Variational study of vacuum wave functional in QCD

We develop a variational method in order to study non-perturbative structure of the vacuum wave functional in QCD. To retain gauge invariance, we employ a vacuum test functional motivated by the structure of perturbation theory. The resultant integral equation contains only renormalizable logarithmic divergences and is reliable in the weak coupling region. We find that this equation contains a non-perturbative solution besides the perturbative one, and the energy in the former state is lower. Further it is shown that the gluon condensation <G _μv ^a2 > calculated using this non-perturbative solution agrees with the result of several authors.     

Unified description of rapidity gaps and energy flows in DIS final states

We show that the ‘orthogonal’ characteristics of the observed rapidity gaps and large forward energy flows in deep inelastic scattering at HERA, can be described within a single framework. Our Monte Carlo model is based on perturbative QCD matrix elements and parton showers together with Lund string model hadronization, but has in addition a new mechanism for soft colour interactions which modifies the perturbative colour structure and thereby the hadronization. Effects of perturbative multiparton emission are investigated and the non-perturbative treatment of the proton remnant is discussed and comparison to the observed transverse energy flow is made. We investigate the resulting diffractive-like properties of the model; such as rapidity gap events, t- and M _X -distributions and the diffractive structure function in comparison to H1 data.     

Heavy quark correlations ine + e − annihilations

In heavy quark jets the quark mass acts as a regulator of collinear singularities, making the quark momentum an infra-red safe variable in perturbative QCD. This allows a direct comparison of measured heavy hadron momentum spectra with perturbative calculations. We exploit the factorisation of heavy quark fragmentation to derive QCD predictions for momentum correlations between heavy hadrons produced ine ⁺ e ^? annihilations. We study the practical feasibility and model sensitivity of our approach using Monte Carlo simulations. Higher order perturbative corrections and contributions from non-perturbative effects are found to be at the level of 10%.     

Energy cone distribution around the jet axis in e+e− annihilation

We study the hadronic energy-weighted angular cross section inside (or outside) a pair of back-to-back cones around the thrust axis in e⁺e^? annihilation. The relevant cross sections. both on and off a quarkonium state (i.e., with three-gluon or quark-antiquark-gluon final states), are calculated in the leading order in perturbative QCD. Our method employs only one variable, viz., the half-radius of the cones, to measure the jet-likeness of events. The usefulness of this “energy-cone” distribution is discussed and compared to the Sterman-Weinberg formula and the energy-correlation distribution.     

Hadroproduction of heavy quarkonia at high energies within the <Emphasis Type="Italic">k</Emphasis><Subscript><Emphasis Type="Italic">T</Emphasis></Subscript>-factorization approach

On the basis of the k _T -factorization approach, heavy-quarkonium \((c\bar c,b\bar b)\) hadroproduction at high energies is considered within nonrelativistic QCD in the leading order in α _s and v. The p _T spectra of various S-and P-wave quarkonium states at the Tevatron collider energies (run I and run II) are fitted, and sets of octet nonperturbative matrix elements are obtained for three different versions of the noncollinear gluon distribution in the proton.     

Strong radiative corrections to annihilations of quarkonia in QCD

The significance of the lowest-order QCD prediction for the annihilations of heavy quark-antiquark bound states is analyzed. The calculation of the leading strong radiative corrections to the hadronic versus electromagnetic annihilation rate ratio R of pseudoscalar quarkonium is presented. In terms of the coupling constant α_s, as defined in the minimal subtraction scheme, we find R = R⁽⁰⁾(1 + 22.14α_s/π). The physical significance of this result is discussed by comparing it with the calculation of the non-leading effects in α_s on the scaling violations in deep inelastic scattering. A bad convergence of the relative perturbative expansion is found, demanding for its safe application a value of the relevant momentum definitely higher than that of charmonium physics.     

Simulation of QCD jets: The choice of the cutoff

In view of the simulation ofe ⁺ e ^? annihilation events corresponding to QCD multi-jet final states, we examine the dependence of the results on the value of the cutoff, which delimits the perturbative from the non-perturbative regimes. We do this by studying in some detail related effects for the lowest order perturbative contributions (including single gluon emission). We conclude that event simulation is considerably affected by the choice of the cutoff. Up to energies where only two and three jet configurations are dominant, though, this does not prevent from having quantitative tests of QCD, if suitable kinematical cuts are applied.     

The production of large transverse momentum jets in plarized photon-photon collisions

A comprehensive survey is presented of the polarization structure of the leading order QCD processes for the production of jets at largep _t in photon-photon collisions which are the result of colliding positrons. Results are given for asymmetries. It is shown that by separating events with various jet topologies it is possible to investigate different aspects of polarization and QCD. For instance the four anf three jet process asymmetries are found to be sensitive to the relative magnitudes of the perturbative anf non-perturbative components of the photon structure function. A discussion is given of the usefulness of polarization in separating the two gluon jet subprocess. It is concluded that such experiments could be very useful in understanding QCD and the strong interactions.     

Energy flow and energy correlations in deep inelastic scattering

We study two examples of infrared-safe quantities in deep inelastic scattering: the flow of energy in a given angular range and the energy-energy angular pattern. We derive expressions for these quantities in perturbative QCD, to order α_s, and show explicitly their infrared safety. Our formulas for the angular energy flow and the energy-energy angular pattern depend only on well-defined QCD factors and on the deep inelastic structure functions. To gauge whether or not these perturbative QCD results are applicable to present day data, we estimate in a simple model the effects of hadronization and primordial parton transverse momentum. In general these non-perturbative effects mask the resulting QCD pattern at present energies, but vanish more rapidly at higher energies than the QCD effects. However, we point out two examples where it may be possible to test the perturbative QCD predictions with available data. One of them involves studying the x-dependence of the azimuthal asymmetry of the energy flow. The other involves studying the angular width of the energy-energy correlation function.     

Sum rule estimate of the subleading non-perturbative contributions to Bs–$\bar{ B}_{s}$ mixing

We use QCD sum rules to compute the matrix elements of the ΔB=2 operators appearing in the heavy-quark expansion of the width difference of the B _s mass eigenstates. The main focus of our analysis is on the subleading operators R ₂ and R ₃, which appear at next-to-leading order in the 1/m _b expansion. The matrix elements of these operators are already essential for precise phenomenology, but their calculation in lattice QCD is lacking and the values given here provide a first estimate of their values. We conclude that the violation of the factorization approximation for these matrix elements due to non-perturbative vacuum condensates is as low as 1–2%.     

Hadroproduction of heavy quark flavors in QCD

Within the framework of perturbative QCD, we investigate the hadroproduction of charmed particles via two-gluon as well as quark-pair annihilation. The total production cross section is found to be sensitive to the choice of the scale parameter Q² and in general not free from non-perturbative effects. Charmed-particle production in the high-p_T region is also studied.     

DSE Perspective on QCD Modeling,Distribution Amplitudes,and Form Factors

We describe results for the pion distribution amplitude (PDA) at the non-perturbative scale μ = 2 GeV by projecting the Poincaré-covariant Bethe–Salpeter wave-function onto the light-front and use it to investigate the ultraviolet behavior of the electromagnetic form factor, F _π (Q ²), on the entire domain of spacelike Q ². The significant dilation of this PDA compared to the known asymptotic PDA is a signature of dynamical chiral symmetry breaking on the light front. We investigate the transition region of Q ² where non-perturbative behavior of constituent-like quarks gives way to the partonic-like behavior of quantum chromodynamics (QCD). The non-perturbative approach is based on the Dyson–Schwinger equation (DSE) framework for continuum investigations in QCD. The leading-order, leading-twist perturbative QCD result for Q ² F _π (Q ²) underestimates the new DSE computation by just 15 % on \({Q^2\gtrsim 8\,}\) GeV², in stark contrast with the result obtained using the asymptotic PDA.     

Finite corrections to quark fragmentation functions in perturbative QCD

The finite corrections of order α _s in perturbative QCD to the cross-sections for semi-inclusive hadron production from deep inelastic leptonhadron scattering and electron-positron annihilation are calculated. We define the effective quark fragmentation functions viae ⁺ e ^? → hadron +X including the finite terms in order to estimate these corrections for the reactions lepton + hadron → lepton + hadron + anything. Contrary to the leading term the next-to-leading order term does not factorize into parts depending on the target and the fragment, respectively. For the processese +p →e + π^± +X andv +p →μ ^? + π^± +X the finite corrections of order α _s turn out to be at most 20% in the range of momenta covered by present experiments.     

Direct photon production beyond leading order in QCD

The significance of the quark-quark scattering process (quark+quark→quark+quark+photon) for the production of large-q_T real photons is discussed in the framework of perturbative QCD. To extract the finite contribution of this process to the differential cross section dσ/dy d²q_T (hadron 1+hadron 2→photon+anything) we define the gluon distribution and the quark-to-photon fragmentation function beyond the leading approximation. The calculations are performed consistently in the dimensional regularization scheme. Our numerical estimates show the resulting finite qq→qqγ contribution to be a small (order α_s/2π) correction in comparison with the basic QCD subprocesses.     

Small QCD corrections in inclusive 0−+ quarkonium decay for the bound-state renormalization scheme

A consistent field theoretic computation of the first-order correction to the total decay of a non-relativistic heavy quarkonium state must consider contributions from the annihilation amplitude, with a typical scale of the order of the quark mass m, and from the bound-state wave function, where the typical scale is of the order of the Bohr momentum α_sm. Therefore, not only the latter smaller scale is the one to be taken for the total decay rate, but also a quite specific renormalization, the “bound-state renormalization scheme”, must be used for a computation of the total inclusive decay rate of 0^?+→hadrons. Due to important cancellations between large individual contributions, the net result turns out to be small, encouraging the use of pure perturbative QCD in such systems.     

Heavy quarkonium production in the regge limit of quantum chromodynamics

Heavy quarkonium \((c\bar c,b\bar b)\) hadronic production at Tevatron (run I and run II) and LHC energies is considered in the framework of nonrelativistic quantum chromodynamics in the leading order with respect to α _s and v using the quasi-multi-Regge kinematics approach. Fitting of p _T spectra of different S and P wave heavy quarkonium states at Tevatron (run I and run II) energies is carried out. The obtained set of octet nonperturbative matrix elements is used for prediction of heavy quarkonium production at LHC energies. The results obtained in the framework of quasi-multi-Regge kinematics are compared with predictions of the collinear parton model.     

Schrödinger vs. dirac bound state spectra of Q\bar Q-systems and a plausible lorentz structure of the effective power-law potential-systems and a plausible lorentz structure of the effective power-law potential

It is shown that a non-relativistic power-law potential model for the heavy quarks in the form V(r)=Ar ^v+V ₀, (A, ν>0) acquires relativistic consistency in generating Dirac bound states of \(Q\bar Q\) -system in agreement with the Schrödinger spectroscopy if the interaction is modelled by equally mixed scalar and vector parts as suggested by the phenomenology of fine-hyperfine splittings of heavy quarkonium systems in a non-relativistic perturbative approach.     

Two-point functions for flavour changing currents in QCD

We complete the calculations of two-point functions in QCD by presenting the results for the flavour changing vector current, including perturbative and non-perturbative contributions (to first order in α_s).     

Non-leptonic weak decay rate of explicitly flavored heavy mesons

It is argued quantitatively that a large difference between the D⁰ and D⁺ lifetimes is mainly due to non-perturbative long-distance effects. The total non-leptonic weak decay rates are related to the soft limit of short-distance processes. Scaling laws for the decay rates of heavy mesons with respect to mass are inferred from the QCD analysis of the soft limit of fragmentation. It is found that the decay rates are not determined by the disconnected spectator diagrams alone even in the limit of the heavy quark mass M going to infinity (< M_W), since the leading term after the QCD correction scales like M⁵ exp √clog M. Some numerical discussion is made for the decay of B mesons and T mesons.