Estimate of the gluonium mass from QCD low-energy theorems

We consider the two-point function of gluonic currents with quantum numbersJ ^PC=O ⁺⁺. Low-energy theorems obtained earlier starting from the QCD lagrangian allow to reconstruct, in gross features, the corresponding spectral density. The mass of the lowestO ⁺ gluonium is estimated.     

Cecotti-Fendley-Intriligator-Vafa index in a box

The Cecotti-Fendley-Intriligator-Vafa (CFIV) index in two-dimensional N=(2,2) models is revisited. We address the problem of “elementary” (nontopological) excitations over a kink solution, in the one-kink sector (using the Wess-Zumino or Landau-Ginzburg models with two vacua as examples). In other words, we limit ourselves to the large-β limit. The excitation spectrum over the BPS-saturated at the classical level kink is discretized through a large box with judiciously chosen boundary conditions. The boundary conditions are designed in such a way that half of supersymmetry is preserved as well as the BPS kink itself, and relevant zero modes. The excitation spectrum acquires a mass gap. All (discretized) excited states enter in four-dimensional multiplets (two bosonic states + two fermionic). Their contribution to indCFIV vanishes level-by-level. The ground state contribution produces |indCFIV|=1.     

Self-assembled, helically stacked anionic aggregates of 2,5,8,11-tetra-tert-butylcycloocta[1,2,3,4-def;5,6,7,8-d'e'f']bisbiphenylene, stabilized by electrostatic interactions

Tetraanions of alkyl-substituted derivatives of cycloocta[1,2,3,4-def;5,6,7,8-d'e'f']bisbiphenylene (BPD) and their counter lithium cations self-assemble to form helically stacked assemblies, including a dimer, a trimer, and a tetramer. NMR self-diffusion measurements and unprecedented magnetic shielding effects for the sandwiched lithium cations support their aggregated nature. The D(2)-tetramer assembly is fully characterized by NMR spectroscopy, providing unequivocal evidence for a helix of four tetraanionic BPD layers with an estimated relative twist angle of about 45 degrees and interlayer spacing of ca. 4 A. The barrier for racemization through the in-plane inter-deck rotation is DeltaG(200)= 9.5 +/- 0.2 kcal mol(-1) in the dimer compared to >15 kcal mol(-1) in the tetramer.     

A theory of the J/gY→η(η′)γ decays

It is argued that the $\text{J}\text{gY}\text{→η(η′)γ}$ decay rates are directly calculable within quantum chromodynamics. The calculation of $\text{Γ(}\text{J}\text{Ψ}\text{→ηγ)}$ is most straightforward and involves no new hypotheses as compared to, say, the $\text{J}\text{Ψ}\text{→}\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}$ decay in detail earlier. To the contrary, evaluation of the $\text{J}\text{Ψ}\text{→η′γ}$ width puts on trial dynamical results concerning the η′ coupling to gluons. The latter depends crucially on non-perturbative power terms in the QCD sum rules. The calculated numbers for $\text{Γ(}\text{J}\text{Ψ}\text{→ηγ)}$ and $\text{Γ(}\text{J}\text{Ψ}\text{→η′γ)}$ agree well with the data.     

Use and misuse of QCD sum rules,factorization and related topics

The purpose of this paper is twofold. First, we are prompted by some recent publications to reply to the criticism of the QCD sum-rules approach contained therein. Hopefully, some of the discussion is of wider interest. In particular, we point out that the multi-gluon operators unlike the multi-quark ones, relevant to the sum rules, do not factorize at large N_c. This implies that the masterfield, even if it is found, will be of no immediate help in evaluating the quarkonium spectrum. Second, we derive new sum rules for light quarks which are sensitive to the mean intensity of the gluon field in the vacuum (the so-called gluon condensate, or 〈vac|G²|vac〉). New sum rules confirm the standard value of 〈vac|G²|vac〉. Some casual remarks on the π⁰ transitions into two virtual photons, π⁰ → γ^*γ^*, are also presented. Finally, we enumerate (in sect. 7) basic points of the sum-rule approach and discuss, im brief, the unsolved problems.     

Quantal problems with partial algebraization of the spectrum

We discuss a new class of spectral problems discovered recently which occupies an intermediate position between the exactly-solvable problems (e.g., harmonic oscillator) and all others. The problems belonging to this class are distinguished by the fact that a part of the eigenvalues, and eigenfunctions can be found algebraically, but not the whole spectrum. The reason explaining the existence of the quasi-exactly-solvable problems is a hidden dynamical symmetry present in the hamiltonian. For one-dimensional motion this hidden symmetry isSL(2,R). It is shown that other groups lead to a partial algebraization in multidimensional quantal problems. In particular,SL(2,R)×SL(2,R),SO(3) andSL(3,R) are relevant to two-dimensional motion inducing a class of quasi-exactly-solvable two-dimensional hamiltonians. Typically they correspond to systems in a curved space, but sometimes the curvature turns out to be zero. Graded algebras open the possibility of constructing quasi-exactlysolvable hamiltonians acting on multicomponent wave functions. For example, with a (non-minimal) superextension ofSL(2,R) we get a hamiltonian describing the motion of a spinor particle.