Status of the lepton g − 2 and effects of hadronic corrections

The electron and muon anomalous magnetic moments (AMM) are measured in experiments and studied in the Standard Model (SM) with the highest precision accessible in particle physics. The comparison of the measured quantity with the SM prediction for the electron AMM provides the best determination of the fine structure constant. The muon AMM is more sensitive to the appearance of New Physics effects and, at present, there appears to be a three- to four-standard deviation between the SM and experiment. The lepton AMMs are pure relativistic quantum correction effects and therefore test the foundations of relativistic quantum field theory in general, and of quantum electrodynamics (QED) and SM in particular, with highest sensitivity. Special attention is paid to the studies of the hadronic contributions to the muon AMM which constitute the main source of theoretical uncertainties of the SM.     

Analysis of the hadronic light-by-light contributions to the muon g − 2

We calculate the hadronic light-by-light contributions to the muon g − 2. We use both 1/N_c and chiral counting to organize the calculation. Then we calculate the leading and next-to-leading order in the 1/N_c expansion low energy contributions using the Extended Nambu-Jona-Lasinio model as hadronic model. We do that to all orders in the external momenta and quark masses expansion. Although the hadronic light-by-light contributions to muon g − 2 are not saturated by these low energy contributions we estimate them conservatively. A detailed analysis of the different hadronic light-by-light contributions to muon g − 2 is done. The dominant contribution is the twice anomalous pseudoscalar exchange diagram. The final result we get is a_μ^{light-by-light} = (−9.2 ± 3.2) × 10⁻¹. This is between two and three times the expected experimental uncertainty at the forthcoming BNL muon g − 2 experiment.     

A computational study of the electron detachment energies of Al2As2 − and Al3As3 −

Ab initio and density functional theory calculations are reported for the low-lying electronic states of Al₂As₂ ^?, Al₂As₂, Al₃As₃ ^?, and Al₃As₃. The ²B_2g ground electronic state of Al₂As₂ ^? has a rhombic structure with the Al atoms occupying the shorter diagonal. In contrast, the As atoms occupy the shorter diagonal of the ground state rhombic structure of Al₂As₂. Electron detachment energies computed for Al₂As₂ ^? are presented and discussed. The adiabatic electron affinity of Al₂As₂ ^? is calculated to be 2.1 eV at the CCSD(T) level, using B3LYP and MP2 optimized geometries. The ground states of both Al₃As₃ ^? (²A₁′) and Al₃As₃ (¹A₁′) have planar hexagonal D_3h geometry. Electron detachment energies computed for the anion are reported. At the CCSD(T)//B3LYP level, the electron affinity of Al₃As₃ is calculated to be 2.47 eV.     

NO 3 2− and CO 2 − centers in synthetic hydroxyapatite: Features of the formation under γ- and UV-irradiations

The EPR studies of synthetic hydroxyapatite containing carbonate and nitrate ions exposed to γ-ray and UV irradiations have been performed. It has been found that γ irradiation leads to the formation of both NO₃²⁻ and CO₂⁻ paramagnetic centers, while the UV irradiation induces only NO₃²⁻ centers. To explain this fact, the hypothesis has been proposed, according to which in the hydroxyapatites studied, there coexist complexes consisting of nitrate ions and shallow electron traps that serve as sources of secondary electrons during UV irradiation. The EPR spectroscopy parameters (g and A) of the detected centers have been determined and compared with similar centers in hydroxyapatite with a different impurity composition. The study of the thermal stability of the centers has demonstrated that, in the temperature range 20–300°C, the NO₃²⁻ centers formed by UV irradiation are more stable than the same centers created by γ-ray irradiation.     

Assessment of role of iron ions on the physical and spectroscopic properties of multi-component Na2O−PbO−Bi2O3−SiO2 glass ceramics

Multi-component glass ceramics composition Na₂O?PbO?Bi₂O₃?SiO₂ doped with different concentrations of Fe₂O₃ as nucleating agent were characterised by XRD, SEM (scanning electron microscope) and DTA (differential thermal analysis) techniques. Optical absorption, EPR, FTIR and Raman studies are also carried out on these glass ceramics. Absorption bands observed at about 457, 489, 678 and 820 nm are the characteristics of Fe³⁺ ions whereas the band observed at about 964 nm is due to Fe²⁺ ions. EPR studies suggested that Fe³⁺ ions entered in the lattice as tetragonally distorted octahedral symmetry or rhombic sites at low concentration of Fe₂O₃, whereas at higher concentration of Fe₂O₃ (beyond 1 mol%), the super exchange type of interactions between multivalency iron ions begin to dominate. FTIR and Raman spectra have revealed the behaviour of various structural units in the glass ceramic matrix. The analysis of these spectroscopic studies indicates that iron ions do exist in Fe³⁺ and Fe²⁺ state.     

Measurement of the Electric Quadrupole Moment of the 9/2− and 21/2− Isomers in 173Ta

The electric quadrupole moments of the 9/2⁻ and 21/2⁻ isomeric states of ¹⁷³Ta at 165.8 keV and 1713.2 keV, respectively, were measured as Q(9/2⁻)=2.92(15) b and Q(21/2⁻)=6.23(18) b for the first time using the TDPAD technique. A 66 MeV pulsed ¹²C ion beam from the 15UD pelletron accelerator facility of the Nuclear Science Centre at New Delhi was used in the reaction ¹⁶⁵Ho(¹²C, 4nγ)¹⁷³Ta. The experimental values of equilibrium deformations β₂(9/2⁻)=0.251(7) and β₂(21/2⁻)=0.391(7) were extracted. This revised version was published online in July 2006 with corrections to the Cover Date.     

Influence of CO 3 2− and OH− groups on dielectric losses of NaCl crystals

The results of measuring the dielectric losses of NaCl crystals with a different concentration of Na₂CO₃ and NaOH admixtures in the melt are given in the present paper. From a comparison of the curves found for the dielectric losses of the crystals studied it can be seen that the course of tan and the positions of the relaxation maxima, corresponding to the measured specimens with CO ₃ ^2– or OH^– admixtures, hardly differ. From these measurements and from a comparison with the results of other authors it follows that the admixture is probably the same in both groups of crystals.In conclusion the author thanks Dr. A. Bohun for discussions on the results and for his continuous interest in this work.     

Comparison of semiempirical and ab initio absolute probabilities of rovibronic transitions for the I 1Π g − , J 1Δ g − →C 1Π u ± system of bands of the H2 molecule

The absolute values of probabilities of the I ¹Π _g ^? , v′, J′; J ¹ Δ _g ^? , v′, J′→C ¹Π _u ^± , v″, J″ spontaneous transitions in the H₂ molecule (for the vibrational and rotational quantum numbers v′=v″=0–3, J′=1–6, and J″=J′, J′ ±1) are calculated by using ab initio and semiempirical data on the dipole moments of the 3dπ ¹Π_g, 3dδ¹Δ_g→2pπ¹Π_u electronic transitions. In both cases, the calculations are performed both in the adiabatic approximation and with an allowance for the nonadiabatic effect of electronic-rotational interaction. The coefficients of expansion of the wave functions of perturbed rovibronic states in the Born-Oppenheimer basis functions used in the calculations were obtained in the approximation of pure precession from experimental values of the terms. It was found that the values of transition probabilities based on the ab initio calculations systematically exceed the corresponding semiempirical data by a factor of 1.2–1.9 for the I ¹Π_g→C ¹Π _u ^± transition and by a factor of 1.4–1.6 for the J ¹Δ _g ^? →C ¹Π _u ^± transition. It was established that the difference between the ab initio and semiempirical values of electronic transition moments virtually has no effect on the dependence of the transition probabilities on the vibrational quantum numbers. The discrepancies between the results of adiabatic and nonadiabatic calculations are significant and reach two orders of magnitude, which is indicative of the important role of perturbations in the probabilities of the transitions considered.     

Magnetic behavior of the alloys CeCuyGa4−y and Ce1−xLaxCuGa3

The results of magnetic susceptibility (x), electrical resistivity (ρ) and heat-capacity (C) measurements of the alloys CeCu_yGa_4−y (y = 0.5, 1.0, 1.25 and 1.5) and Ce_1−xLa_xCuGa₃ (x = 0.2 and 0.9), crystallizing in the BaAl₄-type tetragonal structure, are reported. The Kondo effect tends to dominate with increasing y. All the data for the y = 0.5 alloy are consistent with the onset of ferromagnetic ordering at 6 K. For y = 1.0 and 1.25, though ρ gradually drops below 6 K, the C data do not show the existence of magnetic ordering above 2 K; presumably, for y = 1.0, 1.25 and 1.5, long-range magnetic ordering sets in below 2 K. Above all, C tends to increase with decreasing temperature before the onset of long range magnetic ordering and the values of C/T per Ce mol are considerably diminished for x = 0.9. It is proposed that this C/T enhancement lies in the magnetic precursor effects and not on the heavy-fermion behaviour.     

Observation of perturbations in the rovibronic transition probabilities for the (4d)r 3Π g − , (4d) s 3 Δ g − → (2p) c 3Π u ± band systems of the H2 molecule

The ratios of the radiative transition probabilities for the lines of the P, Q, and R branches of the (4d)r ³Π _g ^? , (4d)s ³Δ _g ^? → (2p) c ³Π _u ^± band systems of the H₂ molecule have been measured for the first time. Significant (to two orders of magnitudes) differences are found between the experimental values and the adiabatic theory predictions. It is established that the results of the nonadiabatic calculation performed by us in the pure-precession approximation taking into account the electronic-rotational interaction of the 4d ³Π_g and 4d ³Δ_g states are in agreement with the experimental data. The optimal energies of rovibronic levels of the r ³Π _g ^? , s ³Δ _g ^? , c ³Π _u ^? , and c ³Π _u ⁺ states have been found and reidentification of 11 from 54 spectral lines, assigned previously to the (0-0) and (1-1) bands, was performed.     

Reevaluation of the hadronic contributions to the muon g−2 and to \alpha (M^{2}_{Z})

We reevaluate the hadronic contributions to the muon magnetic anomaly, and to the running of the electromagnetic coupling constant at the Z-boson mass. We include new π ⁺ π ^? cross-section data from KLOE, all available multi-hadron data from BABAR, a reestimation of missing low-energy contributions using results on cross sections and process dynamics from BABAR, a reevaluation of all experimental contributions using the software package HVPTools together with a reanalysis of inter-experiment and inter-channel correlations, and a reevaluation of the continuum contributions from perturbative QCD at four loops. These improvements lead to a decrease in the hadronic contributions with respect to earlier evaluations. For the muon g?2 we find lowest-order hadronic contributions of (692.3±4.2)?10^?10 and (701.5±4.7)?10^?10 for the e ⁺ e ^?-based and τ-based analyses, respectively, and full Standard Model predictions that differ by 3.6σ and 2.4σ from the experimental value. For the e ⁺ e ^?-based five-quark hadronic contribution to $\alpha(M_{Z}^{2})$ we find $\varDelta \alpha_{\mathrm{had}}^{(5)}(M_{Z}^{2}) =(274.9\pm1.0)\cdot10^{-4}$ . The reduced electromagnetic coupling strength at M _Z leads to an increase by 12 GeV in the central value of the Higgs boson mass obtained by the standard Gfitter fit to electroweak precision data.     

Hadronic contributions to (g−2) of the leptons and to the effective fine structure constant α(M Z 2 )

The new experiment planned at Brookhaven to measure the anomalous magnetic moment of the muona _μ≡(g _μ?2)/2 will improve the present accuracy of 7 ppm by about a factor of 20. This requires a careful reconsideration of the theoretical uncertainties of theg?2 predictions, which are dominated by the error of the contribution from the light quarks to the photon vacuum polarization. This issue is cruicial also for the precise determination of the running fine structure constant at theZ-peak as LEP/SLC experiments continue to increase their precision. In this paper we present an updated analysis of the hadronic vacuum polarization using all presently availablee ⁺e^? data. This seems to be justified because previous work on the subject was based to some extent on preliminary or incomplete experimental data. Contributions from different energy ranges are presented separately forg?2 of the muon and the τ-lepton and for α(M _Z ² ). We obtain the resultsa _μ ^had* =(725±16)×10^?10 anda _τ ^had* =(351±10)×10^?8, where the asterisk indicates the dressed (renormalization group improved) value. For the effective fine structure constant atM _Z=91.1888 GeV we obtainΔα _had ⁽⁵⁾ =0.0280±0.0007 and α(M _Z ² )^?1=128.896±0.090. Further improvement in the accuracy of theoretical predictions which depend on the hadronic vacuum polarization requires more precise measurements ofe ⁺e^? cross-sections at energies below about 12 GeV in future experiments.     

Comparative study of the specific heat of superconducting and non-superconducting YBa2Cu3O7−x

We have measured the specific heat, the electrical resistance and the magnetic susceptibility of YBa₂Cu₃O_7–x in a superconducting (sc) and in a non-superconducting (nsc) version. The latter was obtained by inducing a small loss of oxygen. In the sc sample we find a jump of the specific heat with C=3.6 J mole^–1 K^–1. Below the maximum nearT _c the specific heat of the sc version drops too fast for an electronic effect alone: there is a cross-over from excess to deficiency already at 0.9T _c . The specific heat of the nsc version shows a change of slope in the temperature range between 70 and 80 K, which indicates the existence of a second specific heat anomaly, which apparently exists independently of that due to the onset of superconductivity and explains at least partially the premature crossover.Alexander von Humboldt fellow. On leave in absence from Centro Atomico Bariloche—CNEA Argentina     

High-resolution spectroscopy of the a4Σ−3/2 − X12Π3/2 system of gold monosulphide in the near infrared

ABSTRACT

We have recorded the a⁴Σ^? _3/2 ? X₁ ²Π_3/2 (0,0), (1,0), and (2,0) bands of gaseous gold monosulphide (AuS) at sub-Doppler resolution in the near-infrared region. The molecules were made in a hollow cathode discharge source by the reaction of sputtered gold with carbonyl sulphide. The high resolution of the laser excitation spectrum enabled the determination of molecular constants describing the rotational and ¹⁹⁷Au hyperfine structure in both states, as well as the spin–rotation interaction in the a⁴Σ^? _3/2 state. The natures of the two electronic states are discussed in the context of the observed hyperfine structure.     

On the rotational intensity distribution in the a1Δg → X3Σg− magnetic dipole transition of oxygen molecule

The relative intensity distribution in the rotational structure of the a¹Δ_g → X³Σ_g⁻ magnetic dipole transition of molecular oxygen is examined. Use is made of experimental data obtained from the high-resolution (0.02 cm⁻¹) FTS recording of the 0-0 band published by C. Amiot and J. Verges (Canad. J. Phys. 59, 1391–1398 (1981)). Comparison of the experimental and theoretical intensities indicates that rotational linestrength formulas containing purely vibronic transition moments are inadequate and need to be supplemented by two additional parameters of rovibronic origin.     

High-resolution spectroscopy of difference and combination bands of SF6 to elucidate the ν3 + ν1 − ν1 and ν3 + ν2 − ν2 hot band structures in the ν3 region

The strong infrared absorption in the ν₃ S–F stretching region of sulphur hexafluoride (SF₆) near 948 cm^?1 makes it a powerful greenhouse gas. Although its present concentration in the atmosphere is very low, it is increasing rapidly, due to industrial pollution. The ground state population of this heavy species is only 32% at room temperature and thus many hot bands are present. Consequently, a reliable remote-sensing spectroscopic detection and monitoring of this species require an accurate modelling of these hot bands. We used two experimental set-ups at the SOLEIL French synchrotron facility to record some difference and combination bands of SF₆: (1) a new cryogenic multiple pass cell with 93 m optical path length and regulated at 163 ± 2 K temperature and (2) the Jet-AILES supersonic expansion set-up. With this, we could obtain high-resolution absorption spectra of the ν₃ ? ν₁, ν₃ ? ν₂, ν₁ + ν₃ and ν₂ + ν₃ bands at low temperature. These spectra could be assigned and analysed, thanks to the SPVIEW and XTDS computer programs developed in Dijon. We performed two global fits of effective Hamiltonian parameters. The first one is a global fit of the ground state, ν₂, ν₃, ν₃ ? ν₂, ν₂ + ν₃, 2ν₃ and 2ν₃ ? ν₃ rovibrational parameters, using the present spectra and previous infrared, Raman and two-photon absorption data. This allows a consistent refinement of the effective Hamiltonian parameters for all the implied vibrational levels and a new simulation of the 2ν₃ + ν₂ ? ν₂ hot band. The second global fit involves the present ν₃ ? ν₁ and ν₁ + ν₃ lines, together with previous ν₁ Raman data, in order to obtain refined ν₁ parameters and also ν₁ + ν₃ parameters in a consistent way. This allows to simulate the ν₃ + ν₁ ? ν₁ hot band.