Weak Lagrangian Research Articles

Generic one-loop matching conditions for rare meson decays

Leptonic and semileptonic meson decays that proceed via flavour-changing neutral currents provide excellent probes of physics of the standard model and beyond. We present explicit results for the Wilson coefficients of the weak effective Lagrangian for these decays in any perturbative model in which these processes proceed via one-loop contributions. We explicitly show that our results are finite and gauge independent, and provide Mathematica code that implements our results in an easily usable form.

Novel Soft-Pion Theorem for Long-Range Nuclear Parity Violation.

The parity-odd effect in the standard model weak neutral current reveals itself in the long-range parity-violating nuclear potential generated by the pion exchanges in the ΔI=1 channel with the parity-odd pion-nucleon coupling constant h_{π}^{1}. Despite decades of experimental and theoretical efforts, the size of this coupling constant is still not well understood. In this Letter, we derive a soft-pion theorem relating h_{π}^{1} and the neutron-proton mass splitting induced by an artificial parity-even counterpart of the ΔI=1 weak Lagrangian and demonstrate that the theorem still holds exact at the next-to-leading order in the chiral perturbation theory. A considerable amount of simplification is expected in the study of h_{π}^{1} by using either lattice or other QCD models following its reduction from a parity-odd proton-neutron-pion matrix element to a simpler spectroscopic quantity. The theorem paves the way to much more precise calculations of h_{π}^{1}, and thus a quantitative test of the strangeness-conserving neutral current interaction of the standard model is foreseen.

Weak Polarized Electron Scattering

Scattering polarized electrons provides an important probe of the weak interactions. Precisely measuring the parity-violating left–right cross-section asymmetry (ALR) is the goal of a number of experiments that have recently been completed or are in progress. The experiments are challenging, given that ALR is small, typically between 10−4 and 10−8. By carefully choosing appropriate targets and kinematics, one can isolate various pieces of the weak Lagrangian, providing a search for physics beyond the Standard Model. For other choices, unique features of the strong interaction are being studied, including the radius of the neutron density in heavy nuclei, charge symmetry violation, and higher-twist terms. This article reviews the theory behind the experiments, as well as the general techniques used in the experimental program.

Parity-violating πNN coupling constant in the chiral quark–soliton model

We investigate the parity-violating πNN Yukawa coupling constant hπNN1 within the framework of the SU(2) chiral quark–soliton model, based on the ΔS=0 effective weak Lagrangian derived within the same framework. We find that the parity-violating πNN coupling constant is about 1×10−8 at the scale of 1 GeV. The results of hπNN1 turn out to be sensitive to the Wilson coefficient. We discuss how the gluonic renormalization suppresses the parity-violating πNN coupling constant.

Non-spectator Contributions to Lifetime of Λb**The proejct supported in part by National Natural Science Foundation of China. The preliminary result of this work was presented at the conference organized by National Natural Science Foundation of China

In this work, we study the contributions of non-spectator effects to the lifetimes of Λb and B-mesons comparatively. Based on the well-established theoretical framework about the effective weak Lagrangian, we derive the formulation of the non-spectator effects at the quark level. Especially, for Λb we have considered two pictures: the three-valence-quark picture and the quark-diquark picture. In the two pictures, the interference contributions to the total width are different, in this work, we investigate the interference effects in detail. As a preliminary estimate on the lifetimes, we evaluate the hadronic matrix elements appearing in the final formulas of the lifetimes by means of a simple phenomenological model for both pictures. Our results show that the contributions of the non-spectator effects can reduce the ratio of lifetime of Λb to that of B-mesons by 5 ˜ 7%. It is noted that in the quark-diquark picture the ratio can be further reduced if excited states of the diquark system are taken into account. We conclude that the measured ratio [The Data Group, Phys. Rev. D66 (2002) 010001] can be partly understood by the non-spectator effects, although the problem on the discrepancy between theoretical prediction and experimental measurement is not fully solved.

B−→φφK−decay rate withφφinvariant mass below the charm threshold

We investigate the decay mechanism in the ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\varphi}\ensuremath{\varphi}{K}^{\ensuremath{-}}$ decay with the $\ensuremath{\varphi}\ensuremath{\varphi}$ invariant mass below the charm threshold and in the neighborhood of the ${\ensuremath{\eta}}_{c}$ invariant mass region. Our approach is based on the use of the factorization model and the knowledge of matrix elements of the weak currents. For the B meson weak transition we apply the form factor formalism, while for the light mesons we use effective weak and strong Lagrangians. We find that the dominant contributions to the branching ratio come from the $\ensuremath{\eta},$ ${\ensuremath{\eta}}^{\ensuremath{'}}$ and $\ensuremath{\eta}(1490)$ pole terms of the penguin operators in the decay chains ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\eta}({\ensuremath{\eta}}^{\ensuremath{'}},\ensuremath{\eta}(1490)){K}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\varphi}\ensuremath{\varphi}{K}^{\ensuremath{-}}.$ Our prediction for the branching ratio is in agreement with the Belle Collaboration's result.

Gluonic mechanism forB→Dη′

We present a calculation of the process B --> D eta' within a heavy-light chiral quark model. We assume that the eta' has a large gluonic component, and its coupling is described via the glue-glue-eta' effective vertex. The main contribution comes from the non-factorizable part of the effective weak Lagrangian at quark level. We find, within our model-dependent assumptions, a branching ratio Br(B --> D eta') = (1.7 -- 3.3) 10^(-4), somewhat below the experimental upper bound 9.4 10^(-4).

Rare decayD0→γγ

We present a calculation of the rare decay mode D^0 -> gamma gamma, in which the long distance contributions are expected to be dominant. Using the Heavy Quark Chiral Perturbation Theory Lagrangian with a strong g coupling as recently determined by CLEO from the D^* -> D pi width, we consider both the anomaly contribution which relates to the annihilation part of the weak Lagrangian and the one-loop pi, K diagrams. The loop contributions which are proportional to g and contain the a_1 Wilson coefficient are found to dominate the decay amplitude, which turns out to be mainly parity violating. The branching ratio is then calculated to be (1.0+-0.5)x10^(-8). Observation of an order of magnitude larger branching ratio could be indicative of new physics.

Weak hyperon decays in heavy baryon chiral perturbation theory: Renormalization and applications

The complete renormalization of the weak Lagrangian to chiral order ${q}^{2}$ in heavy baryon chiral perturbation theory is performed using heat kernel techniques. The results are compared with divergences appearing in the calculation of Feynman graphs for the nonleptonic hyperon decay $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Lambda}}p{\ensuremath{\pi}}^{\ensuremath{-}}$ and an estimate for the size of the counterterm contributions to the s-wave amplitudes in nonleptonic hyperon decays is given.

QCD-based analysis of the weak kaon decays

Starting directly from the QCD Lagrangian, effective actions describing weak K-meson decays in different channels have been constructed. To construct effective Lagrangians a bilocal bosonization method, which incorporates the chiral symmetry-breaking mechanism, has been used. The decay rates of K mesons calculated with the derived weak Lagrangians essentially depend on the ``dressing'' mechanism of quarks. This mechanism is generated by the gluonic forces mediated by the two-point gluonic propagators. A reasonable agreement with experiment of calculated decay rates of charged K mesons in leptonic, semileptonic, and the two-pion decay channels has been achieved. The employed parametrization of quark propagators simultaneously gives a correct description of the $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ dynamics.

KL→π0γγ decay and the exchange of vector, scalar and tensor resonances

The exchange of vector, scalar and tensor resonances in KL→π0γγ decay is considered within theO(p6) effective chiral Lagrangian. The weak Lagrangian is constructed using the factorization method. The parameterav, which describes the vector meson exchange, is reinvestigated taking into account two-pion intermediate states and the exchange of scalar and tensor mesons. The contribution of scalar and tensor meson intermediate states to the branching ratio is found to be very small.

Saturation of counterterms by resonances inK →πe + e − decays

The decays $K^{+} \rightarrow \pi^{+} e^{+} e^{-}$, $K_{S} \rightarrow \pi^{0} e^{+} e^{-}$ and $K_{L} \rightarrow \pi^{0} e^{+} e^{-}$ are reinvestigated within the framework of chiral perturbation theory. The counterterms induced by strong, electromagnetic and weak interactions are determined assuming the resonance exchange. The weak deformation model, the factorization model and the large $N_{c}$ limit are used to create a weak Lagrangian. It is found that the results of the first two approaches depend on the $H_{1}$ coupling, defined in the effective chiral Lagrangian of the ${\it O} (p^{4})$ order. The set of parameters used in the extended Nambu and Jona-Lasinio model can accommodete $K^{+} \rightarrow \pi^{+} e^{+} e^{-}$ decay rate within the factorization approach. The CP violating $K_{L} \rightarrow \pi^{0} e^{+} e^{-}$ decay rate is discussed.

Use of summation methods in the calculation of nuclear double beta decay processes.

The use of summation methods, to deal with the calculation of matrix elements involved in the microscopic description of nuclear double beta decay processes, is discussed. The analysis focuses on the accuracy of a procedure which formally expresses the matrix elements of the standard current-current weak interaction, starting from the second-order perturbation treatment of the standard weak Lagrangian, as divergent power series of energy denominators. It is shown that, when properly treated, the summation method leads to results which coincide with the numerical sum of contributions due to virtual intermediate states.

EFFECTIVE CHIRAL LAGRANGIANS FOR STRONG, WEAK AND ELECTROMAGNETIC-WEAK INTERACTIONS OF MESONS FROM QUARK FLAVOR DYNAMICS

Effective chiral Lagrangians for strong, weak and electromagnetic-weak interactions of composite pseudoscalar, vector and axial-vector mesons are derived up to the fourth order in the chiral expansion from quark flavor dynamics based on the Nambu-Jona-Lasinio model. This approach completes earlier work on strong interactions and applies the path-integral bosonization method to the nonleptonic weak quark Lagrangian including the emission of structural photons. As illustrations, the bosonized weak and electromagnetic-weak Lagrangians are applied to the description of K→π(η) and K→π(η)γ* transitions.

On the origin of the enhancement of CP-violating charge asymmetries in K±→3 π decays predicted from chiral theory

We present an analysis of the enhancement of CP-violating charge asymmetries in K ±→3 πdecays. Calculations of decay amplitudes are performed on the basis of bosonized strong and weak lagrangians derived from QCD-motivated quark lagrangians. We show that the interplay of fourth-order contributions of chiral lagrangians for strong interactions and penguin operators in weak interactions significantly enhances the charge asymmetries.

Chiral weak lagrangian for vector mesons and K → 3 π decay amplitudes

We determine the next-order corrections to weak chiral lagrangian induced by vector-meson exchange, and we analyze their effects in K → 3 π decay amplitudes. The result is a substantial improvement of the lowest-order predictions.

Constraints on CP-violating nucleon-nucleon interactions in gauge models from atomic electric dipole moment.

In this paper {ital CP}-violating nucleon-nucleon interactions are studied in several models. The experimental upper bounds on the atomic electric dipole moment (EDM) are used to constrain the {ital CP}-violating parameters of the underlying weak Lagrangian. We compare the constraints from this consideration with those obtained from the upper bound on the neutron EDM. We find that although the constraints from the former consideration are not yet as sensitive as the latter, in some models the constraints from both considerations are within an order of magnitude.

T-symmetry violation as a result of virtual gravitational interaction

T-symmetry violation observed in the weak K-decays is interpreted as a result of an influence of the virtual black holes, inside which the space and time coordinates change places. When this decay happens inside the black hole theP-symmetry violation inherent to (V−A)-type of weak Lagrangian is accepted by the observer asT-symmetry violation.CP-symmetry conservation corresponds toCT-symmetry conservation.

KL,S → l+l− decays in the quark model of superconductivity type

The probabilities of KL,S → l+l− decays are calculated by considering only the dominant two-lepton channel KL,S →γ*γ* → l+l−. The transitions K0 → X, where X=π0,η,η′ orɛ (700) dominating in the KL,S →γ*γ*decay amplitudes, are described by the effective weak Lagrangian. The matrix elements of four-quark operators are calculated within the framework of the quark model of superconductivity type. It is shown that the leading contribution to matrix elements of K0 → X transitions comes from the penguin operator matrix elements.

Chiral weak dynamics.

We derive a chiral weak Lagrangian which interpolates the QCD-corrected-four-fermion weak-interaction Lagrangian to low energies. This is done using the Nambu--Jona-Lasinio model as a guide. The derivation treats SU(3) breaking from the current-quark mass on an equal footing with the spontaneous chiral-symmetry breaking. It leads naturally to an additional factor of 2--4 enhancement of \ensuremath{\Delta}I=1/2 K\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi} decay amplitudes.