Quark-antiquark states and their radiative transitions in terms of the spectral integral equation: Charmonia

Earlier by the authors (Yad. Fiz. 70, 68 (2007)), the bƃ states were treated in the framework of the spectral integral equation, together with simultaneous calculations of radiative decays of the considered bottomonia. In the present paper, such a study is carried out for the charmonium states. We reconstruct the interaction in the c-c sector on the basis of the data for the charmonium levels with J _PC = 0⁻⁺, 1⁻⁻, 0⁺⁺, 1⁺⁺, 2⁺⁺, 1⁺⁻ and radiative transitions ψ(2S) → γχ _c0(1P), γχ _c1(1P), γχ _c2(1P), γχ _c(1S) and χ _c0(1P), χ _c1(1P), χ _c2(1P) → γJ/ψ. The c-c levels and their wave functions are calculated for the radial excitations with n ≤ 6. Also, we determine the c-c component of the photon wave function using the e ⁺ e ⁻-annihilation data: e ⁺ e ⁻ → J/ψ(3097), ψ(3686), ψ(3770), ψ(4040), ψ(4160), ψ(4415) and perform the calculations of the partial widths of the two-photon decays for the n = 1 states η _c0(1S), χ _c0(1P), χ _c2(1P) → γγ and n = 2 states η _c0(2S) → γγ, χ _c0(2P) → γγ. We discuss the status of the recently observed c-c states X(3872) and Y(3941): according to our results, the X(3872) can be either χ _c1(2P) or η _c2(1D), while Y(3941) is χ _c2(2P). The text was submitted by the authors in English.     

Spin-orbit coupling,spin-lattice relaxation,and spin-memory studies ofF-center-molecular-ion pairs in alkali halides

Summary The spin-orbit parameter Δ, spin-lattice relaxation timeT ₁, and spin-mixing parameter ɛ ofF _H(OH⁻) andF _H(CN⁻) centers in several alkali halides have been studied with magnetic circular dichroism at ∼2 K. A close comparison of the experimental results before and after optically induced association of theF center with the molecular ion has been made. In crystals of NaCl structure the negative spin-orbit parameter Δ changes little betweenF andF _H centers in the same host. For CsCl and CsBr two values of Δ have been derived forF _H(CN⁻) centers with axis parallel or perpendicular to the magnetic field. In all studied systems, the spin-lattice relaxation timeT ₁ is already shorter before aggregation compared toF formation. The spin-mixing parameter ɛ decreases slightly forF _H(OH⁻) compared toF centers, while it increases drastically forF _H(CN⁻) defects and reaches its maximum possible value ɛ=0.5 in cesium halides. First attempts to interpret these magneto-optical results will be presented. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

Quark-Antiquark states and their radiative transitions in terms of the spectral integral equation: Bottomonia

In the framework of the spectral integral equation, we consider the states and their radiative transitions. We reconstruct the interaction on the basis of data for the levels of the bottomonium states with J ^PC = 0⁻⁺, 1⁻⁻, 0⁺⁺, 1⁺⁺, 2⁺⁺ as well as the data for the radiative transitions γ (3S) → _γχbJ(2P) and γ(2S) → _γχbJ(1P) with J = 0, 1, 2. We calculate bottomonium levels with the radial quantum numbers n ≤ 6, their wave functions, and corresponding radiative transitions. The ratios Br[_χbJ(2P) → _γγ(2S)]/Br[_χbJ(2P) → _γγ(1S)] for J = 0, 1, 2 are found to be in agreement with data. We determine the component of the photon wave function using the data for the e ⁺ e ⁻ annihilation, e ⁺ e ⁻ → γ(9460), γ(10 023), γ(10 036), γ(10 580), γ(10 865), γ(11 019), and predict partial widths of the two-photon decays ηb0 → γγ, χb0 → γγ, χb2 → γγ for the radial excitation states below the threshold (n ≤ 3). The text was submitted by the authors in English.     

Effect of γ irradiation on the hysteresis phenomena at the incommensurate-commensurate phase transition in Rb2ZnBr4

The effect of γ irradiation on the temperature hysteresis in dielectric permittivity ɛ and loss tangent tan δ of crystalline Rb₂ZnBr₄ has been studied in the vicinity of the incommensurate-commensurate phase transition. The ɛ(T) and tan δ(T) curves were found to exhibit anomalies in the form of maxima. Hysteresis was observed in the measured properties, including the transition temperature T _c (ΔT=T _c ^h −T _c ^c ), in both unirradiated and irradiated samples. It is shown that, as the radiation dose increases the extent of the hysteresis ΔT increases, the values of ɛ _max and tan δ _max at the transition point decrease, and the anomalies wash out. Fiz. Tverd. Tela (St. Petersburg) 40, 1911–1914 (October 1998)     

Photophoresis of coarse aerosol particles with nonuniform thermal conductivity

The photophoresis of a coarse solid spherical aerosol particle in a one-component gas of nonuniform temperature is examined with consideration of the inertial effects in the hydrodynamic equations and the temperature jump in the Knudsen layer. The problem is solved in the spherical coordinates r, Θ, and ϕ. The photophoresis of a homogeneous particle is considered first. Then the results are generalized to an inhomogeneous particle. A particle whose thermal conductivity χ _i varies as a function of r is chosen as a model which describes a broad class of natural and artificially produced aerosol particles. It is shown that the error can be significant if the variable internal thermal conductivity χ _i =χ _i (r) of the particle is ignored and only the value of the thermal conductivity on its surface χ _i (a) is considered, on the assumption that the particle is homogeneous. It is also shown that a particle with a variable internal thermal conductivity χ _i =χ _i (r) and a density of heat sources within it q _i (r,Θ) can be regarded as a homogeneous particle with a thermal conductivity γχ _i (a) and a heat-source density m(r)q _i (r,Θ). Recurrence formulas for gand m(r) in the general case are presented. Analytical expressions for γ and m(r) are found for a model particle with pronounced inhomogeneity. Zh. Tekh. Fiz. 68, 1–6 (April 1998)     

Covariant tensor formalism for partial-wave analyses of ψ decays into γB¯, γγV and ψ(2s)↦γχ<Subscript>c0,1,2</Subscript> with χ<Subscript>c0,1,2</Subscript>↦K¯πand 2π<Superscript>+</Superscript>2π<Superscript>-</Superscript>

With accumulation of high statistics data at BES and CLEO-c, many new interesting channels can get enough statistics for partial-wave analysis (PWA). Among them, ψ↦γpˉ,γΛˉ,γΣˉ,γΞˉ channels provide a good place for studying baryon-antibaryon interactions; the double radiative decays ψ↦γγV with V ≡ ρ,ω,φ have a potential to provide information on the flavor content of any meson resonances (R) with positive charge parity (C = +) and mass above 1 GeV through ψ↦γR↦γγV; ψ(2s)↦γχ_c0,1,2 with χ_c0,1,2↦Kˉπ⁺π^- and 2π⁺2π^- decays are good processes to study χ_cJ charmonium decays. Using the covariant tensor formalism, here we provide theoretical PWA formulae for these channels.     

Magnetic circular dichroism in the absorption of theF A centre in KCl doped with Li and Na

Summary The spin-orbit structure ofF _A centres in KCl:Li and KCl:Na have been studied by means of the magnetic circular dichroism. Due to theirC _4V symmetry theF _A centres have two different spin-orbit parameters, Δ^‖ and Δ^⊥, which only in the KCl:Li case follow the relation: Δ^‖ < Δ_F < Δ^⊥ as expected from the theory. For a close comparison we have also reported our measurement of the spin-orbit coupling ofF centre in KCl. The spin-orbit parameters of theF andF _A centres have been determined using the method of moment.     

New data for the 197Au(γ, nX) and 197Au(γ, 2nX) reaction cross sections

The results from experimental and theoretical studies of the total and partial cross sections of photoneutron reactions on the ¹⁹⁷Au isotope were analyzed. The cross sections for reactions σ(γ, nX) = σ(γ, n) + σ(γ, np) + … + σ(γ, 2nX) = σ(γ, 2n) + σ(γ, 2np) + … were evaluated in the energy range 7 ≤ E _γ ≤ 30 MeV using an approach free of the shortcomings of experimental photoneutron multiplicity sorting methods. The total photoneutron reaction cross sections σ^exp(γ, xn) = σ^exp(γ, nX) + 2σ^exp(γ, 2nX) + … = σ^exp(γ, n) + σ^exp(γ, np) + 2σ^exp(γ, 2n) + 2σ^exp(γ, 2np) + … were used as the initial experimental data. The contributions from the cross sections σ(γ, nX) and σ(γ, 2nX) to the cross sections σ^exp(γ, xn) were separated using the multiplicity transition functions F ₁ ^theor = σ^theor(γ, 1nX)/σ^theor(γ, xn) and F ₂ ^theor = σ^theor(γ, 2nX)/σ^theor(γ, xn), calculated within an updated version of the pre-equilibrium model of photonuclear reactions. New evaluated data for both partial reaction cross sections, i.e., σ^eval (γ, 1nX) = F ₁ ^theorσ^exp(γ, xn) and σ^eval(γ, 2nX) = F ₂ ^theorσ^exp(γ, xn), were obtained. The cross sections σeval(γ, nX) and σ^eval.(γ, 2nX) evaluated using the theoretically calculated functions F _1,2^theor are consistent with the Livermore data, but substantially contradict the Saclay data.     

Effective nonlinear optical properties of shape distributed composite media

The effective linear and nonlinear optical properties of metal/dielectric composite media, in which ellipsoidal metal inclusions are distributed in shape, are investigated. The shape distribution function P(L _x, L _y) is assumed to be 2Δ^-2θ(L _x - 1/3 + Δ/3)θ(L _y - 1/3 + Δ/3)θ(2/3 + Δ/3 - L _x - L _y), where θ( ^{. . .} ) is the Heaviside function, Δ is the shape variance and L_i are the depolarization factors of the ellipsoidal inclusions along i-symmetric axes (i = x, y). Within the spectral representation, we adopt Maxwell-Garnett type approximation to study the effect of shape variance Δ on the effective nonlinear optical properties. Numerical results show that both the effective linear optical absorption α ∼ ωIm() and the modulus of the effective third-order optical nonlinearity enhancement |χ⁽³⁾ _e|/χ⁽³⁾ ₁ exhibit the nonmonotonic behavior with Δ. Moreover, with increasing Δ, the optical absorption and the nonlinearity enhancement bands become broad, accompanied with the decrease of their peaks. The adjustment of Δ from 0 to 1 allows us to examine the crossover behavior from no separation to large separation between optical absorption and nonlinearity enhancement peaks. As Δ → 0, i.e., the ellipsoidal shape deviates slightly from the spherical one, the dependence of |χ⁽³⁾ _e|/χ⁽³⁾ ₁ on Δ becomes strong first and then weak with increasing the imaginary part of inclusions' dielectric constant. In the dilute limit, the exact formula for the effective optical nonlinearity is derived, and the present approximation characterizes the exact results better than old mean field one does. Received 10 December 2002 Published online 4 June 2003 RID="a" ID="a"e-mail: lgaophys@pub.sz.jsinfo.net     

Di-pion emission in heavy quarkonia decays

The dipion spectrum for the ϒ(nS) → ϒ(n′S) transition with n < 4 has the form dw/dq ∼ (phase space) |η − x|², with x = q ² − 4m _π² / (ΔM)² − 4m _π² < q ² ≡ M _ππ², and ΔM = M(nS) − M(n′S). The parameter η is calculated and the spectrum is shown to reproduce the experimental data for all three types of decays: 3 → 1, 2 → 1, and 3 → 2 with η ≈ 0.5, 0, and −3, respectively. The text was submitted by the author in English.     

Scaling functions of susceptibilities toO(1/n) forn-vector models with axial anisotropy

For an axially anisotropicn-vector model withm = O(n) easy – andn – m = O(n) hard components of the order parameter, we derive the susceptibility r ^–1 along one of the equivalent easy axes and the perpendicular one r ^-1 toO(1/n) of the 1/n-expansion in the disordered phase. The results confirm predictions of the scaling theory, e.g.(g, t)=A t ^– X (B g/t ) and (g, t) =A t ^– X (B g/t ), wheret = T – T _c (g = 0),g is the anisotropy parameter andX, X denote the scaling functions. We evaluate the relevant diagrams toO(1/n) which yield the coefficientsA, A and the critical behaviour of the scaling functions and critical amplitudes explicitly for . The extreme anisotropic case, i.e.m = O(1), is discussed briefly in the large-n limit in comparison with the mean field solution.Parts of this paper were presented at the Frühjahrstagung der Deutschen Physikalischen Gesellschaft in Freudenstadt (May 1974).     

Pseudovector heavy quarkonia in e + e −2 collisions

It is shown that BR(χ _b1(1 P)→e ⁺ e ⁻)≃3.3· 10⁻⁷ and BR(χ _c1(1 P)→e ⁺ e ⁻)≃10⁻⁸. This gives realistic possibilities for searching for the production of χ _b1(1 P) and ξ _c1(1 P) states in e ⁺ e ⁻ collisions, even on the present-day colliders, to say nothing of b and c-τ factories. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 8, 569–574 (25 April 1996)     

Static charged spheres with anisotropic pressure in general relativity

We report a generalization of our earlier formalism [Pramana, 54, 663 (1998)] to obtain exact solutions of Einstein-Maxwell’s equations for static spheres filled with a charged fluid having anisotropic pressure and of null conductivity. Defining new variables: w=(4π/3)(ρ+ε)r ², u=4πξr ², v _r=4πp _r r ², v _⊥=4πp _⊥ r ²[ρ, ξ(=−(1/2)F ₁₄ F ¹⁴), p _r, p _⊥ being respectively the energy densities of matter and electrostatic fields, radial and transverse fluid pressures whereas ε denotes the eigenvalue of the conformal Weyl tensor and interpreted as the energy density of the free gravitational field], we have recast Einstein’s field equations into a form easy to integrate. Since the system is underdetermined we make the following assumptions to solve the field equations (i) u=v _r=(a ²/2κ)r ⁿ⁺², v _⊥=k ₁ v _r, w=k ₂ v _r; a ², n(>0), k ₁, k ₂ being constants with κ=((k ₁+2)/3+k ₂) and (ii) w+u=(b ²/2)r ⁿ⁺², u=v _r, v _⊥−v _r=k, with b and k as constants. In both cases the field equations are integrated completely. The first solution is regular in the metric as well as physical variables for all values of n>0. Even though the second solution contains terms like k/r ² since Q(0)=0 it is argued that the pressure anisotropy, caused by the electric flux near the centre, can be made to vanish reducing it to the generalized Cooperstock-de la Cruz solution given in [14]. The interior solutions are shown to match with the exterior Reissner-Nordstrom solution over a fixed boundary. Dedicated to Prof. F A E Pirani.     

Leading-order 2πγ exchange NN interaction: Central potentials proportional to g<Subscript>A</Subscript><Superscript>0</Superscript> and g<Subscript>A</Subscript><Superscript>2</Superscript>

We calculate at two-loop order in chiral perturbation theory the electromagnetic corrections to the leading-order 2π exchange NN interaction proportional to g _A ⁰ and g _A ². The resulting 2πγ exchange potential contains isospin-breaking components which reach up to about -2% of the corresponding isovector 2π exchange potential. With a value of only -17keV at r = m _π ^-1 = 1.4fm the charge-independence breaking central potential obtained here is negligibly small in comparison to the one generated by the isoscalar c₃ contact vertex. Our calculation confirms that the largest long-range isospin-violating NN potentials arise from the 2πγ exchange diagrams involving the large low-energy constants c ₄ ≃ - c ₃ ≃ 3.3GeV^-1 representing the important Δ(1232) dynamics.     

Hadron diffractive processes: the structure of soft pomeron and colour screening

On the basis of the experimental data on diffractive processes in πp, pp and pˉp collisions at intermediate, moderately high and high energies, we restore the scattering amplitude related to the t-channel exchange by vacuum quantum numbers by taking account of the diffractive s-channel rescatterings. At intermediate and moderately high energies, the t-channel exchange amplitude turns, with a good accuracy, into an effective pomeron which renders the results of the additive quark model. At superhigh energies the scattering amplitude provides a Froissart-type behaviour, with an asymptotic universality of cross sections such as σ^tot _πp/σ^tot _pp→ 1 at s→∞. The quark structure of hadrons being taken into account at the level of constituent quarks, the cross sections of pion and proton (antiproton) in the impact parameter space of quarks, σ_π(r _1⊥, r _2⊥; s) and σ_p(r _1⊥, r _2⊥, r _3⊥; s), are found as functions of s. These cross sections implicate the phenomenon of colour screening: they tend to zero at |r _i⊥−r _k⊥|→ 0. The effective colour screening radius for pion (proton) is found for different s. The predictions for the diffractive cross sections at superhigh energies are presented. Received: 15 December 1998     

Quasi-long-range order in the random anisotropy Heisenberg model

The random field and random anisotropy N-vector models are studied with the functional renormalization group in 4−ε dimensions. The random anisotropy Heisenberg (N=3) model has a phase with an infinite correlation length at low temperatures and weak disorder. The correlation function of the magnetization obeys a power law 〈m(r ₁)m(r ₂)〉∼|r ₁−r ₂|^{− 0.62ε}. The magnetic susceptibility diverges at low fields as χ∼H ^−1+0.15ε. In the random field N-vector model the correlation length is finite at arbitrarily weak disorder for any N>3. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 2, 130–135 (25 July 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Photon-pion transition form factor at high photon virtualities within the nonlocal chiral quark model

Recently, the BABAR collaboration reported the measurements of the photon-pion transition form factor F _πγγ*(Q ²), which are in strong contradiction to the predictions of the standard factorization approach to perturbative QCD. In the present work, based on a nonperturbative approach to the QCD vacuum and on rather universal assumptions, we show that there exist two asymptotic regimes for the pion transition form factor. One regime with the asymptotic behavior F _πγ*γ(Q ²) ∼ 1/Q ² corresponds to the result of the standard QCD factorization approach, while other violates the standard factorization and leads to asymptotic behavior as F _πγ*γ(Q ²) ∼ ln(Q ²)/Q ². Furthermore, considering specific nonlocal chiral quark models, we find the region of parameters, where the existing CELLO, CLEO and BABAR data for the pion transition form factor are successfully described.     

Renormalization in Quantum Field Theory and the Riemann--Hilbert Problem II: The β-Function, Diffeomorphisms and the Renormalization Group

We showed in Part I that the Hopf algebra ℋ of Feynman graphs in a given QFT is the algebra of coordinates on a complex infinite dimensional Lie group G and that the renormalized theory is obtained from the unrenormalized one by evaluating at ɛ= 0 the holomorphic part γ₊(ɛ) of the Riemann–Hilbert decomposition γ₋(ɛ)^{− 1}γ₊(ɛ) of the loop γ(ɛ)∈G provided by dimensional regularization. We show in this paper that the group G acts naturally on the complex space X of dimensionless coupling constants of the theory. More precisely, the formula g ₀=gZ ₁ Z ₃ ^−3/2 for the effective coupling constant, when viewed as a formal power series, does define a Hopf algebra homomorphism between the Hopf algebra of coordinates on the group of formal diffeomorphisms to the Hopf algebra ℋ. This allows first of all to read off directly, without using the group G, the bare coupling constant and the renormalized one from the Riemann–Hilbert decomposition of the unrenormalized effective coupling constant viewed as a loop of formal diffeomorphisms. This shows that renormalization is intimately related with the theory of non-linear complex bundles on the Riemann sphere of the dimensional regularization parameter ɛ. It also allows to lift both the renormalization group and the β-function as the asymptotic scaling in the group G. This exploits the full power of the Riemann–Hilbert decomposition together with the invariance of γ₋(ɛ) under a change of unit of mass. This not only gives a conceptual proof of the existence of the renormalization group but also delivers a scattering formula in the group G for the full higher pole structure of minimal subtracted counterterms in terms of the residue. Received: 21 March 2000 / Accepted: 3 October 2000     

Central exclusive quarkonium production with tagged forward protons at RHIC

We study the Central Exclusive Production (CEP) of χ _cJ and η _c mesons at RHIC in proton–proton collisions. We consider the χ _cJ →J/ψ + γ decay channels and, recalling that the J _z =0 suppression of the J=1,2 states can be compensated by their larger branchings to J/ψ + γ, present predictions of rates and distributions for χ _c(0,1,2) production. Particular attention is paid to the impact of p _⊥ cuts applied to the outgoing protons, which can influence the relative rates significantly. The distribution in the azimuthal angle difference between the outgoing protons and the proton p_^²p_{\perp}^{2} is also studied, and shown to depend sensitively on the spin and parity of the centrally produced meson, as well as being affected by the soft-survival factors, S ². Two- and four-body decays, which are particularly relevant for χ _c0 production, are also considered. We show that in the two-body case, backgrounds from ‘direct’ QCD production based on both perturbative and non-perturbative models are expected to be under control.