Perturbative QCD at high energies

A partial review of QCD at high energies is given. Factorization and the use of the renormalization group equation are emphasized. Topics discussed are the parton model, cut vertices in covariant and axial gauges, μ-pair production, jets, form factors, x → 1 limit of structure fu nctions, wide angle elastic scattering and heavy quarkonium exclusive decays. A discussion of mass and infrared singularities and a discussion of Sudakov effects are also included.     

Perturbative QCD corrections in Drell-Yan processes

The influence of lowest-order QCD corrections on the Drell-Yan cross section $\text{Q}{}^4\text{(}\text{dσ}\text{dQ}{}^2\text{)(τ, Q}{}^2\text{)}$ is determined and compared with the asymptotic freedom (AF) corrections. The perturbative calculation exhibits the AF-characteristics of a (strongly) rising Q²-dependence for √τ?0.1 (qg-scattering) and falling for √τ?0.2 (qq?-annihilation). Qualitative agreement between the two calculation methods in the entire √τ-range is obtained with α_s = 0.3.     

Perturbative QCD analysis of the Bjorken sum rule

We study the polarized Bjorken sum rule at low momentum transfer squared Q ² ≤ 3 GeV² in the twist-two approximation and to the next-to-next-to-leading order accuracy.     

虚Compton散射中微扰QCD的可应用性分析

文章阐明微扰色动力学在π介子虚Compton散射过程中的应用性问题.在此过程中,量子色动力学耦合常数除了端点奇点之外还有中心区域的奇点.于是引进一套简单的技术来判断这些奇点的贡献,并认为这些贡献在一定能标上不妨碍微扰色动力学的应用.提出“工作点”判断法来论证微扰色动力学何时对某个遍举过程是适用的.不同的π介子分布振幅的适用性被详细的考察.得到10 GeV²时微扰量子色动力学开始工作;如果放宽限制,工作点将只有4 GeV².     

Perturbative QED and QCD at finite temperatures and densities

The finite temperature and density QED and QCD are discussed from the perturbative viewpoint. A comparison between Abelian QED and non-Abelian QCD is made at every step. The calculation of the thermodynamic potential is performed up to ² In, allowing the masses of the fermions to be arbitrary. The equation of state for QCD plasma is obtained and the phase transition to the hadronic phase is discussed.     

Perturbative and non-perturbative QCD corrections to wide-angle Compton scattering

We investigate corrections to the handbag approach for wide-angle Compton scattering off protons at moderately large momentum transfer: the photon–parton subprocess is calculated to next-to-leading order in and contributions from the generalized parton distribution E are taken into account. Photon and proton helicity flip amplitudes are non-zero due to these corrections, which leads to a wealth of polarization phenomena in Compton scattering. Thus, for instance, the incoming photon asymmetry or the transverse polarization of the proton is non-zero, although small. Received: 31 October 2001 / Revised version: 11 December 2001 / Published online: 8 February 2002     

Perturbative QCD and weak asymmetries in lepton pair production

The interference of electromagnetic and weak production mechanisms for lepton pair production may give rise to several effects which violate parity and charge symmetry. These effects are generally of the order of 1% for dilepton masses of 10 GeV. The theoretical calculations presented here show that experimental studies of these asymmetries may be useful. In particular, measurements of these asymmetries in collisions of pions with polarized protons may lead to a greatly enhanced understanding of the polarization distribution of quarks in a polarized proton. The polarization structure of the d quark is shown to be of special interest. Measurement of the parity-violating asymmetries in proton-polarized proton collisions may prove to be a sensitive probe of the flavor symmetry of the proton antiquark sea. Analysis of the parity conserving charge asymmetry (which is predicted to occur in collisions of unpolarized hadrons) allows a unique further test of the Drell-Yan model for lepton pair production, as well as of our understanding of weak interactions.The above asymmetries mentioned are computed within the framework of the parton model. The focus of this work is on the asymmetries calculated with the inclusion of first-order perturbative QCD effects. The asymmetries are calculated in a differential form for values of the dilepton transverse momentum large compared with the typical (～1 GeV) scale of nonperturbative effects, and also in a form in which this transverse momentum has been integrated over. Corrections to the parton model results, which can be large, show rather different structure for the various asymmetries.A parity-violating asymmetry which may occur in collisions of unpolarized hadrons is also discussed. This asymmetry is very sensitive to the nonperturbative structure of hadrons, and is estimated to be approximately 0.01% for dilepton masses of 10 GeV.     

Perturbative and non-perturbative QCD corrections to wide-angle Compton scattering

The paper contains a sign mistake. In Eqs. (1), (25), (30) and (38) the form factor R _T and the ratio are to be replaced by -R _T and , respectively. The predictions for A _LL = K _LL shown in Fig. 7, are nearly independent of this change while those for A _LS = - K _LS are substantially smaller in absolute value than the results shown in Fig. 8. All other results as well as the conclusions of this paper are not affected by these corrections.Published online: 8 February 2002Erratum published online: 10 October 2003     

Large-Order Estimates in Perturbative QCD and Non-Borel Summable Series

Basic facts about the summation of divergent power series are reviewed, both for series with non vanishing and for series with vanishing convergence radius. Particular attention is paid to the recent development that makes it possible, in the former case, to define summation in the whole Mittag-Leffler star and, in the latter case, to define summation when the point of expansion lies at the tip of a horn-shaped analyticity domain with zero opening angle. Relevance of these results to perturbative QCD is stressed in relation to current discussions concerning large-order estimates of perturbative QCD expansion coefficients.     

A Determination of Nucleon Form Factor Ratios Using Perturbative QCD

Using perturbative QCD in conjunction with CVC and standard electroweak theory, it is shown that at large Q², F₁ⁿ/F₁^P = F₂ⁿ/F₁^P = -0.69. The comparison with other results on form factor ratios from QCD sum rules and/or PQCD is carried out.     

Perturbative chiral violations for domain-wall QCD with improved gauge actions

We investigate, in the framework of perturbation theory at finite Ns$N_s$, the effectiveness of improved gauge actions in suppressing the chiral violations of domain-wall fermions. Our calculations show substantial reductions of the residual mass when it is compared at the same value of the gauge coupling, the largest suppression being obtained when the DBW2 action is used. Similar effects can also be observed for a power-divergent mixing coefficient which is chirally suppressed. No significant reduction instead can be seen in the case of the difference between the vector and axial-vector renormalization constants when improved gauge actions are used in place of the plaquette action. We also find that one-loop perturbation theory is not an adequate tool to carry out comparisons at the same energy scale (of about 2 GeV), and in fact in this case even an enhancement of the chiral violations is frequently obtained.     

Perturbative expansions in QCD and analytic properties of α s

It is shown that analytic properties of standard QCD perturbation theory contradict known spectral properties and contain, in particular, infrared-generated Landau ghost poles and cuts. As an outcome, a rigorous background perturbation theory is developed and its analytic properties are shown to be in agreement with general requirements. In the limiting case of large N _c, where QCD amplitudes contain only pole singularities, the strong coupling constant α _s(Q ²) is shown to be a meromorphic function of external momenta as well. Some simple models and examples are given where nonperturbative β function and α _s(Q ²) can be written explicitly. The general form of amplitudes at large N _c is given in the framework of background perturbation theory, and its correspondence with standard perturbation theory at highmomenta is demonstrated in the example of e ⁺ e ^? annihilation. For timelike momenta, the background coupling constant differs drastically from the standard one, but the background series averaged over energy intervals has the same (AF) behavior at high momenta in the Euclidean and in the Minkowskian region.     

Perturbative versus lattice QCD energy density correlators at high temperatures

Correlators of magnetic and electric field energy density are investigated for SU(N_c) gauge theory at high temperatures T. A separations z ⩽ 2/T the correlators are shown to be dominated by a power-law behavior even for finite gluon screening masses. This continuum behavior is well approximated on current 4 × 16³-lattices in the perturbative limit and leads to a considerable overestimate of screening masses deduced from fitting the lattice correlators with conventional exponential forms. The use of extended sources and sinks to enhance the signal improves the situation for screening masses m ⪢ T but leads to a largely uncontrolled error for masses less than T. In fact, we show that recent lattice QCD data of Grossmann et al., from which a magnetic screening mass m_M ∼ 2.9T was deduced, may even be consistent with a vanishing actual magnetic screening mass.