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Register a new userRevisiting the production of $J/psi+eta_c$ via the $e^+e^-$ annihilation within the QCD light-cone sum rules
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We make a detailed study on the typical production channel of double charmoniums, $e^+e^-to J/psi+eta_c$, at the center-of-mass collision energy $sqrt{s}=10.58$ GeV. The key component of the process is the form factor $F_{rm VP}(q^2)$, which has been calculated within the QCD light-cone sum rules (LCSR). To improve the accuracy of the derived LCSR, we keep the $J/psi$ light-cone distribution amplitude up to twist-4 accuracy. Total cross sections for $e^+e^-to J/psi+eta_c$ at three typical factorization scales are $sigma|_{mu_s} = 22.53^{+3.46}_{-3.49}~{rm fb}$, $sigma|_{mu_k} = 21.98^{+3.35}_{-3.38}~{rm fb}$ and $sigma|_{mu_0} = 21.74^{+3.29}_{-3.33}~{rm fb}$, respectively. The factorization scale dependence is small, and those predictions are consistent with the BABAR and Belle measurements within errors.
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Predictions for $e^+e^-to J/psi eta_c$ from previous studies are made by taking charmonia as a nonrelativistic bound state and by using nonrelativistic QCD(NRQCD) approach. The predicted cross-section is smaller by an order of magnitude than the experimentally observed. We study the process by taking charm quark as a light quark and use light-cone wave-functions to parameterize nonperturbative effects related to charmonia. The total cross section of $e^+e^-to J/psi eta_c$ can be predicted, if these wave-functions are known. Motivated by studies of light-cone wave-functions of light hadrons, we make a reasonable assumption of the forms of light-cone wave-functions. With these light-cone wave-functions we can obtain the cross section which is more closer to the experimentally observed than that from NRQCD approach. We also discuss in detail the difference between two approaches.
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.
Using the method of QCD light-cone sum rules, we calculate the $B to pipi$ hadronic matrix elements with annihilation topology. We obtain a finite result, including the related strong phase. Numerically, the annihilation effects in $Bto pipi$ turn out to be small with respect to the factorizable emission mechanism. Our predictions, together with the earlier sum rule estimates of emission and penguin contributions, are used for the phenomenological analysis of $Bto pipi$ channels. We predict a $Delta I=1/2$ transition amplitude which significantly differs from this amplitude extracted from the current data.
By including the interference effect between the QCD and the QED diagrams, we carry out a complete analysis on the exclusive productions of $e^+e^- to J/psi+chi_{cJ}$ ($J=0,1,2$) at the $B$ factories with $sqrt{s}=10.6$ GeV at the next-to-leading-order (NLO) level in $alpha_s$, within the nonrelativistic QCD framework. It is found that the $mathcal O (alpha^3alpha_s)$-order terms that represent the tree-level interference are comparable with the usual NLO QCD corrections, especially for the $chi_{c1}$ and $chi_{c2}$ cases. To explore the effect of the higher-order terms, namely $mathcal O (alpha^3alpha_s^2)$, we perform the QCD corrections to these $mathcal O (alpha^3alpha_s)$-order terms for the first time, which are found to be able to significantly influence the $mathcal O (alpha^3alpha_s)$-order results. In particular, in the case of $chi_{c1}$ and $chi_{c2}$, the newly calculated $mathcal O (alpha^3alpha_s^2)$-order terms can to a large extent counteract the $mathcal O (alpha^3alpha_s)$ contributions, evidently indicating the indispensability of the corrections. In addition, we find that, as the collision energy rises, the percentage of the interference effect in the total cross section will increase rapidly, especially for the $chi_{c1}$ case.
We investigate the theoretical predictions for thrust distribution in the electron positron annihilation to three-jets process at NNLO for different values of the number of flavors, $N_f$. To determine the distribution along the entire renormalization group flow from the highest energies to zero energy we consider the number of flavors near the upper boundary of the conformal window. In this regime of number of flavors the theory develops a perturbative infrared interacting fixed point. We then consider also the QED thrust obtained as the limit $N_c rightarrow 0$ of the number of colors. In this case the low energy limit is governed by an infrared free theory. Using these quantum field theories limits as theoretical laboratories we arrive at an interesting comparison between the Conventional Scale Setting - (CSS) and the Principle of Maximum Conformality (PMC$_infty$) methods. We show that within the perturbative regime of the conformal window the two methods yield similar results while reducing the number of flavors towards the active number of flavors in the Standard Model the PMC$_infty$ method is the natural extension of the curves within the conformal window and best fits the data.
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