In this paper, we calculate the branching ratios for $B^+\to D_s^+η, B^+\to D_s^+η^{\prime}$, $B^+\to D_s^{*+}η$ and $ B^+\to D_s^{*+}η^{\prime}$ decays by employing the perturbative QCD (pQCD) factorization approach. Under the two kinds of $η-η^{\prime}$ mixing schemes, the quark-flavor mixing scheme and the singlet-octet mixing scheme, we find that the calculated branching ratios are consistent with the currently available experimental upper limits. We also considered the so called "$f_{D_s}$ puzzle", by using two groups of parameters about the $D^{(*)}_s$ meson decay constants, that is $f_{D_s}=241$ MeV, $f_{D^*_s}=272$ MeV and $f_{D_s}=274$ MeV, $f_{D^*_s}=312$ MeV, to calculate the branching ratios for the considered decays. We find that the results change $30\%$ by using these two different groups of paramters.
We calculate the CP averaged branching ratios and CP-violating asymmetries for $B^0 \to ηη, ηη^\prime$ and $η^\prime η^\prime$ decays by employing the perturbative QCD (pQCD) factorization approach. The pQCD predictions for the CP-averaged branching ratios are $Br(B^0 \to ηη) \approx 0.67 \times 10^{-7}$, $Br(B^0 \to ηη^\prime) \approx 0.18 \times 10^{-7}$, and $Br(B^0 \to η^{\prime} η^{\prime}) \approx 0.11 \times 10^{-7}$, which are consistent with currently available experimental upper limits. We also predict large CP-violating asymmetries for the considered three decay modes, which can be …
In this work, we calculate the $CP$-averaged branching ratios and direct $CP$-violating asymmetries of the quasi-two-body decays $B_{(s)}\to P ρ^\prime(1450), Pρ^{\prime\prime}(1700)\to P ππ$ by employing the perturbative QCD (PQCD) factorization approach, where $P$ is a light pseudoscalar meson $K, π, η$ and $η^{\prime}$. The considered decay modes are studied in the quasi-two-body framework by parameterizing the two-pion distribution amplitude $Φ_{ππ}^{\rm P}$. The $P$-wave time-like form factor $F_π$ in the resonant regions associated with the $ρ^\prime(1450)$ and $ρ^{\prime\prime}(1700)$ i…
Perturbative NLO and NNLO QCD evolutions of parton distributions are studied, in particular in the (very) small-$x$ region, where they are in very good agreement with all recent precision measurements of $F_2^p(x,Q^2)$. These predictions turn out to be also rather insensitive to the specific choice of the factorization scheme ($\bar{\rm MS}$ or DIS). A characteristic feature of perturbative QCD evolutions is a {\em{positive}} curvature of $F_2^p$ which increases as $x$ decreases. This perturbatively stable prediction provides a sensitive test of the range of validity of perturbative QCD.
We study the rare decays $B^+ \to D^{(*)+}K^{(*)0}$, which can occur only via annihilation type diagrams in the standard model. We calculate all of the four modes, $B \to PP, VP, PV, VV$, in the framework of perturbative QCD approach and give the branching ratios of the order about $10^{-6}$.
We explain how Regge theory and perturbative evolution may be made compatible at small x. The result not only gives striking support to the two-pomeron description of small-x behaviour, but gives a rather clean test of perturbative QCD itself. When x is very small, or Q^2 is very large, the proton's gluon distribution function is significantly larger than is commonly believed. Perturbative evolution is invalid below Q^2\approx 5 GeV^2.
The $Υ(nS)$ ${\to}$ $B_{c}^{\ast}D$ weak decays ($n$ $=$ $1$, $2$, $3$) are investigated with perturbative QCD approach. It is found that the CKM-favored $Υ(nS)$ ${\to}$ $B_{c}^{\ast}D_{s}$ decays have branching ratio of ${\cal O}(10^{-10})$, which might be potentially accessible to the future LHC and SuperKEKB experiments.
We exploit the fact that within massless perturbative QCD the same Green's function determines the hadronic contribution to the $τ$ decay width and the moments of the $e^+e^-$ cross section. This allows one to obtain relations between physical observables in the two processes up to an unprecedented high order of perturbative QCD. A precision measurement of the $τ$ decay width allows one then to predict the first few moments of the spectral density in $e^+e^-$ annihilations integrated up to $s\sim m_τ^2$ with high accuracy. The proposed tests are in reach of present experimental capabilities.
With the recent investigations of $g^{\ast}g^{\ast}-η^{(\prime)}$ transition form factor and $η-η^{\prime}$ mixing scheme, we present an updated study of the radiative decays $J/Ψ\toη^{(\prime)}γ$ in perturbative QCD. The decays are taken as a test ground for the $g^{\ast}g^{\ast}-η^{(\prime)}$ transition form factors and the $η-η^{\prime}$ mixing scheme. The form factors are found to be working for glunic $η^{(\prime)}$ productions and the mixing angle is constrained to be $ϕ=35.1^{\circ}\pm0.8^{\circ}$.
The strong $D^{*}_sD_{s}η^{(\prime)}$ and $B^{*}_sB_{s}η^{(\prime)}$ vertices are studied and the relevant couplings are calculated in the context of the light-cone QCD sum rule method with twist-4 accuracy by including the next-to-leading order corrections. In the analysis, both the quark and gluon components of the $η$ and $η^{\prime}$ mesons and the axial anomaly corrected higher twist distributions are included.
We review the recent theoretical progress in heavy quarkonium spectroscopy within the boundstate theory based on perturbative QCD. New microscopic pictures of the heavy quarkonium systems are obtained.
Non perturbative results from lattice QCD will be discussed, namely: Vacuum Condensates and QCD Sum Rules; $U_A(1)$ and Topology; Confinement of Color.
Using the global properties of the QCD partition function we determine an all order perturbative beta function in the background gauge field method to find out that it has a simple expressions whose properties and consequences align with other recent results in the QCD literature. We further compute the non-perturbative beta functions for the coupling constant and the theta angle in the background of an instanton field with winding number $n$. We solve for the theta angle in the non-perturbative region to determine that it is approximately zero. By extrapolating to the full QCD beta functions …
Based on parametric reasoning, we provide a simple dynamical picture of how a perturbative parton cascade, in interaction with a QCD medium, fills phase space as a function of time.
Evidence is reviewed suggesting that QCD remains a perturbative theory with a (relatively) small coupling constant down to a distinct infrared boundary on perturbative physics, a boundary corresponding to the momentum scale associated with a beta-function pole.
In these lectures we give a concise introduction to the ideas of renormalon calculus in QED and QCD. We focus in particular on the example of the Adler D function of vacuum polarization, and on relations between perturbative renormalon ambiguities and corresponding non-perturbative Operator Product Expansion (OPE) ambiguities. Recent work on infrared freezing of Euclidean observables is also discussed.
Using recent measurements of the b-quark fragmentation distribution obtained in $e^+e^- \to b \bar{b}$ events registered at the Z pole, the non-perturbative QCD component of the distribution has been extracted independently of any hadronic physics modelling. This distribution depends only on the way the perturbative QCD component has been defined. When the perturbative QCD component is taken from a parton shower Monte-Carlo, the non-perturbative QCD component is rather similar with those obtained from the Lund or Bowler models. When the perturbative QCD component is the result of an analytic N…
We calculate the branching ratios and CP-violating asymmetries for $B^0 \toωη$, $ωη^\prime$, $ϕη$ and $ϕη^\prime$ decays in the perturbative QCD (pQCD) factorization approach. The pQCD predictions for the CP-averaged branching ratios are $Br(B^0 \to ωη) = \left (2.7 ^{+1.1}_{-1.0})\times 10^{-7}$, $Br(B^0 \to ωη^\prime) = \left (0.75 ^{+0.37}_{-0.33}) \times 10^{-7}$, and $Br(B^0 \to ϕη) = \left (6.3 ^{+3.3}_{-1.9}) \times 10^{-9}$, $Br(B^0 \to ϕη^{\prime}) = \left (7.3^{+3.5}_{-2.6}) \times 10^{-9}$ which are consistent with currently available experimental upper limits. The inclusion of the …
The $Ξ_Q^\prime$-$Ξ_Q$ transition magnetic moments are calculated in framework of the light cone QCD sum rules method (LCSR). The values of the transition magnetic moments obtained are compared with the predictions of the other theoretical approaches.
Within the framework of the Fock-Feynman-Schwinger (equivalently, worldline) casting of QCD a four-point process, mediated by a closed quark loop, is studied in the Sudakov kinematical region, first perturbatively and subsequently with the inclusion of non-perturbative contributions through the use of the stochastic vacuum model. Deformations of the, first order, perturbative results are determined. Finally, the resummation of the leading logarithmic terms is performed and physical implications of the result are discussed.
The $η^\prime g^* g^{(*)}$ effective vertex function (EVF) is calculated in the QCD hard-scattering approach, taking into account the $η^\prime$-meson mass. We work in the approximation in which only one non-leading Gegenbauer moment in both the quark-antiquark and gluonic light-cone distribution amplitude for the $η^\prime$-meson is kept. The EVF with one off-shell gluon is shown to have the form $F_{η^\prime g^* g} (q_1^2, 0, m_{η^\prime}^2) = m_{η^\prime}^2 H(q_1^2)/(q_1^2 - m_{η^\prime}^2)$, valid for $|q_1^2| > m_{η^\prime}^2$. An interpolating formulae for the EVF in the space-like regio…
We summarize the current status of our understanding of the structure of the perturbative QCD expressions for the QCD generalization of the Crewther relation.
Using the Kirschner-Lipatov equation as a basis, we study high energy elastic quark-quark amplitudes, which correspond to secondary Reggeons and pion exchange in the double-logarithmic approximation of perturbative QCD.
A brief review of jet physics is presented with an emphasis upon open theoretical problems (non-perturbative domain; hadronization and confinement) and new phenomena (hadroproduction in heavy ion collisions).
This talk brings attention to what is knowable from perturbative QCD theory on two-parton distribution functions in the light of CDF measuruments of the inclusive cross section for double parton scattering.
We perform a study of $W$-boson production in polarized proton-proton collisions through next-to-next-to-leading order (NNLO) in perturbative QCD. This calculation is required to extend the extraction of polarized parton distribution functions to NNLO accuracy. We present differential distributions at $\sqrt{s}=510$ GeV, relevant for comparison to measurements from the Relativistic Heavy Ion Collider (RHIC). The NNLO QCD corrections significantly reduce the scale dependence of the cross section. We compare the longitudinal single-spin asymmetries as a function of lepton pseudorapidity to RHIC …
This is a written version of two lectures given at the First School on Field Theory and Gravitation in Vitoria (Brasil) April 15-19, 1997. We discuss the foundation of QCD as the theory of strong interactions and the perturbative analysis of e^+e^- annihilation into hadrons. Typical concepts of perturbative QCD studies, such as collinear singularities, jets, Sudakov form factors, are explained working out this case.
This is a short write-up of lectures at UK Theory Institute, Swansea UK, Sept.99; and XVII School ``QCD: Perturbative or Non-perturbative?'' Lisbon,Portugal, Oct.99. The covered topic include (i) discussion of the scales at which perturbative description should be changed by the non-perturbative one. A number of various examples are considered, leading to different scales, related to instantons or confinement effects; (ii) Instanton vacuum as an Instanton Liquid; (iii) The phase diagram of QCD at finite temperature and density, and especially description of a recent progress in Color Supercond…
We present the perturbative (PT) and non-perturbative (NP) analysis of the cumulative out-of-event-plane momentum distribution in e+e- annihilation in the near-to-planar three-jet region. A physical interpretation based on simple QCD considerations and kinematical relations will be given, with the aim of extending the described techniques to other multi-jet processes and, possibly, to hadron-hadron collisions.
We present a construction of the pion electromagnetic form factor where the transition from large-Nc Regge vector meson dominance models with infinitely many resonances to perturbative QCD is built in explicitly. The construction is based on an appropriate assignment of residues to the Regge poles, which fulfills the constraints of the parton-hadron duality and perturbative QCD. The model contains a slowly falling off non-perturbative contribution which dominates over the perturbative QCD radiative corrections for the experimentally accessible momenta. The leading order and next-to-leading ord…
We propose that the different angular distributions in two-photon collisions observed at low and high center-of-mass energies $W_{γγ}$ indicate the transition from nonperturbative to perturbative QCD. We calculate the differential cross sections of $γγ\toππ$, $KK$ in the angle $θ$ of one of the final-state mesons using QCD sum rules and the perturbative QCD approach based on $k_T$ factorization theorem. Our predictions from sum rules (perturbative QCD) decrease (increase) with $|\cosθ|$, consistent with the Belle data of $γγ\to K^+K^-$ for $W_{γγ}\approx 1.5$-1.7 (2.2-2.4) GeV.
We calculate the branching ratios and CP asymmetries of the $B\to ϕK$ decays using perturbative QCD approach, which includes $k_T$ and threshold resummations. Our results of branching ratios are consistent with the experimental data and larger than those obtained from the naive factorization assumption and the QCD-improved factorization approach.
A recent form of the Slavnov-Taylor identity for the ghost-gluon vertex of QCD is compared with perturbative results. It is found that this identity, derived assuming ghost-ghost scattering can be neglected, is not consistent with perturbation theory. A new identity is derived at the one-loop perturbative level.
We investigate the non-perturbative effects on the ratio $R=σ_L /σ_T$ in lepton-nucleon deep inelastic scattering by taking into account the lowest dimensional condensate contributions from the QCD vacuum. By combining conventional perturbative QCD corrections and the Georgi- Politzer target-mass effects with the non-perturbative effects from the QCD vacuum, we give a good description of the $Q^2$ and $x$ dependences of $R$ in comparison with the recent experimental data.
I review recent progress in perturbative QCD on two fronts: extending next-to-next-to-leading order QCD corrections to a broader range of collider processes, and applying twistor-space methods (and related spinoffs) to computations of multi-parton scattering amplitudes.
This talk summarizes the presentations given in the Hadronic Physics session at the LEPTRE meeting, emphasizing the importance of LEP data in our quest for a successful approach to non-perturbative QCD.
The perturbative quantum chromodynamics (QCD) is quite successful in the description of main features of multiparticle production processes. Ten most appealing characteristics are described in this brief review talk and compared with QCD predictions. The general perturbative QCD approach is demonstrated and its problems are discussed. It is shown that the analytical calculations at the parton level with the low-momentum cut-off reproduce experimental data on the hadronic final state surprisingly accurately even though the perturbative expansion parameter is not very small. Moreover, the pertur…
I briefly review the progress in perturbative QCD calculations in LEP era and discuss the prospects for the extension of their accuracy to higher orders.
After some general remarks on non-perturbative QCD I present shortly models which lead to a color-electric flux tube formation. The implications of such a flux tube formation especially on high energy scattering are discussed.
We study the $η^\prime g^* g^*$ vertex for arbitrary gluon virtualities in the time-like and space-like regions, using the perturbative QCD hard scattering approach and an input wave-function of the $η^\prime$-meson consistent with the measured $η^\prime γ^* γ$ transition form factor. The contribution of the gluonic content of the $η^\prime$-meson is taken into account, enhancing the form factor over the entire virtuality considered. However, data on the electromagnetic transition form factor of the $η^\prime$-meson is not sufficient to quantify the gluonic enhancement. We also study the effec…
The magnetic moment of the rho-meson is calculated in the framework of QCD sum rules in external fields. Perturbative corrections are taken into account. Bare loop calculations (parton model) give the value 2.0. The nonperturbative effects (operators of dimension 6) result in negative contribution, whereas perturbative corrections -- positive one. The final answer is 1.8.
A new analysis of baryon sum rules is done with modern values of parameters and known perturbative corrections. The restriction for gluon and quark condensates and the new value of nucleon coupling constant are found.
Non-relativistic bound state theories for QED and QCD have become fairly mature and amenable to a textbook-level understanding and computation. In this talk we give an introductory review of the following subjects related to the recent computation of the heavy quarkonium spectrum using perturbative QCD: (1) Technological developments in higher-order computation, (2) Physics predictions, (3) Challenge towards analytic evaluation of the 3-loop static QCD potential.
I give a pedagogical introduction to resummation and power corrections, using the thrust variable in electron-positron annihilation as an example, followed by an discussion of issues of predictability in perturbative QCD.
The Odderon state in perturbative QCD is briefly reviewed. Recent calculations devoted to estimate the diffrative eta_c production at high energies from the leading known Odderon states are discussed.
Using the explicit form of the known single distribution functions (the Green's functions) in the double logarithm approximation of perturbative QCD, we analyze the structure of splitting diagrams as a source of double parton perturbative correlations in the proton. The related phenomenological effects are discussed for the conditions of the LHC experiments.
We analyze the static QCD potential V_QCD(r) in the distance region 0.1 fm < r < 1 fm using perturbative QCD and OPE as basic theoretical tools. We assemble theoretical developments up to date and perform a solid and accurate analysis. The analysis consists of 3 major steps: (I) We study large-order behavior of the perturbative series of V_QCD(r) analytically. (II) In the frame of OPE, we define two types of renormalization schemes for the leading Wilson coefficient. (III) We compare numerically perturbative predictions of the Wilson coefficient and lattice computations of V_QCD(r). We perform…
The radiative transitions $ϕ\to ηγ$ and $ϕ\to η^\prime γ$ are analysed using QCD sum-rules. The results we obtain for ${\cal B}(ϕ\to ηγ)=(1.15 \pm 0.2) 10^{-2}$ and ${\cal B}(ϕ\to η^\prime γ)=(1.18 \pm 0.4) 10^{-4}$ are in very good agreement with existing experimental data. The related issue of $η-η^\prime$ mixing is discussed and we give predictions for the $η$ and $η^\prime$ decay constants in the framework of a mixing scheme in the quark-flavour basis.
These proceedings discuss some of the highlights of recent research in perturbative QCD as it relates to the LHC. Topics covered include the new generation of Monte Carlo event generators, the revolution that is occurring in NLO calculations, progress towards NNLO predictions and developments in the definition and use of jets.
We review on-shell methods for computing multi-parton scattering amplitudes in perturbative QCD, utilizing their unitarity and factorization properties. We focus on aspects which are useful for the construction of one-loop amplitudes needed for phenomenological studies at the Large Hadron Collider.
We compute the decay rates for the exclusive decays $B^{\pm} \to (η^{\prime},η) (K^{\pm}, K^{*\pm})$ and $B^{0}\to (η^{\prime},η) (K^{0}, K^{*0})$ in a QCD-improved factorization framework by including the contribution from the process $b\to sgg \to s (η^{\prime}, η)$ through the QCD anomaly. This method provides an alternative estimate of the contribution $b \to s c\bar{c} \to s(η,η^\prime)$ to these decays as compared to the one using the intrinsic charm content of the $η^{\prime}$ and $η$ mesons determined through the decays $J/ψ\to (η,η^\prime ,η_c) γ$. The resulting branching ratios are c…
Perturbative NLO and NNLO QCD evolutions of parton distributions are studied, in particular in the (very) small-x region, where they are in very good agreement with all recent precision measurements of F_2^p(x,Q^2). These predictions turn out to be also rather insensitive to the specific choice of the factorization scheme (MS or DIS). A characteristic feature of perturbative QCD evolutions is a positive curvature of F_2^p which increases as x decreases. This perturbatively stable prediction provides a sensitive test of the range of validity of perturbative QCD.
We study the radiative decays $h_{c}\rightarrowγη^{(\prime)}$ in the framework of perturbative QCD and evaluate analytically the one-loop integrals with the light quark masses kept. Interestingly, the branching ratios $\mathcal{B}(h_{c}\rightarrowγη^{(\prime)})$ are insensitive to both the light quark masses and the shapes of $η^{(\prime)}$ distribution amplitudes. And it is noticed that the contribution of the gluonic content of $η^{(\prime)}$ is almost equal to that of the quark-antiquark content of $η^{(\prime)}$ in the radiative decays $h_{c} \rightarrow γη^{(\prime)}$. By employing the ra…
