Applicability Of Perturbative QCD Research Articles

Renormalization-scheme variation of a QCD perturbation expansion with tamed large-order behavior

The renormalization-scheme and scale dependence of the truncated QCD perturbative expansions is one of the main sources of theoretical error of the standard model predictions, especially at intermediate energies. Recently, a class of renormalization schemes, parametrized by a single real number $C$, has been defined and investigated in the frame of the standard perturbation expansions in powers of the coupling. In the present paper we investigate the $C$-scheme variation of a Borel-improved QCD perturbation series, which implements information about the large-order divergent character of perturbation theory by means of an optimal conformal mapping of the Borel plane. In the new expansions, the powers of the strong coupling are replaced by a set of expansion functions with properties which resemble those of the expanded correlators, having in particular a singular behavior at the origin of the complex coupling plane. On the other hand, the new expansions have a tamed increase at high orders, as demonstrated by previous studies in the $\overline{\mathrm{MS}}$ renormalization scheme. Using as examples the Adler function and the hadronic decay width of the $\ensuremath{\tau}$ lepton, we investigate the properties of the Borel-improved expansions in the $C$-scheme, in comparison with the standard expansions in the $C$-scheme and the expansions in $\overline{\mathrm{MS}}$. The variation with the renormalization scale and the prescription for the choice of an optimal value of the parameter $C$ are discussed. The good large-order behavior of the Borel-improved expansions is proved also in the $C$-scheme, which is a further argument in favor of using them in applications of perturbative QCD at intermediate energies.

Insights into theγ*N→Δtransition

The \gamma* N -> \Delta(1232) transition is a window on hadron shape deformation, the applicability of perturbative QCD at moderate momentum transfers, and the influence of nonperturbative phenomena on hadronic observables. We explain that the Ash-convention magnetic transition form factor must fall faster than the neutron's magnetic form factor and nonzero values for the associated quadrupole ratios reveal the impact of quark orbital angular momentum within the nucleon and \Delta(1232); and show that these quadrupole ratios do approach their predicted asymptotic limits, albeit slowly.

Introduction to quantum chromodynamics at hadron colliders

A basic introduction to the application of QCD at hadron colliders is presented. I briefly review the phenomenological and theoretical origins of QCD, and then discuss factorization and infrared safety, parton distributions, the computation of hard scattering amplitudes and applications of perturbative QCD.

SPIN CONSTRAINTS ON REGGE PREDICTIONS AND PERTURBATIVE EVOLUTION IN HIGH ENERGY COLLISIONS

Two key issues in the application of perturbative QCD and Regge predictions to high energy processes are whether the hard and soft pomerons should be considered as two separate distinct exchanges and whether the Regge intercepts are Q2 independent or not. Models involving a distinct hard pomeron exchange predict much larger values for the LHC total cross-section. Here we argue that there is a polarized analogue of this issue in the isovector part of the spin structure function g1 and that the spin data appear to favour a distinct hard exchange.

Applicability of perturbative QCD and NLO power corrections for the pion form factor

In many years ago, Isgur and Llewellyn Smith addressed that PQCD is inapplicable to exclusive processes, such as the pion form factor.The main problem is that the asymptotic of PQCD is only about one fourth of the experimental value. We reexamine this PQCD deep problem. By including NLO power corrections to the pion form factor, we may arrive at a perturbative explanation for the data. The key realization is that we need to interprete that the strong interaction coupling constant involved in the PQCD result should be taken as an effective coupling constant under nonperturbative QCD vaccum. This implies that one can equally identify the relevant scale for the effective coupling constant as the factorization scale about 1 GeV. We also find that the average momentum fraction variable locates about 0.5, which is in favor of the asymptotic pion wave function. By employing photon-pion form factor with NLO power corrections to factorize out the nonperturbative effects involved in the effective coupling constant, we can extract an effective running coupling constant, which represents an effective coupling involving in the hard scattering subprocesses. The difference between the effective running coupling constant and the usual perturbative running coupling constant ($\Lambda_{QCD}=0.3$ GeV) is very small for $Q^2> 1 GeV^2$. The effective running coupling constant $\alpha_s/\pi$ is smaller than 0.2 for $Q^2>1 GeV^2$. This directly showes that PQCD is applicable to exclusive processes at energy $Q^2> 1 GeV^2$. In summary, with NLO power corrections, PQCD can completely explain the $Q^2$ spectrum of pion form factor.

Tensor polarization in elastic electron-deuteron scattering to the highest possible momentum transfers

In elastic electron-deuteron scattering, the tensor polarization moments t 20 , t 21 and t 22 , together with the unpolarized cross-sections, have been measured up to a momentum transfer of 1.8 (GeV/c) 2 , or 6.8 fm −1 . The experiment was performed at Jefferson Laboratory using the recoil deuteron polarimeter POLDER. Preliminary results are presented and discussed, especially in view of their significance concerning the applicability of perturbative QCD to this exclusive process.

Heavy-Quark Production in the Target Fragmentation Region

Fixed-target experiments permit the study of hadron production in the target fragmentation region. It is expected that the tagging of specific particles in the target fragments can be employed to introduce a bias in the hard scattering process towards a specific flavour content. The case of hadrons containing a heavy quark is particularly attractive because of the clear experimental signatures and the applicability of perturbative QCD. The standard approach to one-particle inclusive processes based on fragmentation functions is valid in the current fragmentation region and for large transverse momenta $p_T$ in the target fragmentation region, but it fails for particle production at small $p_T$ in the target fragmentation region. A collinear singularity, which cannot be absorbed in the standard way into the phenomenological distribution functions, prohibits the application of this procedure. This situation is remedied by the introduction of a new set of distribution functions, the target fragmentation functions. They describe particle production in the target fragmentation region, and can be viewed as correlated distribution functions in the momentum fractions of the observed particle and of the parton initiating the hard scattering process. It is shown in a next-to-leading-order calculation for the case of deeply inelastic lepton-nucleon scattering that the additional singularity can be consistently absorbed into the renormalized target fragmentation functions on the one-loop level. The formalism is derived in detail and is applied to the production of heavy quarks. The renormalization group equation of the target fragmentation functions for the perturbative contribution is solved numerically, and the results of a case study for deeply inelastic lepton-nucleon scattering at DESY (H1 and ZEUS at HERA), at CERN (NA47) and at Fermilab (E665) are discussed. We also comment briefly on the case of an intrinsic heavy-quark content of the proton.

Effects of QCD resummation on distributions of top-quark–top-antiquark pairs produced at the Fermilab Tevatron

We study the kinematic distributions of top--antitop quark pairs produced at the Tevatron, including the effects of initial state and final state multiple soft gluon emission, using the Collins--Soper--Sterman resummation formalism. The resummed results are compared with those predicted by the showering event generator PYTHIA for various distributions involving the top--antitop quark pair and the individual top quark or antiquark. The comparison between the experimental and predicted distributions will be a strong test of our understanding and application of perturbative QCD. Our results indicate that the showering event generators do not produce enough radiation. We reweight the PYTHIA distributions to agree with our resummed calculation, then use the reweighted events to better estimate the true hadronic activity in top--antitop quark pair production at hadron colliders.

On the applicability of perturbative QCD to exclusive processes at currently available momentum transfer

We re-examine the problems connected with the end-point dominance in the calculation of exclusive processes in perturbative QCD. In a re-analysis we construct nucleon quark distribution amplitudes from the respective moments obtained from a QCD sum rule approach. These functions lead to acceptable values for the e.m. Dirac form factorsF 1 p,n of the nucleon if effective gluon masses of ca. 300–600 MeV are included into the hard-scattering amplitude. In addition we also find a reasonable Q2 — dependence of the proton form factor. The results point at the importance of the end-point k⊥-dependence of distribution amplitude and hard-scattering amplitude in the calculation of exclusive processes.

Applications of perturbative QCD to few body systems

Applications of perturbative QCD to few body systems

The photon structure function F2γ, vector meson dominance and the applicability of perturbative QCD

A phenomenological analysis of the Q 2 evolution of the photon structure function F 2 γ ( x, Q 2) is presented, using the recent TPC data in the range 0.3⩽ Q 2⩽1.6 GeV 2 as a starting point. It is found that although these data are well described by the vector meson dominance (VMD) model and exhibit scaling, they cannot be used as a starting point for an analysis using perturbative QCD. This conclusion that the region described by VMD is outside the perturbative region invalidates all previous arguments over the sensitivity of F 2 γ to the QCD mass scale Λ, which use VMD to estimate the effect of the boundary conditions.

Gluon bremsstrahlung by confined sources

We study the effect of confinement on gluon bremsstrahlung. A natural infrared cutoff emerges both at small gluon momenta and at small angles. If the confinement potential is of the linear “string” type, the cutoff is controlled by the tension parameter and is thus about 1GeV for the transverse momentum of a hard gluon relative to its parent quark. We propose that this confinement effect may remove the necessity for introducing ad hoc cutoffs by a large “intrinsic partonp T ” in phenomenological applications of perturbative QCD.