Light-cone distribution amplitudes of axial-vector mesons

Abstract

We have presented a detailed study of twist-2 and twist-3 light-cone distribution amplitudes of 1 3 P 1 and 1 1 P 1 axial-vector mesons, based on QCD conformal partial wave expansion. Applying equations of motion, the twist-three two-parton light-cone distribution amplitudes can be expressed in terms of leading-twist and twist-three three-parton light-cone distribution amplitudes. The relevant G-parity invariant and violating parameters, containing the corrections due to the SU(3) breaking effects, are evaluated from the QCD sum rule method. The results for axial-vector decay constants of 1 3 P 1 states are presented. The values of tensor decay constants and Gegenbauer moments of the leading twist distribution amplitudes for 1 1 P 1 states are updated. Using Gell-Mann-Okubo mass formula, the mixing angle for the f 8 and f 1 of 1 3 P 1 states is θ3 P 1 ∼ 38 • , and that for h 8 and h 1 of 1 1 P 1 states is θ1 P 1 ∼ 10 • . The detailed properties for physical states f 1 (1285), f 1 (1420), h 1 (1170), and h 1 (1380) are given. Assuming the mixing angle between K 1A and K 1B to be θ K = 45 • or −45 • , we also give the detailed study for K 1 (1270) and K 1 (1400). Using the conformal partial wave expansion, we obtain the models for light-cone distribution amplitudes, containing contributions up to conformal spin 9/2. It is interesting to note that some distribution amplitudes have significant asymmetric behaviors, which should be phenomenologically attractive.

Erratum:B→K1γdecays in the light-cone QCD sum rules [Phys. Rev. D77, 094023 (2008)]

“…Following Ref. [27], we adopt the convention: f K 1A > 0, f ⊥ K 1B > 0 and ǫ 0123 = −1. Thus, the signs of theB →K 1A,B tensor form factors also depend on the definition mentioned above.…”

“…In terms of LCDAs, the leading twist LCDAs of theK 1B do not vanish, so thatB →K 1B tensor form factors are not zero. As a matter of fact, due to the G-parity, the leading-twist LCDA Φ K 1A ⊥ (Φ K 1B ) of theK 1A (K 1B ) meson defined by the nonlocal tensor current (nonlocal axialvector current) is antisymmetric under the exchange of quark and anti-quark momentum fractions in the SU(3) limit, whereas the Φ K 1A (Φ K 1B ⊥ ) is symmetric [27,28]. The above properties were not well-recognized in the previous light-cone (LC) sum rule calculation [7,29].…”

“…The correct forms of LCDAs for the axial-vector mesons have been studied in details in Ref. [27]. Using the LCDAs in Ref.…”

“…Using the LCDAs in Ref. [27], B → K 1 γ decays have recently been investigated in the perturbative QCD (PQCD) approach [30].…”

“…[27,28], we study the B → K 1 γ decays. We compute the relevantB →K 1A andK 1B tensor form factors in the LC sum rule approach.…”