Non-perturbative Power Corrections Research Articles

A new determination of the electromagnetic nucleon form factors from QCD Sum Rules

We obtain the electromagnetic form factors of the nucleon, in the space-like region, using three-point function Finite Energy QCD Sum Rules. The QCD calculation is performed to leading order in perturbation theory in the chiral limit, and also to leading order in the non-perturbative power corrections. For the Dirac form factor, F 1 ( q 2 ) , we get a very good agreement with the data for both the proton and the neutron, in the currently accessible experimental region of momentum transfers. Unfortunately this is not the case, though, for the Pauli form factor F 2 ( q 2 ) , which has a soft q 2 -dependence proportional to the quark condensate 0 | q ¯ q | 0 > .

DIJET EVENT SHAPES AS DIAGNOSTIC TOOLS

Event shapes have long been used to extract information about hadronic final states and the properties of QCD, such as particle spin and the running coupling. Recently, a family of event shapes, the angularities, has been introduced that depends on a continuous parameter. This additional parameter-dependence further extends the versatility of event shapes. It provides a handle on nonperturbative power corrections, on non-global logarithms, and on the flow of color in the final state.

Electromagnetic nucleon form factors from QCD sum rules

The electromagnetic form factors of the nucleon, in the space-like region, are determined from three-point function Finite Energy QCD Sum Rules. The QCD calculation is performed to leading order in perturbation theory in the chiral limit, and to leading order in the non-perturbative power corrections. The results for the Dirac form factor, $F_1(q^2)$, are in very good agreement with data for both the proton and the neutron, in the currently accessible experimental region of momentum transfers. This is not the case, though, for the Pauli form factor $F_2(q^2)$, which has a soft $q^2$-dependence proportional to the quark condensate $<0|\bar{q}q|0>$.

Azimuthal correlation in DIS

We introduce a new angular correlation in DIS process and study its differential distribution in the region in which the observable is small. We perform a perturbative resummation at single logarithmic accuracy and estimate leading non-perturbative power corrections.

Quark mass corrections to the perturbative thrust and its effect on the determination of αs

We consider the effects of quark masses to the perturbative thrust in $e^+e^-$ annihilation. In particular we show that perturbative power corrections resulting from non-zero quark masses considerably alters the size of the non-perturbative power corrections and consequently, significantly changes the fitted value of $\alpha_s$.

Azimuthal correlation in DIS

We introduce the azimuthal correlation for the deep inelastic scattering process. We present the QCD prediction to the level of next-to-leading log resummation, matching to the fixed order prediction. We also estimate the leading non-perturbative power correction. The observable is compared with the energy-energy correlation in e+e− annihilation, on which it is modelled. The effects of the resummation and of the leading power correction are both quite large. It would therefore be particularly instructive to study this observable experimentally.

Renormalon analysis of heavy-light exclusiveBdecays

We study two-body exclusive decays of the form $\overline{B}\ensuremath{\rightarrow}{D}^{(*)}L (L=\ensuremath{\pi},\ensuremath{\rho},\dots{})$ in the heavy-quark limit. We perform a renormalon analysis of such processes to determine the order at which nonperturbative factorization-breaking power corrections enter the amplitude. We find that a class of leading power corrections to the color octet matrix element, of $\mathcal{O}({\ensuremath{\Lambda}}_{\mathrm{QCD}}{/m}_{b}),$ vanishes in the limit of a symmetric light meson parton distribution function. We discuss the phenomenological significance of this result.

Nonperturbative corrections to the Drell-Yan transverse momentum distribution

We study nonperturbative corrections to the transverse momentum distribution of vector bosons in the Drell-Yan process. Factorizing out the Sudakov effects due to soft gluons we express their contribution to the distribution in the form of the vacuum averaged Wilson loop operator. We calculate the nonperturbative contribution to the Sudakov form factor using the expansion of the Wilson loop over vacuum fields supplemented with the expression for nonlocal gauge invariant field strength correlator. Although the Wilson loop is defined in an essentially Minkowski kinematics, the part of the nonperturbative contribution depending on the invariant mass of the produced vector bosons is governed by asymptotics of the correlator at large space-like (Euclidean) separations and therefore can be calculated using conventional nonperturbative methods. Applying the results of lattice calculations we found that the obtained expression for the nonperturbative power corrections is in qualitative agreement with known phenomenological expressions at large transverse momenta and deviate from them at small transverse momenta.

Analyticity and power corrections in hard-scattering hadronic functions

Demanding the analyticity of hadronic observables (calculated in terms of power series of the running coupling) as a whole, we show that they are free of the Landau singularity. Employing resummation and dispersion-relation techniques, we compute in a unifying way power corrections to two different hard-scattering functions in perturbative QCD: the electromagnetic pion form factor to leading order and the inclusive cross section of the Drell–Yan process. In the second case, the leading nonperturbative power correction in bΛ QCD gives rise to a Sudakov-like exponential factor in the impact parameter space which provides enhancement rather than suppression.

Nonperturbative power corrections to two-loopα¯s(q2)in an analytic approach to QCD

The analytic approach to perturbative QCD which allows one to remove nonphysical singularities of the QCD running coupling constant ${\overline{\ensuremath{\alpha}}}_{s}{(q}^{2})$ in the infrared region is applied to standard as well as to iterative solutions of the two-loop renormalization group equation. Nonleading at large momentum nonperturbative contributions in ${\overline{\ensuremath{\alpha}}}_{s}{(q}^{2})$ are obtained in explicit form. The coefficients of nonperturbative contribution expansions in inverse powers of the squared Euclidean momentum are calculated. For both cases considered, power series of negative terms convergent at ${q}^{2}&gt;{\ensuremath{\Lambda}}^{2}$ with different dependences appear on term numbers.

Heavy quark expansion and preasymptotic corrections to decay widths in the ’t Hooft model

We address nonperturbative power corrections to inclusive decay widths of heavy flavor hadrons in the context of the 't Hooft model (two-dimensional QCD at ${N}_{c}\ensuremath{\rightarrow}\ensuremath{\infty}),$ with the emphasis on the ``spectator-dependent'' effects, i.e., those sensitive to the flavor of the spectator. The summation of exclusive widths is performed analytically using the 't Hooft equation. We show that the ${1/m}_{Q}$ expansion of both the weak annihilation and Pauli interference widths coincides with the OPE predictions to the computed orders. Violation of local duality in the inclusive widths is quantified, and the new example is identified where the OPE prediction and the actual effect are completely saturated by a single final state. The qualitative aspects of quark hadronization emerging from the analysis in the 't Hooft model are discussed. Certain aspects of the summation of spectator-independent hadronic weak decay widths are given in more detail, which were not spelled out previously. We also give some useful details of the ${1/m}_{Q}$ expansion in the 't Hooft model.

Measurement of the quark and gluon fragmentation functions in Z $^0$ hadronic decays

The transverse, longitudinal and asymmetric components of the fragmentation function are measured from the inclusive charged particles produced in $e^+e^-$ collisions at LEP. As in deep inelastic scattering, these data are important for tests of QCD. The transverse $\sigma_T$ and longitudinal $\sigma_L$ components of the total hadronic cross section $\sigma_{tot}$ are evaluated from the measured fragmentation functions. They are found to be $\sigma_T/\sigma_{tot}=0.949\pm 0.001(stat.)\pm 0.007(syst.)$ and $\sigma_L/\sigma_{tot}=0.051\pm 0.001(stat.)\pm 0.007(syst.)$ respectively. The strong coupling constant is calculated from $\sigma_L/\sigma_{tot}$ in next-to-leading order of perturbative QCD, giving \[ \alpha_s(M_Z)=0.120\pm 0.002(stat.)\pm 0.013(syst.)\pm 0.007(scale) . \] Including non-perturbative power corrections leads to \[ \alpha_s(M_Z)=0.101\pm 0.002(stat.)\pm 0.013(syst.)\pm 0.007(scale) . \] The measured transverse and longitudinal components of the fragmentation function are used to estimate the mean charged multiplicity, \[ \langle n^{ch}\rangle = 21.21 \pm 0.01(stat.)\pm 0.20(syst.) \] The fragmentation functions and multiplicities in $b\overline{b}$ and light quark events are compared. The measured transverse and longitudinal components of the fragmentation function allow the gluon fragmentation function to be evaluated.

QCD power corrections from a simple model for the running coupling

A simple parametrization of the QCD running coupling at low scales is introduced and used to illustrate various schemes for the estimation of non-perturbative power corrections. The `infrared matching' scheme proposed earlier gives satisfactory results when combined with next-to-leading (or higher) order perturbative predictions. Estimates based on renormalons are shown to be inconsistent with universal behaviour of the running coupling.

Resummed C-parameter distribution in e+e− annihilation

We give perturbative predictions for the distribution of the $C$-Parameter event shape variable in $e^+e^-$ annihilation, including resummation of large logarithms in the two-jet (small-$C$) region, matched to next-to-leading order results. We also estimate the leading non-perturbative power correction and make a preliminary comparison with experimental data.

Numerical analysis of renormalon technique in quantum mechanics

We discuss the ways of extracting a low-energy scale of an underlying theory using high-energy scattering data. Within an exactly solvable model of quantum mechanics we analyze a technique based on introduction of nonperturbative power corrections accounting for asymptotically small terms and an alternative approach exploiting a modified running coupling constant of the model and nonperturbative continuation of evolution equations into an infrared region. Numerical estimates show that the latter is more efficient in approximating low-energy data of the model.

Infrared factorization in inclusive B meson decays

We perform infrared factorization of differential rates of rediative and semileptonic inclusive decays of the B meson in the end-point region of photon and charged lepton spectrum, respectively, in the leading heavy quark mass limit. We find that the differential rates are expressed in terms of hard, jet and soft functions, which satisfy evolution equations. Solving these equations, we find expressions for the moments of the differential rates in their end-point regions, which take into account all leading and nonleading logarithmic corrections in perturbation theory, as well as large nonperturbative power corrections. Expanded to the one-loop level, our predictions coincide with the results of existing lowest order calculations for B→ γX s and B→l vX u . Nonperturbative corrections appear in our formalism from the boundary value of the soft function in the evolution equation. The soft function is a universal process-independent function, which describes the distribution of the b quark in the B meson. Its behavior in the end-point region is governed by the nonperturbative asymptotics of a Wilson line expectation value. By considering the contributions of infrared renormalons, we find an ansatz for the Wilson line, which leads to a Gaussian model for the heavy quark distribution function.

Power corrections to QCD sum rules for Compton scattering

We extend previous work on sum rules for the invariant amplitudes of pion Compton scattering by deriving a complete lowest-order perturbative spectral functin — and its leading non-perturbative power corrections — for a specific combination of the two helicities ( H 1 + H 2) of this process. Using some properties of a modified version of the Borel transform, we develop a method of calculation of the gluonic corrections which can be easily extended to other similar reactions, such as proton Compton scattering. A preliminary comparison of the new sum rule with the pion form factor sum rule is made.

The first infrared renormalon in QED

The asymptotic behaviour of perturbation series due to the first infrared renormalon is calculated in QED including 1/ n-corrections to the large- n behaviour. We use the operator product expansion in a purely perturbative framework. The result agrees with what one finds in QCD, relating infrared renormalons to nonperturbative power corrections.

Energy-energy correlations in e +e − annihilation

We calculate energy-energy correlation (EEC) up to O( α s) 2 in perturbative QCD. The effects of heavy quark masses and experimental resolution in the spirit of Sterman-Weinberg on the EEC functions are also calculated to the same order. We find that the EEC function is sensitive to both the radiative corrections and experimental resolution criterion. The asymmetric EEC function is, in contrast, stable with respect to both the radiative and power corrections in perturbation theory. It is argued that both the data and perturbation theory indicate substantial non-perturbative power corrections to the EEC but modest effects in the asymmetry for Q⩾25 GeV. We show that limited- p T fragmentation models without long-range colour correlations are in agreement with the expectations and data. A phenomenological analysis of the PETRA/PEP data is performed to determine the QCD scale parameter. We determine Λ MS = 120 −47 +60 MeV with no power corrections, and Λ MS = 168 −40 +60 MeV if limited- p T fragmentation effects are included. The small non-perturbative power correction to the asymmetric EEC is a characteristics feature of the limited- p T independent parton-fragmentation models and is testable at PETRA energies.

Kaon and ?-decay rates in QCD

Using techniques developed by Shifman, Vainshtein and Zakharov for QCD, we have computed the non-perturbative power corrections tofK and the semi-leptonic decay rate of τ. These corrections, though small, are found to improve agreement with experiments.