Search

A key issue in making precise predictions in QCD is the uncertainty in setting the renormalization scale $\mu_R$ and thus determining the correct values of the QCD running coupling $\alpha_s(\mu_R^2)$ at each order in the perturbative expansion of a QCD observable. It has often been conventional to simply set the renormalization scale to the typical scale of the process $Q$ and vary it in the range $\mu_R \in [Q/2,2Q]$ in order to estimate the theoretical error. This is the practice of Conventional Scale Setting (CSS). The resulting CSS prediction will however depend on the theorist's choice of renormalization scheme and the resulting pQCD series will diverge factorially. It will also disagree with renormalization scale setting used in QED and electroweak theory thus precluding grand unification. A solution to the renormalization scale-setting problem is offered by the Principle of Maximum Conformality (PMC), which provides a systematic way to eliminate the renormalization scale-and-scheme dependence in perturbative calculations. The PMC method has rigorous theoretical foundations, it satisfies Renormalization Group Invariance (RGI) and preserves all self-consistency conditions derived from the renormalization group. The PMC cancels the renormalon growth, reduces to the Gell-Mann--Low scheme in the $N_C\to 0$ Abelian limit and leads to scale- and scheme-invariant results. The PMC has now been successfully applied to many high-energy processes. In this article we summarize recent developments and results in solving the renormalization scale and scheme ambiguities in perturbative QCD. [full abstract is in the paper]., Comment: 79 pages ; 21 figures; Review article submitted to Prog. Part. Nucl. Phys

In this paper, we study the properties of the pion-photon transition form factor (TFF), $\gamma\gamma^{\ast} \rightarrow \pi^{0}$, by using the principle of maximum commonality (PMC) to deal with its perturbative QCD contribution up to next-to-next-to-leading order (NNLO) QCD corrections. Applying the PMC, we achieve precise pQCD approximant for the TFF in large $Q^2$-region without conventional renormalization scale ambiguity. We also discuss the power suppressed non-valence quark contribution to the TFF, which is important for a sound prediction in low and intermediate $Q^2$-region, e.g. the non-valence quark components affect the TFF by about $1\%$ to $23\%$ when $Q^{2}$ changes down from $40~{\rm GeV^{2}}$ to $4~{\rm GeV^{2}}$. The resultant pion-photon TFF shows a better agreement with previous Belle data. It is hoped that previous discrepancies between the experimental measurements and theoretical predictions could be clarified by the forth-coming precise data on the Belle II measurements., Comment: 7 pages, 6 figures

We introduce four supersymmetric (SUSY) axion models in which the strong CP problem and the $\mu$ problem are solved with the help of the Peccei-Quinn mechanism and the Kim-Nilles mechanism, respectively. The axion physics enriches the SUSY model by introducing axion as a dark matter candidate and, therefore, the lightest supersymmetric particle (LSP) could just be a part of the total dark matter. For this reason, axion relieves the tensions between SUSY models and numerous experimental measurements, such as the dark matter direct detection experiments and the precise measurements of anomalous magnetic moment of the muon $a_\mu$. In the present paper, we investigate the constraints imposed by the latest $a_\mu$ measurements and LUX-ZEPLIN (LZ) experiment on the relic density of the Higgsino-like LSP. Additionally, we consider the constraints arising from the cosmology of saxions and sxinos, and their impacts on the parameter space of our models are carefully examined. For the axion constituting the remaining portion of dark matter, we find that the conventional misalignment mechanism can successfully account for the correct dark matter relic density observed by the Planck satellite.

The $η^{(\prime)}$-mesons in the quark-flavor basis are mixtures of two mesonic states $|η_{q}\rangle=|\bar u u+\bar d d\rangle/\sqrt 2$ and $|η_{s}\rangle=|\bar s s\rangle$. In the previous work, we have made a detailed study on the $η_{s}$ leading-twist distribution amplitude. As a sequential work, in the present paper, we fix the $η_q$ leading-twist distribution amplitude by using the light-cone harmonic oscillator model for its wave function and by using the QCD sum rules within the QCD background field to calculate its moments. The input parameters of $η_q$ leading-twist distribution amplitude $ϕ_{2;η_q}$ at an initial scale $μ_0\sim 1$ GeV are then fixed by using those moments. The sum rules for the $0_{\rm th}$-order moment can also be used to fix the magnitude of $η_q$ decay constant, which gives $f_{η_q}=0.141\pm0.005$ GeV. As an application of the present derived $ϕ_{2;η_q}$, we calculate the transition form factors $B(D)^+ \toη^{(\prime)}$ by using the QCD light-cone sum rules up to twist-4 accuracy and by including the next-to-leading order QCD corrections to the twist-2 part, and then fix the related CKM matrix element and the decay width for the semi-leptonic decays $B(D)^+ \toη^{(\prime)}\ell^+ ν_\ell$., 14 pages, 7 figures, Comments welcome

We present a novel method for precisely determining the QCD running coupling from $R_{\rm uds}$ measurements in electron-positron annihilation. When calculating the fixed-order perturbative QCD (pQCD) approximant of $R_{\rm uds}$, its effective coupling constant $α_s(Q_*^2)$ is determined by using the principle of maximum conformality, a systematic scale-setting method for gauge theories, whose resultant pQCD series satisfies all the requirements of renormalization group. Contribution due to the uncalculated higher-order (UHO) terms is estimated by using the Bayesian analysis. Using $R_{\rm uds}$ data measured by the KEDR detector at $22$ centre-of-mass energies between $1.84$ GeV and $3.72$ GeV, we obtain $α_s(M_Z^2)=0.1227^{+0.0117}_{-0.0132}({\rm exp.})\pm0.0016({\rm the.})$, where the theoretical uncertainty (the.) is negligible compared to the experimental one (exp.). Numerical analyses confirm that the new method for calculating $R_{\rm uds}$ removes conventional renormalization scale ambiguity, and the residual scale dependence due to the UHO-terms will also be highly suppressed due to a more convergent pQCD series. This leads to a significant stabilization of the perturbative series, and a significant reduction of theoretical uncertainty. It thus provides a reliable theoretical basis for precise determination of the QCD running coupling from $R_{\rm uds}$ measurements at future Tau-Charm Facility. It can also be applied for the precise determination of the hadronic contributions to muon $g-2$ and QED coupling $α(M_Z^2)$ within the tau-charm energy range., 22 pages, 8 figures. To be published in JHEP

We present a new determination of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{\rm cb}|$ by using the three-loop perturbative QCD corrections for the $B\to D^{\ast}$ semi-leptonic decay. The decay width of $B\to D^{\ast}$ semi-leptonic decay can be factorized as perturbatively calculable short-distance part and the non-perturbative but universal long-distance part. We adopt the principle of maximum conformality (PMC) single-scale setting approach to deal with the perturbative series so as to achieve a precise fixed-order prediction for the short-distance parameter $\eta_{A}$. By applying the PMC, an overall effective $\alpha_s$ value is achieved by recursively using the renormalization group equation, which inversely results in a precise scale-invariant pQCD series. Such scale-invariant series also provides a reliable basis for predicting the contributions from uncalculated perturbative terms. We then obtain $\eta_{A}=0.9225^{+0.0117}_{-0.0168}$, where the error is the squared average of those from $\Delta\alpha_{s}(M_Z)=\pm0.0010$ and the uncertainties caused by the uncalculated higher-order perturbative terms. By using the data of $B\to D^{\ast}\ell\bar{\nu}_{\ell}$, we finally obtain $|V_{\rm cb}|_{\rm PMC} =(40.60^{+0.53}_{-0.57})\times10^{-3}$, which is consistent with the PDG value within errors., Comment: 7 pages,2 figures

In this paper, we make a detailed study on the hadronic production of the $Ξ_{bc}$ baryon at a fixed target experiment at the LHC (After@LHC). In estimating the production cross sections, the $(g+g)$, $(g+c)$ and $(g+b)$ production mechanisms are considered. For the initial heavy quarks, in addition to the extrinsic component, we also consider the intrinsic component. It is found that the $(g+c)$ and $(g+b)$ production mechanisms give sizable contributions to the $Ξ_{bc}$ production, and the $(g+b)$ mechanism dominates the production. The results show that there are about $3.40\times10^5$ $Ξ_{bc}$ events can be produced per year at After@LHC if the integrated luminosity of After@LHC can be up to $2\,{\rm fb}^{-1}$ per year. Moreover, the intrinsic heavy quarks can have significant impact on the production, which inversely makes the intrinsic component be possibly tested at the After@LHC., 13 pages, 18 figures

In this paper, we calculate the ratio of Cabibbo-Kobayashi-Maskawa matrix elements, $|V_{ub}|/|V_{cb}|$, based on the semileptonic decay $B_s^0\to K^-μ^+ν_μ$. Its key component, the $B_s\to K$ transition form factor $f^{B_s\to K}_+(q^2)$, is studied within the QCD light-cone sum rules approach by using a chiral correlator. The derived $f^{B_s\to K}_+(q^2)$ is dominated by the leading-twist part, and to improve its precision, we construct a new model for the kaon leading-twist distribution amplitude $ϕ_{2;K}(x,μ)$, whose parameters are fixed by using the least squares method with the help of the moments calculated by using the QCD sum rules within the background field theory. The first four moments at the initial scale $μ_0 = 1~{\rm GeV}$ are, $\langle ξ^1\rangle _{2;K} = -0.0438^{+0.0053}_{-0.0075}$, $\langle ξ^2\rangle _{2;K} = 0.262 \pm 0.010$, $\langle ξ^3\rangle _{2;K} = -0.0210^{+0.0024}_{-0.0035}$ and $\langle ξ^4\rangle _{2;K} = 0.132 \pm 0.006$, respectively. And their corresponding Gegenbauer moments are, $a^{2;K}_1 = -0.0731^{+0.0089}_{-0.0124}$, $a^{2;K}_2 = 0.182^{+0.029}_{-0.030}$, $a^{2;K}_3 = -0.0114^{+0.0008}_{-0.0016}$ and $a^{2;K}_4 = 0.041^{-0.003}_{+0.005}$, respectively. At the large recoil region, we obtain $f^{B_s\to K} _+ (0) = 0.270^{+0.022}_{-0.030}$. By extrapolating $f^{B_s\to K}_+(q^2)$ to all the physical allowable region, we obtain a $|V_{ub}|$-independent decay width for the semileptonic decay $B_s^0\to K^-μ^+ν_μ$, $5.626^{+1.271}_{-0.864} \times 10^{-12}\ {\rm GeV}$, which then leads to $|V_{ub}|/|V_{cb}| = 0.072\pm0.005$., 34 pages, 11 figures, comments welcome

It has been found that at a high luminosity $e^+ e^-$ collider, sizable $η_c+c\bar{c}X$ and $η_b+b\bar{b}X$ events can be produced when it works around the $Z$ peak. In this paper, we calculate the decay widths of $Z \to η_c+c+\bar{c}+X$ and $Z \to η_b+b+\bar{b}+X$ up to next-to-leading order (NLO) accuracy. We find that the NLO corrections are significant in these two processes. After including the NLO corrections, the decay widths of $Z \to η_c+c+\bar{c}+X$ and $Z \to η_b+b+\bar{b}+X$ are enhanced by about $37\%$ and $28\%$ for the case of $μ_R=2m_c$ and $μ_R=2m_b$, respectively. The differential decay widths $dΓ/ds_1$ and $dΓ/dz$ for these two decay processes are also analyzed., 10 pages, 11 figures

In this paper, moments of $a_0(980)$-meson twist-2 light-cone distribution amplitudes were deeply researched by using QCD sum rules approach within background field theory. Up to 9th-order accuracy, we present $\langleξ_{2;a_0}^n\rangle|_{μ_0}$ at the initial scale $μ_0 = 1~{\rm GeV}$, i.e. $\langleξ^1_{2;a_0}\rangle|_{μ_0} = -0.307(43)$, $\langleξ^3_{2;a_0}\rangle|_{μ_0} = -0.181(34)$, $\langleξ^5_{2;a_0}\rangle|_{μ_0} = -0.078(28)$, $\langleξ^7_{2;a_0}\rangle|_{μ_0} = -0.049(26)$, $\langleξ^9_{2;a_0}\rangle|_{μ_0} = -0.036(24)$, respectively. An improved light-cone harmonic oscillator model for $a_0(980)$-meson twist-2 light-cone distribution amplitudes is adopted, where its parameters are fixed by using the least squares method based on the $\langleξ_{2;a_0}^n\rangle|_{μ_0}$, and their goodness of fit reach to $95.4\%$. Then, we calculate the $D\to a_0(980)$ transition form factors within the light-cone sum rules approach, and at largest recoil point, we obtain $f_+^{D\to a_0}(0) = 1.058^{+0.068}_{-0.035}$ and $f_-^{D\to a_0}(0) = 0.764^{+0.044}_{-0.036}$. As a further application, the branching fractions of the $D\to a_0(980)\ell\barν_\ell$ semileptonic decays are given. Taking the decay $a_0(980)\to ηπ$ into consideration, we obtain ${\cal B}(D^0 \to a_0(980)^- (\to ηπ^-) e^+ν_e) =(1.330^{+0.216}_{-0.134})\times10^{-4}$, ${\cal B}(D^+\to a_0(980)^0(\to ηπ^0)e^+ν_e)=(1.675^{+0.272}_{-0.169})\times10^{-4}$, which are consistent with the BESIII collaboration and PDG data within errors. Finally, we present the angle observables of forward-backward asymmetries, $q^2$-differential flat terms and lepton polarization asymmetry of the semileptonic decay $D\to a_0(980)\ell\barν_\ell$., 14 pages, 6 figures, more discussions added, accepted for publication in Nuclear Physics A

In the present paper, we study the photoproduction of various $S$-wave $B_c$ states, i.e. $B_c(1{}^1S_0)$, $B_c^*(1{}^1S_0)$, $B_c(2{}^1S_0)$ and $B^*_c(2{}^3S_1)$, at future $e^+e^-$ colliders within the framework of non-relativistic QCD. Two sources of the initial photons can be realized in the production, i.e., the LBS photon and the WWA photon. In addition to the direct photoproduction via the sub-process, $\gamma + \gamma \rightarrow B_c + b + \bar{c}$, we also calculate the resolved photoproduction via the sub-processes, $\gamma + g \rightarrow B_c + b + \bar{c}$ and $q + \bar{q} \rightarrow B_c + b + \bar{c}$ with $q=u,d,s,g$, respectively. Numerical results indicate that the contributions from the single resolved photoproduction are significant and even dominant at certain collision configuration. At the future high-energy and high-luminosity $e^+e^-$ colliders, the $B_c$ meson generated via the photoproduction mechanism is promisingly observable and can be well studied.

In the paper, we study the $B_s\to D_s$ transition form factors by using the light-cone sum rules within the framework of heavy quark effective field theory. We adopt a chiral current correlation function to do the calculation, the resultant transition form factors $f_+^{B_s\to D_s}(q^2)$ and $f_0^{B_s\to D_s}(q^2)$ are dominated by the contribution of $D_s$-meson leading-twist distribution amplitude, while the contributions from less certain $D_s$-meson twist-3 distribution amplitudes are greatly suppressed. At the largest recoil point, we obtain $f_{+,0}^{B_s \to D_s}(0)=0.533^{+0.112}_{-0.094}$. By further extrapolating the transition form factors into all the physically allowable $q^2$ region with the help of the $z$-series parametrization approach, we calculate the branching fractions $\mathcal{B}(B_s \to D_s \ell^\prime ν_{\ell^\prime})$ with $(\ell^\prime= e,μ)$ and $\mathcal{B}(B_s \to D_s τν_τ)$, which gives $\mathcal{R}(D_s)=0.334\pm 0.017$., 9 pages, 7 figures

We make a detailed study on the properties of the total decay width of Higgs decay channel $H\to gg$ up to $\alpha_s^6$-order QCD corrections by using the newly suggested infinite-order scale-setting approach, which is based on the ideas of both the principle of maximum conformality and the intrinsic conformality. This approach is called as the PMC$_\infty$ approach. By using the PMC$_\infty$ approach, we observe that the conventional renormalization scale ambiguity in perturbative QCD calculation is eliminated and the residual scale dependence due to unknown higher-order terms can also be highly suppressed. We then obtain an accurate perturbative QCD prediction on the total decay width, e.g. $\Gamma (H \to gg)|_{\rm PMC_\infty} =336.42^{+7.01}_{-6.92}$ KeV, where the errors are squared averages of those from all the mentioned error sources., Comment: 7 pages, 3 figures, to be published in Chinese Physics C

In this paper, we calculate the $B_c\to J/ψ$ helicity form factors (HFFs) up to twist-4 accuracy by using the light-cone sum rules (LCSR) approach. After extrapolating those HFFs to the physically allowable $q^2$ region, we investigate the $B^+_c$-meson two-body decays and semi-leptonic decays $B_c^+ \to J/ψ+(P, V, \ell^+ ν_\ell)$ with $P/V$ stands for light pseudoscalar/vector meson, respectively. The branching fractions can be derived by using the CKM matrix element and the $B_c$ lifetime from the Particle Data Group, and we obtain ${\cal B}(B_c^+ \to J/ψπ^+)=(0.136^{+0.002}_{-0.002})\%$, ${\cal B}(B_c^+ \to J/ψK^+)=(0.010^{+0.000}_{-0.000})\%$, ${\cal B}(B_c^+ \to J/ψρ^+) =(0.768^{+0.029}_{-0.033})\%$, ${\cal B}(B_c^+ \to J/ψK^{\ast +})=(0.043^{+0.001}_{-0.001})\%$, ${\cal B}(B_c^+ \to J/ψμ^+ν_μ)=(2.802^{+0.526}_{-0.675})\%$ and ${\cal B}(B_c^+ \to J/ψτ^+ν_τ)=(0.559^{+0.131}_{-0.170})\%$. We then obtain ${\cal R}_{π^+/μ^+ν_μ} = 0.048^{+ 0.009}_{-0.012}$ and ${\cal R}_{K^+ / π^+} = 0.075^{+0.005}_{-0.005}$, which agree with the LHCb measured value within $1σ$-error. We also obtain ${\cal R}_{J/ψ}=0.199^{+ 0.060}_{-0.077}$, which like other theoretical predictions, is consistent with the LHCb measured value within $2σ$-error. Those imply that the HFFs under the LCSR approach are also applicable to the $B^+_c$ meson two-body decays and semi-leptonic decays $B_c^+ \to J/ψ+(P, V, \ell^+ ν_\ell)$, and the HFFs obtained by using LCSR in a new way implies that there may be new physics in the $B_c\to J/ψ\ell^+ ν_\ell$ semi-leptonic decays., 10 pages, 4 figures, published version

The QCD coupling $α_s$ is the most important parameter for achieving precise QCD predictions. By using the well measured effective coupling $α^{g_1}_{s}(Q)$ defined from the Bjorken sum rules as a basis, we suggest a novel and self-consistency way to fix the $α_s$ at all scales: The QCD light-front holographic model is adopted for its infrared behavior, and the fixed-order pQCD prediction under the principle of maximum conformality (PMC) is used for its high-energy behavior. Using the PMC scheme-and-scale independent perturbative series, and by transforming it into the one under the physical $V$-scheme, we observe that a precise $α_s$ running behavior in both the perturbative and nonperturbative domains with a smooth transition from small to large scales can be achieved., 6 pages,3 figures

In this paper, we present a new analysis on the $P$-wave charmonium annihilation into two photons up to next-to-next-to-leading order (NNLO) QCD corrections by using the principle of maximum conformality (PMC). The conventional perturbative QCD prediction shows strong scale dependence and deviates largely from the BESIII measurements. After applying the PMC, we obtain a more precise scale-invariant pQCD prediction, which also agrees with the BESIII measurements within errors, i.e. $R={��_{����}(��_{c2})} /{��_{����}(��_{c0})}=0.246\pm0.013$, where the error is for $����_s(M_��)=\pm0.016$. By further considering the color-octet contributions, even the central value can be in agreement with the data. This shows the importance of a correct scale-setting approach. We also give a prediction for the ratio involving $��_{b0, b2} \to����$, which could be tested in future Belle II experiment.

In the paper, we analyze the properties of Gross-Llewellyn Smith (GLS) sum rule by using the $\mathcal{O}(��_s^4)$-order QCD corrections with the help of principle of maximum conformality (PMC). By using the PMC single-scale approach, we obtain an accurate renormalization scale-and-scheme independent fixed-order pQCD contribution for GLS sum rule, e.g. $S^{\rm GLS}(Q_0^2=3{\rm GeV}^2)|_{\rm PMC}=2.559^{+0.023}_{-0.024}$, where the error is squared average of those from $����_s(M_Z)$, the predicted $\mathcal{O}(��_s^5)$-order terms predicted by using the Pad�� approximation approach. After applying the PMC, a more convergent pQCD series has been obtained, and the contributions from the unknown higher-order terms are highly suppressed. In combination with the nonperturbative high-twist contribution, our final prediction of GLS sum rule agrees well with the experimental data given by the CCFR collaboration., 6 pages, 5 figures

We make a detailed study on the typical production channel of double charmoniums, $e^+e^-\to J/��+��_c$, 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 $J/��$ light-cone distribution amplitude up to twist-4 accuracy. Total cross sections for $e^+e^-\to J/��+��_c$ at three typical factorization scales are $��|_{��_s} = 22.53^{+3.46}_{-3.49}~{\rm fb}$, $��|_{��_k} = 21.98^{+3.35}_{-3.38}~{\rm fb}$ and $��|_{��_0} = 21.74^{+3.29}_{-3.33}~{\rm fb}$, respectively. The factorization scale dependence is small, and those predictions are consistent with the BABAR and Belle measurements within errors., 8 pages, 3 figures, version to be published in Physical Review D

In this paper, we make a detailed discussion on the $��$ and $��'$-meson leading-twist light-cone distribution amplitude $��_{2;��^{(\prime)}}(u,��)$ by using QCD sum rules approach under the background field theory. Taking both the non-perturbative condensates up to dimension-six and NLO QCD corrections to the perturbative part, its first three moments $\langle��^n_{2;��^{(\prime)}}\rangle|_{��_0} $ with $n = (2,4,6)$ at initial scale $��_0 = 1$ GeV can be determined. e.g. $\langle��_{2;��}^2\rangle|_{��_0} =0.231_{-0.013}^{+0.010}$, $\langle��_{2;��}^4 \rangle|_{��_0} =0.109_{-0.007}^{+0.007}$, and $\langle��_{2;��}^6 \rangle|_{��_0} =0.066_{-0.006}^{+0.006}$ for $��$-meson, $\langle��_{2;��'}^2\rangle|_{��_0} =0.211_{-0.017}^{+0.015}$, $\langle��_{2;��'}^4 \rangle|_{��_0} =0.093_{-0.009}^{+0.009}$, and $\langle��_{2;��'}^6 \rangle|_{��_0} =0.054_{-0.008}^{+0.008}$ for $��'$-meson. Next, we calculate $D_s\to��^{(\prime)}$ TFFs $f^{��^{(\prime)}}_+(q^2)$ within QCD light-cone sum rules approach up to NLO level. The values at large recoil region are $f^��_+(0) = 0.476_{-0.036}^{+0.040}$ and $f^{��'}_+(0) = 0.544_{-0.042}^{+0.046}$. After extrapolating TFFs to the allowable physical regions within the series expansion, we obtain the branching fractions of the semi-leptonic decay, i.e. $D_s^+\to��^{(\prime)}\ell^+ ��_\ell$, i.e. ${\cal B}(D_s^+\to��^{(\prime)} e^+��_e)=2.346_{-0.331}^{+0.418}(0.792_{-0.118}^{+0.141})\times10^{-2}$ and ${\cal B}(D_s^+\to��^{(\prime)} ��^+��_��)=2.320_{-0.327}^{+0.413}(0.773_{-0.115}^{+0.138})\times10^{-2}$ for $\ell = (e, ��)$ channels respectively. And in addition to that, the mixing angle for $��-��'$ with $��$ and ratio for the different decay channels ${\cal R}_{��'/��}^\ell$ are given, which show good agreement with the recent BESIII measurements., 52 pages, 11 figures, version to be published in EPJC

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 $\langle \xi^n\rangle _{2;D_s}$ are calculated up to dimension-six condensates. At the scale $\mu = 2{\rm GeV}$, we obtain: $\langle \xi^1\rangle _{2;D_s}= -0.261^{+0.020}_{-0.020}$, $\langle \xi^2\rangle _{2;D_s} = 0.184^{+0.012}_{-0.012}$, $\langle \xi^3\rangle _{2;D_s} = -0.111 ^{+0.007}_{-0.012}$ and $\langle \xi^4\rangle _{2;D_s} = 0.075^{+0.005}_{-0.005}$. 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 $f^{B_s\to D_s}_+(q^2)$ 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 $f^{B_s\to D_s}_+(q^2)$ 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 $\mathcal{B}(\bar B_s^0 \to D_s^+ \ell\nu_\ell) = (2.03^{+0.35}_{-0.49}) \times 10^{-2}$ and $|V_{cb}|=(40.00_{-4.08}^{+4.93})\times 10^{-3}$.

Heavy fermion pair production in $e^+e^-$ annihilation is a fundamental process in hadron physics and is of considerable interest for various phenomena. In this paper, we will apply the Principle of Maximum Conformality (PMC) to provide a comprehensive analysis of these processes. The PMC provides a systematic, unambiguous method for determining the renormalization scales of the QCD coupling constant for single-scale and multiple-scale applications. The resulting predictions eliminate any renormalization scheme-and-scale ambiguities, eliminate the factorial renormalon divergences, and are consistent with the requirements of the renormalization group. It is remarkable that two distinctly different scales are determined by using the PMC for heavy fermion pair production near the threshold region. One scale is the order of the fermion mass $m_f$, which enters the hard virtual corrections, and the other scale is of order $ v\,m_f$, where $v$ is the quark velocity, which enters the Coulomb rescattering amplitude. The PMC scales yield the correct physical behavior and reflect the virtuality of the propagating gluons (photons) for the QCD (QED) processes. Moreover, we demonstrate the consistency of PMC scale setting from QCD to QED. Perfect agreement between the Abelian unambiguous Gell-Mann-Low and the PMC scale-setting methods in the limit of zero number of colors is demonstrated., 8 pages, 6 figures, published version

In the paper, we study the properties of the $Z$-boson hadronic decay width by using the $\mathcal{O}(��_s^4)$-order quantum chromodynamics (QCD) corrections with the help of the principle of maximum conformality (PMC). By using the PMC single-scale approach, we obtain an accurate renormalization scale-and-scheme independent perturbative QCD (pQCD) correction for the $Z$-boson hadronic decay width, which is independent to any choice of renormalization scale. After applying the PMC, a more convergent pQCD series has been obtained; and the contributions from the unknown $\mathcal{O}(��_s^5)$-order terms are highly suppressed, e.g. conservatively, we have $����_{\rm Z}^{\rm had}|^{{\cal O}(��_s^5)}_{\rm PMC}\simeq \pm 0.004$ MeV. In combination with the known electro-weak (EW) corrections, QED corrections, EW-QCD mixed corrections, and QED-QCD mixed corrections, our final prediction of the hadronic $Z$ decay width is $��_{\rm Z}^{\rm had}=1744.439^{+1.390}_{-1.433}$ MeV, which agrees with the PDG global fit of experimental measurements, $1744.4\pm 2.0$ MeV., 7 pages, 3 figures

In the paper, we study the properties of the top-quark $\overline{\rm MS}$ running mass computed from its on-shell mass by using both the four-loop $\overline{\rm MS}$-on-shell relation and the principle of maximum conformality (PMC) scale-setting approach. The PMC adopts the renormalization group equation to set the correct magnitude of the strong running coupling of the perturbative series, its prediction avoids the conventional renormalization scale ambiguity, and thus a more precise pQCD prediction can be achieved. After applying the PMC to the four-loop $\overline{\rm MS}$-on-shell relation and taking the top-quark on-shell mass $M_t=172.9\pm0.4$ GeV as an input, we obtain the renormalization scale-invariant $\overline{\rm MS}$ running mass at the scale $m_t$, e.g., $m_t(m_t)\simeq 162.6\pm 0.4$ GeV, in which the error is the squared average of those from $\Delta \alpha_s(M_Z)$, $\Delta M_t$, and the approximate error from the uncalculated five-loop terms predicted by using the Pad\'{e} approximation approach., Comment: 8 pages, 2 figures

In the paper, we present QCD predictions for $��_{c} + ��$ production at an electron-position collider up to next-to-next-to-leading order (NNLO) accuracy without renormalization scale ambiguities. The NNLO total cross-section for $e^{+}+e^{-}\to��+��_{c}$ using the conventional scale-setting approach has large renormalization scale ambiguities, usually estimated by choosing the renormalization scale to be the $e^+ e^-$ center-of-mass collision energy $\sqrt{s}$. The Principle of Maximum Conformality (PMC) provides a systematic way to eliminate such renormalization scale ambiguities by summing the nonconformal $��$ contributions into the QCD coupling $��_s(Q^2)$. The renormalization group equation then sets the value of $��_s$ for the process. The PMC renormalization scale reflects the virtuality of the underlying process, and the resulting predictions satisfy all of the requirements of renormalization group invariance, including renormalization scheme invariance. After applying the PMC, we obtain a scale-and-scheme independent prediction, $��|_{\rm NNLO, PMC}\simeq 41.18$ fb for $\sqrt{s}$=10.6 GeV. The resulting pQCD series matches the series for conformal theory and thus has no divergent renormalon contributions. The large $K$ factor which contributes to this process reinforces the importance of uncalculated NNNLO and higher-order terms. Using the PMC scale-and-scheme independent conformal series and the $\rm Pad\acute{e}$ approximation approach, we predict $��|_{\rm NNNLO, PMC+Pade} \simeq 21.36$ fb, which is consistent with the recent BELLE measurement $��^{\rm obs}$=$16.58^{+10.51}_{-9.93}$ fb at $\sqrt{s} \simeq 10.6$ GeV. This procedure also provides a first estimate of the NNNLO contribution., 8 pages, 5 figures. Discussions improved and references updated. Revised version to be published in JHEP

In this paper, we calculate the total decay widths for the $W^+$-boson decays, $W^+ \to B_c+b+\bar{s}+X$ and $W^+ \to B^*_c+b+\bar{s}+X$, up to next-to-leading order (NLO) accuracy within the framework of the nonrelativistic QCD theory. Both the fixed-order and the fragmentation approaches are adopted to do the calculation. Differential decay widths $d\Gamma/dz$ and $d\Gamma/ds_1$ are also given. We find that the NLO corrections are significant in those two $W^+$ decay channels. Our numerical results show that at the LHC, there are about $7.03\times 10^4$ $B_c$-meson events and $5.10\times 10^4$ $B^*_c$-meson events to be produced via the $W^+$-boson decays per operation year., Comment: 11 pages, 9 figures

Invited "News & Views" for the journal, SCIENCE CHINA: Physics, Mechanics & Astronomy, on a recently new search for the doubly charmed baryon $��_{cc}^+$ at the LHC, which is done by the LHCb Collaboration, arXiv:1909.12273., 2 pages

In the present paper, we present detailed discussions on the hadronic production of $��_{cc}$ at a fixed target experiment at the LHC (After@LHC). The charm quarks in hadron could be either extrinsic or intrinsic. By using the BHPS model as the intrinsic charm distribution function in proton, we observe that even if by setting the proportion of finding the intrinsic charm in a proton as $A_{\rm in}=1\%$, total cross sections for the $g+c$ and $c+c$ production mechanisms shall be enhanced by nearly two times. Thus the number of $��_{cc}$ events to be generated at the After@LHC can be greatly enhanced. Since the total cross sections and differential distributions for the $��_{cc}$ production at the After@LHC are sensitive to the value of $A_{\rm in}$, the After@LHC could be a good platform for testing the idea of intrinsic charm., 13 pages, 17 figures

The heavy quark effective field theory (HQEFT) provides an effective way to deal with the heavy meson decays. In the paper, we adopt two different correlators to derive the light-cone sum rules of the $B \to ��$ transition form factors (TFFs) within the framework of HQEFT. We label those two LCSR results as LCSR-${\cal U}$ and LCSR-${\cal R}$, which are for conventional correlator and right-handed correlator, respectively. We observe that the correlation parameter $|��_{\rm RU}|$ for the branching ratio ${\cal B}(B \to ��l ��_{l})$ is $\sim 0.85$, implying the consistency of the LCSRs under different correlators. Moreover, we obtain $|V_{\rm ub}|_{{\rm LCSR}-{\cal U}}=(3.45^{+0.28}_{-0.20}\pm{0.13}_{\rm{exp}})\times10^{-3}$ and $|V_{\rm ub}|_{{\rm LCSR}-{\cal R}} =(3.38^{+0.22}_{-0.16} \pm{0.12}_{\rm{exp}})\times10^{-3}$. We then obtain $\mathcal{R}_��|_{{\rm LCSR}-{\cal U}}=0.68^{+0.10}_{-0.09}$ and $\mathcal{R}_��|_{{\rm LCSR}-{\cal R}}=0.65^{+0.13}_{-0.11}$, both of them agree with the Lattice QCD predictions. Thus the HQEFT provides a useful framework for studying the $B$ meson decays. Moreover, by using right-handed correlator, the twist-2 terms shall dominant the TFF $f^+(q^2)$, which approaches over $\sim97\%$ contribution in the whole $q^2$-region; and the large twist-3 uncertainty for the conventional correlator is greatly suppressed. One can thus adopt the LCSR-${\cal R}$ prediction to test the properties of the various models for the pion twist-2 distribution amplitudes.

The fragmentation functions for $c$ or $\bar{b}$ quark to $B_c$ or $B_c^*$ meson are derived up to QCD next-to-leading order (NLO). They are further computed numerically and presented in figures precisely. In order to reach a higher accuracy, we have also tried properly to apply them to estimating the $B_c$ and $B_c^*$ production at a $Z$-factory (an $e^+e^-$ collider running at the energy of the $Z$-boson pole)., Comment: 20 pages, 13 figures

In the paper, we study the $��(1S)$ leptonic decay width $��(��(1S)\to \ell^+\ell^-)$ by using the principle of maximum conformality (PMC) scale-setting approach. The PMC adopts the renormalization group equation to set the correct momentum flow of the process, whose value is independent to the choice of the renormalization scale and its prediction thus avoids the conventional renormalization scale ambiguities. Using the known next-to-next-to-next-to-leading order perturbative series together with the PMC single scale-setting approach, we do obtain a renormalization scale independent decay width, $��_{��(1S) \to e^+ e^-} = 1.262^{+0.195}_{-0.175}$ keV, where the error is squared average of those from $��_s(M_{Z})=0.1181\pm0.0011$, $m_b=4.93\pm0.03$ GeV and the choices of factorization scales within $\pm 10\%$ of their central values. To compare with the result under conventional scale-setting approach, this decay width agrees with the experimental value within errors, indicating the importance of a proper scale-setting approach., 6 pages, 4 figures

In this paper, we calculate the $B\to D$ transition form factors (TFFs) within the light-cone sum rules (LCSR) and predict the ratio $\mathcal{R}(D)$. More accurate $D$-meson distribution amplitudes (DAs) are essential to get a more accurate theoretical prediction. We construct a new model for the twist-3 DAs $\phi^p_{3;D}$ and $\phi^\sigma_{3;D}$ based on the QCD sum rules under the background field theory for their moments as we have done for constructing the leading-twist DA $\phi_{2;D}$. As an application, we observe that the twist-3 contributions are sizable in whole $q^2$-region. Taking the twist-2 and twist-3 DAs into consideration, we obtain $f^{B\to D}_{+,0}(0) = 0.659^{+0.029}_{-0.032}$. As a combination of the Lattice QCD and the QCD LCSR predictions on the TFFs $f^{B\to D}_{+,0}(q^2)$, we predict $\mathcal{R}(D) = 0.320^{+0.018}_{-0.021}$, which improves is about $1.5\sigma$ deviation from the HFAG average of the Belle and BABAR data. At present the data are still of large errors, and we need further accurate measurements of the experiment to confirm whether there is signal of new physics from the ratio $\mathcal{R}(D)$., Comment: 15 pages,9 figures

The Higgs boson decay channel, $H\to����$, is one of the most important channels for probing the properties of the Higgs boson. In the paper, we reanalyze its decay width by using the QCD corrections up to $��_s^4$-order level. The principle of maximum conformality has been adopted to achieve a precise pQCD prediction without conventional renormalization scheme-and-scale ambiguities. By taking the Higgs mass as the one given by the ATLAS and CMS collaborations, i.e. $M_{H}=125.09\pm0.21\pm0.11$ GeV, we obtain $��(H\to ����)|_{\rm LHC}=9.364^{+0.076}_{-0.075}$ KeV., 6 pages, 6 figures

We make a detailed study on the $J/��$ meson longitudinal leading-twist distribution amplitude $��_{2;J/��}^\|$ by using the QCD sum rules within the background field theory. By keeping all the non-perturbative condensates up to dimension-six, we obtain accurate QCD sum rules for the moments $\langle��_{n;J/��}^\|\rangle$. The first three ones are $\langle��_{2;J/��}^\|\rangle=0.083(12)$, $\langle��_{4;J/��}^\|\rangle=0.015(5)$ and $\langle��_{6;J/��}^\|\rangle=0.003(2)$, leading to a single peaked behavior for $��_{2;J/��}^\|$ which is sharper than the previous ones around the region of $x\sim0.5$. As an application, we adopt the QCD light-cone sum rules to calculate the $B_c$ meson semileptonic decay $B_c^+ \to J/��\ell^+ ��_\ell$. We obtain $��(B_c^+ \to J/��\ell^+ ��_\ell) = (89.67^{+24.76}_{-19.06}) \times 10^{-15}~{\rm GeV}$ and $\Re(J/��\ell^+ ��_\ell) = 0.217^{+0.069}_{-0.057}$, which agree with the next-to-leading order pQCD prediction and the new CDF measurement within errors., 10 pages, 4 figures

The next-to-next-to-leading order (NNLO) pQCD prediction for the $����^* \to ��_c$ form factor was evaluated in 2015 using nonrelativistic QCD (NRQCD). A strong discrepancy between the NRQCD prediction and the BaBar measurements was observed. Until now there has been no solution for this puzzle. In this paper, we present a NNLO analysis by applying the Principle of Maximum Conformality (PMC) to set the renormalization scale. By carefully dealing with the light-by-light diagrams at the NNLO level, the resulting high precision PMC prediction agrees with the BaBar measurements within errors, and the conventional renormalization scale uncertainty is eliminated. The PMC is consistent with all of the requirements of the renormalization group, including scheme-independence. The application of the PMC thus provides a rigorous solution for the $����^* \to ��_c$ form factor puzzle, emphasizing the importance of correct renormalization scale-setting. The results also support the applicability of NRQCD to hard exclusive processes involving charmonium., 5 pages, 4 figures. References updated. To be published in Phys.Rev.D

We study the $B \to ��$ 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 $��$-meson longitudinal component contributes to the HFFs, and we have $\mathcal{H}_{��,0}(0)=0.435^{+0.055}_{-0.045}$ and $\mathcal{H}_{��,\{1,2\}}(0)\equiv 0$. We extrapolate the HFFs to physically allowable $q^2$-region and apply them to the $B \to ��$ semileptonic decay. We observe that the $��$-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., 11 pages, 7 figures, 8 tables

In the paper, we make a comprehensive study on the hadroproduction of the $B_c (B_c^*)$ meson via the gluon-gluon fusion mechanism at the RHIC and LHC colliders. Total and differential cross sections via the proton-nucleus ($p$-N) and nucleus-nucleus (N-N) collision modes have been discussed under various collision energies. To compare with those via the proton-proton collision mode at the LHC, we observe that sizable number of $B_c (B_c^*)$-meson events can also be produced via the $p$-N and N-N collision modes at the RHIC and LHC. If assuming the spin-triplet $B^*_c$ meson directly decays to the spin-singlet $B_c$ meson with $100\%$ probability, $1.2 \times 10^5$ and $4.7 \times 10^5$ $B_c$-meson events can be produced via the $p$-Au and Au-Au collision modes at the RHIC in one operation year; $5.8 \times 10^6$ and $4.6 \times 10^6$ $B_c$-meson events can be produced via the $p$-Pb and Pb-Pb collision modes at the LHC in one operation year., Comment: 9 pages, 7 figures. Revised version to be published in Phys.Rev.D

The measured branching ratio of the $D$ meson semileptonic decay $D \to ��e^+ ��_e$, which is based on the $0.82~{\rm fb^{-1}}$ CLEO data taken at the peak of $��(3770)$ resonance, disagrees with the traditional SVZ sum rules analysis by about three times. In the paper, we show that this discrepancy can be eliminated by applying the QCD light-cone sum rules (LCSR) approach to calculate the $D\to ��$ transition form factors $A_{1,2}(q^2)$ and $V(q^2)$. After extrapolating the LCSR predictions of these TFFs to whole $q^2$-region, we obtain $1/|V_{\rm cd}|^2 \times ��(D \to ��e ��_e) =(55.45^{+13.34}_{-9.41})\times 10^{-15}~{\rm GeV}$. Using the CKM matrix element and the $D^0(D^+)$ lifetime from the Particle Data Group, we obtain ${\cal B} (D^0\to ��^- e^+ ��_e) = (1.749^{+0.421}_{-0.297}\pm 0.006)\times 10^{-3}$ and ${\cal B} (D^+ \to ��^0 e^+ ��_e) = (2.217^{+0.534}_{-0.376}\pm 0.015)\times 10^{-3}$, which agree with the CLEO measurements within errors. We also calculate the branching ratios of the two $D$ meson radiative processes and obtain ${\cal B}(D^0\to ��^0 ��)= (1.744^{+0.598}_{-0.704})\times 10^{-5}$ and ${\cal B}(D^+ \to ��^+ ��) = (5.034^{+0.939}_{-0.958})\times 10^{-5}$, which also agree with the Belle measurements within errors. Thus we think the LCSR approach is applicable for dealing with the $D$ meson decays., 12 pages, 7 figures, version to be published in EPJC

In this paper, we compute the forward-backward asymmetry and the isospin asymmetry of the $B \to K^* ��^+ ��^-$ decay. The $B \to K^*$ transition form factors (TFFs) are key components of the decay. To achieve a more accurate QCD prediction, we adopt a chiral correlator for calculating the QCD light-cone sum rules for those TFFs with the purpose of suppressing the uncertain high-twist distribution amplitudes. Our predictions show that the asymmetries under the Standard Model and the Minimal Supersymmetric Standard Model with minimal flavor violation are close in shape for $q^2 \ge 6~{\rm GeV}^2$ and are consistent with the Belle, LHCb and CDF data within errors. When $q^2 < 2~{\rm GeV}^2$, their predictions behave quite differently. Thus a careful study on the $B \to K^* ��^+ ��^-$ decay within small $q^2$-region could be helpful for searching new physics beyond the Standard Model. As a further application, we also apply the $B \to K^*$ TFFs to the branching ratio and longitudinal polarization fraction of the $B\to K^*��\bar��$ decay within different models., 11 pages, 6 figures, references updated and revised version to be published in Phys. Rev. D

In this paper, we study the $B \to K^*$ transition form factors (TFFs) within the QCD light-cone sum rules (LCSR) approach. Two correlators, i.e. the usual one and the right-handed one, are adopted in the LCSR calculation. The resultant LCSRs for the $B \to K^*$ TFFs are arranged according to the twist structure of the $K^*$-meson light-cone distribution amplitudes (LCDAs), whose twist-2, twist-3 and twist-4 terms behave quite differently by using different correlators. We observe that the twist-4 LCDAs, though generally small, shall have sizable contributions to the TFFs $A_{1/2}$, $V$ and $T_1$, thus the twist-4 terms should be kept for a sound prediction. We also observe that even though different choices of the correlator lead to different LCSRs with different twist contributions, the large correlation coefficients for most of the TFFs indicate that the LCSRs for different correlators are close to each order, not only for their values at the large recoil point $q^2=0$ but also for their ascending trends in whole $q^2$-region. Such a high degree of correlation is confirmed by their application to the branching fraction of the semi-leptonic decay $B \to K^* \mu^+ \mu^-$. Thus, a proper choice of correlator may inversely provide a chance for probing uncertain LCDAs, i.e. the contributions from those LCDAs can be amplified to a certain degree via a proper choice of correlator, thus amplifying the sensitivity of the TFFs, and hence their related observables, to those LCDAs., Comment: 17 pages, 6 figures. Discussions improved and references updated. To be published in Phys.Rev.D

The $B\to D$ transition form factor (TFF) $f^{B\to D}_+(q^2)$ is determined mainly by the $D$-meson leading-twist distribution amplitude (DA) , $\phi_{2;D}$, if the proper chiral current correlation function is adopted within the light-cone QCD sum rules. It is therefore significant to make a comprehensive study of DA $\phi_{2;D}$ and its impact on $f^{B\to D}_+(q^2)$. In this paper, we calculate the moments of $\phi_{2;D}$ with the QCD sum rules under the framework of the background field theory. New sum rules for the leading-twist DA moments $\left_D$ up to fourth order and up to dimension-six condensates are presented. At the scale $\mu = 2 \rm GeV$, the values of the first four moments are: $\left_D = -0.418^{+0.021}_{-0.022}$, $\left_D = 0.289^{+0.023}_{-0.022}$, $\left_D = -0.178 \pm 0.010$ and $\left_D = 0.142^{+0.013}_{-0.012}$. Basing on the values of $\left_D(n=1,2,3,4)$, a better model of $\phi_{2;D}$ is constructed. Applying this model for the TFF $f^{B\to D}_+(q^2)$ under the light cone sum rules, we obtain $f^{B\to D}_+(0) = 0.673^{+0.038}_{-0.041}$ and $f^{B\to D}_+(q^2_{\rm max}) = 1.124^{+0.053}_{-0.058}$. The uncertainty of $f^{B\to D}_+(q^2)$ from $\phi_{2;D}$ is estimated and we find its impact should be taken into account, especially in low and central energy region. The branching ratio $\mathcal{B}(B\to Dl\bar{\nu}_l)$ is calculated, which is consistent with experimental data., Comment: 12 pages, 8 figures

In the paper, we analyze the $��_c$ decays into light hadrons at the next-to-leading order QCD corrections by applying the principle of maximum conformality (PMC). The relativistic correction at the ${\cal{O}}(��_s v^2)$-order level has been included in the discussion, which gives about $10\%$ contribution to the ratio $R$. The PMC, which satisfies the renormalization group invariance, is designed to obtain a scale-fixed and scheme-independent prediction at any fixed order. To avoid the confusion of treating $n_f$-terms, we transform the usual $\overline{\rm MS}$ pQCD series into the one under the minimal momentum space subtraction scheme. To compare with the prediction under conventional scale setting, $R_{\rm{Conv,mMOM}-r}= \left(4.12^{+0.30}_{-0.28}\right)\times10^3$, after applying the PMC, we obtain $R_{\rm PMC,mMOM-r}=\left(6.09^{+0.62}_{-0.55}\right) \times10^3$, where the errors are squared averages of the ones caused by $m_c$ and $��_{\rm mMOM}$. The PMC prediction agrees with the recent PDG value within errors, i.e. $R^{\rm exp}=\left(6.3\pm0.5\right)\times10^3$. Thus we think the mismatching of the prediction under conventional scale-setting with the data is due to improper choice of scale, which however can be solved by using the PMC., 5 pages, 2 figures

We revisit the $��$-meson longitudinal leading-twist distribution amplitude (DA) $��_{2;��}^\|$ by using the QCD sum rules approach within the background field theory. To improve the accuracy of the sum rules for its moments $\langle��_{n;��}^\|\rangle$, we include the next-to-leading order QCD correction to the perturbative part and keep all non-perturbative condensates up to dimension-six consistently within the background field theory. The first two moments read $\langle ��_{2;��}^\| \rangle|_{1{\rm GeV}} = 0.241(28)$ and $\langle ��_{4;��}^\| \rangle|_{1{\rm GeV}} = 0.109(10)$, indicating a double humped behavior for $��_{2;��}^\|$ at small energy scale. As an application, we apply them to the $B\to ��$ transition form factors within the QCD light-cone sum rules, which are key components for the decay width $��(B\to ��\ell ��_\ell)$. To compare with the world-average of $��(B\to ��\ell ��_\ell)$ issued by Particle Data Group, we predict $|V_{\rm ub}| = 3.19^{+0.65}_{-0.62}$, which agrees with the BABAR and Omn��s parameterization prediction within errors., 10 pages, 5 figures. Revised version to be published in Phys.Rev.D

We make a detailed study on the photoproduction mechanism of the doubly heavy flavored $B_c^{(*)}$ meson at the purposed Large Hadron Electron Collider (LHeC) within the framework of nonrelativistic QCD. In addition to the photoproduction mechanism via the gluon-induced channel $\gamma + g \to B_c^{(*)} + b + \bar{c}$, the extrinsic heavy quark mechanism via the two channels $\gamma + c \to B_c^{(*)} + b $ and $\gamma + \bar{b} \to B_c^{(*)} + \bar{c}$ has also been studied. Those two extrinsic channels are generally suppressed by the heavy quark distribution functions in proton, which however provide significant contributions in low and intermediate $p_T$ region. A detailed comparison of those channels together with the theoretical uncertainties has been presented. By summing up all the mentioned photoproduction channels, we observe that about $(1.04^{+0.90}_{-0.53})\times 10^{5}$ $B_c$ and $(4.86^{+3.72}_{-2.30})\times 10^{5}$ $B_c^*$ events can be generated at the LHeC in one operation year with the proton-electron collision energy $\sqrt{S}=1.30$ TeV and the luminosity ${\mathcal L}\simeq 10^{33}$ ${\rm cm}^{-2} {\rm s}^{-1}$. Here the errors are for $m_c=1.50\pm0.20$ GeV and $m_b=4.9\pm0.40$ GeV. Thus, in addition to the hadronic experiments, the LHeC shall provide another helpful platform for studying the $B_c^{(*)}$ meson properties, especially to test the extrinsic heavy quark mechanism.

A primary problem for perturbative QCD analyses is how to set the renormalization scale of the QCD running coupling in order to achieve maximally precise fixed-order predictions for physical observables. The Principle of Maximum Conformality (PMC) eliminates the ambiguities associated with the conventional renormalization scale-setting procedure, giving predictions which are independent of the choice of renormalization scheme. The scales of the QCD couplings and the effective number of quark flavors are set order by order in the pQCD series. The PMC has a solid theoretical foundation, satisfying the standard renormalization group invariance and all of the the self-consistency conditions derived from the renormalization group......In this brief report, we summarize the results of our recent PMC applications for a number of collider processes, emphasizing their generality and applicability....... These results demonstrate that the application of the PMC systematically eliminates a major theoretical uncertainty for pQCD predictions, thus increasing the sensitivity of the colliders to possible new physics beyond the Standard Model., 10 pages, 4 figures. The title has been changed. This review, submitted to Frontiers of Physics, is based on a contribution by S.J.B. at the Conference {\it Workshop on Physics at a Future High Intensity Collider @ 2-7 GeV in China} Hefei, China January 14-16, 2015

We present a systematical study on the prompt $J/��$ production in association with a $c\bar{c}$ pair via the process, $����\to H(c\bar{c}) +c+\bar{c}$, within the framework of non-relativistic QCD at the future high-energy $e^{+}e^{-}$ collider - International Linear Collider (ILC), including both direct and feed-down contributions. For direct $J/��$ production, the states with color-octet channels, especially the $^3P_J^{[8]}$ and $^1S_0^{[8]}$ ones, provide dominant contribution to the production cross-section, which are about fifty-two times over that of the color-singlet one. This is clearly shown by the transverse momentum ($p_t$) and rapidity distributions. The feed-down contribution from $��'$ and $��_{cJ}$ ($J=0,1,2$) is sizable, which is about $20\%$ to the total prompt cross-section. Besides the yields, we also calculate the $J/��$ polarization parameter $��$. In small $p_t$ region, the polarization of the prompt $J/��$ is longitudinal due to large contributions through the $^3P_J^{[8]}$ channel, and becomes transverse in high $p_t$ region due to $^3S_1^{[8]}$ channel. Thus the $J/��$ production via photon-photon collisions at the ILC shall provide a useful platform for testing the color-octet mechanism., 8 pages, 8 figures. References updated and discussions improved. To be published in Phys.Rev.D

We study the decay width of the Higgs-boson $H\to gg$ up to order $��_s^5$ under the minimal momentum space subtraction scheme (mMOM-scheme). To improve the accuracy of perturbative QCD prediction, we adopt the principle of maximum conformality (PMC) to set its renormalization scales. A detailed comparison of the total decay width and the separate decay widths at each perturbative order before and after the PMC scale setting is presented. The PMC adopts the renormalization group equation to fix the optimal scales of the process. After the PMC scale setting, the scale-dependence for both the total and the separate decay widths are greatly suppressed, and the convergence of perturbative QCD series is improved. By taking the Higgs mass $M_H=125.09\pm 0.21\pm 0.11$ GeV, as recently given by the ATLAS and CMS collaborations, we predict $��(H\to gg)|_{\rm mMOM, PMC} = 339.1\pm 1.7^{+4.0}_{-2.4}$ keV, where the first error is for Higgs mass and the second error is the residual scale dependence by varying the initial scale $��_r\in[M_H/2,4M_H]$., 9 pages, 3 figures. Revised version to be published in J.Phys.G

A newly upgraded version of the BCVEGPY, a generator for hadronic production of the meson $B_c$ and its excited states, is available. In comparison with the previous one [C.H. Chang, J.X. Wang and X.G. Wu, Comput. Phys. Commun. {\bf 175}, 624 (2006)], the new version is to apply an improved hit-and-miss technology to generating the un-weighted events much more efficiently under various simulation environments. The codes for production of $2S$-wave $B_c$ states are also given here., Comment: 4 pages, 1 figures

The complete next-to-next-to-next-to-leading order short-distance and bound-state QCD corrections to $��(1S)$ leptonic decay rate $��(��(1S)\to \ell^+\ell^-)$ has been finished by Beneke {\it et al.} \cite{Beneke:2014qea}. Based on those improvements, we present a renormalization group (RG) improved pQCD prediction for $��(��(1S)\to \ell^+\ell^-)$ by applying the principle of maximum conformality (PMC). The PMC is based on RG-invariance and is designed to solve the pQCD renormalization scheme and scale ambiguities. After applying the PMC, all known-type of $��$-terms at all orders, which are controlled by the RG-equation, are resummed to determine optimal renormalization scale for its strong running coupling at each order. We then achieve a more convergent pQCD series, a scheme- independent and more accurate pQCD prediction for $��(1S)$ leptonic decay, i.e. $��_{��(1S) \to e^+ e^-}|_{\rm PMC} = 1.270^{+0.137}_{-0.187}$ keV, where the uncertainty is the squared average of the mentioned pQCD errors. This RG-improved pQCD prediction agrees with the experimental measurement within errors., 11 pages, 4 figures. Numerical results and discussions improved, references updated, to be published in JHEP

The QCD light-cone sum rules (LCSR) provides an effective way for dealing with the heavy-to-light transition form factors (TFFs), whose non-perturbative dynamics are parameterized into the light-meson's light-cone distribution amplitudes (LCDAs) with various twist structures. By taking the chiral correlator as the starting point, we calculate the LCSRs for the $B\to��$ TFFs up to twist-4 accuracy. As for the TFFs at the large recoil region, we observe that the twist-2 transverse DA $��_{2;��}^\bot$ provides the dominant contribution, while the contributions from the remaining twist-3 and twist-4 terms are $��^2$-suppressed. Thus, our present improved LCSRs provides a good platform for testing the $��_{2;��}^\bot$ behavior. For the purpose, we suggest a convenient WH-model for the $��$-meson leading-twist wavefunction, in which the parameter $B_{2;��}^\bot\sim a^\bot_2$ dominantly controls its longitudinal distribution. Typically, its DA $��_{2;��}^\bot$ is CZ-like as $B_{2;��}^\bot\simeq-0.20$, which changes to be asymptotic-like as $B_{2;��}^\bot\simeq0.00$. By varying $B_{2;��}^\bot\in[-0.20,0.20]$, we present a detailed comparison of the LCSR estimation for the $B\to��$ TFFs with those of pQCD and Lattice QCD predictions. Furthermore, by using the extrapolated TFFs, we estimate the CKM-matrix element $|V_{\rm ub}|$ with the help of two $B\to��$ semi-leptonic decays. The predicted value for $|V_{\rm ub}|$ increases with the increment of $B_{2;��}^\bot$, i.e. we have $\Vub=(2.91\pm0.19)\times 10^{-3}$ for $B_{2;��}^\bot=-0.20$ and $\Vub=(3.11\pm0.19)\times 10^{-3}$ for $B_{2;��}^\bot=0.00$. If using the BABAR prediction as a criteria, we observe that $B^{\perp}_{2;��}\in[-0.2,0.10]$, which indicates that the $��$-meson DA $��_{2;��}^\bot$ prefers a single-peak behavior rather than a double-humped behavior., 14 pages, 3 figures and 12 tables. References updated and discussions improved. To be published in J. Phys. G

We present a detailed calculation on the $B\to K^*$ transition form factors (TFFs), $A_{0,1,2}$, $V$ and $T_{1,2,3}$, within the QCD light-cone sum rules (LCSR). To suppress the contributions from high-twist light-cone distribution amplitudes, we adopt a right-handed chiral correlator to do the LCSR calculation. In the resultant LCSRs for the TFFs, the transverse leading-twist distribution amplitude $��_{2;K^*}^\bot$ provides over $90\%$ contribution, thus those TFFs provide good platforms for testing the property of $��_{2;K^*}^\bot$. We suggest a model for $��_{2;K^*}^\bot$, in which two parameters $B_{2;K^*}^\bot$ and $C_{2;K^*}^\bot$ dominantly control its longitudinal distribution. With a proper choice of $B_{2;K^*}^\bot$ and $C_{2;K^*}^\bot$, our predictions on $B\to K^*$ TFFs are consistent with those of lattice QCD predictions. As an application, we also calculate the branching fraction of the $B$-meson rare decay $B \to K^* ��^+ ��^-$. The predicted differential branching fraction $d{\cal B}/dq^2(B\to K^{*}��^+��^-)$ is consistent with the LHCb and Belle measurements within errors. After integrating over the allowable $q^2$-region, we get the branching fraction, ${\cal B}(B\to K^*��^+��^-) = \left(1.088^{+0.261}_{-0.205} \right)\times 10^{-6}$, where the errors are squared average of the mentioned error sources. When the precision of experimental measurements or the other source of theoretical uncertainties for this process have been further improved in the future, we may get a definite conclusion on the behavior of $��_{2;K^*}^\bot$., 15 pages, 10 figures. Revised version to be published in J.Phys.G