On the miracle of the Coleman-Glashow and other baryon mass formulas

Due to a new measurement of the Xi(0) mass,the Coleman-Glashow formula for the baryon octet e.m. masses (derived using unbroken SU(3) is satisfied to an extraordinary level of precision.The same unexpected precision exists for the Gell-Mann Okubo formula and for its octet-decuplet extension (G.Morpurgo,Phys.Rev.Lett. 68(1992)139).We show that the old question "why do they work so well?" is now answered by the general parameterization method.Comment: 12 pages,Late

The baryon octet magnetic moments to all orders in flavor breaking; an application to the problem of the strangeness in the nucleon

Using the general QCD parametrization (GP) we display the magnetic moments of the octet baryons including all flavor breaking terms to any order. The hierarchy of the GP parameters allows to estimate a parameter $g_{0}$ related to the quark loops contribution of the proton magnetic moment; its order of magnitude is predicted to be inside a comparatively small interval including the value given recently by Leinweber et al. by a lattice QCD calculationComment: (13 pages- version accepted for publication Phys.Rev.D. Note added in last section, 2 references adde

Chiral QCD, General QCD Parameterization and Constituent Quark Models

Several recent papers -using effective QCD chiral Lagrangians- reproduced results obtained with the general QCD parameterization (GP). These include the baryon 8+10 mass formula, the octet magnetic moments and the coincidental nature of the "perfect" -3/2 ratio between the magnetic moments of p and n. Although we anticipated that the GP covers the case of chiral treatments, the above results explicitly exemplify this fact. Also we show by the GP that -in any model or theory (chiral or non chiral) reproducing the results of exact QCD- the Franklin (Coleman Glashow) sum rule for the octet magnetic moments must be violated.Comment: 10 pages, Latex; abridged version (same results), removed some reference

Adams inequalities on measure spaces

In 1988 Adams obtained sharp Moser-Trudinger inequalities on bounded domains of R^n. The main step was a sharp exponential integral inequality for convolutions with the Riesz potential. In this paper we extend and improve Adams' results to functions defined on arbitrary measure spaces with finite measure. The Riesz fractional integral is replaced by general integral operators, whose kernels satisfy suitable and explicit growth conditions, given in terms of their distribution functions; natural conditions for sharpness are also given. Most of the known results about Moser-Trudinger inequalities can be easily adapted to our unified scheme. We give some new applications of our theorems, including: sharp higher order Moser-Trudinger trace inequalities, sharp Adams/Moser-Trudinger inequalities for general elliptic differential operators (scalar and vector-valued), for sums of weighted potentials, and for operators in the CR setting.Comment: To appear in Advances in Mathematics. 54 Pages, minor changes and corrections in v2 (page 1, proof of Corollary 13, some typos). In v3 the more relevant changes/corrections were made on pages 9, 10, 27, 32, 34, 36, 40, 41, 47. Minor corrections in v

A relation between the charge radii of \pi^{+},\K^{+},K^{o} derived by the general QCD parametrization

We derive,using the general QCD parametrization,the approximate relation r^{2}(\pi^{+}) - r^{2}(K^(+)) approximately equal to -r^{2}(K^(o), where the r's are the charge radii.The relation is satisfied but the experimental errors are still sizeable.The derivation is similar to (but even simpler than) that for r^{2}(p) -r^{2}(n) approximately equal to r^{2}({\Delta})[Phys.Lett.B 448,107 (1999)].Comment: latex,5 pages,no figures.To appear in Europhysics Letters [two typos in Abstract corrected