Leading-twist pion and kaon distribution amplitudes from the QCD instanton vacuum

Abstract

Twist-3 distribution amplitudes of the pion and kaon are studied in this paper. We calculate the fist several moments for the twist-3 distribution amplitudes (φ π p,σ and φ K p,σ) of the pion and kaon by applying the QCD sum rules. Our results show that, (i) the first three moments of φ K p and the first two moments of φ π p and φ π,K σ of the pion and kaon can be obtained with 30% uncertainty; (ii) the fourth moment of the φ π p and the second moment of the φ K σ can be obtained when the uncertainty are relaxed to 35%; (iii) the fourth moment of the φ π σ can be obtained only when the uncertainty are relaxed to 40%; (iv) we have m p 0π = 1.10 ± 0.08 GeV and m p 0K = 1.25 ± 0.15 GeV after including the α s-corrections to the perturbative part. These moments will be helpful for constructing the twist-3 wave functions of the pion and kaon.

Two-particle twist-3 distribution amplitudes of the pion and kaon in the light-front quark model

“…For the kaon case, the odd moments are nonzero due to the flavor SU(3) symmetry breaking effects. We again note that the sign of Gegenbauer and ξ moments are the same between our LFQM and χQM [17] predictions but different from QCDSR [9] and DSE [22] predictions.…”

“…We also should note for the same reason that our LFQM results are in good agreement with DSE results in the chiral-symmetry limit of φ σ 3;π (x). In Table III, we list the calculated Gegenbauer-and ξ-moments of the pseudotensor twist-3 kaon φ σ 3;K (x) obtained from the Gaussian wave function with linear and HO potential models and PL wave function and compare them with other model estimates [9,17,22]. For the kaon case, the odd moments are nonzero due to the flavor SU(3) symmetry breaking effects.…”

“…The twist-3 pseudoscalar DA φ P 3;M (x) and pseudotensor DA φ σ 3;M (x) are usually expanded in terms of the Gegenbauer polynomials C 1/2 n and C 3/2 n , respectively, as follows [17]:…”

“…In particular, the shape of the pion DA has been extensively discussed due to the nature of the pion as the massless Nambu-Goldstone boson [5,6]. Finding the fundamental nonperturbative information of QCD motivated many theoretical studies to calculate meson DAs using nonperturbative methods such as the QCD sum rule [3,[7][8][9][10][11][12][13][14][15], the chiral-quark model from the instanton vacuum [16][17][18], the Nambu-JonaLasinio (NJL) model [19,20], the Dyson-Schwinger equation (DSE) approach [21,22], and the light-front quark model (LFQM) [23,24]. Among them, the LFQM appears to be one of the most effective and efficient tools in studying hadron physics as it takes advantage of the distinguished features of the light-front dynamics (LFD) [25].…”

Quark–gluon mixed condensate for the SU(2) light-flavor sector at finite temperature

“…This value is well consistent with those from the chiral quark and instanton models in Refs. [8,26]: k 2 T π ≈= (0.20 ∼ 0.23) GeV 2 . All the numerical results for QC, MC, and m 2 0 are summarized for some different T values in Table I.…”