Extracting m_s From Flavor Breaking in Hadronic Tau Decays

New finite energy sum rules (FESR's) for extracting m_s from hadronic tau decay data are constructed which (1) significantly reduce potential theoretical uncertainties present in existing sum rule analyses and (2) remove problems associated with both the poor convergence of the OPE representation of the longitudinal part of the $us$ vector and axial vector correlators and the large statistical errors in the $us$ spectral data above the K^* region.Comment: 4 pages, 1 figure. Report of presentations to International Conference on Quark Nuclear Physics, Adelaide, Feb. 21-25, 2000, 16th International Conference on Problems in Few-Body Physics, Taipei, March 6-10, 2000, and 7th Conference on the Intersections of Particle and Nuclear Physics, Quebec City, May 22-28, 200

Two-loop analysis of axial vector current propagators in chiral perturbation theory

We perform a calculation of the isospin and hypercharge axial vector current propagators [ΔA3μν(q) and ΔA8μν(q)] to two loops in SU(3)×SU(3) chiral perturbation theory. A large number of O(p6) divergent counterterms are fixed, and complete two-loop renormalized expressions for the pion and eta masses and decay constants are obtained. The calculated isospin and hypercharge axial vector polarization functions are used as input in new chiral sum rules, valid to second order in the light quark masses. Some phenomenological implications of these sum rules are considered

Final State Interactions and Khuri-Treiman Equations in η → 3π decays

Using extended Khuri-Treiman equations, we evaluate the final state interactions due to two-pion rescatterings to the decays η → (π^0)(π^+)(π^-) and η → (π^0)(π^0)(π^0). As subtraction to the dispersion relation we take the one-loop chiral perturbation theory result of Gasser and Leutwyler. The calculated corrections are moderate and amount to about 14% in the amplitude at the center of the decay region. A careful analysis of the errors inherent to our approach is given. As a consequence, the experimental rate of the decay can only be reproduced if the double quark mass ratio Q^(-2) ≡ (m_d - m_u)/(m_s - m̂) * (m_d + m_u)/(m_s + m̂) is increased from the usual value of 1/(24.1)^2 to 1/(22.4 ± 0.9)^2. We have also calculated the ratio of the rates of the two decays and various Dalitz Plot parameters. In particular, the linear slope a in the charged decay is different from the one-loop value and agrees better with experiment

Systematic 1/M expansion for spin 3/2 particles in baryon chiral perturbation theory

Starting from a relativistic formulation of the pion-nucleon-delta system, the most general structure of 1/M corrections for a heavy baryon chiral lagrangian including spin 3/2 resonances is given. The heavy components of relativistic nucleons and delta fields are integrated out and their contributions to the next-to-leaing order lagrangians are constructed explicitly. The effective theory obtained admits a systematic expansion in terms of soft momenta, the pion mass $m_\pi$ and the delta-nucleon mass difference $\Delta$. As an application, we consider neutral pion photoproduction at threshold to third order in this small scale expansion

K -> 3 pi Final State Interactions at NLO in CHPT and Cabibbo's Proposal to Measure a_0-a_2

We present the analytical results for the K -> 3 pi final state interactions at next-to-leading order (NLO) in CHPT. We also study the recent Cabibbo's proposal to measure the pi-pi scattering lenghts combination a_0-a_2 from the cusp effect in the pi^0-pi^0 energy spectrum at threshold for K^+ -> pi^0 pi^0 pi^+ and K_L -> pi^0 pi^0 pi^0$, and give the relevant formulas to describe it at NLO. For that, we use the NLO CHPT expression to fit the real part of K -> 3 pi to data while the pi-pi scattering lenghts are treated non-perturbatively. Using them, we make a quantitative estimate of the theoretical uncertaintity of the a_0-a_2 determination at NLO in our approach and obtain that it is not smaller than 5 % if added quadratically and 7 % if linearly for K^+ -> pi^0 pi^0 pi^+. One gets similar theoretical uncertainties if the neutral K_L -> pi^0 pi^0 pi^0 decay data below threshold are used instead. For this decay, there are very large theoretical uncertainties above threshold due to cancellations and data above threshold cannot be used to get the scattering lenghts. All the numbers we present are in the isospin limit apart of two-pion phase space factors which are physical. We compare our results for the cusp effect with Cabibbo and Isidori's results and discuss the differences and agreements. We also comment on the apperance of the singularity at the K -> 3 pi pseudo-threshold s=(m_K-m_pi)^2 in the discontinuity that defines the cusp.Comment: 31 pages, 8 figures. v2=v3 Added the full contributions to the cusp from the real part of the discontinuity. v4 Improved text. Matches published versio

Strong rescattering in K-> 3pi decays and low-energy meson dynamics

We present a consistent analysis of final state interactions in ${K\rightarrow 3\pi}$ decays in the framework of Chiral Perturbation Theory. The result is that the kinematical dependence of the rescattering phases cannot be neglected. The possibility of extracting the phase shifts from future $K_S-K_L$ interference experiments is also analyzed.Comment: 14 pages in RevTex, 3 figures in postscrip

The Chiral Anomaly in Non-Leptonic Weak Interactions

The interplay between the chiral anomaly and the non-leptonic weak Hamiltonian is studied. The structure of the corresponding effective Lagrangian of odd intrinsic parity is established. It is shown that the factorizable contributions (leading in $1/N_C$) to that Lagrangian can be calculated without free parameters. As a first application, the decay K^+ \ra \pi^+ \pi^0 \gamma is investigated.Comment: 10 pages, LaTe

Dispersion relations and soft pion theorems for K -> pi pi

We propose a new method to obtain the K -> pi pi amplitude from K -> pi which allows one to fully account for the effects of final state interactions. The method is based on a set of dispersion relations for the K -> pi pi amplitude in which the weak Hamiltonian carries momentum. The soft pion theorem, which relates this amplitude to the K -> pi amplitude, can be used to determine one of the two subtraction constants - the second constant is at present known only to leading order in chiral perturbation theory. We solve the dispersion relations numerically and express the result in terms of the unknown higher order corrections to this subtraction constant.Comment: Latex, 10 pages, 1 figure. Typo in eqs. (13,14) corrected, some rephrasing in the introductio