Right now, we have not enough knowledge to determine the hadron distribution amplitudes (DAs) which are universal physical quantities in the high energy processes involving hadron for applying pQCD to exclusive processes. Even for the simplest pion, one can't discriminate from different DA models. Inversely, one expects that processes involving pion can in principle provide strong constraints on the pion DA. For example, the pion-photon transition form factor (TFF) can get accurate information of the pion wave function or DA, due to the single pion in this process. However, the data from Belle and BABAR have a big difference on TFF in high $Q^2$ regions, at present, they are helpless for determining the pion DA. At the present paper, we think it is still possible to determine the pion DA as long as we perform a combined analysis of the most existing data of the processes involving pion such as $\pi \to \mu \bar{\nu}$, $\pi^0 \to \gamma \gamma$, $B\to \pi l \nu$, $D \to \pi l \nu$, and etc. Based on the revised light-cone harmonic oscillator model, a convenient DA model has been suggested, whose parameter $B$ which dominates its longitudinal behavior for $\phi_{\pi}(x,\mu^2)$ can be determined in a definite range by those processes. A light-cone sum rule analysis of the semi-leptonic processes $B \to \pi l \nu$ and $D \to \pi l \nu$ leads to a narrow region $B = [0.01,0.14]$, which indicate a slight deviation from the asymptotic DA. Then, one can predict the behavior of the pion-photon TFF in high $Q^2$ regions which can be tested in the future experiments. Following this way it provides the possibility that the pion DA will be determined by the global fit finally.Comment: 9 pages, 6 figure

We investigate the hadronic production of the doubly heavy baryon Ξ bc at the large hadron collider (LHC), where contributions from the four (bc)-diquark states (bc)3 ,6 [ 1 S0] and (bc)3 ,6 [ 3 S1] have been taken into consideration. Numerical results show that under the condition of pT > 4 GeV and |y| < 1.5, sizable Ξ bc events about 1.7 × 10 7 and 3.5 × 10 9 per year can be produced for the center-of-mass energy √ S = 7 TeV and √ S = 14 TeV respectively. For experimental usage, the total and the interested differential cross-sections are estimated under some typical pT -and y-cuts for the LHC detectors CMS, ATLAS and LHCb. Main uncertainties are discussed and a comparative study on the hadronic production of Ξcc, Ξ bc and Ξ bb at LHC are also presented.

The pion-photon transition form factor (TFF) provides strong constraints on the pion distribution amplitude (DA). We perform an analysis of all existing data (CELLO, CLEO, BaBar, Belle) on the pion-photon TFF by means of light-cone pQCD approach in which we include the next-to-leading order correction to the valence-quark contribution and estimate the non-valence-quark contribution by a phenomenological model based on the TFF's limiting behavior at both Q 2 → 0 and Q 2 → ∞. At present, the pion DA is not definitely determined, it is helpful to have a pion DA model that can mimic all the suggested behaviors, especially to agree with the constraints from the pion-photon TFF in whole measured region within a consistent way. For the purpose, we adopt the conventional model for pion wavefunction/DA that has been constructed in our previous paper [14], whose broadness is controlled by a parameter B. We fix the DA parameters by using the CELLO, CLEO, BABAR and Belle data within the smaller Q 2 region (Q 2 ≤ 15 GeV 2 ), where all the data are consistent with each other. And then the pion-photon TFF is extrapolated into larger Q 2 region. We observe that the BABAR favors B = 0.60 which has the behavior close to the Chernyak-Zhitnitsky DA, whereas the recent Belle favors B = 0.00 which is close to the asymptotic DA. We need more accurate data at large Q 2 region to determine the precise value of B, and the definite behavior of pion DA can be concluded finally by the consistent data in the coming future. The pion-photon transition form factor (TFF), F πγ (Q 2 ), which relates two photons with one lightest meson, provides a good platform to study the property of pion distribution amplitude (DA). Because higher helicity and higher twist structures give negligible contributions to the pion-photon TFF [1, 2], one can extract useful information on the shape of the leading-twist pion DA by comparing the estimated result of F πγ (Q 2 ) with the measured one.Experimentally, the pion-photon TFF is determined by measuring the process e + e − → e + e − π 0 in the singletag mode, where one of the outing electron (tagged) is detected while the other electron (untagged) is scattered at a small angle. The tagged electron emits a highly offshell photon with momentum transfer Q 2 and the momentum transfer to the untagged electron is near zero. The pion-photon TFF has first been measured by the CELLO collaboration with Q 2 < 3 GeV Instead of a pronounced growth of the TFF at high Q 2 region, observed by BABAR, the Belle data are compatible with the well-known asymptotic prediction [7], i.e. Q 2 F πγ (Q 2 ) tends to be a constant (2f π ) for asymptotic DA φ as π (x, Q 2 )| Q 2 →∞ = 6x(1 − x). Here the pion decay constant f π = 92.4 ± 0.25 MeV [8].At present, there is still no definite conclusion on whether pion DA is in asymptotic-like form [7] or in Chernyak-Zhitnitsky (CZ)-like form [9], or in a flat-like form [10]. It would be helpful to have a consistent pion DA model that can mimic all these behaviors and can explain the pion-photon TFF...

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.