The heavy quarkonium spectrum at order mαslnαs

We compute the complete leading-log terms of the next-to-next-to-next-to-leading-order corrections to potential NRQCD. As a by-product we obtain the leading logs at O(mα_s⁵) in the heavy quarkonium spectrum. These leading logs, when Λ_QCDmα_s², give the complete O(mα_s⁵lnα_s) corrections to the heavy quarkonium spectrum.     

On the rise of the proton structure function F2 towards low x

A measurement of the derivative (∂ lnF₂/∂ lnx)_Q²≡−λ(x,Q²) of the proton structure function F₂ is presented in the low x domain of deeply inelastic positron–proton scattering. For 5×10⁻⁵x0.01 and Q²1.5 GeV², λ(x,Q²) is found to be independent of x and to increase linearly with lnQ².     

The low temperature electric quadrupole orientation of184Ir and185Ir in rhenium

The half-lives of¹⁸⁴Ir,¹⁸⁵Ir and¹⁸⁶Ir have been determined to be 3.14(2) h, 14.4(1) h and 16.64(3) h, respectively. The quadrupole frequenciesv _Q = e²qQ_s/h of¹⁸⁴Ir and¹⁸⁵Ir in rhenium single crystal have been determined to be Q_s(¹⁸⁴Ir) = + 2.0(3) b MHz and Q_s(¹⁸⁵Ir) = +2.0(3) b MHz. Adopting the value of –3.6(2)×10¹⁷ V·cm^–2 for the electric field gradient eq at T=0 K, the values of the ground-state spectroscopic quadrupole moments of these isotopes are determined to be Q_s(¹⁸⁴Ir)=+2.0(3) b and Q_s(¹⁸⁵Ir)=–2.5(3) b. The¹⁸⁵Ir moment is only consistent with the ground state Nilsson configuration , the¹⁸⁴Ir moment is consistent with K4 with a predominant K=4 component, in disagreement with K=0,1 found for¹⁸⁶Ir. Our analysis differs in detail from the recent nuclear orientation study by Hagn et al.[1].     

Mirror supersymmetry in the space of (super) extended Poincaré algebras p(p,q)

We classify extended Poincaré Lie superalgebras and Lie algebras of any signature (p, q), i.e. Lie superalgebras and ₂-graded Lie algebras g = g₀ + g₁, where g₀ = s₀(V) + V is the (generalized) Poincaré Lie algebra of the pseudo Euclidean vector space V = ^{p, q} of signature (p, q) and g₁ is a spin 1/2 s₀(V)-module extended to a s₀-module with kernel V.As a result of the classification, we obtain, if g₁ = S is the spinor module, the numbers L ⁺(n, s) (resp. L ^–(n, s)) of independent such Lie super algebras (resp. Lie algebras), which are periodic functions of the dimension n=p+q (mod 8) and the signature s=p–q (mod 8) and satisfy: L ⁺(–n, s)=L ^– (n, s).Supported by Max-Planck-Institut für Mathematik (Bonn).Supported by the Alexander von Humboldt Foundation, MSRI (Berkeley) and SFB 256 (Bonn University).     

A new numerical method for inverse Laplace transforms used to obtain gluon distributions from the proton structure function

We recently derived a very accurate and fast new algorithm for numerically inverting the Laplace transforms needed to obtain gluon distributions from the proton structure function F₂^gp(x,Q²)F_{2}^{\gamma p}(x,Q^{2}). We numerically inverted the function g(s), s being the variable in Laplace space, to G(v), where v is the variable in ordinary space. We have since discovered that the algorithm does not work if g(s)→0 less rapidly than 1/s as s→∞, e.g., as 1/s ^β for 0<β<1. In this note, we derive a new numerical algorithm for such cases, which holds for all positive and non-integer negative values of β. The new algorithm is exact if the original function G(v) is given by the product of a power v ^β−1 and a polynomial in v. We test the algorithm numerically for very small positive β, β=10⁻⁶ obtaining numerical results that imitate the Dirac delta function δ(v). We also devolve the published MSTW2008LO gluon distribution at virtuality Q ²=5 GeV² down to the lower virtuality Q ²=1.69 GeV². For devolution, β is negative, giving rise to inverse Laplace transforms that are distributions and not proper functions. This requires us to introduce the concept of Hadamard Finite Part integrals, which we discuss in detail.     

The NLO Parton Distribution in the (x, Q 2)-Plane: A Relativistic Quark-Exchange Approach to A = 3 Mirror Nuclei

A next-to-leading order QCD analysis of polarized and unpolarized structure functions of the proton in the (x, Q²)-plane is discussed within the scheme of the radiation parton formalism. The valence quark distribution is obtained from the application of the relativistic quark-exchange model to A = 3 mirror nuclei, i.e., ³He and ³H. The sea quark and gluon distributions are calculated using the inverse Mellin technique in the NLO approximation. A comparison is made with the corresponding available experimental data. We find a good fit for F₂^p(x, Q²) to the data. It is shown that our new NLO calculation improves our previous works. We argue that the valence quark scenario at some μ₀² ≪ Q² is a reasonable assumption in the framework of the DGLAP evolution equation. In agreement with the data, it is demonstrated that the asymmetry A₁^p(x, Q²) has no significant Q²-dependence as we go to the small x, even at NLO limit. Finally we argue that for small x ≤ 0.2 it is a good approximation to consider ³He and ³H structure functions as those of neutrons and protons, respectively.     

α(Q) corrections to particle multiplicity ratios in gluon and quark jets

The order α(Q²) correction to the particle multiplicity ratio in gluon and quark jets is calculated in QCD. Through α(Q²) we find , with r = <n>_{gluon jet}/<n>_{quark jet}. This ratio is independent of the opening angle chosen to define the jets.     

Spin structure function g 1 (x, Q) and the DHGHY integral I(Q) at low Q: predictions from the GVMD model

Theoretical predictions for the polarized nucleon structure function g ₁ (x, Q ² ) at low Q² are obtained in the framework of the generalized vector meson dominance model. Contributions from both light and heavy vector mesons are evaluated. In the photoproduction limit the first moment of g₁ is related to the static properties of the nucleon via the Drell-Hearn-Gerasimov-Hosoda-Yamamoto sum rule. This property is employed to fix the magnitude of the light vector meson contribution to g₁, using the recent measurements in the region of baryonic resonances. The results are compared to the data on g ₁ (x, Q ² ). Finally, the DHGHY moment function I(Q ² ) is calculated, and our theoretical predictions are confronted with the recent preliminary data obtained at the Jefferson Laboratory. Received: 9 July 2002 / Published online: 7 October 2002 RID="a" ID="a" e-mail: badelek@fuw.edu.pl RID="b" ID="b" e-mail: jan.kwiecinski@ifj.edu.pl RID="c" ID="c" e-mail: ziaja@tsl.uu.se     

Spectroscopic Study of the Na2 2Σg State by cw Perturbation-Facilitated Optical-Optical Double-Resonance Spectroscopy

The Na₂(3sσ_g)(4sσ_g) 2³Σ⁺_g state of Na₂ has been observed and studied by cw perturbation-facilitated optical-optical double-resonance (PFOODR) spectroscopy for the first time. A single-mode dye laser and a Ti-sapphire laser served as the pump and the probe lasers, respectively. A total of 543 PFOODR excitation signals have been assigned to the 2³Σ⁺_g ← b³Π_1u transitions. Absolute vibrational numbering was determined by counting nodes in the 2³Σ⁺_g → a³Σ⁺_u bound-free spectra. Spectroscopic constants and the corresponding RKR potential energy curve are presented in this vsork. The values of T_e, R_e, and D_e, are found to be 25 551.237(49) cm⁻¹, 3.53463(35) Å, and 6211.5(1) cm⁻¹ respectively.     

Modelling the quark propagator

We are interested in developing covariant, confining, and asymptotically free models of hadrons. With this goal in mind we have carried out a study of dynamical chiral symmetry breaking without imposing the frequently used approximation α_s(−(p−k)²) α₅(−p_>²), where p_>² ≡ max(p², k²) for the running coupling constant in the quark Schwinger-Dyson equation. We present numerical results in Landau gauge and compare these with earlier results obtained when using this approximation. We see in this context that a gluon propagator which has the form 1/q⁴ in the infrared is too singular and must be regulated. We derive a suitably generalized expression for the pion decay constant f_π. With essentially one free parameter we are able to reproduce reasonable results for various physical quantities of interest including , and Λ_QCD.     

Propagator of the Lattice Domain Wall Fermion and the Staggered Fermion

We calculate the propagator of the domain wall fermion (DWF) of the RBC/UKQCD collaboration with 2 + 1 dynamical flavors of 16³ × 32 × 16 lattice in Coulomb gauge, by applying the conjugate gradient method. We find that the fluctuation of the propagator is small when the momenta are taken along the diagonal of the 4-dimensional lattice. Restricting momenta in this momentum region, which is called the cylinder cut, we compare the mass function and the running coupling of the quark-gluon coupling α _s,g1(q) with those of the staggered fermion of the MILC collaboration in Landau gauge. In the case of DWF, the ambiguity of the phase of the wave function is adjusted such that the overlap of the solution of the conjugate gradient method and the plane wave at the source becomes real. The quark-gluon coupling α _s,g1(q) of the DWF in the region q > 1.3 GeV agrees with ghost-gluon coupling α _s (q) that we measured by using the configuration of the MILC collaboration, i.e., enhancement by a factor (1 + c/q ²) with c ≃ 2.8 GeV² on the pQCD result. In the case of staggered fermion, in contrast to the ghost-gluon coupling α _s (q) in Landau gauge which showed infrared suppression, the quark-gluon coupling α _s,g1(q) in the infrared region increases monotonically as q→ 0. Above 2 GeV, the quark-gluon coupling α _s,g1(q) of staggered fermion calculated by naive crossing becomes smaller than that of DWF, probably due to the complex phase of the propagator which is not connected with the low energy physics of the fermion taste. An erratum to this article can be found at     

Study of nucleon spin-dependent properties in the resonance region

In this paper, the spin-dependent structure functions of nucleon g ₁, and photoabsorption cross sections σ_1/2, σ_3/2 and σ_T in the resonance region are estimated based on the constituent quark model and the properties of the five phenomenological Breit-Wigner resonances P ₃₃(1232), S ₁₁(1535), D ₁₃(1520), P ₁₁(1440), and F ₁₅(1680). Our results are compared to the recent E143 data of the polarized structure functions g ₁(W ², Q ²) at points Q ²=0.5 GeV² and Q ²=1.2 GeV² and the data of the total inclusive photoabsorption cross sections. Received: 7 October 1997     

Electronic absorption spectrum of Ni2+ in lithium potassium sulphate single crystal

Single crystals of nickel-doped lithium potassium sulphate were grown by slow evaporation method at room temperature. From the nature and position of the bands observed, a successful interpretation of all the bands could be made assumingO _h symmetry for the Ni²⁺ ion in the crystal. The bands have been assigned transitions from the ground³A_2g(F) state to the excited³T_2g(F),¹E_g(D),³T_1g(F),¹T_2g(D) and³T_1g(P) states. The crystal field parameters derived areDq=910cm^–1,B=890cm^–1 andC=3560cm^–1.The authors wish to express their thanks to Prof. K. Sreerama Murthy for his constant encouragement throughout this investigation. The authors are also thankful to Prof. Mihir Chowdhury, Indian Association for the cultivation of Science, Calcutta for giving permission to take the spectra.     

Resonances in at rest

Data on at rest show two resonant processes: (a) f₀(1370)η,f₀(1370)→σσ and ρρ, (b) η(1440)σ, η(1440)→ηπ⁺π⁻. The branching ratio BR[f₀(1370)→ρρ]/BR[f₀(1370)→σσ]=0.98±0.25 in the mass range available here. Using data on , the ratio Γ_4π/Γ_2π5 for f₀(1370). The effects of the strongly s-dependent width of f₀(1370) are discussed in some detail.The η(1440) is observed decaying to ησ and a₀(980)π, with strong destructive interference between them. In its decay to a₀(980)π, a narrow peak appears in the ηπ mass spectrum, but 30–50 MeV above that usually attributed to a₀(980) and significantly above the KK threshold. This effect is explained naturally by a two-step process: η(1440)→K^*(890)K followed by rescattering of the two kaons through a₀(980) to ηπ above the KK threshold.     

On the high spin expansion in the SYM theory

We study the form of the high spin expansion of the minimal anomalous dimension for long operators belonging to the sl(2) sector of SYM. Keeping fixed the ratio j between the twist and the logarithm of the spin, the minimal anomalous dimension expands as γ(g,j,s)=f(g,j)lns+f⁽⁰⁾(g,j)+O(1/lns). This particular double scaling limit is efficiently described, including the desired accuracy O((lns)⁰), in terms of a linear integral equation. By its use, we are able to evaluate both at weak and strong coupling the subleading scaling function f⁽⁰⁾(g,j) as a series in j, up to the order j⁵. Thanks to these results, the possible extension of the liaison with the O(6) non-linear sigma model may be tackled on a solid ground.     

A new approach to calculate the gluon polarization

We derive the Leading-Order (LO) master equation to extract the polarized gluon distribution G(x,Q ²)=xδg(x,Q ²) from polarized proton structure function, g^p₁(x,Q²)g^{p}_{1}(x,Q^{2}). By using a Laplace-transform technique, we solve the master equation and derive the polarized gluon distribution inside the proton. The test of accuracy which is based in our calculations on two different methods, confirms that we achieve to the correct solution for the polarized gluon distribution. To determine the polarized gluon distribution xδg(x,Q ²) more accurately, we only need to have more experimental data on the polarized structure functions, g₁^p(x,Q²)g_{1}^{p}(x,Q^{2}). Our result for polarized gluon distribution is in good agreement with some phenomenological models.     

Optical absorption spectrum of Ni2+ ions doped in sodium potassium sulphate single crystal

Single crystals of nickel-doped sodium potassium sulphate were grown by slow evaporation method at room temperature. From the nature and position of the bands observed, a successful interpretation of all the observed bands could be made assuming the octahedral symmetry for the Ni^{2 +} ion in the crystal. The bands have been ascribed to transitions from the ground³A_2g(F) state to the excited³T_2g(F),¹E_g(D),³T_1g(F),¹T_2g(D) and³T_1g(P) states. The experimental and calculated energies are in good agreement. The crystal field parameters derived areDq= =880 cm^–1,B= 900cm^–1 andC=3600 cm^–1.One of the authors, Sujatha John expresses her thanks to the Secretary and the Principal, R. B. V. R. Reddy College, Hyderabad for according her permission to pursue the M. Phil. course.     

Q 2 dependence of the measured asymmetry A 1: A test of the Bjorken sum rule

We analyze the proton and deutron data on the spin-dependent asymmetry A ₁(x, Q ²), supposing that the DIS structure functions g ₁(x, Q ²) and F ₃(x, Q ²) have a similar Q ² dependence. As a result, we have found that Λ ₁ ^p −Λ ₁ ⁿ =0.190±0.038 at Q ²=10 GeV² and Λ ₁ ^p −Λ ₁ ⁿ =0.165±0.026 at Q ²=3 GeV²; these values are in the best agreement with the Bjorken sum rule predictions. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 1, 9–14 (10 January 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Correlator of the quark scalar currents and Γtot(H → hadrons) at O(αs) in pQCD

We present the results of the analytical evaluation of the massless four-loop

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(α³_s) correction to the correlator of the quark scalar currents and the Higgs decay rate into hadrons. In numerical form we found (in

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scheme) that Γ (H →

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b ) = (3G_F/4

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π) M_Hm²_b (M_H) [1 + 5.667α_s/π + (35.94 − 1.359n_f) (α_s/π)² + (164.139 − 25.771n_f + 0.259n²_f) (α_s/π)³] where n_f is the number of quark flavour and α_s = α_s(M_H).     

Excitation of the 7s2P1/2, 3/2 levels of Xe+ due to charge exchange in the negative glow of a glow discharge in a neon-xenon mixture

It is shown that in the negative glow of a glow discharge in mixtures of neon with xenon (xenon contents of 5.5·10^–3 to 2% of the total pressure P of the mixture) with P=15 torr and discharge currents i=40 mA (cathode diameter 30 mm), the 7s²P_{1/2, 3/2} levels of the Xe⁺ ion are excited by the charge exchange reaction Xe ^m + Ne⁺ Xe^+* + Ne.The effective cross section Q_3/2 for excitation of the 7s²P_3/2 level is estimated to lie between 10^–14 and 10^–15 cm² and Q_3/26.5 × Q_1/2, where Q_1/2 is the effective cross section for excitation of the 7s²P_1/2 level.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 3, pp. 96–99, March, 1979.