Radiative Ke3 decays revisited

Motivated by recent experimental results and ongoing measurements, we review the chiral perturbation theory prediction for radiative Ke3 decays (neutral kaons). Special emphasis is given on the stability of the inner bremsstrahlung-dominated relative branching ratio vs. the Ke3 form factors, and on the separation of the structure dependent amplitude in differential distributions over the phase space. For the structure dependent terms, an assessment of the order p^6 corrections is given. In particular, a full next-to-leading order calculation of the axial component is performed. The experimental analysis of the photon energy spectrum is discussed, and other potentially useful distributions are introduced.Comment: Version published in Eur.Phys.J.C.: 23 pages (LaTeX), 10 figures. Minor changes in text, typos removed, references updated, Springer style file use

πK\pi K Scattering in Three Flavour ChPT

We present the scattering lengths for the $\pi K$ processes in the three flavour Chiral Perturbation Theory (ChPT) framework at next-to-next-to-leading order (NNLO). The calculation has been performed analytically but we only include analytical results for the dependence on the low-energy constants (LECs) at NNLO due to the size of the expressions. These results, together with resonance estimates of the NNLO LECs are used to obtain constraints on the Zweig rule suppressed LECs at NLO, $L_4^r$ and $L_6^r$. Contrary to expectations from NLO order calculations we find them to be compatible with zero. We do a preliminary study of combining the results from $\pi\pi$ scattering, $\pi K$ scattering and the scalar form-factors and find only a marginal compatibility with all experimental/dispersive input data.Comment: 23 page

An upper bound on the Kaon B-parameter and Re(epsilon_K)

New precise data in B physics and theoretical developments in K physics lead us to reconsider the weak K^0-\bar{K}^0 transition from a large-N_c viewpoint, N_c being the number of colors. In this framework, we infer an upper limit on \hat{B}_K and the Kaon indirect CP violation.Comment: 11 pages, 4 figures. V2 : Minor corrections, final version accepted for publication in JHE

Resumming QCD vacuum fluctuations in three-flavour Chiral Perturbation Theory

Due to its light mass of order Lambda_QCD, the strange quark can play a special role in Chiral Symmetry Breaking (ChSB): differences in the pattern of ChSB in the limits N_f=2 (m_u,m_d->0, m_s physical) and N_f=3 (m_u,m_d,m_s->0) may arise due to vacuum fluctuations of s-bar s pairs, related to the violation of the Zweig rule in the scalar sector and encoded in particular in the O(p^4) low-energy constants L_4 and L_6. In case of large fluctuations, we show that the customary treatment of SU(3)xSU(3) chiral expansions generate instabilities upsetting their convergence. We develop a systematic program to cure these instabilities by resumming nonperturbatively vacuum fluctuations of s-bar s pairs, in order to extract information about ChSB from experimental observations even in the presence of large fluctuations. We advocate a Bayesian framework for treating the uncertainties due to the higher orders. As an application, we present a three-flavour analysis of the low-energy pi-pi scattering and show that the recent experimental data imply a lower bound on the quark mass ratio 2m_s/(m_u+m_d) > 14 at 95 % confidence level. We outline how additional information may be incorporated to further constrain the pattern of ChSB in the N_f=3 chiral limit.Comment: 58 pages, 8 figure

Electromagnetic Corrections in Partially Quenched Chiral Perturbation Theory

We introduce photons in Partially Quenched Chiral Perturbation Theory and calculate the resulting electromagnetic loop-corrections at NLO for the charged meson masses and decay constants. We also present a numerical analysis to indicate the size of the different corrections. We show that several phenomenologically relevant quantities can be calculated consistently with photons which couple only to the valence quarks, allowing the use of gluon configurations produced without dynamical photons.Comment: 11 page

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

Radiative corrections to neutral pion-pair production

We calculate the one-photon loop radiative corrections to the neutral pion-pair photoproduction process $\pi^-\gamma \to \pi^-\pi^0\pi^0$. At leading order this reaction is governed by the chiral pion-pion interaction. Since the chiral $\pi^+\pi^-\to\pi^0\pi^0$ contact-vertex depends only on the final-state invariant-mass it factors out of all photon-loop diagrams. We give analytical expressions for the multiplicative correction factor $R\sim \alpha/2\pi$ arising from eight classes of contributing one-photon loop diagrams. An electromagnetic counterterm has to be included in order to cancel the ultraviolet divergences generated by the photon-loops. Infrared finiteness of the virtual radiative corrections is achieved (in the standard way) by including soft photon radiation below an energy cut-off $\lambda$. The radiative corrections to the total cross section vary between $+2\%$ and $-2\%$ for center-of-mass energies from threshold up to $7m_\pi$. The finite part of the electromagnetic counterterm gives an additional constant contribution of about $1\%$, however with a large uncertainty.Comment: 10 pages, 6 figures, submitted to Eur. Phys. J.

Pion pole contribution to hadronic light-by-light scattering and muon anomalous magnetic moment

We derive an analytic result for the pion pole contribution to the light-by-light scattering correction to the anomalous magnetic moment of the muon, $a_\mu = (g_\mu-2)/2$. Using the vector meson dominance model (VMD) for the pion transition form factor, we obtain $a_\mu^{{\rm LBL},\pi^0} = +56 \times 10^{-11}$.Comment: 4 pages, revte

Soft-photon corrections in multi-body meson decays

The effects due to soft-photon emission (and the related virtual corrections) in multi-body decays of B, D, and K mesons are analysed. We present analytic expressions for the universal O(alpha) correction factors which can be applied to all multi-body decay modes where a tight soft-photon energy cut in the decaying-particle rest-frame is applied. All-order resummations valid in the limit of small and large velocities of the final-state particles are also discussed. The phenomenological implications of these correction factors in the distortion of Dalitz-plot distributions of K -> 3 pi decays are briefly analysed.Comment: 8 pages, 2 figures (v2: minor modifications - published version