A guide to the QCD light-cone sum rule for bb-quark decays

We overview the current status and future perspectives of the QCD-based method of light-cone sum rules. The two main versions of these sum rules, using light-meson and $B$-meson distribution amplitudes are introduced and the most important applications of the method are discussed. We also outline open problems and future perspectives of this method.Comment: Invited review for EPJST, 48 pages, 8 table

Λb→p,Λ\Lambda_b \to p, \Lambda transition form factors from QCD light-cone sum rules

Light-cone sum rules for the $\Lambda_b \to p, \Lambda$ transition form factors are derived from the correlation functions expanded by the twist of the distribution amplitudes of $\Lambda_b$ baryon. In terms of the $\Lambda_b$ three-quark distribution amplitudes models constrained by the QCD theory, we calculate the form factors at small momentum transfers and compare the results with that estimated in the conventional light-cone sum rules (LCSR) and perturbative QCD approaches. Our results indicate that the two different version of sum rules can lead to the consistent numbers of form factors responsible for $\Lambda_b \to p$ transition. The $\Lambda_b \to \Lambda$ transition form factors from LCSR with the asymptotic $\Lambda$ baryon distribution amplitudes are found to be almost one order larger than that obtained in the $\Lambda_b$-baryon LCSR, implying that the pre-asymptotic corrections to the baryonic distribution amplitudes are of great importance. Moreover, SU(3) symmetry breaking effect between the form factors $f_1^{\Lambda_b \to p}$ and $f_1^{\Lambda_b \to \Lambda}$ are computed as $28^{+14}_{-8}$ in the framework of $\Lambda_b$-baryon LCSR.Comment: 18 pages, 5 figure

Weak productions of new charmonium in semi-leptonic decays of B_c

We study the weak productions of novel heavy mesons, such as $\eta_c^{\prime}$, $h_c$, $h_c^{\prime}$, $\chi_{c0}^{\prime}$, X(3940), Y(3940), X(3872), and Y(4260), in the semi-leptonic $B_c$ decays. Since there is still no definite answer for the components of X(3940), Y(3940), X(3872), Y(4260) so far, we will assign them as excited charmonium states with the possible quantum numbers constrained by the current experiments. As for the weak transition form factors, we calculate them in the framework of light-cone QCD sum rules approach, which is proved to be a powerful tool to deal with the non-perturbative hadronic matrix element. Our results indicate that different interpretations of X(3940) can result in remarkable discrepancy of the production rate in the $B_c$ decays, which would help to clarify the inner structure of the X(3940) with the forthcoming LHC-b experiments. Besides, the predicted large weak production rates of X(3872) and Y(3940) in $B_c$ decays and the small semi-leptonic decay rate for $B_c \to Y(4260)$ all depend on their quantum number $J^{PC}$ assignments. Moreover, the $S-D$ mixing of various vector charmonium states in the weak decay of $B_c$ is also discussed in this work. The future experimental measurements of these decays will test the inner structures of these particles, according to our predictions here.Comment: 26 pages, with 7 figures, revTex

Twist-3 distribution amplitudes of scalar mesons from QCD sum rules

We study the twist-3 distribution amplitudes for scalar mesons made up of two valence quarks based on QCD sum rules. By choosing the proper correlation functions, we derive the moments of the scalar mesons up to the first two order. Making use of these moments, we then calculate the first two Gegenbauer coefficients for twist-3 distribution amplitudes of scalar mesons. It is found that the second Gegenbauer coefficients of scalar density twist-3 distribution amplitudes for $K^{*}_0$ and $f_0$ mesons are quite close to that for $a_0$, which indicates that the SU(3) symmetry breaking effect is tiny here. However, this effect could not be neglected for the forth Gegenbauer coefficients of scalar twist-3 distribution amplitudes between $a_0$ and $f_0$. Besides, we also observe that the first two Gegenbauer coefficients corresponding to the tensor current twist-3 distribution amplitudes for all the $a_0$, $K^{*}_0$ and $f_0$ are very small. The renormalization group evolution of condensates, quark masses, decay constants and moments are considered in our calculations. As a byproduct, it is found that the masses for isospin I=1, ${1 \over 2}$ scalar mesons are around $1.27 \sim 1.41$ GeV and $1.44 \sim 1.56$ GeV respectively, while the mass for isospin state composed of $\bar{s} s$ is $1.62 \sim 1.73$ GeV.Comment: replaced with revised version, to be published in Phys. Rev.

Exploring Final State Hadron Structure and SU(3) Flavor Symmetry Breaking Effects in D->PP and D->PV Decays

The nonleptonic two body decays $D\to PP$ and $D\to PV$ are investigated based on the diagrammatic decomposition in a generalized factorization formalism. It is shown that to fit the experimental data, the SU(3) flavor symmetry breaking effects of the coefficients $a_i$s should be considered in $D\to PP$ decay modes. In $D\to PV$ decays, the final state hadron structure due to the pseudoscalar and vector mesons has more important effects on the coefficients $a_i$s than the SU(3) symmetry breaking effects. It is found that the nonfactorizable contributions as well as that of the exchange and annihilation diagrams are significant in these decays.Comment: 20 pages, 6 tables, to appear in Eur.Phys.J.

Three-parton contribution to the B→πB\to\pi form factors in kTk_T factorization

We calculate the three-parton twist-3 contribution to the $B\to\pi$ transition form factors in the $k_T$ factorization theorem. Since different mesons are involved in the initial and final states, two(three)-parton-to-three(two)-parton amplitudes do not vanish. It is found that the dominant contribution arises from the diagrams with the additional valence gluon attaching to the leading-order hard gluon. Employing the three-parton meson distribution amplitudes from QCD sum rules, we show that this subleading piece amounts only up to few percents of the form factors at large recoil of the pion. The framework for analyzing three-parton contributions to $B$ meson decays in the $k_T$ factorization is established.Comment: 8 pages, 3 figure