Heavy Quarkonium Production at LHC through WW Boson Decays

The production of the heavy $(c\bar{c})$-quarkonium, $(c\bar{b})$-quarkonium and $(b\bar{b})$-quarkonium states ($(Q\bar{Q'})$-quarkonium for short), via the $W^+$ semi-inclusive decays, has been systematically studied within the framework of the non-relativistic QCD. In addition to the two color-singlet $S$-wave states, we also discuss the production of the four color-singlet $P$-wave states $|(Q\bar{Q'})(^1P_1)_{\bf 1}>$ and $(Q\bar{Q'})(^3P_J)_{\bf 1}>$ (with $J=(1,2,3)$) together with the two color-octet components $|(Q\bar{Q'})(^1S_0)_{\bf 8}>$ and $|(Q\bar{Q'})(^3S_1)_{\bf 8}>$. Improved trace technology is adopted to derive the simplified analytic expressions at the amplitude level, which shall be useful for dealing with the following cascade decay channels. At the LHC with the luminosity ${\cal L}\propto 10^{34}cm^{-2}s^{-1}$ and the center-of-mass energy $\sqrt{S}=14$ TeV, sizable heavy-quarkonium events can be produced through the $W^+$ boson decays, i.e. $2.57\times10^6$ $\eta_c$, $2.65\times10^6$ $J/\Psi$ and $2.40\times10^6$ $P$-wave charmonium events per year can be obtained; and $1.01\times10^5$ $B_c$, $9.11\times10^4$ $B^*_c$ and $3.16\times10^4$ $P$-wave $(c\bar{b})$-quarkonium events per year can be obtained. Main theoretical uncertainties have also been discussed. By adding the uncertainties caused by the quark masses in quadrature, we obtain $\Gamma_{W^+\to (c\bar{c})+c\bar{s}} =524.8^{+396.3}_{-258.4}$ KeV, $\Gamma_{W^+\to (c\bar{b})+b\bar{s}} =13.5^{+4.73}_{-3.29}$ KeV, $\Gamma_{W^+\to (c\bar{b})+c\bar{c}}= 1.74^{+1.98}_{-0.73}$ KeV and $\Gamma_{W^+\to (b\bar{b})+c\bar{b}}= 38.6^{+13.4}_{-9.69}$ eV.Comment: 24 pages, 12 figures. References updated. To be published in Phys.Rev. D. To match the published versio

Eliminating the Renormalization Scale Ambiguity for Top-Pair Production Using the Principle of Maximum Conformality

It is conventional to choose a typical momentum transfer of the process as the renormalization scale and take an arbitrary range to estimate the uncertainty in the QCD prediction. However, predictions using this procedure depend on the renormalization scheme, leave a non-convergent renormalon perturbative series, and moreover, one obtains incorrect results when applied to QED processes. In contrast, if one fixes the renormalization scale using the Principle of Maximum Conformality (PMC), all non-conformal $\{\beta_i\}$-terms in the perturbative expansion series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. The PMC scale $\mu^{\rm PMC}_R$ and the resulting finite-order PMC prediction are both to high accuracy independent of the choice of initial renormalization scale $\mu^{\rm init}_R$, consistent with renormalization group invariance. As an application, we apply the PMC procedure to obtain NNLO predictions for the $t\bar{t}$-pair production at the Tevatron and LHC colliders. The PMC prediction for the total cross-section $\sigma_{t\bar{t}}$ agrees well with the present Tevatron and LHC data. We also verify that the initial scale-independence of the PMC prediction is satisfied to high accuracy at the NNLO level: the total cross-section remains almost unchanged even when taking very disparate initial scales $\mu^{\rm init}_R$ equal to $m_t$, $20\,m_t$, $\sqrt{s}$. Moreover, after PMC scale setting, we obtain $A_{FB}^{t\bar{t}} \simeq 12.5$, $A_{FB}^{p\bar{p}} \simeq 8.28$ and $A_{FB}^{t\bar{t}}(M_{t\bar{t}}>450 \;{\rm GeV}) \simeq 35.0$. These predictions have a $1\,\sigma$-deviation from the present CDF and D0 measurements; the large discrepancy of the top quark forward-backward asymmetry between the Standard Model estimate and the data are thus greatly reduced.Comment: 4 pages. Detailed derivations for the top-quark pair total cross-sections and forward-backward asymmetry can be found in Refs.[arXiv:1204.1405; arXiv:1205.1232]. To match the published version. To be published in Phys.Rev.Let

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 {\beta_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.Comment: 5 pages, 1 figure, revised to match the published versio

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 \beta-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 \beta-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 \alpha_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 [...]Comment: 20 pages; Appendix added. This version matches the published pape

The Renormalization Scale-Setting Problem in QCD

A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The conventional scale-setting procedure assigns an arbitrary range and an arbitrary systematic error to fixed-order pQCD predictions. In fact, this {\it ad hoc} procedure gives results which depend on the choice of the renormalization scheme, and it is in conflict with the standard scale-setting procedure used in QED. Predictions for physical results should be independent of the choice of scheme or other theoretical conventions. We review current ideas and points of view on how to deal with the renormalization scale ambiguity and show how to obtain renormalization scheme- and scale- independent estimates. We begin by introducing the renormalization group (RG) equation and an extended version, which expresses the invariance of physical observables under both the renormalization scheme and scale-parameter transformations. The RG equation provides a convenient way for estimating the scheme- and scale- dependence of a physical process. We then discuss self-consistency requirements of the RG equations, such as reflexivity, symmetry, and transitivity, which must be satisfied by a scale-setting method. Four typical scale setting methods suggested in the literature, {\it i.e.,} the Fastest Apparent Convergence (FAC) criterion, the Principle of Minimum Sensitivity (PMS), the Brodsky-Lepage-Mackenzie method (BLM), and the Principle of Maximum Conformality (PMC), are introduced. Basic properties and their applications are discussed. We pay particular attention to the PMC, which satisfies all of the requirements of RG invariance...... [full Abstract is in the paper].Comment: 75 pages, 19 figures. Review article to be published in Prog. Part. Nucl. Phy

B_c Meson Production Around the Z^0 Peak at a High Luminosity e^+ e^- Collider

Considering the possibility to build an e{sup +}e{sup -} collider at the energies around the Z{sup 0}-boson resonance with a planned luminosity so high as L {proportional_to} 10{sup 34} {approx} 10{sup 36} cm{sup -2}s{sup -1} (super Z-factory), we make a detailed discussion on the (c{bar b})-quarkonium production through e{sup +}e{sup -} {yields} (c{bar b})[n] + b + {bar c} within the framework of non-relativistic QCD. Here [n] stands for the Fock-states |(c{sub b}){sub 1}[{sup 1}S{sub 0}]>, |(c{bar b})8[{sup 1}S{sub 0}]g>, |(c{bar b} ){sub 1}[{sup 3}S{sub 1}]>, |(c{bar b}){sub 8}[{sup 3}S{sub 1}]g>, |(c{bar b}){sub 1}[{sup 1}P{sub 1}]> and |(c{bar b}){sub 1}[{sup 3}P{sub J}]> (with J = (1, 2, 3)) respectively. To simplify the hard-scattering amplitude as much as possible and to derive analytic expressions for the purpose of future events simulation, we adopt the 'improved trace technology' to do our calculation, which deals with the hard scattering amplitude directly at the amplitude level other than the conventional way at the squared-amplitude level. Total cross-section uncertainties caused by the quark masses are predicted by taking m{sub c} = 1.50 {+-} 0.30 GeV and m{sub b} = 4.90 {+-} 0.40 GeV. If all higher (c{bar b})-quarkonium states decay to the ground state B{sub c} (|(c{bar b}){sub 1}[{sup 1}S{sub 0}]>) with 100% efficiency, we obtain {sigma}{sub e{sup +}+e{sup -}{yields}B{sub c}+b+{bar c}} = 5.190{sub -2.419}{sup +6.222} pb, which shows that about 10{sup 5} {approx} 10{sup 7} B{sub c} events per operation year can be accumulated in the super Z-factory. If taking the collider energy runs slightly off the Z{sup 0}-peak, i.e. {radical}S = (1.00 {+-} 0.05)m{sub Z}, the total cross-section shall be lowered by about one-order from its peak value. Such a super Z-factory shall provide another useful platform to study the properties of B{sub c} meson, or even the properties of its excited P-wave states, in addition to its production at the hadronic colliders Tevatron and LHC