Gluon condensate in charmonium sum rules with three-loop corrections

Charmonium sum rules are analyzed with the primary goal to obtain the restrictions on the value of the dimension 4 gluon condensate. The moments M _n (Q ² ) of the polarization operator of the vector charm currents are calculated and compared with the experimental data. The three-loop () perturbative corrections, the contribution of the gluon condensate with corrections and the contribution of the dimension 6 operator G³ are accounted. It is shown that the sum rules for the moments do not work at Q ² = 0, where the perturbation series diverges and the G³ contribution is large. The domain in the (n, Q ² ) plane where the sum rules are legitimate is found. A strong correlation of the values of gluon condensate and charm quark mass is determined. The absolute limits are found to be for the gluon condensate and for the charm quark mass in the scheme. Received: 16 July 2002 / Revised version: 6 November 2002 / Published online: 24 January 2003 RID="a" ID="a" e-mail: ioffe@vitep1.itep.ru RID="b" ID="b" e-mail: zyablyuk@heron.itep.ru     

QCD sum rules for masses of excited heavy mesons

The masses of excited heavy mesons are studied with sum rules in the heavy quark effective theory. A set of interpolating currents creating (annihilating) excited heavy mesons with arbitrary spin and parity are proposed and their properties are discussed. Numerical results at the leading order of the O(1/m_Q) expansion are obtained for the lowest doublets (0⁺, 1⁺) and (1⁺, 2⁺).     

Equation of state for systems of soft diatomic molecules

A new potential that is a modification of the BBL (Bratko, D.,Blum, L., and Luzar, A.,1985, J. chem. Phys., 83, 6367; Blum, L., Vericat, F., and Bratko, D., 1995, J. chem. Phys., 102, 1461) potential and of the one recently solved analytically by Blum and Vericat (BV) (1995, Molec. Phys., 86, 809; 1996, J. phys. Chem., 100, 1197) is studied by Monte Carlo simulation. The main feature of this potential is that it can be solved using only a small number of parameters (3 in the case treated by BV), and therefore produces a substantial simplification of earlier work. The new potential has an orientational octupole–octupole interaction term which is found necessary to reproduce the broad peak of the oxygen–oxygen structure function due to the tetrahedral position of the second nearest neighbour water molecule. This important feature was absent in the original BBL potential. This model agrees also with the experimental pair correlation functions for oxygen–hydrogen and hydrogen–hydrogen, and yields 42·6 kJ mol^-1 for the internal energy of water, also in agreement with experiment. The hard core central repulsion causes the sharpness of the first peaks in all three correlation functions. This is not necessary but convenient for an analytical solution.     

Excitons in monoclinic zinc diphosphide. Longitudinal exciton and the mixed mode

Exciton absorption spectra in high-quality β-ZnP₂ single crystals have been investigated at T=1.7 K for various directions of the wave vector and various polarization states of the radiation. It has been unambiguously established that the additional high-energy A series, which in some works has been called a D series and ascribed to ZnP₂ crystals, of so-called “rhombic” symmetry,^1,8,10,11 is an intrinsic exciton of the β-ZnP₂ series. A mixed mode has been detected for the first time, and the energy of the longitudinal exciton has been determined. The selection rules for the exciton transitions have been analyzed by a group-theoretical approach, and the symmetry of the nS states of the single exciton has been established on the basis of the experimental data — Γ ₂ ⁻ (z). Fiz. Tverd. Tela (St. Petersburg) 41, 193–202 (February 1999)     

On invariant and covariant Schwartz distributions in the case of a compact linear group

A proof is given for the representations of invariant and covariant (Schwartz) distributions onR ⁿ , which are often used in theoretical physics. We express invariant distributions as distributions of standard polynomial invariants and decompose covariant distributions in standard polynomial covariants. Our consideration is restricted to compact groups acting linearly onR ⁿ . The representation for invariant distributions is obtained provided the standard invariants form an algebraically independent generating set in the ring of invariant polynomials. As for the standard covariants we assume that in the class of covariant polynomials they provide a unique decomposition into a sum of the standard covariants multiplied with invariant polynomials.     

Multilevel rotational transitions in the intermediate stage of three-photon ionization of molecules

Ionization and dissociation of diatomic molecules induced by a weak field (after preliminarily populating an intermediate level) and by intense, linearly polarized monochromatic radiation have been studied. Field-induced mixing of rotational components of various electronic-vibrational states of molecules (such as CO, NO, etc.) at field strength f∼10⁻⁴–10⁻⁵ atomic units can lead to migration among states with different angular momenta J. Therefore, ions with rotational momenta J ⁺ much higher than those prescribed by selection rules for three-photon absorption can be formed from molecules in the ground state. The possibility of selective formation of ions with J ⁺≫1 and zero projection of the angular momentum on the polarization vector of the external electromagnetic radiation has been investigated. Zh. éksp. Teor. Fiz. 111, 1624–1632 (May 1997)     

Perturbation theory for the angular correlation function

A perturbation expression for the angular pair correlation function g ⁽²⁾(r ₁₂, ω₁, ω₂) is derived for systems interacting via non central potentials based on the method developed by Gubbins and Gray [1]. The method uses the ‘correct’ (in the sense of Rushbrooke [3] and Cook and Rowlinson [4]) angle-averaged potential as the reference system about which the perturbation is made. A preliminary comparison between the original Gubbins-Gray expression for g ⁽²⁾(r ₁₂, ω₁, ω₂) and the present expression is made for a system of two-dimensional point dipoles.     

On the possibility of quantization of the conductance in the microwave-induced resistive state of layered superconductors

It was observed that a microwave field induces constant differential resistance steps, close in magnitude to the reciprocal of the conductance quantum h/2e ², in the current-voltage characteristics (IVCs) of layered structures with an intrinsic Josephson effect under conditions of transport in a direction perpendicular to the layers. A qualitative explanation of this result is proposed. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 1, 68–71 (10 January 1998)     

New approach to achieving the potentially high conductivity of polydiacetylene

It is postulated that only the surface layers of the structural formations are doped in single crystals of various polydiacetylenes because of the high packing density of their macromolecules and that this is the reason for the low level of conductivity attained in these conjugated polymers. For the purpose of raising the efficacy of the doping process by increasing the surface-to-volume ratio of the polymer, single crystals of the polydiacetylene poly-1,1,6,6-tetraphenylhexadiinediamine (poly-THD) are ground by various methods. A correlation between the particle size of the ground single crystals and their dc conductivity in the doped state is discovered. A record value of the conductivity (3×10⁻² S/cm) for polydiacetylenes, which is more than two orders of magnitude higher than published values (10⁻³–10⁻⁵ S/cm), is achieved. Fiz. Tverd. Tela (St. Petersburg) 39, 774–777 (April 1997)     

<Emphasis Type="Italic">B</Emphasis>→<Emphasis Type="Italic">D</Emphasis><Superscript>(*)</Superscript> form factors from QCD light-cone sum rules

We derive new QCD sum rules for B→D and B→D ^* form factors. The underlying correlation functions are expanded near the light-cone in terms of B-meson distribution amplitudes defined in HQET, whereas the c-quark mass is kept finite. The leading-order contributions of two- and three-particle distribution amplitudes are taken into account. From the resulting light-cone sum rules we calculate all B→D ^(*) form factors in the region of small momentum transfer (maximal recoil). In the infinite heavy-quark mass limit the sum rules reduce to a single expression for the Isgur–Wise function. We compare our predictions with the form factors extracted from experimental B→^(*) l ν _l decay rates fitted to dispersive parameterizations.     

Parton distributions,small-x physics and the spin structure of the nucleon

Several theoretical aspects in leading (1-loop) and higher (2-loop) order as well as various approaches of extracting leading twist-2 parton distributions from structure function measurements are discussed and summarized. Their implications for the small-x region (x⩽10⁻²) are analyzed and compared with alternative approaches where higher twist contributions (‘fans’) are added to the twist-2 LO terms in the evolution equations. The second part of these lectures deals with longitudinally polarized parton distributions related to the structure functiong ₁, in particular with various scenarios to explain the total spin structure of nucleons, including the gluon anomaly as well. Specific (realistic) tests for discriminating between these alternatives are discussed as well asx-dependent expectations, in particular for neutron targets in connection with the Bjorken sum rule. Furthermore, various theoretical expectations and sum rules for the transverse (chiral-even) structure functiong ₂ are presented and very recent developments of transverse chiral-odd (‘transversity’) distributions are briefly discussed.     

The distance dependence and spatial distribution of the molecular quadrupole moments of P2, S2 and Cl2

The quadrupole moments (Θ) of the molecules P₂, S₂ and Cl₂ have been computed at the SCF, CASSCF and CASSCF + 1 + 2 levels of theory, using augmented correlation consistent basis sets. The convergence of Θ as a function of basis set and level of theory is discussed. The variation of Θ from the separated atoms to the equilibrium region is reported. Θ is written as the sum of a sigma and pi contribution, and inaccuracies in the SCF values for P₂ and S₂ are due to the poor representation of the pi system in the SCF theory. A reference state dependent quadrupole moment density, - ½(3cos² θ- 1)r ²δη(r; R), is defined whose integral is the mole2 cular quadrupole moment, and the spatial distributions of the density and its relationship to the density difference δη(r; R) are examined.     

Sum rules for the decays of the c-even charmonium states

Sum rules for the decays of the C-even charmonium levels (¹S₀, ³P₀, ³P₂, ¹D₂) are derived. These rules are based on the asymptotic freedom of the quantum chromodynamics at small distances and on the analyticity. They refer to the various vacuum amplitudes involving products of charmed quark currents: electromagnetic current as well as currents with quantum numbers J^PC=0^?+,0⁺⁺,2⁺⁺,2^?+. The contribution of the continuum to some of the sum rules is small, and they are saturated by the contribution of the lowest charmonium levels. In this way we predict the widths of the two-photon decays of the charmonium states and estimate their total hadronic widths.     

Dynamical Correlation Functions for an Impenetrable Bose Gas with Neumann or Dirichlet Boundary Conditions

Abstract

We study the time and temperature dependent correlation functions for an impenetrable Bose gas with Neumann or Dirichlet boundary conditions ψ(x ₁, 0)ψ ^?(x ₂ , t) _±,T . We derive the Fredholm determinant formulae for the correlation functions, by means of the Bethe Ansatz. For the special case x ₁ = 0, we express correlation functions with Neumann boundary conditions ψ(0, 0)ψ ^?(x ₂ , t) _+,T , in terms of solutions of nonlinear partial differential equations which were introduced in [1] as a generalization of the nonlinear Schrödinger equations. We generalize the Fredholm minor determinant formulae of ground state correlation functions ψ(x ₁)ψ ^?(x ₂) _±,0 in [2], to the Fredholm determinant formulae for the time and temperature dependent correlation functions ψ(x ₁, 0)ψ ^?(x ₂ , t) _±,T , t ∈ R, T ≥ 0.     

πNN coupling determined beyond the chiral limit

Within the conventional QCD sum rules, we calculate the πNN coupling constant, g _πN, beyond the chiral limit using two-point correlation function with a pion. For this purpose, we consider the Dirac structure, iγ₅, at m _π ² order in the expansion of the correlator in terms of the pion momentum. For a consistent treatment of the sum rule, we include the linear terms in quark mass as they constitute the same chiral order as m _π ². In this sum rule, we obtain g _πN= 13.3 ± 1.2, which is very close to the empirical πNN coupling. This demonstrates that going beyond the chiral limit is crucial in determining the coupling. Received: 8 July 1999 / Revised version: 20 August 1999     

Lattice structure and magnetization of LaCoO<Subscript>3</Subscript> thin films

We investigate the structure and magnetic properties of thin films of the LaCoO₃ compound. Thin films are deposited by pulsed laser deposition on various substrates in order to tune the strain from compressive to tensile. Single-phase (001) oriented LaCoO₃ layers were grown on all substrates despite large misfits. The tetragonal distortion of the films covers a wide range from -2% to 2.8%. Our LaCoO₃ films are ferromagnetic with Curie temperature around 85 K, contrary to the bulk. The total magnetic moment is below 1μ _B /Co³⁺, a value relatively small for an exited spin-state of the Co³⁺ ions, but comparable to values reported in literature. A correlation of strain states and magnetic moment of Co³⁺ ions in LaCoO₃ thin films is observed.     

Topological orbifold models and quantum cohomology rings

We discuss the topological sigma model on an orbifold target space. We describe the moduli space of classical minima for computing correlation functions involving twisted operators, and show, through a detailed computation of an orbifold ofCP ¹ by the dihedral groupD ₄, how to compute the complete ring of observables. Through this procedure, we compute all the rings of dihedralCP ¹ orbifolds. We then considerCP ²/D ₄, and show how the techniques of topologicalanti-topological fusion might be used to compute twist field correlation functions for nonabelian orbifolds.Supported in part by Fannie and John Hertz Foundation     

Theoretical design of azaacene-based non-fullerene electron transport material used in inverted perovskite solar cells

ABSTRACT

Inverted perovskite solar cells (PSCs) have attracted much attention due to their low-temperature and solution-based process. Electron transport layers are important components in inverted PSCs. Non-fullerene n-type organic small molecules seem to be more attractive as electron transport layers, because their structures are easy to be synthesised and modified. In this paper, density functional theory and semi-classical Marcus electron transfer theory were used to explore the electron transport properties in three azaacene derivatives, including one experimentally reported molecule, 1,4,9,16-tetrakis((triisopropylsilyl)ethynyl)quinoxalino[2^?,3^?:4^″,5^″]cyclopenta[1^″,2^″,3^″:5^′,6^′]acenaphtho[1^′,2^′:5,6]pyrazino[2,3-b]phenazine (1), and two theoretically designed molecules (2 and 3). Compound 2 is formed by substituting i-Pr groups in compound 1 with H atoms, which is designed to evaluate the effect of i-Pr groups on the electron transport properties. Compound 3 is designed by adding one more benzopyrazine group to the conjugation structure of compound 1. It shows that i-Pr group can increase HOMO and LUMO energy levels and improve solubility in organic solvent and hydrophobicity. Enlarging conjugation can not only decrease LUMO energy level and electron reorganisation energy, but also can increase solubility and electron mobility. So our designed compound 3 is expected to be a potential electron transport material in inverted PSCs.     

Bd,s– mass-differences from QCD spectral sum rules

We present the first QCD spectral sum rules analysis of the SU(3) breaking parameter ξ and an improved estimate of the renormalization group invariant (RGI) bag constant both entering into the B⁰_d,s– mass-differences. The averages of the results from the Laplace and moment sum rules to order α_s are and

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, in units where f_π=130.7 MeV. Combined with the experimental data on the mass-differences ΔM_d,s, one obtains the constraint on the CKM weak mixing angle |V_ts/V_td|²20.0(1.1). Alternatively, using the weak mixing angle from the analysis of the unitarity triangle and the data on ΔM_d, one predicts ΔM_s=18.6(2.2) ps⁻¹ in agreement with the present experimental lower bound and within the reach of Tevatron 2.