Observation of the Heavy Baryons Sigma b and Sigma b*

We report an observation of new bottom baryons produced in pp collisions at the Tevatron. Using 1.1 fb(-1) of data collected by the CDF II detector, we observe four Lambda b 0 pi+/- resonances in the fully reconstructed decay mode Lambda b 0-->Lambda c + pi-, where Lambda c+-->pK* pi+. We interpret these states as the Sigma b(*)+/- baryons and measure the following masses: m Sigma b+=5807.8 -2.2 +2.0(stat.)+/-1.7(syst.) MeV/c2, m Sigma b- =5815.2+/-1.0(stat.)+/-1.7(syst.) MeV/c2, and m(Sigma b*)-m(Sigma b)=21.2-1.9 +2.0(stat.)-0.3+0.4(syst.) MeV/c2.     

Dirac Sigma Models

We introduce a new topological sigma model, whose fields are bundle maps from the tangent bundle of a 2-dimensional world-sheet to a Dirac subbundle of an exact Courant algebroid over a target manifold. It generalizes simultaneously the (twisted) Poisson sigma model as well as the G/G-WZW model. The equations of motion are satisfied, iff the corresponding classical field is a Lie algebroid morphism. The Dirac Sigma Model has an inherently topological part as well as a kinetic term which uses a metric on worldsheet and target. The latter contribution serves as a kind of regulator for the theory, while at least classically the gauge invariant content turns out to be independent of any additional structure. In the (twisted) Poisson case one may drop the kinetic term altogether, obtaining the WZ-Poisson sigma model; in general, however, it is compulsory for establishing the morphism property.     

Poisson Sigma Model on the Sphere

We evaluate the path integral of the Poisson sigma model on the sphere and study the correlators of quantum observables. We argue that for the path integral to be well-defined the corresponding Poisson structure should be unimodular. The construction of the finite dimensional BV theory is presented and we argue that it is responsible for the leading semiclassical contribution. For a (twisted) generalized Kähler manifold we discuss the gauge fixed action for the Poisson sigma model. Using the localization we prove that for the holomorphic Poisson structure the semiclassical result for the correlators is indeed the full quantum result.     

Sigma Terms of Light-Quark Hadrons

A calculation of the current-quark mass dependence of hadron masses can help in using observational data to place constraints on the variation of nature’s fundamental parameters. A hadron’s σ-term is a measure of this dependence. The connection between a hadron’s σ-term and the Feynman-Hellmann theorem is illustrated with an explicit calculation for the pion using a rainbow-ladder truncation of the Dyson-Schwinger equations: in the vicinity of the chiral limit σ_π = m_π/2. This truncation also provides a decent estimate of σ_ρ because the two dominant self-energy corrections to the ρ-meson’s mass largely cancel in their contribution to σ_ρ. The truncation is less accurate for the ω, however, because there is little to compete with an ω → ρπ self-energy contribution that magnifies the value of σ_ω by ≲25%. A Poincaré-covariant Faddeev equation, which describes baryons as composites of confined-quarks and -nonpointlike-diquarks, is solved to obtain the current-quark mass dependence of the masses of the nucleon and Δ, and thereby σ_N and σ_Δ. This “quark-core” piece is augmented by the “pion cloud” contribution, which is positive. The analysis yields σ_N ≃ 60 MeV and σ_Δ ≃ 50 MeV.     

CP Violation in the Linear Sigma Model

Motivated by the possibility of the formation of CP-odd domains in heavy ion collisions, we investigate the effects of CP violation on the chiral transition within the linear sigma model with two flavors of quarks. We also study how the CP-odd system is affected by the presence of a strong magnetic field, that is presumably generated in a non-central heavy ion collision. We find that both ingredients play an important role, influencing drastically the nature of the phase transition and the critical temperature.     

On the AKSZ Formulation of the Poisson Sigma Model

We review and extend the Alexandrov–Kontsevich–Schwarz–Zaboronsky construction of solutions of the Batalin–Vilkovisky classical master equation. In particular, we study the case of sigma models on manifolds with boundary. We show that a special case of this construction yields the Batalin–Vilkovisky action functional of the Poisson sigma model on a disk. As we have shown in a previous paper, the perturbative quantization of this model is related to Kontsevich's deformation quantization of Poisson manifolds and to his formality theorem. We also discuss the action of diffeomorphisms of the target manifolds.     

Phase Structure of the Semi-Classical Linear Sigma Model

In order to establish a quantitative framework for assessing the reliability of dynamical simulations of DCC phenomena with the semi-classical mean-field treatment of the linear model, we determine and discuss the phase structure implied by this approximate treatment. While the results appear to be physically reasonable for realistic scenarios, where the pion mass and the volume are finite, the approximate treatment might be less appropriate for idealized scenarios involving small masses and large volumes.     

Sigma models in the presence of dynamical point-like defects

Point-like Liouville integrable dynamical defects are introduced in the context of the Landau–Lifshitz and Principal Chiral (Faddeev–Reshetikhin) models. Based primarily on the underlying quadratic algebra we identify the first local integrals of motion, the associated Lax pairs as well as the relevant sewing conditions around the defect point. The involution of the integrals of motion is shown taking into account the sewing conditions.