The Skyrme Model Revisited: An Effective Theory Approach and Application to the Pentaquarks

The Skyrme model is reconsidered from an effective theory point of view. Starting with the most general Lagrangian up to including terms of order $p^4$, $N_c$ and $\delta m^2$ ($\delta m\equiv m_s-m$), we obtain new interactions, which have never been discussed in the literature. We obtain the parameter set best fitted to the low-lying baryon masses by taking into account the representation mixing up to $\bm{27}$. A prediction for the mainly anti-decuplet excited nucleon $N'$ and $\Sigma'$ is given.Comment: talk given at International Workshop PENTAQUARK04, July 20-23 (2004) at SPring-8, based on the work (hep-ph/0410145) done in collaboration with Y. Mitsunari and N. Yamashita; 8 page

Apparently noninvariant terms of U(N)×U(N)U(N)\times U(N) nonlinear sigma model in the one-loop approximation

We show how the Apparently Noninvariant Terms (ANTs), which emerge in perturbation theory of nonlinear sigma models, are consistent with the nonlinearly realized symmetry by employing the Ward-Takahashi identity (in the form of an inhomogeneous Zinn-Justin equation). In the literature the discussions on ANTs are confined to the SU(2) case. We generalize them to the U(N) case and demonstrate explicitly at the one-loop level that despite the presence of divergent ANTs in the effective action of the "pions", the symmetry is preserved.Comment: two paragraphs added in Introduction, typos in Eqs. fixe

More about the Wilsonian analysis on the pionless NEFT

We extend our Wilsonian renormalization group (RG) analysis on the pionless nuclear effective theory (NEFT) in the two-nucleon sector in two ways; on the one hand, (1) we enlarge the space of operators up to including those of $\mathcal{O}(p^4)$ in the $S$ waves, and, on the other hand, (2) we consider the RG flows in higher partial waves ($P$ and $D$ waves). In the larger space calculations, we find, in addition to nontrivial fixed points, two ``fixed lines'' and a ``fixed surface'' which are related to marginal operators. In the higher partial wave calculations, we find similar phase structures to that of the $S$ waves, but there are \textit{two} relevant directions in the $P$ waves at the nontrivial fixed points and \textit{three} in the $D$ waves. We explain the physical meaning of the $P$-wave phase structure by explicitly calculating the low-energy scattering amplitude. We also discuss the relation between the Legendre flow equation which we employ and the RG equation by Birse, McGovern, and Richardson, and possible implementation of Power Divergence Subtraction (PDS) in higher partial waves.Comment: 39 pages, 5 figures, the final versio

A study of the origin of Scottish Presbyterianism (1560-1638)

This dissertation seeks to explore the origin of Presbyterianism in Scotland. Hence, every effort has been made to describe the process of the emergence of the Presbyterian government and its development during the period from the 1520s to the point before the Second Reformation of 1638. This study covers the following main aspects: first, the goals of the Scottish Reformation; secondly, the grounds on which the General Assembly championed the Presbyterian system; thirdly, the process of how the Second Book of Discipline was formed; fourthly, the contents of the Second Book of Discipline; and fifthly, how presbyteries developed between 1581 and 1638. It should be remembered, of course, that as a result of the government’s overall preference for an Episcopalian system, the General Assembly’s desire for Presbyterianism met with resistance and on occasions, substantial setbacks until final success was achieved in 1690. This study aims to trace the emergence and development of Presbyterianism in Scotland. As such, chapters follow an essentially chronological pattern, covering the key persons, pressures, struggles and events which deeply affected the way in which the Reformation succeeded after several attempts to overcome the problems for introducing the Presbyterian system in the Church. Several approaches are employed in this study. The modern approach to the Scottish Reformation is various indeed. W. Ian P. Hazlett offers the best useful summary concerning its method of approach classified into eight types: first, Catholic perspectives on the Scottish Reformation; secondly, Lutheran roots and emphasis on the Scottish Reformation; thirdly, influence of Calvinism on Presbyterian church polity; fourthly, the simple political motivation for the Reformation; fifthly, Queen Mary’s religious policy; sixthly, re-examination from contemporary local and urban contexts; seventhly, the Gaelic perspective on the Scottish Reformation; and eighthly, application of Max Weber’s thesis of the pairing of Calvinism and Capitalism for the Scottish Reformation. This study attempts to synthesize the third, fourth and sixth approaches mentioned in Hazlett’s classification. In the study of church polity, we have to identify what were the ‘means’ and ‘ends’ of that polity. These are inevitably related to each other, as the form of church government (such as its ‘system’ or ‘construction’) is designed as a means to accomplish particular ends. It is important therefore, to identify the goals of the Reformation before we proceed to discuss the form of Presbyterian church government which grew out of it. Hence, chapter one deals with the primary goals at the time of the Reformation in connection with the church government which the Reformers introduced. Subsequently, chapter two describes the process of how the Second Book of Discipline was formed and what its contents were. The third chapter focuses on the process of the institution of the Presbyterian government after its approval by the General Assembly in 1578. Finally, chapter four focuses on the development of the presbyteries between 1581 and 1638. This study will synthesize various views on early Presbyterianism in Scotland up to 1638 to provide a historically reliable account of this formative period in Scottish church history. (quotation from 'Introduction' of this thesis