On the Corrections to Dashen's Theorem

The electromagnetic corrections to the masses of the pseudoscalar mesons $\pi$ and $K$ are considered. We calculate in chiral perturbation theory the contributions which arise from resonances within a photon loop at order $O(e^2 m_q)$. Within this approach we find rather moderate deviations to Dashen's theorem.Comment: 14 pages, sligthly enlarged version; a numerical error is corrected and the embedding of the figures is improved. The complete paper, including figures, is also available via anonymous ftp at ftp://www-ttp.physik.uni-karlsruhe.de/ , or via www at http://www-ttp.physik.uni-karlsruhe.de/cgi-bin/preprints/; to be published in Phys.Rev.

Resonance Contributions to the Electromagnetic Low Energy Constants of Chiral Perturbation Theory

The effective chiral Lagrangian of the strong and electromagnetic interactions of the pseudoscalar mesons at low energies depends on a set of low energy constants. We determine the contributions to the electromagnetic coupling constants at order $O(e^2 p^2)$, which arise from resonances within a photon loop. We give some implications of our results, in particular we discuss in detail the effects on the corrections to Dashen's theorem.Comment: LaTex (uses epsfig.sty), 35 pages including 3 Postscript figures. The complete paper is also available via anonymous ftp at ftp://www-ttp.physik.uni-karlsruhe.de/ , or via www at http://www-ttp.physik.uni-karlsruhe.de/cgi-bin/preprints/ ; slightly enlarged version. Accepted for publication in Nucl. Phys.

Virtual Photons in Chiral Perturbation Theory

In the framework of chiral perturbation theory virtual photons are included. We calculate the divergences of the generating functional to one loop and determine the structure of the local action that incorporates the counterterms which cancel the divergences. As an application we discuss the corrections to Dashen's theorem at order [e^2*m(quark)].Comment: 19 pages , LaTex, 1 figure appended as PostScript file, (little corrections on the pages 8 and 17 - the physical results are not affected), BUTP-94/

Rho - omega mixing in chiral perturbation theory

In order to calculate the rho - omega mixing we extend the chiral couplings of the low-lying vector mesons in chiral perturbation theory to a lagrangian that contains two vector fields. We determine the momentum dependence of the two-point function and recover an earlier result for the on-shell expression. We discuss the off-shell behaviour of the mixing.Comment: Latex, 12 pages. The paper is also available via anonymous ftp at (129.13.102.139) ftp://ttpux2.physik.uni-karlsruhe.de/ttp95-08/ttp95-08.ps, or via www at http://ttpux2.physik.uni-karlsruhe.de/cgi-bin/preprints

Extension of the Chiral Perturbation Theory Meson Lagrangian to Order P6P^6

We have derived the most general chirally invariant Lagrangian ${\cal L}_6$ for the meson sector at order $p^6$. The result provides an extension of the standard Gasser-Leutwyler Lagrangian ${\cal L}_4$ to one higher order, including as well all the odd intrinsic parity terms in the Lagrangian. The most difficult part of the derivation was developing a systematic strategy so as to get all of the independent terms and eliminate the redundant ones in an efficient way. The 'equation of motion' terms, which are redundant in the sense that they can be transformed away via field transformations, are separated out explicitly. The resulting Lagrangian has been separated into groupings of terms contributing to increasingly more complicated processes, so that one does not have to deal with the full result when calculating $p^6$ contributions to simple processes.Comment: 59 pages in LaTex, using RevTex macro, TRIUMF preprint TRI-PP-94-6

Tau Decays and Chiral Perturbation Theory

In a small window of phase space, chiral perturbation theory can be used to make standard model predictions for tau decays into two and three pions. For $\tau \to 2\pi \nu_\tau$, we give the analytical result for the relevant form factor $F_V$ up to two loops, then calculate the differential spectrum and compare with available data. For $\tau \to 3 \pi \nu_\tau$, we have calculated the hadronic matrix element to one loop. We discuss the decomposition of the three pion states into partition states and we give detailed predictions for the decay in terms of structure functions. We also compare with low energy predictions of meson dominance models. Overall, we find good agreement, but also some interesting discrepancies, which might have consequences beyond the limit of validity of chiral perturbation theory.Comment: 39 pages, Latex, including 8 Postscript figures. The complete paper is also available via anonymous ftp at ftp://www-ttp.physik.uni-karlsruhe.de/ , or via www at http://www-ttp.physik.uni-karlsruhe.de/cgi-bin/preprint