Quasi-particle model for lattice QCD: quark–gluon plasma in?heavy ion collisions

We propose a quasi-particle model to describe the lattice QCD equation of state for pure SU(3) gauge theory in its deconfined state, for T≥1.5T _c. The method involves mapping the interaction part of the equation of state to an effective fugacity of otherwise non-interacting quasi-gluons. We find that this mapping is exact. Using the quasi-gluon distribution function, we determine the energy density and the modified dispersion relation for the single particle energy, in which the trace anomaly is manifest. As an application, we first determine the Debye mass, and then the important transport parameters, viz., the shear viscosity, η, and the shear viscosity to entropy density ratio, h/S\eta/{\mathcal{S}}. We find that both η and h/S\eta/{\mathcal{S}} are sensitive to the interactions, and that the interactions significantly lower both η and h/S\eta/\mathcal{S}.     

Magnetic moments of baryons in higher symmetry schemes including charm

Relations among the magnetic moments of charmed and uncharmed baryons are derived in the framework of SU(4) and SU(8) symmetries. The SU(3) resultμ (Σ ^o)=−μ(Λ) is not present in SU(4), but is obtained in SU(8). Higher order effects are further considered to improve the situation.     

Charm changing weak decays 1/2+ → 3/2+ + 0−/γ in SU(4) and SU(8) w

Weak decay modes (1/2⁺ → 3/2⁺ + 0⁻/γ) of charmed baryons are studied. Relations among the various decay amplitudes are derived in isospin, SU(3), SU(4) and SU(8) _w symmetries. Sextet dominance in SU(3) forbidsB(3) →D(10) +P(3*) decays. 20″ dominance in SU(4) specifies all the decays in terms of Θ⁻ decays. Weak decays of Θ* ₃ ⁺⁺ and Θ⁻ are also discussed. SU(8) _w symmetry predictsα , which is consistent with the experimental value.     

Generalized interacting boson model and the collective behaviour in nuclei

The effect of including the high spin bosons on the manifestation of collective behaviour in nuclei is examined by plotting theB(E2; 2⁺→0⁺) rates as a function of neutron number for various values ofη, whereη is the highest angular momentum of the bosons included in the calculation.B(E2; 2⁺→0⁺) values of a large number of nuclei in various regions of the nuclear periodic table are calculated with a single value for the effective charge in the generalized scheme. Irreducible representations of SU(3) contained in the symmetric partition [N] of U(15) are worked out for integersN uptoN=15, to enable the explicit inclusion of theg boson into calculations. The experimentally observed odd-K bands in²³⁴U and¹⁸⁴W are described as a direct consequence of theg boson.     

Photoproduction of η -mesons off protons

Photoproduction of η -mesons was studied with the Crystal-Barrel detector at ELSA for photon energies in the range from 0.75 to 3GeV. Total and differential cross-sections are presented. The η mesons are detected in two decay modes, in η → 2γ and in η → 3π⁰ → 6γ . The cross-sections vary slowly as functions of energy and η production angle suggesting that only few resonances make significant contributions to the cross-section. For photon energies above 1.5GeV, the differential cross-sections show a strong forward peak due to meson exchanges in the t channel. A comparison of the η -photoproduction cross-sections with SAID and MAID as well as with a partial-wave analysis performed on our data in combination with other data sets shows good agreement. The Bonn-Gatchina partial-wave analysis suggests that the largest contribution to η photoproduction for energies below 3GeV proceeds via three resonances, the well-known N(1535)S ₁₁ , via N(1720)P ₁₃ , and a newly suggested N(2070)D ₁₅ .     

Analysis of the low-energy ηNN-dynamics within a three-body formalism

The interaction of an η-meson with two nucleons is studied within a three-body approach. The major features of the ηNN-system in the low-energy region are accounted for by using a s-wave separable ansatz for the two-body ηN and NN amplitudes. The calculation is confined to the (J ^π;T) = (0^-;1) and (1^-;0) configurations which are assumed to be the most promising candidates for virtual or resonant ηNN-states. The eigenvalue three-body equation is continued analytically into the nonphysical sheets by contour deformation. The position of the poles of the three-body scattering matrix as a function of the ηN-interaction strength is investigated. The corresponding trajectory, starting on the physical sheet, moves around the ηNN three-body threshold and continues away from the physical area giving rise to virtual ηNN-states. The search for poles on the nonphysical sheets adjacent directly to the upper rim of the real energy axis gives a negative result. Thus no low-lying s-wave ηNN-resonances were found. The possible influence of virtual poles on the low-energy ηNN-scattering is discussed. Received: 27 June 2000 / Accepted: 3 August 2000     

Sum rules for the baryon20, baryon20′ and meson 16-plet coupling constants in broken SU (4) and SU (3) symmetry

Sum rules for the coupling constants for D (20), B (20′) and P (16) are given taking into account first order breaking of SU (4) and SU (3) symmetries. The D (20) and B (20′) contain the usual 3/2⁺ baryon decuplet and 1/2⁺ baryon octet of SU (3), while the P (16) contains the usual pseudoscalar octet of pions, etc. These sum rules generalize the decuplet → octet + octet sum rules of broken SU (3 to a broken SU (4) symmetry scheme, in particular the charm SU (4) for hadrons. It is pointed out that, of the many sum rules, it may be possible to check some of them experimentally (see Section 5) and thus provide a test for an underlying SU (4 symmetry for strong interactions.     

Low-energy ηd-resonance

Elastic ηd-scattering is considered within the Alt-Grassberger-Sandhas (AGS) formalism for various ηN input data. A three-body resonant state is found close to the ηd threshold. This resonance is sustained for different choices of the two-body ηN-scattering length a _ηN. The position of the resonance moves towards the ηd threshold when Rea _ηN is increased, and turns into a quasi-bound state at Rea _ηN∼ 0.7-0.8 fm depending on the choice of Ima _ηN. Received: 12 June 2000 / Accepted: 3 August 2000     

Measurement of η photoproduction on the proton from threshold to 1500 MeV

Beam asymmetry and differential cross-section for the reaction γp → ηp were measured from production threshold to 1500MeV photon laboratory energy. The two dominant neutral decay modes of the η -meson, η → 2γ and η → 3π⁰ , were analyzed. The full set of measurements is in good agreement with previously published results. Our data were compared with three models. They all fit satisfactorily the results but their respective resonance contributions are quite different. The possible photoexcitation of a narrow state N(1670) was investigated and no evidence was found.     

Revisiting toric SU(3) structures

Three‐dimensional smooth compact toric varieties (SCTV) admit SU(3) structures, and may thus be relevant for string compactifications, if they have even first Chern class (c₁). This condition can be fulfilled by infinitely many SCTVs, including ℂℙ³ and ℂℙ¹ bundles over all two‐dimensional SCTVs. We show that as long as c₁ is even, toric SU(3) structures can be constructed using a method proposed in [1]. We perform a systematic study of the parametric freedom of the resulting SU(3) structures, with a particular focus on the metric and the torsion classes. Although metric positivity constrains the SU(3) parameters, we find that every SCTV admits several toric SU( 3) structures and that parametric choices can sometimes be made to match requirements of string vacua. We also provide a short review on the constraints that an SU(3) structure must meet to be relevant for four‐dimensional, maximally symmetric �� = 1 or �� = 0 string vacua.     

Anisotropy of the local field in anisotropic films of conjugated polymers

Using the data on dispersion of refractive indices in the visible region, the experimental values of the components L _j of the Lorentz tensor have been obtained for uniaxial (crystalline, oriented on a substrate, and stretched) films of conjugated polymers from nanometer to micrometer thicknesses. The dependence of the components L _j on the axial and planar orientations of macromolecules with respect to the optical axis of the film, technology of fabricating the films, and chemical structure of macromolecules has been elucidated. The correlation between the components L _j and the measured parameter η has been determined and the analytical dependence L _j (η) for films with both types of macromolecular orientation has been established. In the visible region (0 ≤ η ≤ 0.5), the presence of one point (η = 1/3) of isotropization of the tensor L and three points (η = 0, 1/3, and 0.5) of isotropization of the local field tensor f has been revealed. The point η = 1/3 of isotropization of the tensors L and f has been determined. A comparison has been made between the values of L _j (η) with predictions of known models of the local field for conjugated polymers.     

Mixing parameters of η and η′ mesons

Mixing angles of η and η′ mesons are obtained in the scheme of octet-singlet mixing θ_η = −15.4°, θ′_η = −17.9°, and in the scheme connected with expansion in the quark basis $ \bar q $ \bar q q − $ \bar s $ \bar s s φ = 39.3°. The constants gV _ηγ, g _η′ V _γ of radiative decays η′ → V _γ and V → ηγ (V ≡ ρ, ω, φ) and the ratios of constants of weak decays of η and η′ mesons are calculated. The numerical values that were found are in agreement with the experimental data.     

Hadron production near threshold

Final state interaction effects inpp→ pΛK ⁺ andpd →³Heη reactions are explored near threshold to study the sensitivity of the cross-sections to thepΛ potential and theηN scattering matrix. The final state scattering wave functions between Λ andp andη and³He are described rigorously. The Λ production is described by the exchange of one pion and aK-meson between two protons in the incident channel. Theη production is described by a two-step model, where in the first step a pion is produced. This pion then produces anη by interacting with another nucleon     

η- mixing in U(3) chiral perturbation theory

We investigate η- mixing in infrared regularized U(3) chiral perturbation theory by calculating the η and masses up to one-loop order. From this analysis it becomes obvious that even at leading order η--mixing does not obey the usually assumed one-mixing-angle scheme if large N _c counting rules are not employed. Received: 12 March 2001 / Accepted: 4 July 2001     

A method of η′ decay product selection to detect partial chiral symmetry restoration

In case of chiral U _A(1) symmetry restoration the mass of the η′ boson (the ninth, would-be Goldstone boson) is decreased, thus its production cross section is heavily enhanced [1], The η′ decays (through one of its decay channels) into five pions. These pions will not be correlated in terms of Bose-Einstein correlations, thus the production enhancement changes the strength of two-pion correlation functions at low momentum [2). Preliminary results strongly support the mass decrease of the η′ boson [3–5]. In this paper we propose a method to select pions coming from η′ decays. We investigate the efficiency of the proposed kinematical cut in several collision systems and energies with several simulators. We prove that our method can be used in all investigeted collision systems.     

Evolution of a Model Quantum System¶ Under Time Periodic Forcing:¶Conditions for Complete Ionization

We analyze the time evolution of a one-dimensional quantum system with an attractive delta function potential whose strength is subjected to a time periodic (zero mean) parametric variation η(t). We show that for generic η(t), which includes the sum of any finite number of harmonics, the system, started in a bound state will get fully ionized as t→∞. This is irrespective of the magnitude or frequency (resonant or not) of η(t). There are however exceptional, very non-generic η(t), that do not lead to full ionization, which include rather simple explicit periodic functions. For these η(t) the system evolves to a nontrivial localized stationary state which is related to eigenfunctions of the Floquet operator. Received: 1 November 2000 / Accepted: 5 February 2001     

How the recent BABAR data for P → γγ* affect the Standard Model predictions for the rare decays P → l+l?

Measuring the lepton anomalous magnetic moments (g − 2) and the rare decays of light pseudoscalar mesons into lepton pairs P → l ⁺ l ⁻, serve as important tests of the Standard Model. To reduce the theoretical uncertainty in the standard model predictions, the data on the charge and transition form factors of the light pseudoscalar mesons play a significant role. Recently, new data on the behavior of the transition form factors P → γγ* at large momentum transfer were supplied by the BABAR collaboration. There are several problems with the theoretical interpretation of these data: (1) An unexpectedly slow decrease of the pion transition form factor at high momenta, (2) the qualitative difference in the behavior of the pion form factor and the η and η′ form factors at high momenta, (3) the inconsistency of the measured ratio of the η and η′ form factors with the predicted one. We comment on the influence of the new BABAR data on the rare decay branchings.     

Gravity-induced weak symmetry breaking and supergravity

We give here a review of the recent developments of grand unified theories based onN=1 supergravity. We start with a brief introduction of supersymmetry and supergravity multiplets, and then discuss the construction of an invariant Lagrangian. The phenomena of gravity-induced weak symmetry breaking via the super Higgs effect at the tree level, corresponding to the conventional SU(5) gauge group, are then considered. We then extend this idea to the larger group SO(10), showing two possible breaking chains given as (i) SO(10)×susy→SU(2) _L ×U(1) _R ×U(1) _B-L ×SU(3) _C (≡ G₂₁₁₃)×susy→U(1)_em×SU(3) _C (G _LE ) predicting a secondZ-boson having mass lower than 1 TeV, and (ii) SO(10)×susy→SU(2) _L ×SU(2) _R ×SU(4)→(≡G₂₂₄)×susy→ SU(2) _L ×U(1) _Y ×SU(3) _C (≡ G₂₁₃)×susy→U(1)_em×SU(3) _C . We also consider the radiative breaking of weak symmetry via renormalisation group effects, which predicts the top quark mass. Some experimental signatures of the supersymmetric particles are investigated and possible future outlook is discussed. Invited talk presented at the International Symposium on Theoretical Physics, Bangalore, November 1984.     

Symmetry breaking for theBBP-couplings

The B-A system of CP molecule has been reinvestigated. The rotational structures in the (0, 0) and (1, 1) bands have been photographed in the second order of a 10.6 m grating with 25μ slit width. The molecular constants have been determined using a weighted least squares fit computer program. It is found that the spin-splitting constant in the B-state is negative and not positive as reported by previous workers. An accurate value ofα in the A-state could be determined. The present analysis also suggests that the spin-splitting constant in the ground state of CP should be positive, hence the assignment of theR ₁ andR ₂ orP ₁ andP ₂ branches in the B-X system of CP by Barwaldet al should be interchanged.     

Reconciling φ radiative decays with other data for a0(980), f0(980), ππ→KK and ππ→ηη

Data for φ→γ(ηπ⁰) are analysed using the KK loop model and compared with parameters of a₀(980) derived from Crystal Barrel data. The ηπ mass spectrum agrees closely and the absolute normalisation lies just within errors. However, BES parameters for f₀(980) predict a normalisation for φ→γ(π⁰π⁰) at least a factor 2 lower than is observed. This discrepancy may be eliminated by including constructive interference between f₀(980) and σ. The magnitude required for σ→KK is consistent with data on ππ→KK. A dispersion relation analysis by Büttiker, Descotes-Genon and Moussallam of ππ→KK leads to a similar conclusion. Data on ππ→ηη also require decays of σ to ηη. Four sets of ππ→KK data all require a small but definite f₀(1370) signal. PACS 13.25.Gv; 14.40.Gx; 13.40.Hq