Improvement of perturbation theory in QCD for e + e − →hadrons and the problem of α s freezing

A method of improving perturbation theory in QCD is developed which can be applied to any polarization operator. The case of the polarization operator Π(q ²), corresponding to the process e ⁺ e ⁻→ hadrons, is considered in detail. By the use of the analytical properties of Π(q ²) and a perturbation expansion of Π(q ²) for q ²<0, the function ImΠ(q ²) at q ²>0 is defined in such a way that the infrared pole is eliminated. The convergence of the perturbation series for R(q ²)=σ(e ⁺ e ⁻ →hadrons)/(e ⁺ e ⁻→μ ⁺ μ ⁻) is improved. After substitution of R(q ²) into the dispersion relation an improved Adler function D(q ²) is obtained, having no infrared pole and a frozen α _s (q ²). Good agreement with experiment is achieved. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 3, 167–170 (10 August 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Study of Bs→φ?+?? decay in a single universal extra dimension model

Using form factors derived from the light-cone sum rules, we investigate B _s →φℓ ⁺ ℓ ⁻ (ℓ=e,μ,τ) in a single universal extra dimension model (UED). In UED, there is only one new parameter with respect to the Standard Model (SM), which is the inverse of the compactification radius R of the extra dimension. In this work, the branching ratios, the dilepton invariant mass spectra, the forward–backward asymmetries, and the lepton polarization asymmetries of B _s →φℓ ⁺ ℓ ⁻ are calculated. For a lower value of 1/R, there are some considerable discrepancies between the UED and SM. However, with the increase of 1/R, the effect of UED tends to diminish; in particular for 1/R≥1000 GeV, two models have approximately the same predictions. Compared with data from CDF for B _s →φμ ⁺ μ ⁻, we find that the 1/R tends to be larger than 350 GeV. We also find that the zero crossing point of the forward–backward asymmetry of B _s →φμ ⁺ μ ⁻ becomes smaller, which would be an important platform for probing the UED effect. These results could be tested in the Large Hadron Collider (LHC) at CERN and the future super-B factory.     

e -μ+→e +μ- process in a model with theSU(2)L×SU(2)R×U(1)B−L gauge group

A model based on theSU(2)_L×SU(2)_R×U(1)_B−L gauge group is used to study the lepton recharging processe ^-μ⁺→e ⁺μ^-. It should be possible to observe this process on a muon collider in the fixed-electron-target regime or the electron-beam regime. It is shown that the given process can be used to measure not only the characteristics of physical Higgs bosons, but also the parameters of neutrino oscillations. Grodno University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 83–88, November, 1998.     

The superconducting properties of YBa2(Cu1−xMx)3O7 for M=Zn and Ni

Transverse and zero-field μSR measurements were made on YBa₂(Cu_1−xNi_x)₃O_7−y withx=0.1 and 0.2, and YBa₂(Cu_1−x Zn _x )₃O_7−y withx=0.03, 0.06, 0.1, and 0.16, wherey≈0.1. Since doping may lead to magnetic ordering this was searched for with both zero and transverse field μSR, but no evidence was found over the temperature range studied: 10–100 K. However, depolarization rates as functions of temperature were obtained, and the low temperature values of these are σ=3.2 μs⁻¹.1.6μs⁻¹, and 1 μs⁻¹ forx=0.01, and 0.2 Ni, respectively, and σ=0.8 μs⁻¹, 0.75 μs⁻¹, 0.65 μs⁻¹, and 0.4 μs⁻¹ forx=0.03, 0.06, 0.1, and 0.16 Zn, respectively. Estimates for the effect of decreasing electron concentration for Zn are made, but these alone do not account for the drop in σ. Estimates for the effect of scattering on λ and hence σ are made. The reduction in σ for Ni dopant is in surprisingly good agreement with these estimates. For Zn the order of magnitude is correct, but the relative lack of further change in σ after the effect of the first 0.03 addition seems to imply a saturation of the effect of scattering.     

An interpolation of the vacuum polarization function for the evaluation of hadronic contributions to the muon anomalous magnetic moment

We propose a simple parameterization of the two-point correlator of hadronic electromagnetic currents for the evaluation of the hadronic contributions to the muon anomalous magnetic moment. The parameterization is explicitly done in the Euclidean domain. The model function contains a phenomenological parameter which provides an infrared cutoff to guarantee the smooth behavior of the correlator at the origin in accordance with experimental data in e ⁺e^- annihilation. After fixing a numerical value for this parameter from the leading order hadronic contribution to the muon anomalous magnetic moment, the next-to-leading order results related to the vacuum polarization function are accurately reproduced. The properties of the four-point correlator of hadronic electromagnetic currents as for instance the so-called light-by-light scattering amplitude relevant for the calculation of the muon anomalous magnetic moment are briefly discussed. Received: 14 December 2001 / Published online: 7 June 2002     

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

Chiral phenomenological relations between rates of rare radiative decays of kaon to pion and leptons and the meson form factors

In the framework of the chiral perturbation theory we obtain the phenomenological relations between decay branches of rare radiative kaon to pion and leptons K ⁺ → π⁺ l ⁺ l ⁻ and K _S ⁰ → π⁰ l ⁺ l ⁻ and meson form factors. The comparison of these results with the present-day experimental data shows us that the ChPT relations for a charge kaon can determine meson form factors from already measured decay rates at high precision level. However, in the case of the neutral kaon decays K ⁰ → π⁰ e ⁺ e ⁻(μ⁺μ⁻) the form factor data are known to a higher precision than data on the differential rates of radiative kaon decay K ⁰ π⁰ e ⁺ e ⁻(μ⁺μ⁻).     

Fine structure of the muonic <Superscript>4</Superscript>He ion

On the basis of quasi-potential approach to the bound state problem in QED we calculate the vacuum polarization, recoil and structure corrections of orders α⁵ and α⁶ to the fine splitting interval ΔE ^fs = E(2P _3/2) − E(2P _1/2) in muonic ₂⁴He ion. The resulting value ΔE ^fs = 146180.68 μeV provides reliable guideline in performing a comparison with the relevant experimental data.     

Generalized holographic and Ricci dark energy models

In this paper, we consider generalized holographic and Ricci dark energy models where the energy densities are given as ρ _R =3c ² M _pl² Rf(H ²/R) and ρ _h =3c ² M _pl² H ² g(R/H ²), respectively; here f(x), g(y) are positive defined functions of the dimensionless variables H ²/R or R/H ². It is interesting that holographic and Ricci dark energy densities are recovered or recovered interchangeably when the function f(x)=g(y)≡1 or f(x)=Id and g(y)=Id are taken, respectively (for example f(x),g(x)=1−ε(1−x), ε=0or1, respectively). Also, when f(x)≡xg(1/x) is taken, the Ricci and holographic dark energy models are equivalent to a generalized one. When the simple forms f(x)=1−ε(1−x) and g(y)=1−η(1−y) are taken as examples, by using current cosmic observational data, generalized dark energy models are considered. As expected, in these cases, the results show that they are equivalent (ε=1−η=1.312), and Ricci-like dark energy is more favored relative to the holographic one where the Hubble horizon was taken as an IR cut-off. And the suggested combination of holographic and Ricci dark energy components would be 1.312R−0.312H ², which is 2.312H²+1.312[(H)\dot]2.312H^{2}+1.312\dot{H} in terms of H ² and [(H)\dot]\dot{H} .     

Total rates of nuclear capture of negative muons in the isotopes 132Xe and 40Ar

The lifetimes of a negative muon in the isotopes ¹³²Xe and ⁴⁰Ar in the solid phase are measured. The lifetime of μ ⁻ in the 1s state of the isotope ¹³²Xe is τ(¹³²Xe)=101.7±1.7 ns, which corresponds to a total nuclear capture rate Λ_c(¹³²Xe)=9.4±0.2 μs⁻¹. The lifetime of μ ⁻ in the isotope ⁴⁰Ar, viz., τ (⁴⁰Ar)=568±6 ns, corresponding to a capture rate Λ_c(⁴⁰Ar)=1.31±0.01 μs⁻¹, is obtained to several times better accuracy as compared to previously published results. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 3, 181–183 (10 February 1999)     

Experimental study of the reaction e + e − → K S K L in the energy range √S = 1.04−1.38 GeV

We present a measurement of the e ⁺ e ⁻ → K _S K _L cross section in the energy range √s = 1.04−1.38 GeV. For an energy of √s ≥ 1.2 GeV the cross section exceeds vector meson dominance model predictions with only ρ(770), ω(783), and ϕ(1020) mesons taken into account. The measured cross section agrees well with previous measurements. Published in Russian in Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2006, Vol. 130, No. 5, pp. 831–839. This article was translated by the authors.     

B→K1?+?? decays in a family non-universal Z′ model

The implications of the family non-universal Z′ model in the B→K ₁(1270,1400)ℓ ⁺ ℓ ⁻(ℓ=e ,μ ,τ) decays are explored, where the mass eigenstates K ₁(1270, 1400) are the mixtures of ¹ P ₁ and ³ P ₁ states with the mixing angle θ. In this work, considering the Z′ boson and setting the mixing angle θ=(−34±13)^○, we analyze the branching ratio, the dilepton invariant mass spectrum, the normalized forward–backward asymmetry and lepton polarization asymmetries of each decay mode. We find that all observables of B→K ₁(1270)μ ⁺ μ ⁻ are sensitive to the Z′ contribution. Moreover, the observables of B→K ₁(1400)μ ⁺ μ ⁻ have a relatively strong θ-dependence; thus, the Z′ contribution will be buried by the uncertainty of the mixing angle θ. Furthermore, the zero crossing position in the FBA spectrum of B→K ₁(1270)μ ⁺ μ ⁻ at low dilepton mass will move to the positive direction with Z′ contribution. For the tau modes, the effects of Z′ are not remarkable due to the small phase space. These results could be tested in the running LHC-b experiment and Super-B factory.     

A Measurement of the ψ′ to J/ψ production ratio in 920?GeV proton-nucleus interactions

Ratios of the ψ^′ over the J/ψ production cross sections in the dilepton channel for C, Ti and W targets have been measured in 920 GeV proton-nucleus interactions with the HERA-B detector at the HERA storage ring. The ψ^′ and J/ψ states were reconstructed in both the μ⁺μ^- and the e⁺e^- decay modes. The measurements covered the kinematic range -0.35≤x_F≤0.1 with transverse momentum p_T≤4.5 GeV/c. The angular dependence of the ratio has been used to measure the difference of the ψ^′ and J/ψ polarization. All results for the muon and electron decay channels are in good agreement: their ratio, averaged over all events, is R_ψ′(μ)/R_ψ′(e)=1.00±0.08±0.04. This result constitutes a new, direct experimental constraint on the double ratio of branching fractions, (B^′(μ)B(e))/(B(μ)B^′(e)), of ψ^′ and J/ψ in the two channels. The ψ^′ to J/ψ production ratio is almost constant in the covered x_F range and shows a slow increase with p_T.     

Quantum chromodynamics studies at LEP2

Several studies have been made to the hadronic final states in e ⁺ e ⁻ collisions at LEP. Studies of the annihilation process at LEP2 have given rise to results on jet rate, event shape, heavy flavour production, inclusive momentum spectra, Bose-Einstein correlation and colour reconnection effects. Event shape studies have given rise to accurate determination of the strong coupling constant α _s using O (α _s ² ) with resummed leading and next-to-leading log calculation and also with power law corrections. Studies of 2-photon processes have yielded results on γγ cross-section, heavy flavour production, photon structure function and γ*γ* scattering.     

Renormalization-group improved prediction for Higgs production at hadron colliders

We use renormalization-group methods in effective field theory to improve the theoretical prediction for the cross section for Higgs-boson production at hadron colliders. In addition to soft-gluon resummation at N³LL, we also resum enhanced contributions of the form (C _A π α _s ) ⁿ , which arise in the analytic continuation of the gluon form factor to time-like momentum transfer. This resummation is achieved by evaluating the matching corrections arising at the Higgs-boson mass scale at a time-like renormalization point μ ²<0, followed by renormalization-group evolution to μ ²>0. We match our resummed result to NNLO fixed-order perturbation theory and give numerical predictions for the total production cross section as a function of the Higgs-boson mass. Resummation effects are significant even at NNLO, where our improved predictions for the cross sections at the Tevatron and the LHC exceed the fixed-order predictions by about 13% and 8%, respectively, for m _H =120 GeV. We also discuss the application of our technique to other time-like processes such as Drell–Yan production, e ⁺ e ⁻→hadrons, and hadronic decays of the Higgs boson.     

Laser photoacoustic spectroscopy of iodine molecule: Single and two-photon absorption

Photoacoustic spectroscopy of iodine molecule has been studied in gas phase using nitrogen laser-pumped tunable dye laser. The experiment yielded the vibrational spectrum corresponding toX ¹Σ⁺(0 _g ⁺ )→B ³Π(0 _g ⁺ ) transition up to the convergence limit. The photo-acoustic spectrum in the region 17580–18850 cm⁻¹ is presented along with the vibrational analysis. Five of the vibrational bands reported earlier by Venkateswarlu, Kumar and McGlynn have been partially resolved and the structure of one of them has been analyzed and shown to be due to an overlap of (14, 2) and (12, 1) bands. The analysis was based on a comparison with the highly resolved spectrum of Gerstenkorn and Luc. The structure observed in the region 20200–20750 cm⁻¹ which is beyond the convergence limit of the transitionX ¹Σ⁺(0 _g ⁺ )→B ³Π(0 _u ⁺ ) has been analyzed as due to two-photon absorption. Most of the bands could be assigned to two transitions both originating in the ground state and terminating in two different electronic states 1 _g andE(0 _g ⁺ ), atT _e=40821 cm⁻¹ (orT ₀=41355 cm⁻¹) andT _e=41411 cm⁻¹ (orT ₀=41355 cm⁻¹) respectively.     

Next-to-next-leading order correction to 3-jet rate and event-shape distribution

The hadronic events from the e ⁺ e ⁻ annihilation data at the centre-of-mass energies ranging from 60 to 197 GeV were studied. The AMY and OPAL Collaborations offered a unique opportunity to test QCD by measuring the energy dependence of different observables. The coupling constant, α _s, was measured by two different methods: first by employing the three-jet observables. Combining all the data, the value of as at next-to-next leading order (NNLO) was determined to be 0.117 ± 0.004(hard) ± 0.006(theo). Secondly, from the event-shape distributions, the strong coupling constant, α _s, was extracted at NNLO and it’s evaluation was tested with the energy scale. The results were consistent with the running of α _s, expected from QCD predictions. Averaging over different observables, α _s was determined to be 0.115 ± 0.007(hard) ± 0.003(theo).     

Wilson line correlator in the MV model: relating the glasma to deep inelastic scattering

In the color glass condensate framework the saturation scale measured in deep inelastic scattering of high energy hadrons and nuclei can be determined from the correlator of Wilson lines in the hadron wavefunction. These same Wilson lines give the initial condition of the classical field computation of the initial gluon multiplicity and energy density in a heavy ion collision. In this paper the Wilson line correlator in both adjoint and fundamental representations is computed using exactly the same numerical procedure as has been used to calculate gluon production in a heavy ion collision. In particular the discretization of the longitudinal coordinate has a large numerical effect on the relation between the color charge density parameter g²μ and the saturation scale Q_s. Our result for this relation is Q_s≈0.6g²μ, which results in the classical Yang–Mills value for the “gluon liberation coefficient” c≈1.1. PACS  24.85.+p; 25.75.-q; 13.60.Hb     

Spectroscopic and structural proprieties of LiAr and LiAr<Subscript>2</Subscript> molecules

We determined and tried to understand the spectroscopic and structural properties of small LiAr and LiAr₂ molecules within a simple model considering LiAr as a result of interaction between a valence electron and a LiAr⁺ molecular ion. Potential energy curves, spectroscopic constants, and vibrational levels corresponding to the Li(2s, 2p, 3s, and 3p)+Ar dissociation are reported for the LiAr molecule. The depth of the potential well for the X ²Σ⁺ ground state is found to be 50 cm⁻¹ (the corresponding experimental value is (42.5±1.2) cm⁻1 [1]). R _e is determined to be 9.36 a.u. (the experimental value is 9.24 a.u.). For the first excited state A, R _e = 4.97 a.u. and D _e = 993cm ⁻¹ (the corresponding experimental values are 4.68 a.u. and (925−40) cm⁻¹, respectively [1]). The spacing between the vibrational levels for the ground and first excited states is in very good agreement with the experiment. For the ground state, the difference between our results and the data of the most recent experiment is about 1 cm⁻¹. The model has been extended to study the LiAr₂ molecule in two forms (linear and triangular). We have determined the potential energy surfaces of the states dissociating to Li(2s, 2p)+Ar₂ and thus found the triangular form to be more stable as compared to the linear one. We have also calculated the transition energy between the ground state and first excited states of this molecule. The emission spectrum of the Li(2s)+Ar₂→Li(2p)+Ar₂ transition in both forms redshifts as compared to the Li(2s)→Li(2p) atomic transition.