Heavy particle content in QCD jets

We calculate the multiplicity of heavy quark pairs in gluon jets in lowest order QCD, along with the non-perturbative correction related to the gluon condensate 〈(α/π)F²〉. The value of the non-perturbative correction is

where M is the mass of the heavy quark, N is the number of colors, and C_F and C_A are the values of the Casimir operators in the fundamental and adjoint representation respectively. α(M) is the running coupling constant at the scale of the heavy quark, and 〈F²〉 is the gluon condensate, usually determined to be 〈α/πF²〉 ∼ 0.012 GeV⁴. The non-perturbative correction is extremely small.     

Sensitivity of polarization observables in elastic ed scattering to the neutron form factors

The deuteron elastic form factors are calculated within the Bethe-Salpeter approach with separable interaction. The charge, quadrupole, and magnetic form factors [F _C(q ²), F _Q(q ²), and F _M(q ²), respectively]; the structure functions A(q ²) and B(q ²); and the tensor polarization components T ₂₀(q ², T ₂₁(q ²), and T ₂₂(q ²) are investigated up to ?q ²=50 fm^?2. The role of relativistic effects is discussed, and a comparison with nonrelativistic calculations is performed. The effect of the neutron form factors on the deuteron form factors and especially on tensor polarization components is discussed too.     

Higher order QCD corrections to an exclusive two-photon process

We calculate the next-to-leading order QCD corrections in the $\text{MS}$ scheme to the coefficient functions in an operator product expansion of the amplitude T(q², p²) for the process $\text{γ}{}^1\text{(q) + γ}{}^1\text{(p) →}\text{helicity-zero}$, flavour non-singlet meson in which ?q² is large and ?p² ? 0. For an asymptotic wave function the complete O(α_s) correction for a pseudoscalar meson is about 16% for p² = 0 and α_s = 0.3; most of this correction can be removed by using a modified evolution equation for the wave function, leaving a correction of about 7%. For large p² the complete O(α_s) correction for a pseudoscalar meson is about 10%. We discuss how our results can be combined with similar calculations for the pion form factor F_π(Q²) to give a prediction: F_π(Q²) = Aα_s(Q²)T_π²(q², 0)(1 + Bα_s) that is independent of the as yet unknown two-loop anomalous dimension matrix.     

Studies of vibrational surface modes in ionic crystals: III. Vibrational contributions to the surface thermodynamic functions for the (001) face of LiF,MgO, NaF,NaCl, Nal,RbF, and RbCl

The temperature dependence of the vibrational contributions to surface specific heat, surface entropy, surface energy, and surface Helmholtz free energy have been calculated for the (001) face of seven crystals having the rocksalt structure. The calculations assume a perfect, unrelaxed surface and make use of shell models fitted to bulk phonon spectra determined from inelastic neutron scattering. In terms of the bulk zero-temperature Debye temperature θ₀, the surface specific heat C_v^s exhibits an effective power law behavior, T^α, from at least T = 0.02 θ₀ up to 0.05 θ₀ in most cases (and up to 0.07 θ₀ for NaF), with α ≈ 2.5 in most cases — in contrast with the result of α = 2 in a Debye-like model. (Below 0.02 θ₀, results derived for our 15-layer films depart significantly from intrinsic surface effects because of the finite thickness.) C_v^s attains a maximum at a temperature T(C_max^s) ranging from 0.14 θ₀ to 0.20 θ₀, in contrast with the result T(C_max^s) = 0.21 θ₀ for the Debye-like model. The peak value C_max^s ranges from 0.34 k_BA_SUC to 0.41 k_BA_SUC, where A_SUC is the area of the surface unit cell. The shap the peak in C_v^s differs characteristically between that class of crystals in which there is some overlap of the acoustical and optical bulk bands and that class in which there is an appreciable absolute gap between the acoustical and optical bulk bands; in the latter class the peak is flattened on the low side of the maximum, with the maximum pushed to somewhat higher temperature. On those points of comparison with the rather sparse existing data for surface-excess heat capacity in which the value of specific surface area is not required (e.g., the value of T(C^s_max)), the agreement ranges from encouraging to equivocal. On those comparisons which require the surface area of the experimental samples (e.g., the magnitude of C^s_max) the agreement ranges from only fair to bad. Further experimental work is needed, and great care in surface area determinations is necessary.     

Braided m-Lie Algebras

Braided m-Lie algebras induced by multiplication are introduced, which generalize Lie algebras, Lie color algebras and quantum Lie algebras. The necessary and sufficient conditions for the braided m-Lie algebras to be strict Jacobi braided Lie algebras are given. Two classes of braided m-Lie algebras are given, which are generalized matrix braided m-Lie algebras and braided m-Lie subalgebras of End _F M, where M is a Yetter–Drinfeld module over B with dimB < . In particular, generalized classical braided m-Lie algebras sl _{q, f} (GM _G (A), F) and osp _{q, t} (GM _G (A), M, F) of generalized matrix algebra GM _G (A) are constructed and their connection with special generalized matrix Lie superalgebra sl _{s, f} (GM _{Z_2}(A ^s ), F) and orthosymplectic generalized matrix Lie super algebra osp _{s, t} (GM _{Z_2}(A ^s ), M ^s , F) are established. The relationship between representations of braided m-Lie algebras and their associated algebras are established.This revised version was published online in March 2005 with corrections to the cover date.     

Hadronisation effects in event-shape moments

We study the moments of hadronic event shapes in e ⁺ e ^? annihilation within the context of next-to-next-to-leading order (NNLO) perturbative QCD predictions combined with non-perturbative power corrections in the dispersive model. This model is extended to match the NNLO perturbative prediction. The resulting theoretical expression has been compared to experimental data from JADE and OPAL, and a new value for α _s (M _Z ) has been determined, as well as of the average coupling α ₀ in the non-perturbative region below μ _I =2 GeV within the dispersive model: $$\begin{array}{rcl}\alpha_s(M_Z)&=&0.1153\pm0.0017(\mathrm{exp})\pm0.0023(\mathrm{th}),\\[5pt]\alpha_0&=&0.5132\pm0.0115(\mathrm{exp})\pm0.0381(\mathrm{th}).\end{array}$$ The precision of the α _s (M _Z ) value has been improved in comparison to the previously available next-to-leading order analysis. We observe that the resulting power corrections are considerably larger than those estimated from hadronisation models in multi-purpose event generator programs.     

Measurement of polarization angular coefficients in <Emphasis Type="Italic">Z</Emphasis> boson leptonic decays with ATLAS at the LHC

This paper presents the complete set of polarization angular coefficients A _0?7 describing lepton angular distributions in Z boson decay, which were measured at the ATLAS experiment in proton–proton collisions with the energy √s = 8 TeV. Theoretical values for the difference A ₀ ? A ₂ calculated in the fixed-order QCD perturbation theory O(α _s ² ), demonstrate significant deviation from the measured data, which indicates the necessity of taking into account higher order corrections. The evidence of nonzero coefficients A _5,6,7 was obtained for the first time, in accordance with theoretical calculations in O(α _s ² ) approximation. Measurement of the polarization angular coefficients A _i is important for subsequent precision measurement of parameters of the electroweak model at the LHC, such as the sine of Weinberg electroweak mixing angle sin² θ _W and the W boson mass.     

A new method to determine the electroweak couplings of individual light flavours at LEP

A method is presented for determining the yields and properties of individual light quark flavours in Z ⁰ decays that is essentially free of detailed assumptions about hadronisation. The method uses an equation system with the number of events which are single and double tagged by high energy hadrons as inputs. In addition, SU(2) isospin symmetry and the flavour independence of QCD are used to derive general relations between hadron production from the various primary light quarks. Assuming the branching fractions R _q of the Z ⁰ into down and strange quarks to be the same, five million hadronic Z ⁰ decays may allow precisions of δ(R _d = R _s)/(R _d = R _s) ～ 0.05 and δA _FB(d = s) ～ δA _fb(u) ～ 0.015 for the corresponding asymmetries. The method can be extended to include somewhat more model dependent symmetries of hadron production, which then allows the electroweak observables for each of the individual light quarks to be determined.     

Note on the two inequivalent spin 1/2 baryon field operators

There are two inequivalent spin 1/2 local baryon field operators that can be constructed from 3 quarks. A priori theJ ^P =1/2⁺ baryons can couple to any linear combination of these operators. We show however that the coupling of the 1/2⁺ baryons to these operators is determined by the value of theSU(3) ratio ofF toD type pseudoscalar-baryon couplings. The experimental value of this ratio implies, for example, that the proton couples strongly to (u ^T C _γ d)u and weakly to (u ^T C d)γ _s u. This is of interest in QCD sum rule applications.     

The twistM λ,T=0 giant modes in spherical nuclei

The theory of twisting nuclear vibrations developed by Holzwarth and Eckart to elucidate the nature of the 2^? giant mode is extended to high-multipole, spin-independentM λ,T=0 resonances. Within the framework of the distorted Fermi-surface model the parameters of inertia and stiffness against multipolarity for the nuclear incompressible Fermi-drop are derived. The energies and probabilities of the twistingM λ,T=0 modes calculated in fact without adjustable constants readE(M λ)=?ω _F \(\left[ {\frac{{(2\lambda + 3)(\lambda - 1)}}{5}} \right]^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}} \) andB(M λ) = γ_λ Z² A ^(2λ-4)/3 μ² fm^(2λ-2)respectively. The comparison with data for the 2^? resonance and predictions for higher multipoles are presented.     

The 2009 world average of <Emphasis Type="Italic">α</Emphasis><Subscript><Emphasis Type="Bold">s</Emphasis></Subscript>

Measurements of α _s, the coupling strength of the Strong Interaction between quarks and gluons, are summarised and an updated value of the world average of a_s(M_Z⁰)\alpha_{\mathrm{s}}(M_{\mathrm{Z}^{0}}) is derived. Special emphasis is laid on the most recent determinations of α _s. These are obtained from τ-decays, from global fits of electroweak precision data and from measurements of the proton structure function F₂, which are based on perturbative QCD calculations up to O(a_s⁴)\mathcal{O}(\alpha_{\mathrm{s}}^{4}); from hadronic event shapes and jet production in e⁺e⁻ annihilation, based on O(a_s³)\mathcal{O}(\alpha_{\mathrm{s}}^{3}) QCD; from jet production in deep inelastic scattering and from ϒ decays, based on O(a_s²)\mathcal{O}(\alpha_{\mathrm{s}}^{2}) QCD; and from heavy quarkonia based on unquenched QCD lattice calculations. A pragmatic method is chosen to obtain the world average and an estimate of its overall uncertainty, resulting in

Two-photon exchange in p⊆)p→ℓ+ℓ−X and a comparison with QCD

A thorough study of lepton-pair production from two-photon annihilation in p?)p collisions is presented. The differential cross section is calculated over a large range of energies (27?√s?800 GeV as a function of the dilepton mass M as well as the dilepton transverse momentum Q_T and the Feynman variable x_F. No kinematical approximations (such as the equivalent photon approximation) are made. For Q_T ≈ 0 the two-photon mechanism represents an important fraction of the pp→e⁺e^?X cross section already at ISR energies, whereas at ISABELLE energies it dramatically dominates in the interval 0?Q_T?1 GeV. At ISR energies these conclusions follow from a direct comparison of the two-photon contribution with pp→e⁺e^?X data. For the ISABELLE energy range the expected O(α_s) QCD contribution to pp→?⁺?^?X, corrected for soft gluon radiation to all orders (in leading bilogarithmic approximation), was taken as a reference. At larger Q_T and ISR energies the γγ contribution is negligible, whereas at √s = 800 GeV γγ/QCD? 10–20% almost everywhere. Furthermore, two-photon candidate events from the ISR are shown to be in reasonable agreement with theory. A decomposition of the γγ cross section into contributions from both proton vertices being elastic, inelastic and of mixed configuration is given. The results provide important clues for a future isolation of the two-photon mechanism.     

High precision measurements of the hyperfine structure of seven metastable atomic states of57Fe by laser-Rf double-resonance

The hyperfine structure of the metastable atomic states (3d ⁷4s)⁵ F _2,3,4,5 and (3d ⁷ 4s)³ F _2,3,4 of⁵⁷Fe has been measured using theABMR- LIRF method (atomic beam magnetic resonance detected by laser induced resonance fluorescence). From these measurements the following hfs constantsA of the magnetic dipole interaction have been obtained (corrected for second order effects):A(⁵ F ₂)=55.994(7) MHzA(⁵ F ₃)=69.632(5) MHzA(⁵ F ₄)=78.435(4) MHzA(⁵ F ₅)=87.246(3) MHzA(³ F ₂)=143.328(4) MHzA(³ F ₃)=50.602(10) MHzA(³ F ₄)=13.456(5) MHz     

Light thresholds in Grand Unified Theories

In a generic Grand Unified Theory with a relatively small dispersion of the spectrum around the Z-boson and the unification masses, a connection is established, exact at one loop level, between M_Z, G_F, α(M_Z and the strong coupling constant α₃(M_Z. At this level of precision, this avoids the logical and phenomenological inconsistency of predicting α₃(M_Z) by means of the electroweak couplings as extracted from the data in the Standard Model rather than in the complete theory. Attention is paid to the independence of the physical results from regularization and/or renormalization schemes.As a particularly relevant example, the analysis is specialized to the case of the Minimal Supersymmetric Standard Model, with emphasis on light charginos and neutralinos.     

A Monte Carlo program for QCD event simulation ine +e− annihilation at LEP energies

We present a Monte Carlo program for event simulation of Quantum Chromodynamics ine ⁺e^? annihilation, which includes multi-emission of quanta treated in the leading-logarithm approximation. Some difficulties of currentO(α _s ) phenomenology, associated with the treatment of divergences, are eliminated, without essentially altering the results of the analysis of the data from PETRA. At the same time a direct extension is provided of current QCD phenomenology to LEP energies, where multi-emission effects cannot be ignored. Detailed predictions for hadrons within the LEP energy interval are reported. With respect to conventionalO(α _s ) calculations, some new predicted features are: i) an average hadron multiplicity rising faster than logW, whereW is the c.m. energy, ii) a slower increase of the average hadron transverse momentum, 〈p _T ² 〉∝αα _s (W ²)W instead of the ∝α _s (W ²)W ² behaviour expected in theOα _s ) approximation. Implications for detector design and pattern recognition at LEP are also discussed.     

Optical and electrical characterization of cadmium selenide doped with cobalt

The optical and electrical properties of Co²⁺ ions in CdSe have been investigated. Absorption, photoluminescence, electron paramagnetic resonance, and Hall measurements were used to characterize a cobalt-doped (1×10¹⁹ cm⁻³) single crystal. Infrared absorption and emission spectra associated with transitions between the ⁴A₂(F) ground state and the ⁴T₁(F) and ⁴T₂(F) excited states are described. At 10 K, spin-orbit splittings result in three structured absorption bands associated with the ⁴A₂(F) to ⁴T₁(F) transition having zero-phonon lines at 4926, 5101, and 5724 cm⁻¹. The ⁴A₂(F) to ⁴T₂(F) transition shows two zero-phonon lines at 2874 and 3286 cm⁻¹, also accompanied by vibronic structure. Intrinsic lattice modes explain most of the sharp-line structure observed at low temperature, except for a subset of peaks where local modes (25-30 cm⁻¹) are invoked. Using below-band-gap light, selective excitation allows detection of the ⁴T₁(F) to ⁴A₂(F) recombination at liquid-helium temperatures. The activation of free carriers in our n-type material containing shallow donors is affected by the presence of cobalt, and we find the Co^+/++ level to be about 34 meV below the conduction band of CdSe.     

On the applicability of finite order perturbative QCD calculations of jet rates ine + e − annihilation

We have studied the measurement of α _s using exact second order QCD matrix element calculations of jet rates ine ⁺ e ^?→hadrons. We investigate the dependence of α _s (M _Z ² ), measured by experiments at theZ ⁰ resonance, on the choice of renormalisation scale in terms of the functional form of the three-jet matrix element. We find that only a restricted domain of the jet resolution parametery _c , $\Lambda _{\overline {MS} } $ , and scale gives a perturbation series which is well-behaved to second order, and that this domain is different for the various jet algorithms in current use.     

Effects of QCD multi-jet contributions in electron-positron annihilation

By means of a recently proposed Monte Carlo procedure for computing QCD multi-jet finals states in the leading-logarithm approximation, we calculate the effects of multi-emission on the hadronic final state in electron-positron annihilation. In particular, we present quantitative predictions for the growth with energy of the average multiplicity, which increases faster than log W, and for the average transverse momentum, for which ee find 〈p_T²〉 ∝ α_s(W²) W, in contrast with the ∝ α_s(W²) W² behaviour expected in lowest perturbative order calculations.     

αS(KT2) versus αS(K2) in QCD jet development: Some quantitative remarks

Properties of QCD jets for two proposed choices of the variable appearing in the QCD running coupling constant, α_S(K²) or α_S(K_T²) with K_T²=z(1?z)K², have been studied in detail by the use of Monte Carlo techniques. Contrary to expectations based on approximate analytic calculations it is found that when substituting K² with K_T² in α_S the growth with energy of the multiplicity of the quanta is not sensibly altered, and it is even slowed down for extreme values of the non-perturbative cutoff, which delimits the minimum virtual mass of the quanta. It appears, therefore, that the analysis of subleading effects may be totally misleading if phase-space constraints are not taken into account exactly, which is possible to do in Monte Carlo calculations.     

The effect of 1Q2 and αs corrections on tests of QCD

We discuss in detail the use of the structure function F₃(x, Q²) of deep-inelastic neutrino scattering for testing quantum chromodynamics. QCD is entirely consistent with all data. However, we show that higher-twist (order $\text{1}\text{Q}{}^2$) 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 $\text{1}\text{Q}{}^2$ contributions within the context of QCD. Furthermore, the possible presence of higher-twist terms makes it impossible to unambiguously detect the logarithmic Q² dependence and anomalous dimensions which distinguish QCD from hypothetical alternative theories. As a result, more precise data with higher Q² 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.