In 2017, LHCb collaboration reported their first observation of the rare decays $B_s \to ϕ(f_0(980)$ $/f_2(1270) \to ) π^+π^-$ and the evidence of $B^0 \to ϕ(f_0(980)/f_2(1270)\to)π^+π^-$. Motivated by this, we study these quasi-two-body decays in the perturbative QCD approach. The branching fractions, $CP$ asymmetries and the polarization fractions are calculated. We find that within the appropriate two-meson wave functions, the calculated branching fractions are in agreement with the measurements of LHCb. Based on the narrow-width approximation, We also calculate the branching fractions of the quasi-two-body $B_{d,s}\to ϕ(f_0(980)/f_2(1270)\to) π^0π^0$ and $B_{d,s}\to ϕ(f_2(1270)\to) K^+K^-$, and hope the predictions to be tested in the ongoing LHCb and Belle II experiments. Moreover, the processes $B_{d,s}\to ϕf_2(1270)$ are also analyzed under this approximation. We note that the $CP$ asymmetries of these decays are very small, because these decays are either penguin dominant or pure penguin processes.
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.
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…
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.
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.
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.
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 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 present a global fit of current available experimental results on $χ_c$ decays within next-to-leading-order perturbative QCD. The quality and reduced errors of recent data improve the agreement between theory and experiment.
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.
We compare two approaches to the description of pion Compton scattering at moderate momentum transfer, one being based on local duality QCD sum rules for the invariant amplitudes of the process, which have been derived recently, and the other on the modified factorization formula with Sudakov effects included. We find that perturbative QCD predictions are dominant over those from QCD sum rules only for the scattering angle greater than 90$^o$.
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.
Pion Compton scattering is studied in perturbative QCD for real and space--like initial photons. Different methods for the convolution of the hard amplitude with the pion wave--functions, which have in the past led to conflicting results, are compared.
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.
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…
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.
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.
The multiple hadroproduction in the perturbative QCD is briefly reviewed. There are a number of quantities which can be analysed with the use of the high-luminosity TRISTAN data. The analysis will contribute to clarifying some unsolved questions, and to the deeper understanding of the jet physics.
Recent developments of perturbation theory at finite temperature based on effective field theory methods are reviewed. These methods allow the contributions from the different scales to be separated and the perturbative series to be reorganized. The construction of the effective field theory is shown in detail for phi^4 theory and QCD. It is applied to the evaluation of the free energy of QCD at order g^5 and the calculation of the g^6 term is outlined. Implications for the application of perturbative QCD to the quark-gluon plasma are also discussed.
We review the main results of next-to-leading order QCD analyses of polarized deep-inelastic scattering data, with special attention to the assessment of theoretical uncertainties.
In the framework of the perturbative QCD approach, we study the charmless pure weak annihilation Bc->KK decay and find that the branching ratio BR(Bc->KK) O(10^-7). This prediction is so tiny that the Bc->KK decay might be unmeasurable at the Large Hadron Collider.
A brief overview of some recently active topics in perturbative QCD, including: string-inspired recursion techniques at tree level; recursion approaches and automation of standard techniques for 1-loop calculations; the status of NNLO jet calculations; and non-trivial structures that appear in higher-order calculations.
It is known that the correlator of one axial and two vector currents, that receives leading contributions through one-loop fermion triangle diagrams, is not modified by QCD radiative corrections at two loops. It was suggested that this non-renormalization of the VVA correlator persists in higher orders in perturbative QCD as well. To check this assertion, we compute the three-loop QCD corrections to the VAA-correlator u sing the technique of asymptotic expansions. We find that these corrections do not vanish and that they are proportional to the QCD beta-function.
The recent calculation of the four-loop beta function in QCD provides further evidence that the Banks-Zaks expansion in 16half-n_f is sufficiently well behaved to be useful even for n_f=2 light flavours. This expansion inherently predicts "freezing" of the QCD couplant at low energies as a perturbative effect. We consider the e+e- and Bjorken-sum-rule cases as examples.
We review the current status of the high order perturbative QCD evaluation of the hadronic decay rates of the Z and Higgs bosons. A systematic classification of the various types of QCD corrections to $O(α_s^2)$ and $O(α_s^3)$ is made and their numerical status is clarified.
This is a comprehensive review on the perturbative hot QCD including the recent developments. The main body of the review is concentrated upon dealing with physical quantities like reaction rates. Contents: \S1. Introduction, \S2. Perturbative thermal field theory: Feynman rules, \S3. Reaction-rate formula, \S4. Hard-thermal-loop resummation scheme in hot QCD, \S5. Effective action, \S6. Hard modes with $|P^2| \leq O (g^2 T^2)$, \S7. Application to the computation of physical quantities, \S8. Beyond the hard-thermal-loop resummation scheme, \S9. Conclusions.
Integral kernels describing the pair interaction of reggeized gluons and quarks are reconstructed in terms of conformal symmetric 4-point functions in the transverse plane of impact parameters.
Theoretical ideas related to the existence of glueballs in QCD are reviewed. These include non-perturbative phenomena such as confinement, instantons, vacuum condensates and renormalons. We also discuss glueball dominance of the trace of the stress-tensor, the mass content of the nucleon and a theorem on the lightest glueball state.
Effective field theory methods provide a convenient approach to study static observables in field theory at finite temperature. In this talk, I will outline the construction of the effective field theory that describes effective observables in QCD at high temperature. An analysis of the convergence of the perturbative series for the free energy of QCD will also be presented.
We study both polarized and unpolarized proton structure functions in the kinematical region of large Bjorken x and four-momentum transfer of few GeV^2. In this region the phenomenon of parton-hadron duality takes place between the smooth continuation of the deep inelastic scattering curve and the average of the nucleon resonances. We present results on a perturbative-QCD analysis using all recent accurate data with the aim of extracting the infrared behavior of the nucleon structure functions.
