Hulthén potential models for <Emphasis Type="BoldItalic">α−α</Emphasis> and <Emphasis Type="BoldItalic">α−</Emphasis>He<Superscript><Emphasis Type="BoldItalic">3</Emphasis></Superscript> elastic scattering

Simple Hulthén-type potential models are proposed to treat the α?α and \(\alpha {-} \text {He}^{3}\) elastic scattering. The merit of our approach is examined by computing elastic scattering phases through the judicious use of the phase function method. Reasonable agreements in scattering phase shifts are obtained with the standard data.     

Complementarity of the CERN Large Hadron Collider and the <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> International Linear Collider

The next-generation high-energy facilities, the CERN Large Hadron Collider (LHC) and the prospective e ⁺ e ⁻ International Linear Collider (ILC), are expected to unravel new structures of matter and forces from the electroweak scale to the TeV scale. In this report we review the complementary role of LHC and ILC in drawing a comprehensive and high-precision picture of the mechanism breaking the electroweak symmetries and generating mass, and the unification of forces in the frame of supersymmetry. Extended version of Ref. [1] to be published in “Supersymmetry on the Eve of the LHC”, a special volume of European Physical Journal C, Particles and Fields (EPJC) in memory of Julius Wess.     

Hypersurfaces Satisfying <Emphasis Type="BoldItalic">τ</Emphasis><Subscript><Emphasis Type="BoldItalic">2</Emphasis></Subscript><Emphasis Type="BoldItalic">(ϕ) = ητ(ϕ)</Emphasis> in Pseudo-Riemannian Space Forms

In this paper, we derived the equations for the hypersurface \({M^{n}_{r}}\) of a pseudo-Riemannian space form \(N^{n+1}_{q}(c)\) to satisfy τ ₂(?) = η τ(?) (η a constant) with τ(?) and τ ₂(?) be the tension and bitension fields of \({M^{n}_{r}}\). As applications, we prove that a hypersurface \({M^{n}_{r}}\) satisfying τ ₂(?) = η τ(?) in \(N^{n+1}_{q}(c)\) has constant mean curvature, under the assumption that \({M^{n}_{r}}\) has diagonalizable shape operator with at most three distinct principal curvatures. Then, using this result, we classify partially such hypersurface. We also make a preliminary study of hypersurfaces satisfying τ ₂(?) = f τ(?) with f be function.     

Another tetraquark structure in the <Emphasis Type="Italic">π</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">χ</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis>1</Subscript> invariant mass distribution

In this article, we assume that there exists a scalar hidden charm tetraquark state in the π ⁺ χ _c1 invariant mass distribution, and we study its mass using the QCD sum rules. The numerical result M _Z =(4.36±0.18) GeV is consistent with the mass of the Z(4250). The Z(4250) may be a tetraquark state, but other possibilities, such as a hadro-charmonium resonance and a molecular state, are not excluded.     

Near-threshold radiative 3<Emphasis Type="Italic">π</Emphasis> production in <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> annihilation

We consider the π⁺π^?π₀γ final state in electron-positron annihilation at c.m.s. energies not far from the threshold. Both initial-and final-state radiations of the hard photon are considered, but without interference between them. The amplitude for the final-state radiation is obtained by using the effective Wess-Zumino-Witten Lagrangian for pion-photon interactions valid for low energies. In real experiments, energies are never so small that ρ and ω mesons would have a negligible effect. So a phenomenological Breit-Wigner factor is introduced in the final-state radiation amplitude to account for the vector mesons' influence. Using radiative 3π production amplitudes, a Monte Carlo event generator was developed which could be useful in experimental studies.     

On mass corrections to the decay <Emphasis Type="Italic">P</Emphasis> → <Emphasis Type="Italic">l</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">l</Emphasis><Superscript>−</Superscript>

The Mellin-Barnes representation is used to improve the theoretical estimate of mass corrections to the width of a light pseudoscalar meson decay into a lepton pair, P → l ⁺ l ⁻. The full resummation of the terms ln(m _l ²/Λ²)(m _l ²/Λ²) ⁿ and (m _l ²/Λ²) ⁿ to the decay amplitude is performed, where m _l is the lepton mass and Λ ≈ m _ρ is the characteristic scale of the P → γ*γ* form factor. The total effect of the mass corrections for the e ⁺ e ⁻ channel is negligible and, for the μ⁺μ⁻channel, its order is of a few percent. The text was submitted by the authors in English.     

One-loop electro-weak corrections to three-jet observables of <Emphasis Type="Italic">b</Emphasis>-quarks <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> annihilations

We compute the full one-loop EW contributions of entering the electron–positron into two b-quarks and one gluon cross section at the Z peak and LC energies. We include both factorisable and non-factorisable virtual corrections, photon bremsstrahlung but not the real emission of W ^± and Z bosons. Their importance for the measurement of α _S from jet rates and shape variables is explained qualitatively and illustrated quantitatively. Their impact on the forward–backward asymmetry is also analysed. Work supported in part by the U.K. Science and Technology Facilities Council (STFC), by the European Union (EU) under contract MRTN-CT-2006-035505 (HEPTOOLS FP6 RTN) and by the Italian Ministero dell’Istruzione, dell’Università e della Ricerca (MIUR) under contract 2006020509_004. An erratum to this article can be found at     

One-loop electro-weak corrections to three-jet observables of <Emphasis Type="Italic">b</Emphasis>-quarks <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> annihilations

We compute the full one-loop EW contributions of \({\mathcal{O}}(\alpha_{\mathrm{S}}\alpha_{\mathrm{EM}}^{3})\) entering the electron–positron into two b-quarks and one gluon cross section at the Z peak and LC energies. We include both factorisable and non-factorisable virtual corrections, photon bremsstrahlung but not the real emission of W ^± and Z bosons. Their importance for the measurement of α _S from jet rates and shape variables is explained qualitatively and illustrated quantitatively. Their impact on the forward–backward asymmetry is also analysed.     

<Emphasis Type="Italic">J</Emphasis>/<Emphasis Type="Italic">ψ</Emphasis> suppression and <Emphasis Type="Italic">p</Emphasis><Subscript><Emphasis Type="Italic">T</Emphasis></Subscript> spectra in RHIC and LHC energy collisions

In a hydrodynamic model, we have studied J/ψ production in Au+Au/Cu+Cu collisions at RHIC energy, GeV. At the initial time, J/ψ’s are randomly distributed in the fluid. As the fluid evolves in time, the free streaming J/ψ’s are dissolved if the local fluid temperature exceeds a threshold temperature T _J/ψ . Sequential melting of charmonium states (χ _c , ψ ^′ and J/ψ), with melting temperatures , T _J/ψ ≈2T _c and feed-down fraction F≈0.3, explains the PHENIX data on the centrality dependence of J/ψ suppression in Au+Au collisions. J/ψ p _T spectra and the nuclear modification factor in Au+Au collisions are also well explained in the model. The model however overpredicts the centrality dependence of J/ψ suppression in Cu+Cu collisions by 20–30%. The J/ψ p _T spectra are underpredicted by 20–30%. The model predicts that in central Pb+Pb collisions at LHC energy,  GeV, J/ψ’s are suppressed by a factor of ∼10. The model predicted a J/ψ p _T distribution in Pb+Pb collisions at LHC is similar to that in Au+Au collisions at RHIC.     

Scalar mesons in <Emphasis Type="Italic">η</Emphasis>′ → <Emphasis Type="Italic">ηπ</Emphasis><Superscript>0</Superscript><Emphasis Type="Italic">π</Emphasis><Superscript>0</Superscript> decay

The decay η′ → ηπ ⁰ π ⁰ is studied in the framework of isobar model. It is shown, that good agreement with the experiment is achieved if α ₀- and σ-meson contributions are taken into account. The contribution of α ₀-meson is dominant, but σ-meson is necessary to reproduce the form of the Dalitz plot. Instead of the usual Breit-Wigner form of σ-meson propagator we use parametrization of the ππ-amplitude, which satisfies analyticity, crossing, unitarity and chirality constraints. This amplitude has a pole in the complex plane, which corresponds to σ-meson and describe experimental data on ππ-scattering in K _e4 decay.     

Deviation from the standard model in the decay <Emphasis Type="Italic">π</Emphasis><Superscript>+</Superscript> → <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">νγ</Emphasis>

A precise investigation of radiative pion decay (π⁺ → e⁺νγ) in a pion beam from the meson factory of the Paul Scherrer Institute (Switzerland) was performed by the PIBETA Collaboration with the aid of the PIBETA detector. This resulted in finding 41 601 events of radiative pion decay in three kinematical regions. The absolute values of the branching ratio for radiative pion decay were determined in each of these regions. To a precision approximately four times higher than that known previously, the ratio of the axial-vector to the vector form factor was found to be γ ≡ F _A /F _V = 0.443 (15), the latter being fixed at F _V = 0.0259. The number of events found in the kinematical region specified by photon energies of E_γ > 55.6 MeV, positron energies of E _e > 20.0 MeV, and angles of θ_{γ, e} > 40° between the momenta of the corresponding particles (B region) was 5233. In region B, the measured branching ratio for radiative pion decay, R_π→evγ(expt) = 11.6(3) × 10^?8, proved to be smaller by eight standard deviations than that which follows from the Standard Model, R_π→evγ (theor) = 14.34(1) × 10^?8.     

ALICE-PHOS: acceptance and efficiency correction factors <Emphasis Type="Italic">p</Emphasis>−<Emphasis Type="Italic">p</Emphasis>→<Emphasis Type="Italic">π</Emphasis><Superscript>0</Superscript>+<Emphasis Type="Italic">X</Emphasis> at 10 TeV

In ultra-relativistic Heavy-Ion Collisions (HIC), the properties of the quark gluon plasma (QGP) can be explored, in particular, via measurements of neutral pions. The π ⁰ is an important probe for both proton and heavy ion physics. In the former case, π ⁰ production provides an important mean of testing pQCD as well as useful data to constrain current and future theoretical models. In the latter case, π ⁰ measurements will serve as a baseline for exploring the nature of the HIC hard scattering. In the ALICE experiment, π ⁰ mesons are identified as they decay into two photons (π ⁰→γ γ) using the high-resolution photon spectrometer (PHOS). PHOS will measure π ⁰ transverse momentum over a wide range, from hundreds of MeV/c to several tens of GeV/c. An estimation of π ⁰ production cross-section in proton–proton collisions is calculated in a next-to-leading order (NLO) approximation and first presented. The π ⁰ geometrical acceptance and the identification efficiency along with the analysis on the invariant mass are the two important correction factors for obtaining a realistic π ⁰ spectrum discussed in this paper.     

Two-Photon Channel in <Emphasis Type="Italic">B</Emphasis>−<Emphasis Type="Italic">L</Emphasis> Models

In this paper we examine the possibility of having an exception to the recent observation by L. Randall amd M. Wise, which states that “a significant branching ratios to both e ⁺ e ⁻ and γ γ is possible only if new physics beyond that in the SM couples directly to electrons”. We consider resonances decaying into diphotons and dielectrons final states predicted in U(1) _B−L extensions of the SM. We find that these new resonances can’t decay into e ⁺ e ⁻ and γ γ final states with comparably measurable branching ratios although such resonances are directly coupled to electrons.     

Investigation of the process <Emphasis Type="Italic">J/ψ</Emphasis> → <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> with the KEDR detector

The product of the electron width of the J/ψ meson and the probability for its decay to an electron-positron pair was measured by using data from the KEDR experiment at the VEPP-4M electron-positron collider. The result was Γ _ee × Γ _ee /Γ = 0.3392 ± 0.0068(stat.) ± 0.0063(syst.) keV.     

Lie Superalgebra Structures in <Emphasis Type="Italic">H</Emphasis><Superscript>⋅</Superscript> (<Emphasis Type="Italic">g</Emphasis>;<Emphasis Type="Italic">g</Emphasis>)

Let g=vect(M) be the Lie (super)algebra of vector fields on any connected (super)manifold M; let - be the change of parity functor, C ⁱ and H ⁱ the space of i-chains and i-cohomology. The Nijenhuis bracket makes into a Lie superalgebra that can be interpreted as the centralizer of the exterior differential considered as a vector field on the supermanifold associated with the de Rham bundle on M. A similar bracket introduces structures of DG Lie superalgebra in L ^* and for any Lie superalgebra g. We use a Mathematica-based package SuperLie (already proven useful in various problems) to explicitly describe the algebras l ^* for some simple finite dimensional Lie superalgebras g and their relatives - the nontrivial central extensions or derivation algebras of the considered simple ones.     

Static spherically symmetric solution of (<Emphasis Type="Italic">R</Emphasis> ± <Emphasis Type="Italic">μ</Emphasis><Superscript>4</Superscript>/<Emphasis Type="Italic">R</Emphasis>) gravity

The static spherically symmetric solution for R ± μ ⁴/R model of f(R) gravity is investigated. We obtain the metric for space-time in the solar system that reduces to the Schwarzschild metric, when μ tends to zero. For the obtained metric, the deviation from Einstein gravity is very small. This result is different from the other results have been obtained by equivalence between f(R) gravity and scalar tensor theory. Also it is shown that the vacuum solution in the solar system depends on the shape of matter distribution which differ from the Einstein’s gravity.