We perform the first global QCD analysis of parton distribution functions (PDFs) in the pion, combining πA Drell-Yan data with leading neutron electroproduction from HERA within a Monte Carlo approach based on nested sampling. Inclusion of the HERA data allows the pion PDFs to be determined down to much lower values of x, with relatively weak model dependence from uncertainties in the chiral splitting function. The combined analysis reveals that gluons carry a significantly higher pion momentum fraction, ∼ 30%, than that inferred from Drell-Yan data alone, with sea quarks carrying a somewhat smaller fraction, ∼ 15%, at the input scale. Within the same effective theory framework, the chiral splitting function and pion PDFs can be used to describe thē d −ū asymmetry in the proton.

We use the BLM method to fix the renormalization scale of the QCD coupling in exclusive hadronic amplitudes such as the pion form factor and the photon-to-pion transition form factor at large momentum transfer. Renormalization-scheme-independent commensurate scale relations are established which connect the hard scattering subprocess amplitudes that control exclusive processes to other QCD observables such as the heavy quark potential and the electron-positron annihilation cross section. The commensurate scale relation connecting the heavy quark potential, as determined from lattice gauge theory, to the photon-to-pion transition form factor is in excellent agreement with γe → π 0 e data assuming that the pion distribution amplitude is close to its asymptotic form √ 3f π x(1 − x). We also reproduce the scaling and normalization of the γγ → π + π − data at large momentum transfer. Because the renormalization scale is small, we argue that the effective coupling is nearly constant, thus accounting for the nominal scaling behavior of the data. However, the normalization of the space-like pion form factor F π (Q 2 ) obtained from electroproduction experiments is somewhat higher than that predicted by the corresponding commensurate scale relation. This discrepancy may be due to systematic errors introduced by the extrapolation of the γ

We present a calculation of the quark distribution amplitudes(DAs), the Gegenbauer moments, and decay constants for π, ρ, K and K * mesons using the light-front quark model. While the quark DA for π is somewhat broader than the asymptotic one, that for ρ meson is very close to the asymptotic one. The quark DAs for K and K * show asymmetric form due to the flavor SU(3)symmetry breaking effect. The decay constants for the transversely polarized ρ and K * mesons(f T ρ and f T K * ) as well as the longitudinally polarized ones(fρ and fK * ) are also obtained. Our averaged values for f T V /fV , i.e. (f T ρ /fρ)av = 0.78 and (f T K * /fK * )av = 0.84, are found to be consistent with other model predictions. Especially, our results for the decay constants are in a good agreement with the SU(6) symmetry relation, f T ρ(K * ) = (f π(K) + f ρ(K * ) )/2.

We investigate the exclusive semileptonic Bc → (D, ηc, B, Bs)ℓν ℓ , η b → Bcℓν ℓ (ℓ = e, µ, τ ) decays using the light-front quark model constrained by the variational principle for the QCD motivated effective Hamiltonian. The form factors f+(q 2 ) and f−(q 2 ) are obtained from the analytic continuation method in the q + = 0 frame. While the form factor f+(q 2 ) is free from the zero-mode, the form factor f−(q 2 ) is not free from the zero-mode in the q + = 0 frame. We quantify the zero-mode contributions to f−(q 2 ) for various semileptonic Bc decays. Using our effective method to relate the non-wave function vertex to the light-front valence wave function, we incorporate the zero-mode contribution as a convolution of zero-mode operator with the initial and final state wave functions. Our results are then compared to the available experimental data and the results from other theoretical approaches. Since the prediction on the magnetic dipole B * c → Bc + γ decay turns out to be very sensitive to the mass difference between B * c and Bc mesons, the decay width Γ(B * c → Bcγ) may help in determining the mass of B * c experimentally. Furthermore, we compare the results from the harmonic oscillator potential and the linear potential and identify the decay processes that are sensitive to the choice of confining potential. From the future experimental data on these sensitive processes, one may obtain more realistic information on the potential between quark and antiquark in the heavy meson system.

We present the analysis of exclusive 0 − →0 − semileptonic heavy meson decays using the constituent quark model based on the light-front quantization. Our model is constrained by the variational principle for the well-known linear plus Coulomb interaction motivated by QCD. Our method of analytic continuation to obtain the weak form factors avoids the difficulty associated with the contribution from the nonvalence quark-antiquark pair creation. Our numerical results for the heavy-to-heavy and heavy-to-light meson decays are in a good agreement with the available experimental data and the lattice QCD results. In addition, our model predicts the two unmeasured mass spectra of 1 S 0 (bb) and 3 S 1 (bs) systems as M bb =9657 MeV and M bs = 5424 MeV.