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.     

Dark resonances for ground-state transfer of molecular quantum gases

One possible way to produce ultra-cold, high-phase-space-density quantum gases of molecules in the rovibronic ground state is given by molecule association from quantum-degenerate atomic gases on a Feshbach resonance and subsequent coherent optical multi-photon transfer into the rovibronic ground state. In ultra-cold samples of Cs₂ molecules, we observe two-photon dark resonances that connect the intermediate rovibrational level |v=73,J=2〉 with the rovibrational ground state |v=0,J=0〉 of the singlet X ¹ Σ _g ⁺ ground-state potential. For precise dark resonance spectroscopy we exploit the fact that it is possible to efficiently populate the level |v=73,J=2〉 by two-photon transfer from the dissociation threshold with the stimulated Raman adiabatic passage (STIRAP) technique. We find that at least one of the two-photon resonances is sufficiently strong to allow future implementation of coherent STIRAP transfer of a molecular quantum gas to the rovibrational ground state |v=0,J=0〉.     

On the high-statistics investigation of the <Emphasis Type="Italic">a</Emphasis><Subscript>0</Subscript>(980) resonance in the γγ → π<Superscript>0</Superscript>η reaction

High-statistics data on the γγ → π⁰η reaction will make it possible to conclude whether the K ⁺ K ⁻-loop rescattering mechanism, γγ → K ⁺ K ⁻ → a ₀(980) → π⁰η, is the main mechanism of the production of a ₀(980) isovector resonance. This mechanism provides a reasonable value of 20–30 nb at the maximum for the manifestation of a ₀(980) in the γγ → π⁰η cross section. It also gives rise to a noticeable narrowing of the a ₀(980) peak to its effective (observed) width ≈20–30 MeV in the γγ → π⁰η channel. The decay width averaged over the resonance mass distribution is 〈Γ_{α 0} → K ⁺ K ⁻ → γγ〉_πη ≈ 0.13 keV. The experimental confirmation of this scenario would be important evidence in favor of the q ² $ \bar q $ \bar q ² nature of light scalar mesons.     

Mechanism of the production of the <Emphasis Type="Italic">a</Emphasis><Subscript>0</Subscript>(980) resonance in the γγ → π<Superscript>0</Superscript>η reaction

High-statistics Belle data on the γγ → π⁰η reaction have been analyzed in order to reveal the mechanism of two-photon production and the nature of the a ₀(980) resonance. The solution obtained for the γγ → π⁰η amplitude is in agreement with the predictions of the chiral theory for the πη-scattering length; with the strong coupling of the a ₀(980) resonance with the πη, K $ \bar K $ \bar K , and πη′ channels; and with the key role of the a ₀(980) → (K $ \bar K $ \bar K + π⁰η + π⁰η′) → γγ rescattering mechanisms in the a ₀(980) → γγ decay. This picture is much in favor of the q ² $ \bar q $ \bar q ² nature of a ₀(980) resonance and is consistent with the properties of its partners, σ₀(600) and f ₀(980) resonances, in particular, with those manifested in the γγ → ππ reactions. The important role of vector exchanges in the formation of the nonresonant background in the γγ → π⁰η reaction has been revealed. Preliminary information on the π⁰η → π⁰η reaction has been obtained.     

Learning about flavour structure from τ→eβγ and μ→eγ?

Current and upcoming experiments should improve the sensitivity to e _α →e _β γ decays by an order of magnitude. This paper assumes that one of the τ→e _β γ decays is observed, and explores the structure and consequences of the required new flavoured couplings. In simple models (a low-scale seesaw, leptoquarks) it is shown that the dipole vertex function is proportional to a product of flavoured matrices from the Lagrangian (a “Jarlskog-like” invariant), provided that the loop particles are weakly coupled to the Higgs. Secondly, if the dipole vertex function has a hierarchical structure, this might imply that only some of the τ→e _β γ modes can be observed, due to the “approximate zero” implied by the bound on μ→eγ. The assumptions underlying this potential test of a hierarchical structure are discussed.     

Entanglement and Mixedness of Locally Cloned Non-Maximal W-State

In this work we describe a protocol by which two of three parties generate two bipartite entangled state among themselves without involving third party, from a non maximal W-state or W-type state |X〉=α|001〉₁₂₃+β|010〉₁₂₃+γ|100〉₁₂₃,α ²+β ²+γ ²=1 shared by three distant partners. Also we have considered the case β=γ, to obtain a range for α ², for which the local output states are separable and non local output states are inseparable. We also find out the dependence of the mixedness of inseparable states with their amount of inseparability, for that range of α ².     

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.     

Photon polarization in the two-photon decay of heavy hydrogen-like ions

We have applied the density matrix and second-order perturbation theory in order to re-analyze the two-photon decay of hydrogen-like ions for the polarization of emitted light. Special attention is paid to the linear polarization of one of the photons, while the spin state of the second photon is supposed to be unobserved. For such an “angle-polarization” correlation of the two photons we investigate the contributions that arise from non electric-dipole terms in the expansion of the electron-photon interaction. Detailed calculations are performed for the 2s_1/2 →1s_1/2 and 3d_5/2 →1s_1/2 transitions in neutral hydrogen as well as in hydrogen-like uranium.     

Generalized Two-Mode Squeezed States and Some Nonclassical Characteristics

A class of generalized two-mode squeezed states |φ〉 is presented, which are generated from the generalized two-mode squeezing operator U(γ,λ) acting on the two-mode coherent state |α ₁,α ₂〉. We first investigate some mathematical properties of U(γ,λ) including the squeezing transformation under U(γ,λ), ket-bra integral form in the coordinate representation, normally ordered form. Then we evaluate some nonclassical characteristics of the state |φ〉 such as higher-order squeezing behavior, entanglement analysis and analytical expression of the Wigner function.     

Cross-sections for low-energy πgamma; reactions

We review the cross-sections for low-energy π^-γ reactions in the framework of chiral perturbation theory. Charged-pion Compton scattering, π^-γ → π^-γ , is considered up to one-loop order where the pion's internal structure enters through the difference of the electric and magnetic pion polarizability, α_π - β_π . The ongoing COMPASS experiment aims at measuring this important structure constant with high statistics using the Primakoff effect. In the same way, the reaction π^-γ → π^-π⁰ serves as a test of the QCD chiral anomaly (via the γ3π -coupling constant F _γ3π . Furthermore, we calculate the total cross-sections for neutral and charged pion-pair production, π^-γ → π^-π⁰π⁰ and π^-γ → π^-π⁺π^- , which are governed by the chiral ππ -interaction. Finally, we investigate the radiative (correction) process π^-γ → π^-γγ and calculate the corresponding two-photon mass spectrum. This information will be useful for analyzing the π^- Primakoff scattering events with photons in the final state.     

Electromagnetic decays of radially excited mesons π0′, ρ0′, ω0′, and production of π0′ at lepton colliders

Radiative decays π ⁰(π ^0′) → γ + γ, π ^0′ → ρ ⁰(ω) + γ, ρ ^0′(ω′) → π ⁰ + γ, ρ ^0′(ω′) → π ^0′ + γ, and some processes of π ^0′ production at lepton colliders are considered in the framework of the nonlocal SU(2) × SU(2) Nambu-Jona-Lasinio model. Mixing of the radially excited and the ground meson states is taken into account. Numerical results for the decay and production processes are presented.     

The aγγγ vertex and three-photon axion decay in an external magnetic field

The axion vertex aγγγ, the probability of three-photon axion decay in an external magnetic field, and the cross section of the crossing process aγ→2γ, which CP invariance forbids in vacuum, are calculated for the first time. It is shown that in superstrong magnetic fields B≫F ₀=m ²/|e|=4.41·10¹³ G the probability of three-photon decay is greater than the probability of two-photon decay. The astrophysical aspects of the questions examined are discussed. Zh. éksp. Teor. Fiz. 116, 26–34 (July 1999)     

Two-photon decays of pseudotensor mesons <Emphasis Type="Italic">π</Emphasis><Subscript>2</Subscript>(1670), <Emphasis Type="Italic">π</Emphasis><Subscript>2</Subscript>(2250), and <Emphasis Type="Italic">π</Emphasis><Subscript>2</Subscript>(2510)

In terms of relativistic and gauge-invariant spectral-integral technique, we calculate amplitude for the π ₂ → γγ decay as a three-step transition π ₂ → q $ \bar q $ \bar q (2⁻⁺) → γ + q $ \bar q $ \bar q (1⁻⁻) → γγ. Using wave functions of the q $ \bar q $ \bar q components of photon (hep-ph/0406320) and those of pseudotensor mesons π ₂(1670), π ₂(2000), π ₂(2250), and π ₂(2510) (hep-ph/0511109), we obtain the following values for partial widths: Γ _{π2(1670)→γγ} = 0.072 ± 0.007 keV, Γ _{π2(2000)→γγ} = 0.037 ± 0.004 keV, Γ _{π2(2250)→γγ} = 0.027 ± 0.003 keV, and Γ _{π2(2510)→γγ} = 0.022 ± 0.002 keV. In the calculations, we use the momentum operator expansion, and, in this connection, discuss the problem of nilpotent operators inherent in the considered amplitude. It should be emphasized that measurement of two-photon decays of the π ₂ states can give valuable information about the long-range quark-antiquark forces which, as one may guess, are related to the quark confinement.     

Direct photons in ATLAS@LHC

The ATLAS detector at the LHC is capable of efficiently separating photons and neutral hadrons based on their shower shapes over a wide range in η, ϕ and E _T , either in addition to or instead of isolation cuts. This provides ATLAS with a unique strength for direct photon and γ-jet physics (“tomography”) as well as access to the unique capability to measure non-isolated photons from fragmentation or from the medium. We present a first look at the ATLAS direct photon measurement capabilities in p+p and Pb+Pb collisions at LHC energies over the region |η| < 2.4.     

B ?→ K 1*? (1270)(→ ρ 0 K ?) ? + ? ? in LEET

Flavor changing neutral current (FCNC) decays of the B-meson are a very useful tool for studying possible physics scenarios beyond the standard model (SM), where of the many FCNC modes radiative, purely leptonic and semi-leptonic decays of the B-meson are relatively clean tests. Within this context, the BELLE collaboration has measured the process B→K ^* γ and also searched for the B→K ₁(1270)γ process. Theoretical analyses of these processes are yielding similar values of the relevant form factors. In this work we have used this upper bound in studying the angular correlations for the related semi-leptonic decay mode B ⁻→K ₁⁻(1270)(→ρ ⁰ K ⁻)ℓ ⁺ ℓ ⁻, where we have used the form factors that have already been estimated for the B→K ₁(1270)γ mode. Note that the additional form factors that are required were calculated using large energy effective theory (LEET).     

Direct photons in nuclear collisions at fair energies

Using the extrapolation of existing data, estimations of prompt-photon production at FAIR energies have been made. At y = y _c.m. the rapidity density of prompt photons with p _t > 1.5 GeV/c per central Au + Au event at 25 A GeV is estimated as ∼10⁻⁴. With the planned beam intensity 10⁹ per second and 1% interaction probability, for 10% of most central events one can expect the prompt-photon rate ∼10² photons per second. Direct photons from the hadron scenario of ion collisions generated by the Hadron-String-Dynamics (HSD) transport approach with implemented meson scatterings πρ → πγ, ππ → ργ have been analyzed. Photons from short-living resonances (e.g., ω → π ⁰ γ) decaying during the dense phase of the collision should be considered as direct photons. They contribute significantly in the directphoton spectrum at p _t = 0.5–1 GeV/c. At the FAIR energy 25 A GeV in Au + Au central collisions the HSD generator predicts, as a lower estimate, γ _direct/ ≃ 0.5% in the region p _t = 0.5–1 GeV/c. At p _t = 1.5–2 GeV/c γ _prompt/ ≃ 2%. Thermal direct photons have been evaluated with the Bjorken Hydro-Dynamics (BHD) model. The BHD spectra differ strongly from the HSD predictions. The direct-photon spectrumis very sensitive to the initial temperature parameter T ₀ of the model. The 10-MeV increase in the T ₀ value leads to ∼2 times higher photon yield. The text was submitted by the authors in English.     

Partial wave analysis of πproduction in two-photon collisions at LEP

The reaction γγ → π⁺π^-π⁰ with quasi-real photons is studied with a total integrated luminosity of 663pb^-1, collected by the L3 detector at LEP at center-of-mass energies from 183 to 209GeV. The results of an energy-dependent partial wave analysis in the mass region 1.1≤M(π⁺π^-π⁰)≤2.2GeV are presented. The reaction is dominated by a₂(1320) formation. A strong signal consistent with the first radial excitation of the isovector tensor state, a₂(1700), is present and confirms the previous L3 observation. Its two-photon partial width is found to be Br(3π) = 0.37^+0.12_-0.08keV, the relative branching ratio of ρ(770)π to f₂(1270)π is 3.4±0.4. For all observed states the product of γγ partial width and 3π branching ratios is measured.     

Towards B→Vγ decays at NNLO in SCET

We compute NNLO ((α_s ²)) corrections to the hard-scattering kernels entering the QCD factorization formula for B→Vγ decays, where V is a light vector meson. We give complete NNLO results for the dipole operators Q₇ and Q₈, and partial results for Q₁ valid in the large-β₀ limit and neglecting the NNLO correction from hard-spectator scattering. Large perturbative logarithms in the hard-scattering kernels are identified and resummed using soft-collinear effective theory. We use our results to estimate the branching fractions for B→K^*γ and B_s→φγ decays at NNLO and compare them with the current experimental data.