arXiv subjects

Xing-Gang Wu

Publications and source records attributed to Xing-Gang Wu.

At least 181 records · Page 10Linked to original sources

arXiv2014

An analysis of $H \to γγ$ up to three-loop QCD corrections

The principle of maximum conformality (PMC) provides a convenient way for setting the optimal renormalization scales for high-energy processes, which can eliminate the conventional renormalization scale error via an order-by-order manner. At present, we make a detailed PMC analysis on the Higgs decay $H\rightarrow γγ$ up to three-loop QCD corrections. As an important point of deriving reliable PMC estimation, it is noted that only those $\{β_i\}$-terms that rightly determine the running behavior of coupling constant via the renormalization group equation should be absorbed into the coupling constant, and those $\{β_i\}$-terms that pertain to the quark mass renormalization and etc. should be kept as a separate. To avoid confusion of separating and absorbing different types of $\{β_i\}$-terms into the coupling constant, we first transform the decay width in terms of top quark $\overline{\rm MS}$ mass into that of on-shell mass and then apply the PMC scale setting. After applying PMC scale setting, the final estimation is conformal and is scheme-independent and scale-independent. Up to three-loop QCD corrections, we obtain a PMC scale $μ^{\rm PMC}_{r}=242.3$ GeV $\sim 2M_H$, which is optimal and highly independent of any choice of initial scale. Thus, we obtain a more accurate scale-independent prediction by taking the Higgs mass as the same as that of ATLAS and CMS measurements, i.e., $Γ(H\rightarrow γγ)|_{\rm ATLAS}=9.504^{+0.226}_{-0.252}$ keV and $Γ(H\rightarrow γγ)|_{\rm CMS}=9.568^{+0.195}_{-0.191}$ keV, where the error is caused by the measured Higgs mass, i.e. the Higgs mass $M_{H}$ is taken as $125.5\pm0.2^{+0.5}_{-0.6}$ GeV for ATLAS and $125.7\pm0.3\pm0.3$ GeV for CMS, respectively.

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arXiv2014

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 $\left<ξ^2\right>|_{\rm 1\;GeV} = 0.338 \pm 0.032$, $\left<ξ^4\right>|_{\rm 1\;GeV} = 0.211 \pm 0.030$ and $\left<ξ^6\right>|_{\rm 1\;GeV} = 0.163 \pm 0.030$. 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 $a^π_2|_{\rm 1\;GeV} = 0.403 \pm 0.093$, which is consistent with those obtained in the literature within errors but prefers a larger central value as indicated by lattice QCD predictions.

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arXiv2014

$V_{cb}$ from the semileptonic decay $B\to D \ell \barν_{\ell}$ and the properties of the $D$ 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 ($ϕ_{3D}$), 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.

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arXiv2014

Bottomonium production associated with a photon at a high luminosity $e^+e^-$ collider with next-to-leading order QCD corrections

We make a detailed discussion on the one-loop QCD correction to the bottomonium production associated with a photon, i.e. via the channel $e^{+}e^{-} \toγ^*/Z^0 \to |H_{b\bar{b}}\rangle + γ$, where $|H_{b\bar{b}}\rangle$ stands for the color-singlet bottomonium state as $η_b$, $Υ$, $h_b$ or $χ_{bJ}$ ($J$=0, 1 or 2), respectively. At the super $Z$ factory with the collision energy $E_{cm} \sim m_Z$, by summing up the cross sections for all bottomonium states, we obtain a large one-loop QCD correction, i.e. $|R|\sim 30\%$. This ensures the necessity and importance of the one-loop QCD corrections for the present processes. Further more, for the $η_b$, $h_b$ and $χ_{bJ}$ production, their cross sections are dominated by the $s$-channel diagrams and are enhanced by the $Z^0$ boson resonance effect when $E_{cm}\sim m_Z$. While, for the $Υ$ production, such resonance effect shall be smeared by a large $t(u)$-channel contribution that dominant over the $s$-channel one. Theoretical uncertainties caused by slight change of $E_{cm}$, the $b$-quark mass, the renormalization scale and etc. have been presented. At the super $Z$ factory with a high luminosity up to ${\cal L}=10^{36}{\rm cm}^{-2}{\rm s}^{-1}$, the bottomonium plus one photon events are sizable, especially for $η_b$ and $Υ$, which have large signal significance. Summing up all bottomonium states, we shall totally have $\sim 3.8\times10^{5}$ bottomonium events in one operation year. So, the super $Z$ factory shall provide a good platform for studying the bottomonium properties.

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arXiv2014

Hadronic decays of the spin-singlet heavy quarkomium under the principle of maximum conformality

The principle of maximum conformality (PMC) provides a way to eliminate the conventional renormalization scale ambiguity in a systematic way. By applying the PMC scale setting, all non-conformal terms in perturbative series are summed into the running coupling, and one obtains a unique, scale-fixed prediction at any finite order. In the paper, we make a detailed PMC analysis for the spin-singlet heavy quarkoniums decay (into light hadrons) at the next-to-leading order. After applying the PMC scale setting, the decay widths for all those cases are almost independent of the initial renormalization scales. The PMC scales for $η_c$ and $h_c$ decays are below $1$ GeV, in order to achieve a confidential pQCD estimation, we adopt several low-energy running coupling models to do the estimation. By taking the MPT model, we obtain: $Γ(η_{c} \to LH)=25.09^{+5.52}_{-4.28}$ MeV, $Γ(η_{b} \to LH)=14.34^{+0.92}_{-0.84}$ MeV, $Γ(h_{c} \to LH)=0.54^{+0.06}_{-0.04}$ MeV and $Γ(h_{b} \to LH)=39.89^{+0.28}_{-0.46}$ KeV, where the errors are calculated by taking $m_{c}\in[1.40\rm GeV,1.60\rm GeV]$ and $m_{b}\in[4.50\rm GeV,4.70\rm GeV]$. These decay widths agree with the principle of minimum sensitivity estimations, in which the decay widths of $η_{c,b}$ are also consistent with the measured ones.

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arXiv2014

Hadronic production of $Ξ_{cc}$ at a fixed-target experiment at the LHC

In the paper, we present a detailed discussion on the $Ξ_{cc}$ production at a fixed target experiment at the LHC (After@LHC). The doubly charmed baryon $Ξ_{cc}$ is produced via the channel, ${\rm Proton} + {\rm Proton}\toΞ_{cc}+X$. In estimating its hadroproduction, we discuss three dominant subprocesses, e.g. $g+g\to Ξ_{cc} +\bar{c} +\bar{c}$, $g+c\to Ξ_{cc}+\bar{c}$ and $c+c\to Ξ_{cc}+g$. During the production, it shall first generate a binding diquark and then form the $Ξ_{cc}$ baryon by grabbing soft light-quarks or gluons. We observe that both the two diquark configurations $(cc)[^3S_1]_{\bf\bar 3}$ and $(cc)[^1S_0]_{\bf 6}$ can have sizable contributions to the $Ξ_{cc}$ production. Large number of $Ξ_{cc}$ events can be generated at the After@LHC, whose total production cross section is larger than that of the SELEX experiment by about thirty-five times. It may also possible to study the properties of $Ξ_{bc}$ at the After@LHC. More specifically, we shall have about $8.3 \times 10^6$ $Ξ_{cc}$ events/year and $1.8 \times 10^4$ $Ξ_{bc}$ events/year when its integrated luminosity approaches to $2$ fb$^{-1}$/year. Thus, in addition to SELEX and LHC, the After@LHC shall provide another useful platform for studying the baryon properties.

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arXiv2014

The Higgs boson inclusive decay channels $H \to b\bar{b}$ and $H \to gg$ up to four-loop level

The principle of maximum conformality (PMC) has been suggested to eliminate the renormalization scheme and renormalization scale uncertainties, which are unavoidable for the conventional scale setting and are usually important errors for theoretical estimations. In this paper, by applying PMC scale setting, we analyze two important inclusive Standard Model Higgs decay channels, $H\rightarrow b\bar{b}$ and $H\rightarrow gg$, up to four-loop and three-loop levels accordingly. After PMC scale setting, it is found that the conventional scale uncertainty for these two channels can be eliminated to a high degree. There is small residual initial scale dependence for the Higgs decay widths due to unknown higher-order $\{β_i\}$-terms. Up to four-loop level, we obtain $Γ(H\rightarrow b\bar{b}) = 2.389\pm0.073 \pm0.041$ MeV and up to three-loop level, we obtain $Γ(H\rightarrow gg) = 0.373\pm0.030$ MeV, where the first error is caused by varying $M_H=126\pm4$ GeV and the second error for $H\to b\bar{b}$ is caused by varying the $\overline{\rm MS}$-running mass $m_b(m_b)=4.18\pm0.03$ GeV. Taking $H\to b\bar{b}$ as an example, we present a comparison of three BLM-based scale setting approaches, e.g. the PMC-I approach based on the PMC-BLM correspondence, the $R_δ$-scheme and the seBLM approach, all of which are designed to provide effective ways to identify non-conformal $\{β_i\}$-series at each perturbative order. At four-loop level, all those approaches lead to good pQCD convergence, they have almost the same pQCD series, and their predictions are almost independent on the initial renormalization scale. In this sense, those approaches are equivalent to each other.

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arXiv2014

Heavy and light meson wavefunctions

We present a short review on the properties of heavy and light mesons' light-cone wavefunctions (LCWFs), and their distribution amplitudes (DAs). The B meson LCWFs can be treated by taking the heavy quark limit ($m_b\to\infty$) and by using the heavy quark effective theory. Furthermore, we propose a simple model for the B meson WFs with 3-particle Fock states' contributions, whose behaviors are controlled by two parameters $\barΛ$ and $δ$. Using such model, the form factors $F^{B\toπ}_{+,0,T}$ and $F^{B\to K}_{+,0,T}$ in large recoil region are studied up to ${\cal O}(1/m_b^2)$ within the $k_T$ factorization approach. On the other hand, we adopt Brodsky-Huang-Lepage (BHL) prescription for constructing the WFs of the lighter pseudoscalars as $η_c$, D-meson, pion, kaon, $η^{(\prime)}$ and etc. Such BHL-like model can be conveniently extended to construct the LCWFs for light scalar or vector mesons. Within such model the longitudinal distributions of those WFs are basically determined by a parameter $B$, whose value can be determined via a global fit of experimental data.

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arXiv2014

Systematic Scale-Setting to All Orders: The Principle of Maximum Conformality and Commensurate Scale Relations

We present in detail a new systematic method which can be used to automatically eliminate the renormalization scheme and scale ambiguities in perturbative QCD predictions at all orders. We show that all of the nonconformal β-dependent terms in a QCD perturbative series can be readily identified by generalizing the conventional renormalization schemes based on dimensional regularization. We then demonstrate that the nonconformal series of pQCD at any order can be resummed systematically into the scale of the QCD coupling in a unique and unambiguous way due to a special degeneracy of the β-terms in the series. The resummation follows from the principal of maximum conformality (PMC) and assigns a unique scale for the running coupling at each perturbative order. The final result is independent of the initial choices of renormalization scheme and scale, in accordance with the principles of the renormalization group, and thus eliminates an unnecessary source of systematic error in physical predictions. We exhibit several examples known to order α_s^4; i.e. i) the electron-positron annihilation into hadrons, ii) the tau-lepton decay to hadrons, iii) the Bjorken and Gross-Llewellyn Smith (GLS) sum rules, and iv) the static quark potential. We show that the final series of the first three cases are all given in terms of the anomalous dimension of the gluon field, in accordance with conformality, and with all non-conformal properties encoded in the running coupling. The final expressions for the Bjorken and GLS sum rules directly lead to the generalized Crewther relations, exposing another relevant feature of conformality. The static quark potential shows that PMC scale setting in the Abelian limit is to all orders consistent with QED scale setting. Finally, we demonstrate that the method applies to any renormalization scheme and [...]

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arXiv2013

Next-to-leading order QCD corrections for the charmonium production via the channel $e^+ e^- \to H(|c\bar{c}\rangle) + γ$ round the $Z^0$ peak

In our previous work [2], it has been found that sizable charmonium events via the channel $e^+e^- \to γ^*/Z^0 \to H(|c\bar{c}\rangle) +γ$ can be produced at the suggested super $Z$ factory, where $H(|c\bar{c}\rangle)$ represents the dominant color-singlet $S$-wave and $P$-wave charmonium states $J/ψ$, $η_c$, $h_c$ and $χ_{cJ}$ ($J=0, 1, 2$), respectively. As an important step forward, in the present paper, we present a next-to-leading order (NLO) QCD analysis within the framework of nonrelativistic QCD. In different to the case of $B$ factory in which the single charmonium production is dominated by the channel via a virtual photon, at the super $Z$ factory, its cross-section is dominated by the channel via a $Z^0$ boson. Estimations up to NLO level are done at both the $B$ factory and the super $Z$ factory experimental conditions. We observe that the NLO distributions have the same shapes as those of LO distributions, but their differences are sizable. This indicates that a NLO calculation is necessary and important to achieve a more accurate estimation. Due to $Z^0$ boson resonance effect, at the super $Z$ factory with a high luminosity up to $10^{36}{\rm cm}^{-2}{\rm s}^{-1}$, when summing all the color-singlet states' contribution together, one may observe about $8.0\times10^{4}$ charmonium events via the channel $e^+e^-\to Z^0 \to H(|c\bar{c}\rangle)+γ$ in one operation year. Then, such super $Z$ factory could provide another useful platform to study the charmonium properties, even for the higher charmonium states.

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arXiv2013

BCVEGPY and GENXICC for the hadronic production of the doubly heavy mesons and baryons

Doubly heavy mesons and baryons provide a good platform for testing pQCD. Two generators BCVEGPY and GENXICC for simulating the hadronic production of the doubly heavy mesons and baryons have been developed in recent years. In this talk, we present their main idea and their recent progresses. The dominant gluon-gluon fusion mechanism programmed in those two generators are written based on the improved helicity amplitude approach, in which the hard scattering amplitude are dealt with directly at the amplitude level and the numerical efficiency are greatly improved by properly decomposing the Feynman diagrams and by fully applying the symmetries among them. Moreover, in comparison to the previous versions, we have updated the programs in order to generate the unweighted meson or baryon events much more effectively within various simulation environments. The generators can be conveniently imported into PYTHIA to do further hadronization and decay simulation.

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arXiv2013

Exclusive charmonium production from $e^+ e^-$ annihilation round the $Z^0$ peak

We make a comparative and comprehensive study on the charmonium exclusive productions at the $e^+e^-$ collider with the collision energy either round the $Z^0$-boson mass for a super $Z$ factory or equals to 10.6 GeV for the $B$ factories as Belle and BABAR. We study the total cross sections for the charmonium production via the exclusive processes $e^+e^- \to γ^*/Z^0 \to H_{1}+H_{2}$ and $e^+e^- \to γ^*/Z^0 \to H_{1} +γ$, where $H_{1}$ and $H_{2}$ represent the dominant color-singlet $S$-wave and $P$-wave charmonium states respectively. Total cross sections versus the $e^+e^-$ collision energy $\sqrt{s}$, together with their uncertainties, are presented, which clearly show the relative importance of these channels. At the $B$ factory, the production channels via the virtual $γ^*$ propagator are dominant over the channels via the $Z^0$ propagator by about four orders. While, at the super $Z$ factory, due to the $Z^0$-boson resonance effect, the $Z^0$ boson channels shall provide sizable or even dominant contributions in comparison to the channels via the $γ^*$ propagator. Sizable exclusive charmonium events can be produced at the super $Z$ factory with high luminocity up to $10^{36}{\rm cm}^{-2}{\rm s}^{-1}$, especially for the channel of $e^+e^- \to Z^0 \to H_{1} +γ$, e.g. by taking $m_c=1.50\pm0.20$ GeV, we shall have $(5.0^{+0.8}_{-0.6})\times10^4$ $J/ψ$, $(7.5^{+1.1}_{-0.9})\times10^3$ $η_c$, $(6.2^{+3.3}_{-1.9})\times10^3$ $h_{c}$, $(3.1^{+1.7}_{-0.9})\times10^2$ $χ_{c0}$, $(2.2^{+1.0}_{-0.4})\times10^3$ $χ_{c1}$, and $(7.7^{+4.1}_{-2.4})\times10^2$ $χ_{c2}$ events by one operation year. Thus, in addition to the $B$ factories as BABAR and Belle, such a super $Z$ factory shall provide another useful platform for studying the heavy quarkonium properties and for testing QCD theories.

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arXiv2013

Reanalysis of the BFKL Pomeron at the next-to-leading logarithmic accuracy

We apply the principle of maximum conformality (PMC) to the Balitsky-Fadin-Kuraev-Lipatov (BFKL) Pomeron intercept at the next-to-leading logarithmic (NLL) accuracy. The PMC eliminates the conventional renormalization scale ambiguity by absorbing the non-conformal $\{β_i\}$-terms into the running coupling, and a more accurate pQCD estimation can be obtained. After PMC scale setting, the QCD perturbative convergence can be greatly improved due to the elimination of renormalon terms in pQCD series, and the BFKL Pomeron intercept has a weak dependence on the virtuality of the reggeized gluon. For example, by taking the Fried-Yennie gauge, we obtain $ω_{\rm MOM}^{\rm PMC}(Q^{2},0)\in [0.149,0.176]$ for $Q^2\in[1,100]\;{\rm GeV}^2$. This is a good property to apply to the high-energy phenomenology. Further more, to compare with the data, it is found that the physical ${\rm MOM}$-scheme is more reliable than the $\overline{\rm MS}$-scheme. The ${\rm MOM}$-scheme is gauge dependent, which can also be greatly suppressed after PMC scale setting. We discuss the MOM-scheme gauge dependence for the Pomeron intercept by adopting three gauges, i.e. the Landau gauge, the Feynman gauge and the Fried-Yennie gauge, and we obtain $ω_{\rm MOM}^{\rm PMC}(Q^{2}=15\;{\rm GeV}^2,0) = 0.166^{+0.010}_{-0.017}$; i.e. about $10\%$ gauge dependence is observed. We apply the BFKL Pomeron intercept to the photon-photon collision process, and compare the theoretical predictions with the data from the OPAL and L3 experiments.

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arXiv2013

$J/ψ+χ_{cJ}$ Production at the $B$ Factories under the Principle of Maximum Conformality

Under the conventional scale setting, the renormalization scale uncertainty usually constitutes a systematic error for a fixed-order perturbative QCD estimation. The recently suggested principle of maximum conformality (PMC) provides a principle to eliminate such scale ambiguity in a step-by-step way. Using the PMC, all non-conformal terms in perturbative expansion series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. In the paper, we make a detailed PMC analysis for both the polarized and the unpolarized cross sections for the double charmonium production process, $e^{+} + e^{-} \to J/ ψ(ψ') + χ_{cJ}$ with $(J=0,1,2)$. The running behavior for the coupling constant, governed by the PMC scales, are determined exactly for the specific processes. We compare our predictions with the measurements at the $B$ factories, BABAR and Belle, and the theoretical estimations obtained in the literature. Because the non-conformal terms are different for various polarized and unpolarized cross sections, the PMC scales of these cross sections are different in principle. It is found that all the PMC scales are almost independent of the initial choice of renormalization scale. Thus, the large renormalization scale uncertainty usually adopted in the literature up to $sim40%$ at the NLO level, obtained from the conventional scale setting, for both the polarized and the unpolarized cross sections are greatly suppressed. It is found that the charmonium production is dominated by J=0 channel. After PMC scale setting, we obtain $σ(J/ψ+χ_{c0}) = 12.25^{+3.70}_{-3.13}$ fb and $σ(ψ'+χ_{c0}) =5.23^{+1.56}_{-1.32}$ fb,......

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arXiv2013

Determination of the pion distribution amplitude

Right now, we have not enough knowledge to determine the hadron distribution amplitudes (DAs) which are universal physical quantities in the high energy processes involving hadron for applying pQCD to exclusive processes. Even for the simplest pion, one can't discriminate from different DA models. Inversely, one expects that processes involving pion can in principle provide strong constraints on the pion DA. For example, the pion-photon transition form factor (TFF) can get accurate information of the pion wave function or DA, due to the single pion in this process. However, the data from Belle and BABAR have a big difference on TFF in high $Q^2$ regions, at present, they are helpless for determining the pion DA. At the present paper, we think it is still possible to determine the pion DA as long as we perform a combined analysis of the most existing data of the processes involving pion such as $π\to μ\barν$, $π^0 \to γγ$, $B\to πl ν$, $D \to πl ν$, and etc. Based on the revised light-cone harmonic oscillator model, a convenient DA model has been suggested, whose parameter $B$ which dominates its longitudinal behavior for $ϕ_π(x,μ^2)$ can be determined in a definite range by those processes. A light-cone sum rule analysis of the semi-leptonic processes $B \to πl ν$ and $D \to πl ν$ leads to a narrow region $B = [0.01,0.14]$, which indicate a slight deviation from the asymptotic DA. Then, one can predict the behavior of the pion-photon TFF in high $Q^2$ regions which can be tested in the future experiments. Following this way it provides the possibility that the pion DA will be determined by the global fit finally.

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arXiv2013

A Systematic All-Orders Method to Eliminate Renormalization-Scale and Scheme Ambiguities in PQCD

We introduce a generalization of the conventional renormalization schemes used in dimensional regularization, which illuminates the renormalization scheme and scale ambiguities of pQCD predictions, exposes the general pattern of nonconformal {β_i}-terms, and reveals a special degeneracy of the terms in the perturbative coefficients. It allows us to systematically determine the argument of the running coupling order by order in pQCD in a form which can be readily automatized. The new method satisfies all of the principles of the renormalization group and eliminates an unnecessary source of systematic error.

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arXiv2013

Revisiting the $B^{(*)}_s$-Meson Production at the Hadronic Colliders

The production of heavy-flavored hadron at the hadronic colliders provides a challenging opportunity to test the validity of pQCD predictions. There are two mechanisms for the $B^{(*)}_s$ hadroproduction, i.e. the gluon-gluon fusion mechanism via the subprocess $g+g\rightarrow B^{(*)}_s+b+\bar{s}$ and the extrinsic heavy quark mechanism via the subprocesses $g+\bar{b}\to B^{(*)}_s +\bar{s}$ and $g+s\to B^{(*)}_s +b$, both of which shall have sizable contributions in proper kinematic region. Different from the fixed-flavor-number scheme (FFNS) previously adopted in the literature, we study the $B^{(*)}_s$ hadroproduction under the general-mass variable-flavor-number scheme (GM-VFNS), in which we can consistently deal with the double counting problem from the above two mechanisms. Properties for the $B^{(*)}_s$ hadroproduction are discussed. To be useful reference, a comparative study of FFNS and GM-VFNS is presented. Both of which can provide reasonable estimations for the $B^{(*)}_s$ hadroproduction. At the Tevatron, the difference between these two schemes is small, however such difference is obvious at the LHC. The forthcoming more precise data on LHC shall provide a good chance to check which scheme is more appropriate to deal with the $B^{(*)}_s$-meson production and to further study the heavy quark components in hadrons.

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arXiv2013

Heavy Quarkonium Production through the Semi-Exclusive $e^+ e^-$ Annihilation Channels around the $Z^0$ Peak

Within the framework of the non-relativistic QCD, we present a detailed discussion on the heavy quarkonium production at the leading order in $α_s$ at a $e^+ e^-$ collider with the collision energy around the $Z^0$ peak. Quarkonia are produced through the semi-exclusive channels $e^{+}e^{-} \rightarrow |H_{Q\bar{Q}}\rangle +X$ with $X=Q\bar{Q}$ or $gg$, where $Q$ indicates a heavy quark (respectively $b$ or $c$). It is noted that in addition to the color-singlet 1S-level quarkonium states, the 2S and 1P color-singlet states and the color-octet $|(Q\bar{Q})[1^3S_1^{({\bf 8})}]g\rangle$ state also provide sizable contributions. The heavy quarkonium transverse momentum and rapidity distributions for the $e^+ e^-$ collision energy $E_{cm}=m_Z$ are presented. For both charmonium and bottomonium production via the $Z^0$ propagator, there is approximate "spin degeneracy" between the spin-triplet and spin-singlet quarkonium states. Uncertainties for the total cross sections are estimated by taking $m_c=1.50\pm0.15$ GeV and $m_b=4.90\pm0.15$ GeV. Around $E_{cm}=m_{Z}$, due to the $Z^0$-boson resonance effect, total cross sections for the channels via the $Z^0$-propagator become much larger than the channels via the virtual photon propagator. We conclude that, in addition to the $B$ factories as BaBar and Belle and the hadronic colliders as Tevatron and LHC, such a super $Z$-factory will present an excellent platform for studying the heavy quarkonium properties.

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