The anomalous chiral perturbation theory meson Lagrangian to order p6p^6 revisited

We present a revised and extended construction of the mesonic Lagrangian density in chiral perturbation theory (ChPT) at order $p^6$ in the anomalous (or epsilon) sector, ${\cal{L}}_{6,\epsilon}$. After improving several aspects of the strategy we used originally, i.e., a more efficient application of partial integration, the implementation of so-called Bianchi identities, and additional trace relations, we find the new monomial sets to include 24 $SU(N_f)$, 23 SU(3), and 5 SU(2) elements. Furthermore, we introduce 8 supplementary terms due to the extension of the chiral group to $SU(N_f)_L \times SU(N_f)_R \times U(1)_V$.Comment: 21 pages, Latex, using RevTe

Corrections to Sirlin's Theorem in O(p6)O(p^6) Chiral Perturbation Theory

We present the results of the first two-loop calculation of a form factor in full $SU(3) \times SU(3)$ Chiral Perturbation Theory. We choose a specific linear combination of $\pi^+, K^+, K^0$ and $K\pi$ form factors (the one appearing in Sirlin's theorem) which does not get contributions from order $p^6$ operators with unknown constants. For the charge radii, the correction to the previous one-loop result turns out to be significant, but still there is no agreement with the present data due to large experimental uncertainties in the kaon charge radii.Comment: 6 pages, Latex, 2 LaTeX figure

Physical Nucleon Properties from Lattice QCD

We demonstrate that the extremely accurate lattice QCD data for the mass of the nucleon recently obtained by CP-PACS, combined with modern chiral extrapolation techniques, leads to a value for the mass of the physical nucleon which has a systematic error of less than one percent.Comment: 4 pages, 2 figure

K_L \ra \mu^\pm e^\mp \nu \overline{\nu} as background to K_L \ra \mu^\pm e^\mp

We consider the process K_L \ra \mu^\pm e^\mp \nu \overline{\nu} at next to leading order in chiral perturbation theory. This process occurs in the standard model at second order in the weak interaction and constitutes a potential background in searches for new physics through the modes K_L \ra \mu^\pm e^\mp. We find that the same cut, $M_{\mu e}>489$~MeV, used to remove the sequential decays K_{l3}\ra \pi_{l2} pushes the B(K_L \ra \mu^\pm e^\mp \nu \overline{\nu}) to the $10^{-23}$ level, effectively removing it as a background.Comment: 8 pages, LaTeX, 1 figure appended as postscript file after \end{document}. Fermilab-Pub-93/024-

Enhanced chiral logarithms in partially quenched QCD

I discuss the properties of pions in ``partially quenched'' theories, i.e. those in which the valence and sea quark masses, $m_V$ and $m_S$, are different. I point out that for lattice fermions which retain some chiral symmetry on the lattice, e.g. staggered fermions, the leading order prediction of the chiral expansion is that the mass of the pion depends only on $m_V$, and is independent of $m_S$. This surprising result is shown to receive corrections from loop effects which are of relative size $m_S \ln m_V$, and which thus diverge when the valence quark mass vanishes. Using partially quenched chiral perturbation theory, I calculate the full one-loop correction to the mass and decay constant of pions composed of two non-degenerate quarks, and suggest various combinations for which the prediction is independent of the unknown coefficients of the analytic terms in the chiral Lagrangian. These results can also be tested with Wilson fermions if one uses a non-perturbative definition of the quark mass.Comment: 14 pages, 3 figures, uses psfig. Typos in eqs (18)-(20) corrected (alpha_4 is replaced by alpha_4/2

Isospin Violation in Chiral Perturbation Theory and the Decays \eta \ra \pi \ell \nu and \tau \ra \eta \pi \nu

I discuss isospin breaking effects within the standard model. Chiral perturbation theory presents the appropriate theoretical framework for such an investigation in the low--energy range. Recent results on the electromagnetic contributions to the masses of the pseudoscalar mesons and the $K_{\ell 3}$ amplitudes are reported. Using the one--loop formulae for the $\eta_{\ell 3}$ form factors, rather precise predictions for the decay rates of $\eta \rightarrow \pi \ell \nu$ can be obtained. Finally, I present an estimate of the \tau \ra \eta \pi \nu branching ratio derived from the dominant meson resonance contributions to this decay.Comment: 10 pages, latex, one figure available upon reques

Contributions of order O(mquark2){\cal O}(m_{\rm quark}^2) to Kℓ3K_{\ell 3} form factors and unitarity of the CKM matrix

The form factors for the $K_{\ell 3}$ semileptonic decay are computed to order $O(p^4)$ in generalized chiral perturbation theory. The main difference with the standard $O(p^4)$ expressions consists in contributions quadratic in quark masses, which are described by a single divergence-free low-energy constant, $A_3$. A new simultaneous analysis is presented for the CKM matrix element $V_{us}$, the ratio $F_K/F_{\pi}$, $K_{\ell 3}$ decay rates and the scalar form factor slope $\lambda_0$. This framework easily accommodates the precise value for $V_{ud}$ deduced from superallowed nuclear $\beta$-decays

Chiral condensate thermal evolution at finite baryon chemical potential within Chiral Perturbation Theory

We present a model independent study of the chiral condensate evolution in a hadronic gas, in terms of temperature and baryon chemical potential. The meson-meson interactions are described within Chiral Perturbation Theory and the pion-nucleon interaction by means of Heavy Baryon Chiral Perturbation Theory, both at one loop, and nucleon-nucleon interactions can be safely neglected within our hadronic gas domain of validity. Together with the virial expansion, this provides a systematic expansion at low temperatures and chemical potentials, which includes the physical quark masses. This can serve as a guideline for further studies on the lattice. We also obtain estimates of the critical line of temperature and chemical potential where the chiral condensate melts, which systematically lie somewhat higher than recent lattice calculations but are consistent with several hadronic models. We have also estimated uncertainties due to chiral parameters, heavier hadrons and higher orders through unitarized Chiral Perturbation Theory.Comment: 15 pages, 15 figures, 3 tables, ReVTeX. Version to appear in Phys. Rev. D. References added. More conservative estimate of applicability domain, with new figure. More detailed explanation of final results with two more figures. Results unchange

Baryon chiral perturbation theory with virtual photons and leptons

We construct the general pion-nucleon SU(2) Lagrangian including both virtual photons and leptons for relativistic baryon chiral perturbation theory up to fourth order. We include the light leptons as explicit dynamical degrees of freedom by introducing new building blocks which represent these leptons.Comment: 11 page

Sigma-term physics in the perturbative chiral quark model

We apply the perturbative chiral quark model (PCQM) at one loop to analyse meson-baryon sigma-terms. Analytic expressions for these quantities are obtained in terms of fundamental parameters of low-energy pion-nucleon physics (weak pion decay constant, axial nucleon coupling, strong pion-nucleon form factor) and of only one model parameter (radius of the nucleonic three-quark core). Our result for the piN sigma term of about 45 MeV is in good agreement with the value deduced by Gasser, Leutwyler and Sainio using dispersion-relation techniques and exploiting the chiral symmetry constraints.Comment: 19 pages, LaTeX-file, 2 Figure