Highlights of Recent Results with Clas

Recent results on the study of the electromagnetic structure of nucleon resonances, the spin structure of proton and neutrons at small and intermediate photon virtualities, and the search for exotic pentaquark baryons are presented.Comment: 12 pages, 8 figures, invited talk at MENU2004, Beijin

Baryon octupole moments

We report on a calculation of higher electromagnetic multipole moments of baryons in a non-covariant quark model approach. The employed method is based on the underlying spin-flavor symmetry of the strong interaction and its breaking.We present results on magnetic octupole moments of decuplet baryons and discuss their implications.Comment: 3 page

Distributional representations and dominance of a L\'{e}vy process over its maximal jump processes

Distributional identities for a L\'evy process $X_t$, its quadratic variation process $V_t$ and its maximal jump processes, are derived, and used to make "small time" (as $t\downarrow0$) asymptotic comparisons between them. The representations are constructed using properties of the underlying Poisson point process of the jumps of $X$. Apart from providing insight into the connections between $X$, $V$, and their maximal jump processes, they enable investigation of a great variety of limiting behaviours. As an application, we study "self-normalised" versions of $X_t$, that is, $X_t$ after division by $\sup_{0<s\le t}\Delta X_s$, or by $\sup_{0<s\le t}| \Delta X_s|$. Thus, we obtain necessary and sufficient conditions for $X_t/\sup_{0<s\le t}\Delta X_s$ and $X_t/\sup_{0<s\le t}| \Delta X_s|$ to converge in probability to 1, or to $\infty$, as $t\downarrow0$, so that $X$ is either comparable to, or dominates, its largest jump. The former situation tends to occur when the singularity at 0 of the L\'evy measure of $X$ is fairly mild (its tail is slowly varying at 0), while the latter situation is related to the relative stability or attraction to normality of $X$ at 0 (a steeper singularity at 0). An important component in the analyses is the way the largest positive and negative jumps interact with each other. Analogous "large time" (as $t\to \infty$) versions of the results can also be obtained.Comment: Published at http://dx.doi.org/10.3150/15-BEJ731 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Dibaryon Condensate in Nuclear Matter and Neutron Stars: Exact Analysis in One-Dimensional Models

We investigate dense nuclear matter with a dibaryon Bose-Einstein condensate as a possible intermediate state before the quark-gluon phase transition. An exact analysis of this state of matter is presented in a one-dimensional model. The analysis is based on a reduction of the quantization rules for the N-body problem to N coupled algebraic transcendental equations. We observe that when the Fermi momentum approaches the resonance momentum, the one-particle distribution function increases near the Fermi surface. When the Fermi momentum is increased beyond the resonance momentum, the equation of state becomes softer. The observed behavior can be interpreted in terms of formation of a Bose-Einstein condensate of two-fermion resonances (dibaryons). In cold nuclear matter, it should occur if 2(m_N + epsilon_F) is greater or equal to m_D, where m_N and m_D are respectively the nucleon and dibaryon masses and epsilon_F is the nucleon Fermi energy.Comment: 25 pages, LaTeX, 2 Postscript figures, to appear in Annals of Physic