Three loop gauge β-function for the most general single gauge-coupling theory

We calculate the three loop contribution to the β-function of the gauge coupling constant in a general, anomaly-free, renormalisable gauge field theory involving a single gauge coupling using the background field method in the scheme.     

The static potential in quantum chromodynamics

The effective interaction between a static quark-antiquark pair is computed within the framework of 〈G_μv^aG_a^μv〉 ≠ 0. Due to the static approximation the interaction takes the form of a potential, which is in striking agreement with phenomenological potentials.     

Organocatalysis: quantum chemical modeling of nucleophilic addition to α,β‐unsaturated carbonyl compounds

One of the successful transformations within the field of organocatalysis, the organocatalytic asymmetric addition of nitromethane to α,β‐unsaturated aldehydes and ketones, has been studied by quantum chemical modeling. The level of accuracy of the hybrid density functional theory method B3LYP/6‐31G(d) was compared to a high level ab initio benchmark for this reaction. It is concluded that B3LYP/6‐31G(d) performs very well for this reaction type, giving good estimates of critical energies. The reaction between acrolein and nitromethane was studied in detail. The reaction mechanism revealed an intermediate oxazolidin structure, which is currently unknown. Alkyl substitution in various positions on the amine catalyst or α,β‐unsaturated carbonyl compound influences the reactivity in a predictive fashion. The iminium ion, prop‐2‐en‐iminium, is less activated towards nucleophilic attack compared to protonated acrolein. Copyright © 2007 John Wiley & Sons, Ltd.     

A new method for functionalizing α,γ‐dinitro compounds at the β‐position: application to the cyclization of β‐alkoxy‐α,γ‐dinitro compounds

Treatment of 2,4‐dinitropentane with bromine and sodium methoxide in methanol, affords formation of an ether product, 2,4‐dibromo‐3‐methoxy‐2,4‐dinitropentane, in 59% yield as a mixture of three diastereomers. This observation has led to a general synthesis of 3‐alkoxy‐2,4‐dibromo‐2,4‐dinitropentanes, obtained in 75‐86% yield from 2,4‐dibromo‐2,4‐dinitropentane as the preferred reactant. 4‐Bromo‐2,4‐dinitro‐2‐pentene has been identified as an intermediate in these reactions. The nitroalkene has been isolated and undergoes conjugate addition with alkoxides to afford the same ether products after brominative work‐up. The nitroalkene undergoes conjugate addition with sodium azide to give 3‐azido‐2,4‐dibromo‐2,4‐dinitropentane in 38% yield as a mixture of two isomers in which the (R*,R*) isomer predominates. Sequential treatment of 2,4‐dibromo‐2,4‐dinitropentane with sodium methoxide followed by sodium iodide and acetic acid gives 3‐methoxy‐2,4‐dinitropentane in 63% yield, the overall product of simple methoxylation of 2,4‐dinitropentane. However, attempted complete debromination of 2,4‐dibromo‐3‐methoxy‐2,4‐dinitropentane with excess sodium iodide and acetic acid results only in monodebromination to give 2‐bromo‐3‐methoxy‐2,4‐dinitropentane in 86% yield. Likewise, 2‐bromo‐3‐ethoxy‐2,4‐dinitropentane is formed in 93% yield from the ethoxy analog. A mechanistic rationale is offered for condition‐specific removal of the second Br atom in these reactions. Treatment of 3‐methoxy‐2,4‐dinitropentane with potassium acetate/iodine in dimethyl sulfoxide affords formation of 4,5‐dihydro‐3,4‐dimethyl‐3‐methoxy‐4‐nitroisoxazole 2‐oxide in 30% yield as a single diastereomer. Conversion of 2‐bromo‐3‐methoxy‐2,4‐dinitropentane in 15% yield to 4,5‐dihydro‐3,4‐dimethyl‐3‐methoxy‐4‐nitroisoxazole 2‐oxide is also possible by using potassium acetate in dimethyl sulfoxide. The mechanistic pathways for formation of 4,5‐dihydro‐3,4‐dimethyl‐3‐methoxy‐4‐nitroisoxazole 2‐oxide apparently involve unstable 3‐methoxy‐1,2‐dimethyl‐1,2‐dinitrocyclopropane as the common intermediate. Similarly, 2‐bromo‐3‐ethoxy‐2,4‐dinitropentane affords 4,5‐dihydro‐3‐ethoxy‐3,4‐dimethyl‐4‐nitroisoxazole 2‐oxide in 13% yield. Copyright © 2013 John Wiley & Sons, Ltd.     

Condensates in quantum chromodynamics

The paper presents a short review of our knowledge today on vacuum condensates in quantum chromodynamics (QCD). The condensates are defined as vacuum averages of the operators which arise due to nonperturbative effects. The important role of condensates in determining physical properties of hadrons and of their low-energy interactions in QCD is underlined. The special value of the quark condensate, connected to the existence of baryon masses, is mentioned. Vacuum condensates induced by external fields are discussed. QCD at low energy is checked on the basis of the data on hadronic τ decay. In theoretical analysis, the terms of perturbation theory (PT) up to α _s ³ are accounted for; in the operator product expansion (OPE), those up to dimension 8. The total probability of the decay τ → hadrons (with zero strangeness) and of the τ-decay structure functions are best described at α _s (m _τ ² )=0.330±0.025. It is shown that the Borel sum rules for τ-decay structure functions along the rays in the q ²-complex plane are in agreement with experiment, having an accuracy of ～2% at the values of the Borel parameter |M ²|>0.8 GeV². The magnitudes of dimension 6 and 8 condensates were found, and the limitations on gluon condensates were obtained. The sum rules for the charmed-quark vector-current polarization operator were analyzed in three loops (i.e., in order α _s ² ). The value of the charmed-quark mass (in an \(\overline {MS} \) regularization scheme) was found to be \(\bar m_c (\bar m_c^2 ) = 1.275 \pm 0.015\) GeV, and the value of gluon condensate was estimated as 〈0|(α _s/π)G ²|0〉=0.009±0.007 GeV⁴. The general conclusion is that the QCD described by PT + OPE is in good agreement with experiment at Q ²?1 GeV².     

Solid-state synthesis of potassium β- and β″-gallates

Direct synthesis of K-β- and β″-gallates by Ga₂O₃–K₂O solid-state reaction is described. The formation of K-β- or β″-gallates depends on the initial Ga₂O₃ phase. -Ga₂O₃ leads to K-β-gallate; β-Ga₂O₃ leads to K-β″-gallate. K-β″-Gallate is stable <1200°C. The high temperature stability of K-β″-gallate can be enhanced by doping with aliovalent ions.     

Search for γγ→ηb in ee collisions at LEP 2

A search for the pseudoscalar meson η_b is performed in two-photon interactions at LEP 2 with an integrated luminosity of 699 pb⁻¹ collected at e⁺e⁻ centre-of-mass energies from 181 GeV to 209 GeV. One candidate event is found in the six-charged-particle final state and none in the four-charged-particle final state, in agreement with the total expected background of about one event. Upper limits of Γ_γγ(η_b)×BR(η_b→4 charged particles)<48 eV, Γ_γγ(η_b)×BR(η_b→6 charged particles)<132 eV are obtained at 95% confidence level, which correspond to upper limits of 9.0% and 25% on these branching ratios.     

The quark form factor in quantum chromodynamics

It is shown how leading logarithmic predictions of certain quark form factor effects in QCD, such as the suppression of the Drell-Yan process at small transverse momenta and of the collinear energy-energy correlation in e⁺e^? annihilation, are invalidated by non-leading logarithms corresponding to the vectorial cancellation of gluon transverse momenta. Simple improved expressions incorporating this phenomenon are presented.     

Charmed baryons in quantum chromodynamics

We consider a three-phase model of strongly interacting matter, treating each phase as an ideal gas modified by a simple phenomenological interaction feature. For nuclear matter, we take into account the baryonic repulsion; for the quark-gluon plasma, we include the bag pressure; the constituent quark phase has a non-zero effective quark mass as well as an independent bag pressure. By studying which phase dominates thermodynamically in what region of temperature and baryon number density, we obtain a phase diagram for strongly interacting matter and gain some insight on the relation between deconfinement and chiral symmetry restoration.     

Spectroscopic and structural investigations of α‐, β‐, and γ‐AlH3 phases

With its reputation as a high‐energy density fuel, aluminum hydride (AlH₃) has received renewed attention as a material that is particularly suitable, not only for hydrogen storage but also for rocket propulsion. While the various phases of AlH₃ have been investigated theoretically, there is a shortage of experimental studies corroborating the theoretical findings. In response to this, we present here an investigation of these compounds based primarily on two research areas in which there is the greatest scarcity of information in the literature, namely Raman and infrared (IR) absorption analysis. To the authors' knowledge, this is the first report of experimental far‐IR absorption results on these compounds. Two different samples prepared by broadly similar ethereal reactions of AlCl₃ with LiAlH₄ were analyzed. Both Raman and IR absorption measurements indicate that one sample is purely γ‐AlH₃ and that the other is a mixture of α‐, β‐, and γ‐AlH₃ phases. X‐ray diffraction confirms the spectroscopic findings, most notably for the β‐AlH₃ phase, for which optical spectroscopic data are reported here for the first time. Copyright © 2010 John Wiley & Sons, Ltd.     

On de-globalization in quantum chromodynamics

The recent discovery and resummation of a class of single logarithmic effects (non-global logs), has a significant impact on several QCD observables ranging from the classic Sterman-Weinberg jet definition to currently studied event shapes and rapidity gap observables. The discovery of the above effects overturns, for example, the common wisdom that hadronic energy flow in limited inter-jet regions is dictatedprimarily by the colour flow of the underlying hard partonic subprocess. We discuss some features of non-global logs and the rapid progress being made in estimating and controlling such corrections.     

Multijet structure in quantum chromodynamics

Field theories naturally give rise to multiple jets of hadrons in short-distance processes, such as e⁺ e^? annihilation. In particular, a low-energy jet of hadrons distributed in some cone of opening angle δ would be naively expected to evolve at high energies into multiple jets within the angle δ. We explore to what extent this will happen in quantum chromodynamics.     

The deconfining phase transition in lattice quantum chromodynamics

We present a large-scale Monte Carlo calculation of the deconfining phase transition temperature in lattice quantum chromodynamics without fermions. Using the Wilson action, the transition temperature as a function of the lattice couplingg is consistent with scaling behavior dictated by the perturbativeα function for 6/g²>6.15. Speaker at the conference; on leave from CRIP, Budapest.     

The quark-nucleon phase diagram and quantum chromodynamics

The temperature dependence of a conjectured first-order phase transition between nuclear matter and quark-gluon matter is calculated for temperatures below T = 200 MeV. On the nuclear side a rather successful meson-nucleon mean field theory is applied while quark-gluon matter at large densities and finite temperatures is described perturbatively by quantum chromodynamics. Outside the finite volume of hot and dense quark-gluon matter the physical vacuum is characterized, by the newly determined bag parameter Λ_B = 235 MeV. We observe a dramatic drop in the density of nuclear matter at the phase transition point as the temperature increases, if the scale parameter Λ of QCD is chosen as Λ = 100 MeV. For larger values of Λ the effect is less pronounced. Further work is required to settle this problem.     

ηη′ threshold enhancement in p annihilations into πηη′ at rest

We report on the observation of an ηη′ threshold enhancement produced in p annihilations at rest into π⁰ηη′, which we identify with the recently discovered ƒ₀(1500).     

Observation of χb production in the exclusive reaction ′→γγχb→γγ→γγ(eeorμμ−)

We report on the observation of 1 ³P_J (χ_b) production in the reaction ′→γχ_b→γγ→γγ(e⁺e⁻ or μ⁺μ⁻). The data were recorded with the nonmagnetic CUSB detector at the Cornell Electron Storage Ring, CESR. We observe 124 γγ events with either an electron or muon pair in the final state. In the γγ correlation plot about 40% of the events cluster around (120, 430) MeV.