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Using the soft pion theorem, crossing, and the dispersion relations for the two pion distribution amplitude ($2pi$DA) we argue that the second Gegenbauer moment the $rho$-meson DA ($a_2^{(rho)}$) most probably is negative. This result is at variance with the majority of the model calculations for $a_2^{(rho)}$. Using the instanton theory of the QCD vacuum, we computed $a_2^{(rho)}$ at a low normalisation point and obtain for the ratio $ a_2^{(rho)}/M_3^{(pi)}$ {it definitely negative value} in the range of $a_2^{(rho)}/M_3^{(pi)}in [-2, -1]$. The range of values corresponds to a generous variation of the parameters of the instanton vacuum. The value of the second Gegenbauer moment of pion DA is positive in the whole range and is compatible with its the most advanced lattice measurement. It seems that the topologically non-trivial field configurations in the QCD vacuum (instantons) lead to qualitatively different shapes of the pion and the $rho$-meson DAs.
A new method for the model-independent determination of the light-cone distribution amplitude (LCDA) of the $B$-meson in heavy quark effective theory (HQET) is proposed by combining the large momentum effective theory (LaMET) and the numerical simula
The pion distribution amplitude (DA) can be related to the fundamental QCD Greens functions as a function of the quark self-energy and the quark-pion vertex, which in turn are associated with the pion wave function through the Bethe-Salpeter equation
We present preliminary results for the second moment of the pions distribution amplitude. The lattice formulation and the phenomenological implications are briefly reviewed, with special emphasis on some subtleties that arise when the Lorentz group i
Using the second moment of the pion distribution amplitude as an example, we investigate whether lattice calculations of matrix elements of local operators involving covariant derivatives may benefit from the recently proposed momentum smearing techn
We present the results of a lattice study of the second moment of the light-cone pion distribution amplitude using two flavors of dynamical (clover) fermions on lattices of different volumes and pion masses down to $m_pisim 150 , mathrm {MeV}$. At la