K0ΛK^0\Lambda Photoproduction with Nucleon Resonances

We investigate the reaction mechanism of $K^0 \Lambda$ photoproduction off the neutron target, i.e., $\gamma n \to K^0 \Lambda$, in the range of $W\approx 1.6-2.2$ GeV. We employ an effective Lagrangian method at the tree-level Born approximation combining with a Regge approach. As a background, the $K^*$-Reggeon trajectory is taken into account in the $t$ channel and $\Lambda$ and $\Sigma$ hyperons in the $u$-channel Feynman diagram. In addition, the role of various nucleon resonances listed in the Particle Data Group (PDG) is carefully scrutinized in the $s$ channel where the resonance parameters are extracted from the experimental data and constituent quark model. We present our numerical results of the total and differential cross sections and compare them with the recent CLAS data. The effect of the narrow nucleon resonance $N(1685,1/2^+)$ on cross sections is studied in detail and it turns out that its existence is essential in $K^0 \Lambda$ photoproduction to reproduce the CLAS data.Comment: 4 pages, 3 figures, Proceedings of "8th International Conference on Quarks and Nuclear Physics (QNP2018)", November 13-17, 2018, Tsukuba, Japa

Polygonal words in free groups

A longstanding question of Gromov asks whether every one-ended word-hyperbolic group contains a subgroup isomorphic to the fundamental group of a closed hyperbolic surface. An infinite family of word-hyperbolic groups can be obtained by taking doubles of free groups amalgamated along words that are not proper powers. We define a set of polygonal words in a free group of finite rank, and prove that polygonality of the amalgamating word guarantees that the associated square complex virtually contains a $\pi_1$-injective closed surface. We provide many concrete examples of classes of polygonal words. For instance, in the case when the rank is 2, we establish polygonality of words without an isolated generator, and also of almost all simple height 1 words, including Baumslag--Solitar relator $a^p (a^q)^b$ for $pq\ne0$.Comment: 23 pages, 8 figure