We reformulate the analysis of nuclear parity-violation (PV) within the framework of effective field theory (EFT). To O(Q), the PV nucleon-nucleon (N N ) interaction depends on five a priori unknown constants that parameterize the leadingorder, short-range four-nucleon operators. When pions are included as explicit degrees of freedom, the potential contains additional medium-and long-range components parameterized by PV πN N coupling. We derive the form of the corresponding one-and two-pion-exchange potentials. We apply these considerations to a set of existing and prospective PV few-body measurements that may be used to determine the five independent low-energy constants relevant to the pionless EFT and the additional constants associated with dynamical pions. We also discuss the relationship between the conventional meson-exchange framework and the EFT formulation, and argue that the latter provides a more general and systematic basis for analyzing nuclear PV.

The electric dipole form factor (EDFF) of the nucleon stemming from the QCD θ term and from the quark color-electric dipole moments is calculated in chiral perturbation theory to sub-leading order. This is the lowest order in which the isoscalar EDFF receives a calculable, non-analytic contribution from the pion cloud. In the case of theθ term, the expected lower bound on the deuteron electric dipole moment is |d d | > ∼ 1.4·10 −4θ e fm. The momentum dependence of the isovector EDFF is proportional to a non-derivative time-reversal-violating pion-nucleon coupling, and the scale for momentum variation -appearing, in particular, in the radius of the form factor-is the pion mass.The electric dipole form factor (EDFF) completely specifies the parity (P ) and timereversal (T ) -violating coupling of a spin 1/2 particle to a single photon [1,2]. At zero momentum, it reduces to the electric dipole moment (EDM), and its radius provides a contribution to the Schiff moment (SM) of a bound state containing the particle [3]. The full momentum dependence of the form factor can be used in lattice simulations to extract the EDM by extrapolation from a finite-momentum calculation [4] (in addition to the required extrapolations in quark masses and volume [5]).There has been some recent interest [1,2,6,7,8,9] in the nucleon EDFF motivated by prospects of experiments that aim to improve the current bound on the neutron EDM, |d n | < 2.9 · 10 −13 e fm [10], by nearly two orders of magnitude [11], and to constrain the proton and deuteron EDMs at similar levels [12]. We would like to understand the implications of a possible signal in these measurements to the sources of T violation at the quark level, which include, in order of increasing dimension, the QCDθ term, the quark color-EDM (qCEDM) and EDM, the gluon color-EDM, etc. [13,14]. Unfortunately, as with other low-energy observables, both the EDM and the SM of hadrons and nuclei are difficult to calculate directly in QCD. However, long-range contributions from pions can, to some extent, be calculated using the low-energy effective field theory of QCD, chiral perturbation theory (ChPT) [15,16,17]. ChPT affords a systematic expansion of lowenergy observables in powers of Q/M QCD , where Q represents low-energy scales such as external momenta and the pion mass m π , and M QCD ∼ 1 GeV denotes the characteristic QCD scale. (For introductions, see for example Refs. [18,19].)In Refs. [1,9] the nucleon EDFF stemming from T -violation sources of effective dimension up to 6 was considered in ChPT to the lowest order where momentum dependence appears. It was argued [9] that the nucleon EDFF partially reflects the source of T violation at the quark level. The various sources differ in particular in the expectation for the behavior of the isoscalar EDFF. Forθ and qCEDM, the isoscalar momentum dependence appears only at NLO. The nucleon EDFF fromθ was calculated at LO in Ref.[1], generalizing to finite momenta earlier calculations of the EDM [20, 21] and SM [3]. At this order, the momentum depe...

We assess the importance of final state interactions in D + → K − π + π + , stressing the consistency between two-and three-body interactions. The basic building block in the calculation is a Kπ amplitude based on unitarized chiral perturbation theory and with parameters determined by a fit to elastic LASS data. Its analytic extension to the second sheet allows the determination of two poles, associated with the κ and the K * (1430), and a representation of the amplitude based on them is constructed. The problem of unitarity in the three-body system is formulated in terms of an integral equation, inspired in the Faddeev formalism, which implements a convolution between the weak vertex and the final state hadronic interaction. Three different topologies are considered for the former and, subsequently, the decay amplitude is expressed as a perturbation series. Each term in this series is systematically related to the previous one and a re-summation was performed. Remaining effects owing to single and double rescattering processes were then added and results compared to FOCUS data. We found that proper three-body effects are important at threshold and fade away rapidly at higher energies. Our model, based on a vector weak vertex, can describe qualitative features of the modulus of the decay amplitude and agrees well with its phase in the elastic region. I. MOTIVATIONAbout forty years ago, reactions of the type KN → πKN were used to determine the Kπ amplitude [1]. Such reactions involve the scattering of an incoming kaon and a pion from the nucleon cloud. The dominant one-pion exchange amplitude is isolated by selecting events with low momentum transfer. This is the only Kπ → Kπ scattering data, collected in the range 0.825 < m Kπ < 1.960 GeV/c 2 . In the past decade, heavy flavor decays, in particular decays of D mesons, became a key to the physics of the light scalars. Currently these are the only process in which S-wave amplitudes can be continuously studied, starting from threshold, filling the existing gaps on the scattering data. In addition, very large, high purity samples, in which the initial state has always well defined quantum numbers, became available in the past few years. Multibody decays of heavy flavor particles proceed almost entirely via intermediate states involving resonances that couple to ππ and Kπ. The universal Kπ and ππ amplitudes are, therefore, present in these decays as well. These amplitudes could, in principle, be extracted with great precision. * patricia@if.usp.br † tobias@ita.br ‡ alberto@cbpf.br Most of the existing results come from hadronic decays of D mesons. The golden modes are theand, in the case of the Kπ system, thedecay. These decay modes share some common features: the presence of two identical particles in the final state, and a largely dominant S-wave component. The standard procedure is the analysis of the Dalitz plot, in which the decay amplitude is modeled by a coherent sum of resonant amplitudes, accounting for the possible intermediate states -the so-called isobar...

We derive the parity-and time-reversal-violating nuclear interactions stemming from the QCDθ term and quark/gluon operators of effective dimension 6: quark electric dipole moments, quark and gluon chromo-electric dipole moments, and two four-quark operators. We work in the framework of two-flavor chiral perturbation theory, where a systematic expansion is possible. The different chiral-transformation properties of the sources of time-reversal violation lead to different hadronic interactions. For all sources considered the leading-order potential involves known one-pion exchange, but its specific form and the relative importance of short-range interactions depend on the source. For theθ term, the leading potential is solely given by one-pion exchange, which does not contribute to the deuteron electric dipole moment. In subleading order, a new two-pion-exchange potential is obtained. Its short-range component is indistinguishable from one of two undetermined contact interactions that appear at the same order and represent effects of heavier mesons and other shortrange QCD dynamics. One-pion-exchange corrections at this order are discussed as well.