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Register a new userNew results on Pionic Twist-3 Distribution Amplitudes within the QCD Sum Rules
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We present an improved calculation on the pionic twist-3 distribution amplitudes $phi^{pi}_{p}$ and $phi^{pi}_{sigma}$, which are studied within the QCD sum rules. By adding all the uncertainties in quadrature, it is found that $<xi^2_p>=0.248^{+0.076}_{-0.052}$, $<xi^4_p>=0.262^{+0.080}_{-0.055}$, $<xi^2_sigma>=0.102^{+0.035}_{-0.025}$ and $<xi^4_sigma>=0.094^{+0.028}_{-0.020}$. Furthermore, with the help of these moments, we construct a model for the twist-3 wave functions $psi^{pi}_{p,sigma}(x,mathbf{k}_bot)$, which have better end-point behavior and are helpful for perturbative QCD approach. The obtained twist-3 distribution amplitudes are adopted to calculate the $Btopi$ transition form factor $f^+_{Bpi}$ within the QCD light-cone sum rules up to next-to-leading order. By suitable choice of the parameters, we obtain a consistent $f^+_{Bpi}$ with those obtained in the literature.
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We make a detailed study on the $D_s$ meson leading-twist LCDA $phi_{2;D_s}$ by using the QCD sum rules within the framework of the background field theory. To improve the precision, its moments $langle xi^nrangle _{2;D_s}$ are calculated up to dimension-six condensates. At the scale $mu = 2{rm GeV}$, we obtain: $langle xi^1rangle _{2;D_s}= -0.261^{+0.020}_{-0.020}$, $langle xi^2rangle _{2;D_s} = 0.184^{+0.012}_{-0.012}$, $langle xi^3rangle _{2;D_s} = -0.111 ^{+0.007}_{-0.012}$ and $langle xi^4rangle _{2;D_s} = 0.075^{+0.005}_{-0.005}$. Using those moments, the $phi_{2;D_s}$ is then constructed by using the light-cone harmonic oscillator model. As an application, we calculate the transition form factor $f^{B_sto D_s}_+(q^2)$ within the light-cone sum rules (LCSR) approach by using a right-handed chiral current, in which the terms involving $phi_{2;D_s}$ dominates the LCSR. It is noted that the extrapolated $f^{B_sto D_s}_+(q^2)$ agrees with the Lattice QCD prediction. After extrapolating the transition form factor to the physically allowable $q^2$-region, we calculate the branching ratio and the CKM matrix element, which give $mathcal{B}(bar B_s^0 to D_s^+ ell u_ell) = (2.03^{+0.35}_{-0.49}) times 10^{-2}$ and $|V_{cb}|=(40.00_{-4.08}^{+4.93})times 10^{-3}$.
The QCD sum rule method is formulated for the strangeness +1 pentaquark baryon with isospin I=0 and spin-parity J^P = 3/2^pm. The spin-3/2 states are considered to be narrower than the spin-1/2 ones, and thus may provide a natural explanation for the experimentally observed narrow width of Theta^+. In order to obtain reliable results in QCD sum rule calculations, we stress the importance of establishing a wide Borel window, where convergence of the operator product expansion and sufficient low-mass strength of the spectral function are guaranteed. To this end, we employ the difference of two independent correlators so that the high-energy continuum contribution is suppressed. The stability of the physical quantities against the Borel mass is confirmed within the Borel window. It is found that the sum rule gives positive evidence for the (I, J^P) = (0, 3/2^+) state with a mass of about 1.4 pm 0.2 GeV, while we cannot extract any evidence for the (0, 3/2^-) state.
The axial-vector $a_1(1260)$-meson longitudinal twist-2 distribution amplitude $phi_{2;a_1}^| (x,mu )$ within the framework of QCD sum rules under the background field theory is investigated. By considering the vacuum condensates up to dimension-six and the perturbative part up to next-to-leading order QCD corrections, the moments at initial scale $mu_0=1~{rm GeV}$ are $langle xi_{2;a_1}^{|;2}rangle |_{mu_0} = 0.210 pm 0.018$, $langle xi_{2;a_1}^{|;4}rangle |_{mu_0} = 0.091 pm 0.007$, and $langle xi_{2;a_1}^{|;6}rangle |_{mu_0} = 0.052 pm 0.004$ respectively. Secondly, the transition form factors (TFFs) for $Dto a_1(1260)$ under the light-cone sum rules are given. When taking squared momentum transfer to zero, we obtain $ A(0) = 0.130_{ - 0.015}^{ + 0.013}$, $V_1(0) = 1.899_{ - 0.127}^{ + 0.119}$, $V_2(0) = 0.211_{ - 0.020}^{ + 0.018}$, and $V_0(0) = 0.235_{ - 0.025}^{ + 0.026}$. With the extrapolated TFFs for the physically allowable region, the differential decay widths and total branching ratios for the processes $D^{0(+)} to a_1^{-(0)}(1260)ell^+ u_ell$ can be obtained, i.e. ${cal B}(D^0to a_1^-(1260) e^+ u_e) = (5.421_{-0.697}^{+0.702}) times 10^{-5}$, ${cal B}(D^+to a_1^0(1260) e^+ u_e) = (6.875_{-0.884}^{+0.890}) times 10^{-5}$, ${cal B}(D^0to a_1^-(1260) mu^+ u_mu)=(4.864_{-0.641}^{+0.647}) times 10^{-5}$, ${cal B}(D^+ to a_1^0(1260) mu^+ u_mu)=(6.169_{-0.821}^{+0.813}) times 10^{-5}$.
We study the $B to rho$ helicity form factors (HFFs) by applying the light-cone sum rules up to twist-4 accuracy. The HFF has some advantages in comparison to the conventionally calculated transition form factors, such as the HFF parameterization can be achieved via diagonalizable unitarity relations and etc. At the large recoil point, only the $rho$-meson longitudinal component contributes to the HFFs, and we have $mathcal{H}_{rho,0}(0)=0.435^{+0.055}_{-0.045}$ and $mathcal{H}_{rho,{1,2}}(0)equiv 0$. We extrapolate the HFFs to physically allowable $q^2$-region and apply them to the $B to rho$ semileptonic decay. We observe that the $rho$-meson longitudinal component dominates its differential decay width in low $q^2$-region, and its transverse component dominates the high $q^2$-region. Two ratios $R_{rm low}$ and $R_{rm high}$ are used to characterize those properties, and our LCSR calculation gives, $R_{rm low}=0.967^{+0.305}_{-0.284}$ and $R_{rm high}=0.219^{+0.058}_{-0.070}$, which agree with the BaBar measurements within errors.
In the past years there has been a revival of hadron spectroscopy. Many interesting new hadron states were discovered experimentally, some of which do not fit easily into the quark model. This situation motivated a vigorous theoretical activity. This is a rapidly evolving field with enormous amount of new experimental information. In the present report we include and discuss data which were released very recently. The present review is the first one written from the perspective of QCD sum rules (QCDSR), where we present the main steps of concrete calculations and compare the results with other approaches and with experimental data.
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