Tests Of Quantum Chromodynamics Research Articles

Testing quantum chromodynamics with moment sum rules

We investigate the consistency of ${e}^{+}{e}^{\ensuremath{-}}$ annihilation data with QCD. The gluon-condensate matrix element is determined independent of the value of the strong coupling constant or possible mass-renormalization ambiguities. Our method employs finite-contour sum rules which explicitly consider continuum data. For $c$-quark production the condensate parameter is ${\ensuremath{\varphi}}_{c}=(2.5\ifmmode\pm\else\textpm\fi{}0.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, while for $b$-quark production we find ${\ensuremath{\varphi}}_{b}=(0.4\ifmmode\pm\else\textpm\fi{}1.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, consistent with zero. The concept of duality of moments is proved and its applicability discussed.

Improbability of measuring electron structure functions

Electron structure functions, which are completely calculable, should provide an excellent test of quantum chromodynamics. While their experimental determination is in principle simply done by measuring the wide-angle electron from electron-photon scattering in e/sup +/e/sup -/ collisions, in practice one cannot cover an interesting range in the appropriate variable x/sub ..gamma../ = Q/sup 2//(s+u).

Quantum chromodynamics: Theory and experiment

Abstract For more than a decade a substantial fraction of the high energy experimental program has been devoted to the gathering of data which are sensitive to the short distance behavior of the strong interaction. During the same time period a theory of the strong interaction, quantum chromodynamics (QCD), has been developed. The use of perturbation theory techniques allows some definite predictions to be made which can be tested by such data. This review is intended to give an overview of the program of testing QCD in large momentum transfer processes. For each example considered, the sensitivities of the proposed tests will be discussed and various technical difficulties will be outlined.

Large-angle two-photon exclusive channels in quantum chromodynamics

Detailed leading-order quantum-chromodynamics (QCD) predictions are given for the scaling, angular, and helicity dependence of the reactions $\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}M\overline{M}$ ($M=\ensuremath{\pi},K,\ensuremath{\rho}$, etc.) at large momentum transfer. In addition to providing a basic test of QCD at short distances, measurements can be used to determine the process-independent meson distribution amplitudes ${\ensuremath{\varphi}}_{M}(x,Q)$. Other related two-photon channels such as $\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\rho}$, ${\ensuremath{\gamma}}^{*}\ensuremath{\gamma}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0},{\ensuremath{\eta}}^{0},{\ensuremath{\eta}}^{\ensuremath{'}}$, and ${\ensuremath{\eta}}_{c}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ are also discussed. We also prove the existence of a fixed Regge singularity at $J=0$ which couples to $\ensuremath{\gamma}\ensuremath{\rho}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\rho}$ in the $t$ channel but not to $\ensuremath{\gamma}\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\pi}$.

Photon structure functions and azimuthal asymmetries in two-photon processes

Based on the recently developed framework of Curci, Furmanski, and Petronzio, we derive the photon structure functions in quantum chromodynamics (QCD). Then we perform QCD calculations for the azimuthal asymmetries of jets in two-photon processes. We find that in contrast to the case of lepton-hadron scatterings, the deep-inelastic ${e}^{+}{e}^{\ensuremath{-}}$ reaction via two-photon exchange is expected to show cleaner signatures for the azimuthal asymmetries as a result of enhanced QCD effects. We suggest that these will serve as useful tests of QCD.

Quarkonia and quantum chromodynamics

The $\ensuremath{\psi}$ and $\ensuremath{\Upsilon}$ spectroscopies are analyzed in the framework of a recently proposed potential model which incorporates linear confinement and asymptotic freedom. Given the Regge slope ${\ensuremath{\alpha}}^{\ensuremath{'}}$ (${\ensuremath{\alpha}}^{\ensuremath{'}}$ taken to be 1 ${\mathrm{GeV}}^{\ensuremath{-}2}$) and the quantum-chromodynamics (QCD) scale parameter $\ensuremath{\Lambda}$ (${\ensuremath{\Lambda}}_{\stackrel{-}{\mathrm{MS}}}$ taken to be 0.5 GeV, where $\stackrel{-}{\mathrm{MS}}$ refers to the modified minimal-subtraction scheme) the potential is completely determined. Excellent agreement with experiment is found, including in particular leptonic widths and hyperfine splittings. This supports a short-distance behavior of the quark-antiquark potential as predicted by QCD. We also demonstrate in a model-independent way that the $\ensuremath{\Psi}$ and $\ensuremath{\Upsilon}$ spectra provide a lower bound on the QCD scale parameter $\ensuremath{\Lambda}$; we find ${\ensuremath{\Lambda}}_{\stackrel{-}{\mathrm{MS}}}g0.1$ GeV. The properties of ($b\overline{c}$) and possible ($t\overline{t}$), ($t\overline{c}$), and ($t\overline{b}$) spectroscopies are studied, including weak-interaction effects. The implications of the $\ensuremath{\Psi}$, $\ensuremath{\Upsilon}$, and possible heavier quarkonium families for quantitative tests of QCD are discussed. It is shown that a ($t\overline{t}$) system with $m(t\overline{t})\ensuremath{\ge}40$ GeV would provide an accurate determination of ${\ensuremath{\Lambda}}_{\stackrel{-}{\mathrm{MS}}}$.

Quantum chromodynamics corrections to polarised deep-inelastic electron-nucleon scattering

Quantum chromodynamics corrections to orderα s (the running coupling constant), using the quark-parton approach are calculated for the spin-dependent structure functions in deep-inelastic polarised electron-nucleon scattering. Consequences of these corrections for the Bjorken sum rule and the asymmetry in the case of longitudinally polarised (with respect to the beam) nucleons is discussed which could provide possible tests of quantum chromodynamics. Comparison of our results with the moments of the flavour non-singlet contribution to the structure functions obtained using operator product expansion is also given.

Problem ofRine+e−annihilation

A careful analysis is presented of the most recent data for $R({e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\mathrm{hadrons})$ using improved theoretical techniques. The analysis is based on a generalized method for smoothing $R$. We show why the hadronic cross section is potentially one of the best tests of quantum chromodynamics. The theoretical complications such as unknown parameters and nonperturbative corrections are discussed, and resulting theoretical uncertainties are estimated. Some previously neglected QED corrections are accounted for. We find that for $\sqrt{s}$ near 7 GeV, the data lie about 15-17% above the theory; the experimental uncertainty is \ifmmode\pm\else\textpm\fi{} 10% (dominated by systematics). For $\sqrt{s}$ near 5 GeV, the difference is only 5-8%. This apparent discrepancy may well be due to systematic problems in the experiment. For completeness we consider the possibility that there is a threshold for new particles at $\sqrt{s}\ensuremath{\approx}6$ GeV. We consider new quarks, Higgs bosons, color-sextet quarks, integrally charged and even fractionally charged leptons. While most of these hypotheses are not particularly attractive, some cannot be ruled out.

Transverse Momentum and Angular Distributions of Hadrons in Muon-Proton Scattering and Tests of Quantum Chromodynamics

The properties of the transverse momenta and angular distributions of hadrons produced in muon-proton scattering are compared with first-order quantum-chromodynamics calculations. The quantum-chromodynamics prediction for the ${Q}^{2}$ dependence of the average hadron transverse momentum squared agrees with the data provided a constant term is added in quadrature to the prediction. This additive term is attributed to the intrinsic transverse momentum of the quarks in the nucleon and to the transverse momentum inherent in quark fragmentation.

The effect of [formula omitted] and αs corrections on tests of QCD

We discuss in detail the use of the structure function F 3( x, Q 2) of deep-inelastic neutrino scattering for testing quantum chromodynamics. QCD is entirely consistent with all data. However, we show that higher-twist (order 1 Q 2 ) contributions, which are commonly neglected, can have a dramatic impact on interpretation of this result. At present the data are not accurate enough to determine the magnitudes of these 1 Q 2 contributions within the context of QCD. Furthermore, the possible presence of higher-twist terms makes it impossible to unambiguously detect the logarithmic Q 2 dependence and anomalous dimensions which distinguish QCD from hypothetical alternative theories. As a result, more precise data with higher Q 2 are needed to provide definitive tests of QCD. The corrections of second-order in α s introduce fewer complications for testing QCD, and provide a useful context for understanding critical ambiguities in the definitions of α s and Λ.

Polarization of gluon jets in photon-photon scattering

We show that the linear polarization of a gluon emerging from the reaction e + e → e + e + g + g is large - on the order of 20%. This polarization arises from the process γ + γ → quark loop → g + g, which is expected to dominate the two gluon jet cross section. The polarization can be used to test quantum chromodynamics (QCD), even if the gluon jets cannot be distinguished clearly from the background of quark jets. If the QCD prediction is accepted, our result can be used to enhance the signal of gluon jets, thereby aiding in the study of their properties.

Tests of quantum chromodynamics and a direct measurement of the strong coupling constant αs at √ s=30 GeV

We report the measurement of the reaction e + + e − → hadronic jets at a center-of-mass energy √ s=30 GeV using the MARK-J detector at PETRA. By measuring the energy and angular distribution of both neutrals and charged particles we were able to isolate unambiguously the three-jet events in a kinematic region where the backgrounds from q q and phase space contributions and other processes are small. Various comparisons of the data with quantum chromodynamics were made. The relative yield of three-jet events and the shape distribution of the events enable us to determine α s = 0.23 ± 0.02 (statistical error) with a systematic error of ± 0.04.

Tensor analysis of hadronic jets in quantum chromodynamics

We define tensors in momentum space for the events produced in ${e}^{+}{e}^{\ensuremath{-}}$ annihilation. They are calculable in quantum-chromodynamics (QCD) perturbation theory and therefore can be used as a test of QCD. We have studied their distributions and average values which give characteristics of the global structure of hadronic jets in QCD.

Polarization of High-Transverse-Momentum Single Photons as a Test of Quantum Chromodynamics.

Polarization of High-Transverse-Momentum Single Photons as a Test of Quantum Chromodynamics.

Two-photon processes ine+e−calorimetric experiments and tests of quantum chromodynamics

High-energy two-photon collisions will be responsible for a large fraction of events in e/sup +/e/sup -/ machines such as PETRA, PEP, and LEP. We suggest measuring the energy pattern of the ..gamma gamma.. processes, which would provide very interesting information on the interplay between electromagnetic and strong interactions. The angular distribution of the hadronic energy (antenna pattern) is calculated for photon-photon collisions. By using energy-conservation sum rules, we give a model-independent, reliable computation of the corrections due to color confinement, as well as heavy-quark masses and decays. The contributions from the quantum chromodynamics (QCD) structure of the photon, which are characterized by three or four jets in the final state, are taken into account. The energy correlation, i.e., the hadronic energy radiated through two calorimeters as a function of the relative angle is also calculated. We evaluate the energy pattern and energy correlation for the formation of C-even bound states, and find that an extremely good resolution in the hadronic energy would be needed in order to disentangle the bound-state contribution from the background. We present a detailed discussion of the two-photon processes as a background in the studies of the energy pattern of the e/sup +/e/sup -/ annihilation intomore » hadrons. By requiring that either the total hadronic energy or the invariant hadronic mass is larger than 60% of their maximum value, ..sqrt..s, the ..gamma gamma.. background should be suppressed enough to allow for the experimental tests of QCD in e/sup +/e/sup -/ annihilation which have been recently proposed.« less

Polarization of High-Transverse-Momentum Single Photons as a Test of Quantum Chromodynamics

It is shown that high-transverse-momentum photons originating from the process quark+gluon\ensuremath{\rightarrow}quark+photon exhibit a substantial linear polarization in perturbative quantum chromodynamics. The angular dependence of the polarization is quite sensitive to the non-Abelian structure of the interaction, and can be used to check the equality of the quark-gluon and three-gluon couplings.

Discovery of Three-Jet Events and a Test of Quantum Chromodynamics at PETRA

We report the analysis of the spatial energy distribution of data for e+e hadrons obtained with the MARK-J detector at PETRA. We define the quantity oblateness to describe the flat shape of the energy configuration and the three-jet structure which is unambiguously observed for the first time. Our data can be explained by quantum chromodynamic predictions for the production of quark-antiquark pairs accompanied by hard noncollinear gluons. In previous papers' we have reported the observation of a two-jet structure in the production of multihadronic states in e'e annihilation at PETRA, in terms of thrust and spherocity. At higher energies, the hadrons in each jet become increasingly collimated, and the identification of these hadrons with jets becomes increasingly unambiguous. Detailed analysis of the distribution of hadronic energy in three dimensions therefore can be done in order to see the effects of quantum chromodynamics (QCD), and, in particular, the emission of gluons. The detector we used, known as MARK-J, ' measures the energy distribution of both neutral and charged particles (except neutrinos). It covers a solid angle of cp=2~ and 8=9' to 171' (8 is the polar and y is the azimuthal angle). Lucite Cerenkov counters surround the intersection region, followed by two layers (A and B) of three radiation lengths each of lead-scintillator shower counters, with one fast photomultiplier tube at each end. The counters A and B enable us to locate shower maxima in various 9 and cp directions. They are followed by the sixteen C counters, consisting of twelve layers (twelve radiation lengths) of lead-scintillator sandwich also with one phototube at each end. Surrounding the electromagnetic shower counters are drift chambers which measure tracks from hadron showers and incident muon angle. The next layers are hadron calorimeters consisting of magnetized-iron- scintillator sandwiches. The last layer of calorimeter, composed of the D counters, is used for triggering on muons and for rejecting cosmic rays. The magnetic field in the iron is toroidal and its value is 1V kG. Finally, in the outermost layer there are drift chambers which are used to measure single- and double-muon exit angles and mom enta. In the small-angle region there are four layers of scintillation counters sandwiched between 10cm-thick iron plates to measure shower energy in the region 12 (8&30. The total energy of each interaction and the direction of a particle or group of particles is computed from the time and pulse-height information of the shower counters and calorimeter counters. The azimuthal position is determined by the finely segmented shower counters. This method enables us to determine the 6I and y angles to an accuracy of & 5' for e or y and &15' for hadrons. The jet analysis of the hadronic events was performed with use of the spatial distribution of the energy deposited in the detector. For each counter hit, a vector E' (the energy flow) is constructed, whose direction is given by the position of the signal in the counter, and magnitude by the corresponding deposited energy. To describe the energy distribution, three orthogonal axes are defined for each event as follows: (1) The thrust axis, e„ is defined as the direction along which the projected energy flow is

Equipartitioned Jets: New Tests of Quantum Chromodynamics

We propose a modified definition of hadronic jets in quantum chromodynamics which is more selective than the Sterman-Weinberg criterion. It prohibits any two jet streams from having appreciably different energies. Our more restrictive definition provides new tests of quantum chromodynamics in high-energy experiments. We illustrate this idea for two-"quark"-jet configurations in ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\mathrm{hadrons}$ and for two-"gluon"-jet production. The necessity of exponentiating perturbative jet predictions is also discussed.

Tests of quantum chromodynamics in two-photon collisions and high-pTphoton production

We use the diagrammatic approach to scale breaking to rederive the results of the renormalization-group approach to two-photon, ${\ensuremath{\gamma}}^{*}\ensuremath{\gamma}$, collisions, where one of the photons is highly virtual and the other nearly real. In an axial gauge only ladder diagrams contribute to leading-logarithmic accuracy. When interpreted in terms of the quark distribution of the real photon we obtain the result ${G}_{\frac{q}{\ensuremath{\gamma}}}({q}^{2},x)=[\frac{\ensuremath{\alpha}}{{\ensuremath{\alpha}}_{s}({q}^{2})}]{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{f}}_{q}(x)+O(1)$, where ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{f}}_{q}(x)$ is an exactly calculable scaling function. By virtue of the fact that only ladder diagrams contribute in leading-logarithmic accuracy for this and other short-distance photon-target probes, we find that this form for ${G}_{\frac{q}{\ensuremath{\gamma}}}$ can be employed (to leading-logarithmic accuracy) in any short-distance application involving a photon target. We give a summary of these additional applications with emphasis on high-transverse-momentum phenomena. We present also estimates of the vector-dominance background to the pointlike component of the photon distribution function. In addition we present a convenient summary of leading-logarithmic quantum-chromodynamic corrections including dominant $x\ensuremath{\rightarrow}1$ behaviors.

Tests of quantum chromodynamics in the decay of the τ-lepton and in electron positron annihilation into hadrons

We present a method to derive upper and lower bounds for a large class of quantities measurable ine + e − annihilation into hadrons and in τ-decay. The theoretical input are the asymptotic expansions for the vacuum polarization functions of vector and axial vector currents in the euclidean region as given by QCD. Since our method allows straightforward inclusion of (as yet uncalculated) higher order terms in α s , there is the potential of making high precision tests of QCD even with experiments at rather moderate energies. We argue, therefore, that it may be very worthwhile to pursue experiments ate + e − storage rings below theJ/Ψ resonance and to measure the branching ratios for the decays of the τ-lepton with high accuracy. In the latter case we can also get information on the behaviour of the weak axial vector current which should be very interesting in connection with chiral symmetry breaking.