The Fragmented Glueball: A Personal View

A coupled-channel analysis has been performed to identify the spectrum of scalar mesons. The data include BESIII data on radiative J/ψ decays into π0π0, KS KS, ηη, and ωϕ, 15 Dalitz plots from ¯N annihilation at rest at LEAR, the CERN-Munich multipoles for ππ elastic scattering, the S-wave from BNL data on ππ scattering into KS KS, from GAMS data on ππ π0π0; ηη, and ηη', and NA48/2 data on low-mass ππ interactions from K± → ππe±v decays. The analysis reveals the existence of ten scalar isoscalar resonances. The resonances can be grouped into two classes: resonances with a large SU(3) singlet component and those with a large octet component. The production of isoscalar resonances with a large octet component should be suppressed in radiative J/ψ decays. However, in a limited mass range centered at 1900MeV, these mesons are produced abundantly. Mainly-singlet scalar resonances are produced over the full mass range but with larger intensity at 1900MeV. The total scalar isoscalar yield in radiative decays into scalar mesons shows a clear peak which is interpreted as the scalar glueball of lowest mass.

The $$D_s^+ \rightarrow a_0(980) e^+ \nu _e$$ reaction and the $$a_0(980)-f_0(980)$$ mixing

We perform a study of the $$D_s^+ \rightarrow a_0(980)(f_0(980)) e^+ \nu _e$$ D s + → a 0 ( 980 ) ( f 0 ( 980 ) ) e + ν e reactions investigating the different sources of isospin violation which make the production of the $$a_0(980)$$ a 0 ( 980 ) possible. We find that loops involving kaons in the production mechanism provide a source of isospin violation since they do not cancel due to the different mass of charged and neutral kaons, but we also find that the main source comes from the breaking of isospin in the meson-meson transition T matrices, which contain information on the nature of the low lying scalar mesons. The reaction is thus very sensitive to the nature of the $$a_0(980)$$ a 0 ( 980 ) and $$f_0(980)$$ f 0 ( 980 ) resonances. Our results are consistent with the present upper bound for $$a_0(980)$$ a 0 ( 980 ) production and only a factor three smaller, indicating that future runs with more statistics should find actual numbers for this reaction from where we can learn more about the origin of the scalar resonances and their nature.

Non-perturbative aspects of gauge theories from gauge-gravity dualities

In this Ph.D. Thesis we consider two speci˝c supergravities which are well-established within the literature on holography, and which are known to provide the low-energy e˙ective description of either superstring theory or M-theory: the six-dimensional half-maximal theory of Romans, and the maximal supergravity in seven dimensions.We implement their dimensional reduction by compactifying on an S1 and T 2, respectively, to obtain a ˝ve-dimensional sigma-model coupled to grav-ity. Spectra of bosonic excitations are computed numerically by considering ˝eld ˛uctuations on background geometries which holographically realise con-˝nement. We furthermore propose a diagnostic tool to detect mixing e˙ects between scalar resonances and the pseudo-NambuGoldstone boson associated with spontaneous breaking of conformal invariance: the dilaton. This test con-sists of neglecting a certain component of the spin-0 ˛uctuation variables, ef-fectively disregarding their back-reaction on the underlying geometry; where discrepancies arise compared to the complete calculation we infer dilaton mix-ing. For both theories this analysis evinces a parametrically light dilaton.For each supergravity we uncover a tachyonic instability within their param-eter space; motivated by these pathological ˝ndings we proceed to conduct an investigation into their respective phase structures, reasoning that there must necessarily exist some mechanism by which these instabilities are rendered phys-ically inaccessible. We compile a comprehensive catalogue of geometrically dis-tinct backgrounds admissible within each theory, and derive general expressionsfor their holographically renormalised free energy F. Another numerical rou-tine is employed to systematically extract data for some special deformationparameters, and F is plotted in units of an appropriate universal scale.Our analysis proves fruitful: each theory exhibits clear evidence of a ˝rst-order phase transition which induces the spontaneous decompacti˝cation of the shrinking circular dimension before the instability manifests, favouring instead a class of singular solutions. The aforementioned dilaton resonance appears only along a metastable portion of the branch of con˝ning backgrounds.

Masses of Charmed and Bottom Tetraquarks in the Non-Relativistic Quark Model

Heavy tetraquark states are studied within the diquark-antidiquark picture in the framework of a simple constituent quark model. Considering hyperfine spin and isospin interactions, we predict the masses of the scalar diquarks and of the open and hidden charmed and bottom scalar tetraquarks. Our results indicate the scalar resonances [Formula: see text] and [Formula: see text] have a sizable tetraquark amount in their wave function, while it turns out the scalar state [Formula: see text] should not be considered as being predominately diquark-antidiquark bound states.