Two--loop integrals in chiral perturbation theory

We consider chiral perturbation theory in the meson sector at order $E^6$. In the terminology of the external field technique, the two--loop graphs so generated are of the sunset type. We discuss the evaluation of several of these in the case where the masses of the particles running in the loops are equal. In particular, we present integral representations that are suitable for the evaluation of diagrams in kinematical regions where branch points and cuts are present.Comment: 28 pages, LaTeX, 5 figures embedded with epsf.st

Differential Expression Of Gap Junction mRNAs And Proteins In The Developing Murine Kidney And In Experimentally Induced Nephric Mesenchymes

The expression of three gap junction (GJ) proteins, alpha-1 (Cx43), beta-1 (Cx32), and beta-2 (Cx26), and their transcripts were examined during the ontogeny of the mouse and rat kidney. These proteins were expressed in two non-overlapping patterns. The alpha-1 GJ protein was first observed in mesenchymal cells in the 12-day mouse kidney. By day 14 and thereafter, the ai protein was detected in the transient S-shaped bodies, but not in the podocytes of the maturing glomeruli. After birth the antigen was retained in a small subset of secretory tubules.The beta-1 and beta-2 GJ proteins were similar in their developmental patterns. They were first detected in a small subset of secretory tubules in the subcortical zone of day 17 embryos. These tubules were identified by immunohistochemical markers to be proximal. At birth, practically all proximal tubules expressed the two antigens.This analysis of GJ proteins was consistent with the results of S1 nuclease protection assays showing that, while the alpha-1 mRNA appeared early during kidney development and declined around birth, the two beta mRNAs appeared later and became intensified during the last days of intrauterine development.In experimentally induced metanephric mesenchymes, a transient expression of the alpha-1 GJ protein was seen during the segregation of the tubular anlagen. beta-1 and beta-2 GJ proteins were not detected in such induced mesenchymes cultivated up to 7 days.These observations provide evidence for the cell-specific utilization of different GJ genes during different stages of kidney organogenesis. The alpha-1 gene is activated during the early segregation of the secretory tubule and might contribute to its compartmentalization, while the beta-1 and beta-2 gene products are not detected until advanced stages of development. The latter gene products might be correlated with the physiological activity of the proximal tubules in vivo, as they are not expressed in experimentally induced tubules detectable with markers for proximal tubules

Chiral Condensates in Quark and nuclear Matter

We present a novel treatment for calculating the in-medium quark condensates. The advantage of this approach is that one does not need to make further assumptions on the derivatives of model parameters with respect to the quark current mass. The normally accepted model-independent result in nuclear matter is naturally reproduced. The change of the quark condensate induced by interactions depends on the incompressibility of nuclear matter. When it is greater than 260 MeV, the density at which the condensate vanishes is higher than that from the linear extrapolation. For the chiral condensate in quark matter, a similar model-independent linear behavior is found at lower densities, which means that the decreasing speed of the condensate in quark matter is merely half of that in nuclear matter if the pion-nucleon sigma commutator is six times the average current mass of u and d quarks. The modification due to QCD-like interactions is found to slow the decreasing speed of the condensate, compared with the linear extrapolation.Comment: 12 pages, 7 figures, revtex4 styl

The Contribution of the Light Quark Condensate to the Pion-Nucleon Sigma Term

There has been a discrepancy between values of the pion-nucleon sigma term extracted by two different methods for many years. Analysis of recent high precision pion-nucleon data has widened the gap between the two determinations. It is argued that the two extractions correspond to different quantities and that the difference between them can be understood and calculated.Comment: Modern Physics Letters A (in press