Inclusive Jet Production in γp and γγ Processes: Direct and Resolved Photon Cross Sections in Next-To-Leading Order QCD

The production of jets in low Q² ep scattering (photoproduction) and in low Q² ey⁺ey⁻ scattering (γγ scattering) allows for testing perturbative QCD and for measuring the proton and photon structure functions. This requires exact theoretical predictions for one- and two-jet cross sections. We describe the theoretical formalism, giving sufficient details, for calculating the direct and resolved processes in γp and γγ reactions in next-to-leading order QCD. We present the complete analytical results for the Born terms, the virtual, and the real corrections. To separate singular and regular regions of phase space we use the phase space slicing method with an invariant mass cut-off. In this way, all soft and collinear singularities are either canceled or absorbed into the structure functions. Using a flexible Monte Carlo program, we evaluate the cross sections numerically and perform various tests and comparisons with other calculations. We consider the scale dependence of our results and compare them to data from the experiments H1 and ZEUS at HERA and OPAL at LEP.     

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.     

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%.     

QCD corrections at the Z0

All QCD corrections in hadron-initiated lepton-pair production are questionable for Q²?100 GeV² since a perturbative expansion is not justified in this kinematical range. Application of the renormalization group (RG) program at Z₀ energies is meaningful. We exhibit the size of the non-log correction terms, introduce experimental tests, and point to the assumptiona inherent in Drell-Yan (DY) type analyses.     

Perturbative aspects of dilepton production at finite temperature

First order corrections to the Born term production rate of dileptons in a Quark Gluon Plasma are examined in the framework of finite temperature perturbative QCD. While infrared divergences disappear, mass singularities do not cancel, which might cause large logarithmic terms to appear at order αs     

Spectator interactions and theK-factor in the Drell-Yan process

The precise value of theO(α _s perturbative QCD correction to the Drell-Yan cross-section seems to depend on the calculational procedure. We show how this ambiguity is removed when proper account is taken of the additional interactions involving spectator quarks. Explicit calculations in the scalar quark model reveal that the important contributions come from values of the gluon momentum that are very soft.

     

CMS overview

We discuss the production of γπ⁰ and π⁰ π⁰ pairs with a large invariant mass at collider energies. We present a study based on a perturbative QCD calculation at full next-to-leading order accuracy, implemented in the computer programme DIPHOX. We give estimations for various observables, which concern the reducible background to the Higgs boson search in the channel H → γγ, in the mass range 80-140 GeV at the LHC. We critically discuss the reliability of these estimates due to our imperfect knowledge of fragmentation functions at high z and a subtle interplay between higher order corrections and realistic experimental cuts. Whereas the invariant mass spectrum of photon-pion pairs is theoretically better under control, in the dipion case large uncertainties remain. Finally we comment on the impact of our findings on Higgs boson searches at the LHC. We conclude that the qualitative statement that the pion backgrounds should not be dangerous for the H → γγ search channel remains true at the next-to-leading order level.     

The matrix element of the transverse component of the bilocal vector current and its parton interpretation

In this paper we study the matrix element of the transverse component of the bilocal vector current in the context of deep inelastic scattering. The BJL limit of high energy amplitudes together with light-front current algebra imply the same parton interpretation for its matrix element as that of the plus component. On the other hand, the transverse component depends explicitly on the gluon field operator in QCD, appears as “twist three” and hence its matrix element has no manifest parton interpretation. In this paper we perform calculations in light-front time-ordering perturbative QCD for a dressed quark target to order α_s and demonstrate that the matrix element of the transverse component of the bilocal vector current has the same parton interpretation as that of the plus component.     

Gauge invariance structure of quantum chromodynamics

Perturbative QCD may be subdivided into separately gauge-invariant sectors according to the projection of non-abelian color weights onto linearly independent basis elements. We exploit the general Lie group structure of the theory to give an algorithm for finding these gauge-invariant sets and present several examples of its use. The planar sector and the systematics of the non-planar corrections are defined for any gauge theory. Our gauge set classification has implications for QCD bound states, finite order perturbative QCD calculations, the study of QCD infrared singularities and for the question of convergence of the perturbation series.     

Mass corrections to the tau decay rate

In this note radiative corrections to the total hadronic decay rate of the τ-lepton are studied employing perturbative QCD and the operator product expansion. We calculate quadratic quark mass corrections to the decay rate rationR _τ to the order0(α _s ² m²) and find that they contribute appreciably to the Cabbibo supressed decay modes of the τ-lepton. We also discuss corrections of mass dimensionD=4, where we emphasize the need of a suitable choice of the renormalization scale of the quark and gluon condensates.     

Boundary conditions and amplitude ratios for finite-size corrections of a one-dimensional quantum spin model

We study the influence of boundary conditions on the finite-size corrections of a one-dimensional (1D) quantum spin model by exact and perturbative theoretic calculations. We obtain two new infinite sets of universal amplitude ratios for the finite-size correction terms of the 1D quantum spin model of N sites with free and antiperiodic boundary conditions. The results for the lowest two orders are in perfect agreement with a perturbative conformal field theory scenario proposed by Cardy [J. Cardy, Nucl. Phys. B 270 (1986) 186].     

Space- and time-like electromagnetic pion form factors in light-cone pQCD

We present a combined analysis of the space- and time-like electromagnetic pion form factors in light-cone perturbative QCD with transverse momentum dependence and Sudakov suppression. Including the genuine non-perturbative “soft” QCD and the power suppressed twist-3 corrections to the standard twist-2 perturbative QCD result, the experimental form factor data available at moderate energies/momentum transfers can be explained reasonably well. To this end, the bulk of the existing discrepancy between the space- and time-like experimental data is ostensibly reconciled.     

Improved calculations of quark distributions in hadrons: the case of the pion

The earlier introduced method of calculation of quark distributions in hadrons, based on QCD sum rules, is improved. The imaginary part of the virtual photon forward scattering amplitude on some hadronic current is considered in the case, when initial and final virtualities of the current , and are different, . The operator product expansion (OPE) in , is performed. The sum rule for quark distribution is obtained using double dispersion representation of the amplitude on one side in terms of calculated in QCD OPE and on the other side in terms of physical states contributions. Double Borel transformation in , is applied to the sum rule, killing background non-diagonal transition terms which deteriorated the accuracy in previous calculations. The case of the valence quark distribution in the pion is considered, which was impossible to treat by the previous method. OPE up to dimension 6 operators is performed and leading order perturbative corrections are accounted. Valence u-quark distribution in was found at intermediate x, , and normalization point . These results may be used as input for evolution equations. Received: 14 July 1999 / Published online: 6 March 2000     

Investigation of power corrections to event shape variables measured in deep-inelastic scattering

Deep-inelastic ep scattering data, taken with the H1 detector at HERA, are used to study the event shape variables thrust, jet broadening, jet mass, C parameter and two kinds of differential two-jet rate. The data cover a large range of the four-momentum transfer Q, which is considered to be the relevant energy scale, between 7 GeV and 100 GeV. The Q dependences of the mean values are compared with second order calculations of perturbative QCD applying power law corrections proportional to to account for hadronization effects. The concept of power corrections is investigated by fitting simultaneously a non-perturbative parameter and the strong coupling constant . Received: 22 December 1999 / Published online: 25 February 2000     

Single slepton production associated with a top quark at LHC in NLO QCD

Single slepton production in association with a top quark at the CERN Large Hadron Collider (LHC) is one of the important processes in probing the R-parity violation couplings. We calculate the QCD next-to-leading order (NLO) corrections to the $pp \to t\tilde{\ell}^{-}(\bar{t}\tilde{\ell}^{+})+X$ process at the LHC and discuss the impacts of the QCD corrections on kinematic distributions. We investigate the dependence of the leading order (LO) and the NLO QCD corrected integrated cross section on the factorization/renormalization energy scale, slepton, stop-quark and gluino masses. We find that the uncertainty of the LO cross section due to the energy scale is obviously improved by the NLO QCD corrections, and the exclusive jet event selection scheme keeps the convergence of the perturbative series better than the inclusive scheme. The results show that the polarization asymmetry of the top-quark will be reduced by the NLO QCD corrections, and the QCD corrections generally increase with the increment of the $\tilde{t}_{1}$ or $\tilde {g}$ mass value.     

QCD analysis of the Bjorken sum rule revisited

We present extended analysis of the polarized Bjorken sum rule using the four-loop expression for the coefficient function C _Bj(α_s) available now and the recent low Q ²-data from the Jefferson Lab and COMPASS experiments. We demonstrate that the perturbative series for the function C _Bj gives a hint to its asymptotic nature manifesting itself in the region Q ² ? 1 GeV². It is confirmed by the considered integral model for the perturbative QCD correction. We analyze values of higher-twist terms extracted from the mentioned data and discuss the interplay between higher orders perturbative and higher-twist contributions. We extend our consideration to the Gross-Llewellyn Smith sum rule and investigate the relation between higher twist coefficients in these two sum rules.     

Nonperturbative corrections in resummed cross sections

We show that the resummation of large perturbative corrections in QCD leads to ambiguities in high energy cross sections that are suppressed by powers of large momentum scales. These ambiguities are caused by infrared renormalons, which are a general feature of resummed hardscattering functions in perturbative QCD, even though these functions are infrared safe order-by-order in perturbation theory. As in the case of the operator product expansion, the contributions of infrared renormalons to coefficient functions may be absorbed into the definition of higher-dimensional operators, which induce nonperturbative corrections that are power-suppressed at high energies. The strength of the suppression is determined by the location of the dominant infrared renormalon, which may be identified explicitly in the resummed series. In contrast to the operator product expansion, however, the relevant operators in factorized hadron-hadron scattering and jet cross sections are generally nonlocal in QCD, although they may be expressed as local operators in an effective theory for eikonalized quarks. In this context, we verify and interpret the presence of 1 /Q corrections to the inclusive Drell-Yan cross section with Q the pair mass. In a similar manner, we find exp (-b² In Q) corrections in the impact parameter space of the transverse momentum distributions of the Drell-Yan process and e⁺6^- annihilation. We also show that the dominant nonperturbative corrections to cone-based jet cross sections behave as 1 /(Qδ), with δ the opening angle of the jet and Q the center of mass energy.     

Higher order QCD corrections to charged-lepton deep-inelastic scattering and global fits of parton distributions

We study the perturbative QCD corrections to the heavy-quark structure functions of charged-lepton deep-inelastic scattering and their impact on global fits of parton distributions. We include the logarithmically enhanced terms near threshold due to soft gluon resummation in the QCD corrections at next-to-next-to-leading order. We demonstrate that this approximation is sufficient to describe the available HERA data in most parts of the kinematic region. The threshold-enhanced next-to-next-to-leading order corrections improve the agreement between predictions based on global fits of the parton distribution functions and the HERA collider data even in the small-x region.