplitude from this approach are calculated to all orders.We also show the Wilsonline renormalization which is crucial to remove the power divergences in this approach,and find that it reduces the oscillation at the end points of the distribution amplitude.Our exploratory result shows that the asymptotic form of the pion distribution amplitude favors a single-hump form at 310-MeV.At the same time,the pion distribution amplitudes under the NJL model are introduced.the Pauli-Villars regularization method is used to make the distribution amplitudes satisfy the proper normalization and crossing properties.Recovered the good endpoint behavior of the pion distribution and achieved satisfactory agreement with the analysis of CLEO experimental data.Last,the QCD sum rules with nonlocal condensation are introduced to more accurately recalculate the moments and their confidence intervals of pion distribution amplitudes,including radiation correction.Thus,we are able to construct a set of allowable pion distribution amplitudes to define a reliability region on the a2,a4 plane of the expansion coefficients of the Gegenbauer polynomial.we emphasize that models like CZ,as well as asymptotic forms,are excluded from this group.It shows that the identified a2,a4 region strongly overlaps with those extracted from CLEO.The purpose of the paper that we use SVZ sum rules to study the pion leading-twist distribution amplitude(DA),and we take the background field as a framework.We develop quark propagator and vertex operator up dimension-six to receive new sum rule of the leading-twist DA moments within Quantum Chromodynamics(QCD)in the background field.By calculating,one can get the first two moments of the leading-twist DA when energy scale ?=1GeV,the second moment<?2=0.314±0.035,the fourth moment...