Revisiting the Pion Leading-Twist Distribution Amplitude within the QCD Background Field Theory

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\cdot \tensor{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 \left|_{\rm 1\;GeV} = 0.338 \pm 0.032, \left|_{\rm 1\;GeV} = 0.211 \pm 0.030 and \left|_{\rm 1\;GeV} = 0.163 \pm 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 $a^\pi_2|_{\rm 1\;GeV} = 0.403 \pm 0.093$, which is consistent with those obtained in the literature within errors but prefers a larger central value as indicated by lattice QCD predictions.Comment: 13 pages, 7 figure

Transitions between the quantum Hall states and insulators induced by periodic potentials

Journal ArticleTransitions between two quantum Hall states or between a quantum Hall state and a Mott insulator induced by periodic potentials are studied in the 1 /TV expansion. The transitions are found to be continuous in the large-TV limit and are described by a critical point that depends on a real parameter 0, which is determined by the topological orders in the quantum Hall states involved in the transition. Some critical exponents and universal quantities are calculated in the large-TV limit and shown to be 0 dependent

VcbV_{cb} from the semileptonic decay B→DℓνˉℓB\to D \ell \bar{\nu}_{\ell} and the properties of the DD meson distribution amplitude

The improved QCD light-cone sum rule (LCSR) provides an effective way to deal with the heavy-to-light transition form factors (TFFs). Firstly, we adopt the improved LCSR approach to deal with the $B\to D$ TFF $f^{+}(q^2)$ up to twist-4 accuracy. Due to the elimination of the most uncertain twist-3 contribution and the large suppression of the twist-4 contribution, the obtained LCSR shall provide us a good platform for testing the $D$-meson leading-twist DA. For the purpose, we suggest a new model for the $D$-meson leading-twist DA ($\phi_{3D}$), whose longitudinal behavior is dominantly determined by a parameter $B$. Moreover, we find its second Gegenbauer moment $a^D_2\sim B$. Varying $B$ within certain region, one can conveniently mimic the $D$-meson DA behavior suggested in the literature. Inversely, by comparing the estimations with the experimental data on the $D$-meson involved processes, one can get a possible range for the parameter $B$ and a determined behavior for the $D$-meson DA. Secondly, we discuss the $B\to D$ TFF at the maximum recoil region and present a detailed comparison of it with the pQCD estimation and the experimental measurements. Thirdly, by applying the LCSR on $f^{+}(q^2)$, we study the CKM matrix element \Vcb together with its uncertainties by adopting two types of processes, i.e. the $B^0/\bar{B}^0$-type and the $B^{\pm}$-type. It is noted that a smaller $B \precsim 0.20$ shows a better agreement with the experimental value on \Vcb. For example, for the case of $B=0.00$, we obtain $|V_{cb}|(B^0/\bar{B}^0-{\rm type})=(41.28 {^{+5.68}_{-4.82}} {^{+1.13}_{-1.16}}) \times 10^{-3}$ and $|V_{cb}|(B^{\pm}-{\rm type})=(40.44 {^{+5.56}_{-4.72}} {^{+0.98}_{-1.00}}) \times 10^{-3}$, whose first (second) uncertainty comes from the squared average of the mentioned theoretical (experimental) uncertainties.Comment: 13 pages, 10 figures. Reference updated and discussion improved. To be published in Nucl.Phys.

Twist-3 light-cone distribution amplitudes of the scalar mesons within the QCD sum rules and their application to the B→SB \to S transition form factors

We investigate the twist-3 light-cone distribution amplitudes (LCDAs) of the scalar mesons $a_0$, $K^{\ast}_0$ and $f_0$ within the QCD sum rules. The QCD sum rules are improved by a consistent treatment of the sizable $s$-quark mass effects within the framework of the background field approach. Adopting the valence quark component $(\bar{q}_1 q_2)$ as the dominant structure of the scalar mesons, our estimation for their masses are close to the measured $a_0(1450)$, $K^{\ast}_0(1430)$ and $f_0(1710)$. From the sum rules, we obtain the first two non-zero moments of the twist-3 LCDAs $\phi^{s,\sigma}_{a_0}$: $\langle \xi_{s,a_0}^{2(4)} \rangle=0.369 \;(0.245)$ and $\langle \xi_{\sigma,a_0}^{2(4)} \rangle=0.203 \;(0.093)$; those of the twist-3 LCDAs $\phi_{K^*_0}^{s,\sigma}$: $\langle \xi_{s,K^{\ast}_0}^{1(2)} \rangle =0.004\;(0.355)$ and $\langle \xi_{\sigma,K^{\ast}_0}^{1(2)} \rangle =0.018\;(0.207)$; and those of the twist-3 LCDAs $\phi_{f_0}^{s,\sigma}$: $\langle \xi_{s,f_0}^{2(4)} \rangle=0.335 \;(0.212)$ and $\langle \xi_{\sigma,f_0}^{2(4)} \rangle=0.196 \; (0.088)$, respectively. As an application of those twist-3 LCDAs, we study the $B \to S$ transition form factors by introducing proper chiral currents into the correlator, which is constructed such that the twist-3 LCDAs give dominant contribution and the twist-2 LCDAs make negligible contribution. Our results of the $B \to S$ transition form factors at the large recoil region $q^2 \simeq 0$ are consistent with those obtained in the literature, which inversely shows the present twist-3 LCDAs are acceptable.Comment: 14 pages, 12 figures, 7 table

The ρ\rho-meson longitudinal leading-twist distribution amplitude

In the present paper, we suggest a convenient model for the vector $\rho$-meson longitudinal leading-twist distribution amplitude $\phi_{2;\rho}^\|$, whose distribution is controlled by a single parameter $B^\|_{2;\rho}$. By choosing proper chiral current in the correlator, we obtain new light-cone sum rules (LCSR) for the $B\to\rho$ TFFs $A_1$, $A_2$ and $V$, in which the $\delta^1$-order $\phi_{2;\rho}^\|$ provides dominant contributions. Then we make a detailed discussion on the $\phi_{2;\rho}^\|$ properties via those $B\to\rho$ TFFs. A proper choice of $B^\|_{2;\rho}$ can make all the TFFs agree with the lattice QCD predictions. A prediction of $|V_{\rm ub}|$ has also been presented by using the extrapolated TFFs, which indicates that a larger $B^{\|}_{2;\rho}$ leads to a larger $|V_{\rm ub}|$. To compare with the BABAR data on $|V_{\rm ub}|$, the longitudinal leading-twist DA $\phi_{2;\rho}^\|$ prefers a doubly-humped behavior.Comment: 7 pages, 3 figures. Discussions improved and references updated. To be published in Phys.Lett.