In view of the recent experimental developments on the experimental side in the $η\to π^0 γγ$ decay, and the fact that the Particle Data Group in the on line edition of 2007 reports sizable changes of the radiative decay widths of vector mesons used as input in the theoretical calculations of \cite{eta}, a reevaluation of the decay width of the $η$ in this channel has been done, reducing its uncertainty by almost a factor of two. The new input of the PDG is used and invariant mass distributions and total widths are compared with the most recent results from AGS, MAMI and preliminary ones of KLOE. The agreement of the theory with the AGS and MAMI data is very good, both for the total rates as well as for the invariant mass distributions of the two photons.
We study the masses of the low-lying charmed mesons within the framework of heavy-hadron chiral perturbation theory. We work to third order in the chiral expansion, where meson loops contribute. In contrast to previous approaches, we use physical meson masses in evaluating these loops. This ensures that their imaginary parts are consistent with the observed widths of the D-mesons. The lowest odd- and even-parity, strange and nonstrange mesons provide enough constraints to determine only certain linear combinations of the low-energy constants in the effective Lagrangian. We comment on how latti…
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, ${\cal{L}}_{6,ε}$. 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…
The $σ$-terms are calculated at next-to-leading order in heavy baryon chiral perturbation theory by employing a cutoff regularization. The results do not depend on the cutoff value to the order we are working . The baryon masses and $σ_{πN}(0)$ are used to perform a least-squares fit to the three appearing low-energy constants and predictions for the two $KN$ $σ$-terms and the strange contribution to the nucleon mass are made. The lack of convergence in the chiral expansions of these quantities when regularized dimensionally is overcome in the cutoff scheme. The $σ$-term shifts to the pertinen…
We reconsider the Constituent Chiral Quark Model of Manohar and Georgi in the presence of $SU(3)_{L}\times SU(3)_{R}$ external sources. As recently emphasized by Weinberg, the corresponding effective Lagrangian is renormalizable in the Large--${\rm N_c}$ limit. We show, however, that the number of the required counterterms depends crucially on the value of $g_A$ and it is minimized for $g_A =1$. We then find that with a rather small value for the constituent quark mass, which we fix phenomenologically to $M_Q =(190\pm 40)\MeV$, the model reproduces rather well the values of several well known …
We reexamine critically the chiral expansion for the baryon magnetic moments including the contributions from loops which involve intermediate octet and decuplet baryons. We find that, contrary to some claims, the nonanalytic loop contributions of orders $m_s^{1/2}$ and $m_s ln m_s$ are of the same general size because of large coupling factors for the latter, and that the decuplet contributions are as large as the octet contributions and must be included in a consistent calculation. There is no clear evidence of the convergence of the chiral series. The adequacy of the theory will not be esta…
We reconsider the DMO sum rule in light of our recent two-loop calculations of isospin and hypercharge vector and axialvector current propagators in chiral perturbation theory. A modified derivation valid to second order in the light quark masses is presented, and a phenomenological analysis yields determination of a combination of finite counterterms occurring in the p^4 and p^6 chiral lagrangians. Suggestions are given for further study.
Chiral symmetry breaking may exhibit significantly different patterns in two chiral limits: N_f=2 massless flavours (m_u=m_d=0, m_s physical) and N_f=3 massless flavours (m_u=m_d=0=m_s=0). Such a difference may arise due to vacuum fluctuations of s-bar{s} pairs related to the violation of the Zweig rule in the scalar sector, and could yield a numerical competition between contributions counted as leading order and next-to-leading in the chiral expansions of observables. We recall and extend Resummed Chiral Perturbation Theory (ReChPT), a framework that we introduced previously to deal with suc…
The contribution to the muon anomalous magnetic moment from the fermion triangle loop diagrams connected to the muon line by a photon and a $Z$ boson is reanalyzed in the unitary gauge. With use of the anomalous axial-vector Ward identity, it is shown that the calculation in the unitary gauge exactly coincides with the one in the 't Hooft-Feynman gauge. The part which arises from the ordinary axial-vector Ward identity corresponds to the contribution of the neutral Goldstone boson. For the top-quark contribution, the one-parameter integral form is obtained up to the order of $m_μ^2/m_Z^2$. The…
We re-examine the hadronic loop effects to the masses of $D^*_0$ and $D^*_{s0}$ calculated in quark models in the framework of heavy meson chiral perturbation theory (HMCHPT). The inaccuracy in the choice of the argument of the chiral loop functions in previous works is corrected. Our calculations consider the full one-loop corrections that appear at leading order in the chiral expansion of the effective Lagrangian. Unlike previous approaches, ours leads to satisfactory results in explaining the low mass of the observed scalar charm states reported by the Particle Data Group (PDG). It is found…
While chiral symmetry breaking in the QCD vacuum is attributed to nonzero chiral condensate, an alternative symmetry breaking pattern with no chiral condensate is also possible, as pointed out by Stern. This hypothetical phase was excluded in QCD at zero density long time ago, but nothing forbids it at finite baryon density. In this work, we study the $θ$ dependence of this unorthodox phase on the basis of chiral perturbation theory. Physical observables such as energy density, topological susceptibility, non-local chiral order parameter and meson masses are computed analytically in the epsilo…
We reanalyse the magnetic moments of the baryon octet, decuplet, and antidecuplet within the framework of the chiral quark-soliton model, with SU(3) symmetry breaking taken into account. We consider the contributions of the mixing of higher representations to the magnetic moment operator arising from the SU(3) symmetry breaking. Dynamical parameters of the model are fixed by experimental data for the magnetic moments of the baryon octet and from the masses of the octet, decuplet and of $Θ^{+}$. The magnetic moment of $Θ^{+}$ depends rather strongly on the pion-nucleon sigma term and reads $-1.…
The concept of effective field theory leads in a natural way to a construction principle for phenomenological sensible models known under the name of the Cheshire Cat Principle. We review its formulation in the chiral bag scenario and discuss its realization for the flavor singlet axial charge. Quantum effects inside the chiral bag induce a color anomaly which requires a compensating surface term to prevent breakdown of color gauge invariance. The presence of this surface term allows one to derive in a gauge-invariant way a chiral-bag version of the Shore-Veneziano two-component formula for th…
We revisit the $KN$ scattering amplitude in order to investigate the possibility for the existence of a broad resonance in the $I=0$ $KN$ channel around the energy of 1617 MeV with 305 MeV width. We use the chiral unitary model to describe the $KN$ scattering amplitudes and determine the model parameters so as to reproduce the differential cross sections of the $K^{+}N$ scatterings and the $I=0$ and 1 total cross sections up to $p_{lab} = 800$ MeV/c, from which inelastic contributions start to be significant. Performing analytic continuation of the determined amplitude to the complex energy pl…
Parity violation in a chiral, four-atom molecule is discussed. Given the geometrical positions of the four atoms, we calculate the anapole moment of it. This problem was first discussed by Khriplovich and Pospelov. We give a detailed derivation for it so that it can be more accessible to wider range of scientists. We correct errors in their results and generalize their initial state to |s_{1/2}\rangle and |p_{1/2}\rangle states. We also discuss realistic candidates of the chiral molecules to which this approach can be applied.
We analyze s-wave pion-nucleon scattering in a unitarized chiral effective Lagrangian including all dimension two contact terms. We find that both the S11(1535) and the S11(1650) are dynamically generated, but the S31(1620) is not. We further discuss the structure of these dynamically generated resonances.
A dynamical investigation of the nucleon-nucleon (NN) interaction by using the resonating group method (RGM) in a chiral SU(3) quark model has been revisited. The considered quark-quark interaction includes, besides the one-gluon exchange (OGE) and the phenomenological confinement potential, the nonet scalar and pseudoscalar meson exchanges derived from the spontaneous SU(3) chiral symmetry breaking. The physical consistency requirement that the wave functions of single baryons satisfy the minimums of the Hamiltonian has been strictly imposed in determination of the model parameters. The calcu…
After our work was published, Frink and Meißner \cite{FM06} pointed out that our {\cal O}(q^3) three-flavour meson-baryon chiral Lagrangian was not minimal. Here, we discuss their findings and revise ours accordingly. We find that eight monomials in our ${\cal O}(q^3)$ Lagrangian are not independent, but in addition, two monomials were wrongly discarded, which, as a result, makes the agreement in the number of independent monomials with \cite{FM06} complete.
The anti-kaon nucleon system close to threshold is analyzed in view of the new accurate DEAR kaonic hydrogen data. The calculations are performed using chiral SU(3) effective field theory in combination with non-perturbative schemes based on coupled channels. Several variants of such approaches are compared with experimental data and the differences in the results are discussed. Coulomb and isospin breaking effects turn out to be important and are both taken into account. The pole structure of the Lambda(1405) resonance close to the anti-kaon nucleon threshold is critically examined.
We construct the full p6 order chiral Lagrangians for the unitary group and special unitary groups, including nf-, three- and two-flavor cases, all bilinear currents (scalar, pseudoscalar, vector, axial-vector and tensor currents) and theta parameter. The number of independent operators are 1391, 1326 and 969 for each of the flavor unitary groups. From these results, we find one extra linear relation among the traditional p4 order low-energy constants under the U(3) group, and some more linear relations with tensor sources for the p6 order low-energy constants in the special unitary groups. We…
Motivated by the search for possible CP violating terms in the trace of the energy-momentum tensor in theories coupled to gravity we revisit the problem of trace anomalies in chiral theories. We recalculate the latter and ascertain that in the trace of the energy-momentum tensor of theories with chiral fermions at one-loop the Pontryagin density appears with an imaginary coefficient. We argue that this may break unitarity, in which case the trace anomaly has to be used as a selective criterion for theories, analogous to the chiral anomalies in gauge theories. We analyze some remarkable consequ…
Chiral Ward identities lead to consistent accounting for the sigma's width in the linear sigma model's Feynman rules. Reanalysis of pion scattering data at threshold imply a mass for the sigma of 600+ 200 - 100 MeV.
We re-investigate Adler's PCAC relation in the presence of an external electromagnetic field within the framework of QCD coupled to external fields. We discuss pion electroproduction within a tree-level approximation to chiral perturbation theory and explicitly verify a chiral Ward identity referred to as the Adler-Gilman relation. We critically examine soft-momentum techniques and point out how inadmissable approximations may lead to results incompatible with chiral symmetry. As a result we confirm that threshold pion electroproduction is indeed a tool to obtain information on the axial form …
We report on recent results on the decay of the phi into pi^+ pi^- and phi radiative decays into pi^0 pi^0 gamma and pi^0 eta gamma, which require the consideration of the final state interaction of a pair of mesons in a region inaccessible to Chiral Perturbation Theory. By using nonperturbative chiral unitary methods for the meson meson interaction we can obtain the corresponding decay widths and the results are compared with recent experimental data.
By describing within the chiral unitary approach the s-wave interaction of the vector meson nonet with the octet of pseudoscalar Goldstone Bosons, we find that the main component of the axial vector mesons b_1(1235), h_1(1170), h_1(1380), a_1(1260), f_1(1285) and the two states associated to the K_1(1270) does not follow the QCD dependence on the number of colors for ordinary qqbar mesons.
We study the S-wave kaon-nucleon interactions for strangeness S=-1 in a novel relativistic chiral unitary approach based on coupled channels. Dispersion relations are used to perform the necessary resummation of the lowest order relativistic chiral Lagrangian. A good description of the data in the K^- p, πΣand πΛchannels is obtained. We show how this method can be systematically extended to higher orders, emphasizing its applicability to any scenario of strong self-interactions where the perturbative series diverges even at low energies. Discussions about the differences to existing approaches…
We revisit the chiral kinetic equation from high density effective theory approach, finding a chiral kinetic equation differs from counterpart derived from field theory in high order terms in the $O(1/μ)$ expansion, but in agreement with the equation derived in on-shell effective field theory upon identification of cutoff. By using reparametrization transformation properties of the effective theory, we show that the difference in kinetic equations from two approaches are in fact expected. It is simply due to different choices of degree of freedom by effective theory and field theory. We also s…
The double lepton pair decay modes of the K_L meson are analyzed including all contributions of order p^6 in Chiral Perturbation Theory. The experimentally established e^+ e^- e^+ e^- mode and the recently observed e^+ e^- mu^+ mu^- mode are discussed in detail.
We make a theoretical study of the J/Psi decays into ωππ, ϕππ, ωK \bar{K} and ϕK\bar{K} using the techniques of the chiral unitary approach stressing the important role of the scalar resonances dynamically generated through the final state interaction of the two pseudoscalar mesons. We also discuss the importance of new mechanisms with intermediate exchange of vector and axial-vector mesons and the role played by the OZI rule in the J/Ψϕππvertex, quantifying its effects. The results nicely reproduce the experimental data for the invariant mass distributions in all the channels considered.
Using a manifestly gauge-invariant approach we show that the set of low-energy constants in the electroweak chiral Lagrangian currently used in the literature is redundant. In particular, by employing the equations of motion for the gauge fields, one can choose to remove two low-energy constants which contribute to the self-energies of the gauge bosons. The relation of this result to the experimentally determined values for the oblique parameters S,T and U is discussed. We then evaluate the matching relation between gauge-invariant Green's functions in the full and the effective theory for the…
In view of ongoing experimental activities to determine the pion polarizabilities, we have started to recalculate the available two-loop expressions in the framework of chiral perturbation theory, because they have never been checked before. We make use of the chiral Lagrangian at order p^6 now available, and of improved techniques to evaluate the two-loop diagrams. Here, we present the result for the neutral pions. The cross section for the reaction gamma+gamma->pi0+pi0 agrees with the earlier calculation within a fraction of a percent. We present analytic results for the dipole and quadrupol…
Quantum effects inside the chiral bag induce a color anomaly which requires a compensating surface term to prevent breakdown of color gauge invariance. We show that the presence of this surface term first discovered several years ago allows one to derive in a gauge-invariant way a chiral-bag version of the Shore-Veneziano two-component formula for the flavor-singlet axial charge of the proton. This has relevance to what is referred to as the ``proton spin problem" on the one hand and to the Cheshire-Cat phenomenon in hadron structure on the other. We show that when calculated to the leading or…
The pion and kaon coupled-channel vector form factors are described by making use of the resonance chiral Lagrangian results together with a suitable unitarization method in order to take care of the final state interactions. A very good reproduction of experimental data is accomplished for the vector form factors up to $\sqrt{s}\leq 1.2$ GeV and for the $ππ$ P-wave phase shifts up to $\sqrt{s}\leq 1.5$ GeV.
Pion-nucleon scattering, pion photoproduction, and nucleon Compton scattering are analyzed within a scheme based on the chiral Lagrangian. Partial-wave amplitudes are obtained by an analytic extrapolation of subthreshold reaction amplitudes computed in chiral perturbation theory, where the constraints set by electromagnetic-gauge invariance, causality and unitarity are used to stabilize the extrapolation. Experimental data are reproduced up to energies $\sqrt{s}\simeq 1300$ MeV in terms of the parameters relevant at order $Q^3$. A striking puzzle caused by an old photon asymmetry measurement c…
We make a theoretical study of the $\J$ decays into $ωππ$, $ϕππ$, $ωK \bar{K}$ and $ϕK\bar{K}$ using the techniques of the chiral unitary approach stressing the important role of the scalar resonances dynamically generated through the final state interaction of the two pseudoscalar mesons. We also discuss the importance of new mechanisms with intermediate exchange of vector and axial-vector mesons and the role played by the OZI rule in the $\Jϕππ$ vertex, quantifying its effects. The results nicely reproduce the experimental data for the invariant mass distributions in all the channels conside…
In this talk we report on the use of a chiral unitary approach for the interaction of the octets of meson and baryon and the octet of mesons with the decuplet of baryons. Two octets of $J^π=1/2^-$ baryon states and a singlet are generated dynamically in the first case, resulting in the case of strangeness $S=-1$ in two poles of the scattering matrix close to the nominal $Λ(1405)$ resonance. In the second case many resonances are also generated, among them an exotic baryon with S=1 corresponding to a $ΔK$ resonance. We make suggestions of experiments which could show evidence for the existence …
We have calculated the decay amplitude for the process $K_{S}$ $\to$ $γγ$ at one loop order in chiral perturbation theory. As a new improvement we have included the weak mass term which is only relevant for processes with external fields in the final state. This term was ignored in earlier publications for this decay. We find that the inclusion of $G_{8}^{\prime}$ brings the theoretical decay rate into a good agreement with experiment.
We perform a complete one-loop calculation of meson-meson scattering, and of the scalar and pseudoscalar form factors in U(3) chiral perturbation theory with the inclusion of explicit resonance fields. This effective field theory takes into account the low-energy effects of the QCD U_A(1) anomaly explicitly in the dynamics. The calculations are supplied by non-perturbative unitarization techniques that provide the final results for the meson-meson scattering partial waves and the scalar form factors considered. We present thorough analyses on the scattering data, resonance spectroscopy, spectr…
We study chiral symmetry breaking in QCD, using as ingredients in the quark gap equation recent lattice results for the gluon and ghost propagators. The Ansatz employed for the quark-gluon vertex is purely non-Abelian, introducing a crucial dependence on the ghost dressing function and the quark-ghost scattering amplitude. The numerical impact of these quantities is considerable: the need to invoke confinement explicitly is avoided, and the dynamical quark masses generated are of the order of 300 MeV. In addition, the pion decay constant and the quark condensate are computed, and are found to …
We study the latest $N_f=2+1+1$ and $N_f=2$ ETMC lattice QCD simulations of the nucleon masses and extract the pion-nucleon sigma term utilizing the Feynman-Hellmann theorem in SU(2) baryon chiral perturbation theory with the extended-on-mass-shell scheme. We find that the lattice QCD data can be described quite well already at the next-to-next-to-leading order. The overall picture remains essentially the same at the next-to-next-to-next-to-leading order. Our final result is $σ_{πN}=50.2(1.2)(2.0)$ MeV, or equivalently, $f_{u/d}^N=0.0535(13)(21)$, where the first uncertainty is statistical and…
The recent results from Belle of the $τ^-\toν_τπ^-e^+e^-$ analysis has incentivated us to make a reanalysis of a former work where the Structure Dependent parts are obtained using Resonance Chiral Theory. Here we rely on the same theory accounting for effects that explicitly break such symmetry. A motivation is the involved $Wπγ^\star$ vertex, utterly relevant in computing $τ^- \to ν_τπ^-$ radiative corrections.
The proton burning process p + p -> d + e(+) + ν(e), important for the stellar evolution of main-sequence stars of mass equal to or less than that of the Sun, is computed in effective field theory using chiral perturbation expansion to the next-to-next-to leading chiral order. This represents a model-independent calculation consistent with low-energy effective theory of QCD comparable in accuracy to the radiative np capture at thermal energy previously calculated by first using very accurate two-nucleon wavefunctions backed up by an effective field theory technique with a finite cut-off. The r…
The decays eta, eta-prime --> pi+ pi- l+ l- (with l = e, mu) are investigated within a chiral unitary approach which combines the chiral effective Lagrangian with a coupled-channels Bethe-Salpeter equation. Predictions for the decay widths and spectra are given.
We improve the calculations of the $η\to π^0 γγ$ decay within the context of meson chiral lagrangians. We use a chiral unitary approach for the meson-meson interaction, thus generating the $a_0(980)$ resonance and fixing the longstanding sign ambiguity on its contribution. This also allows us to calculate the loops with one vector meson exchange, thus removing a former source of uncertainty. In addition we ensure the consistency of the approach with other processes. First, by using vector meson dominance couplings normalized to agree with radiative vector meson decays. And, second, by checking…
We make a theoretical study of the charge and forward-backward pion asymmetries in the e+e- --> pi+ pi- gamma process on and off the phi resonance energy. These observables are rather sensitive to the inner details of the theoretical models to describe the reaction. In addition to the standard implementation of the initial state radiation (ISR) and the Bremsstrahlung contribution to the final state radiation (FSR), we use the techniques of the chiral unitary approach to evaluate the contribution from the mechanisms of phi decay into pi+pi-gamma. This contribution involves the implementation of…
An empirically successful mass formula derived long ago from hadronic string models is not explained by symmetries of the QCD lagrangian. Consider that M(rho)^2-M(pi)^2 = M(K*)^2-M(K)^2 to a few percent accuracy. We derive this and other equal spacing relations using chiral symmetry and a novel Z_2 symmetry. We offer an interpretation of this Z_2 symmetry as a manifestation of chiral anomalies in a gauge theory with an intrinsic cutoff.
We first review the current algebra - PCAC approach to nonleptonic octet baryon 14 weak decay B (\to) (B^{\prime})(π) amplitudes. The needed four parameters are independently determined by (Ω\to Ξπ),(ΛK) and (Ξ^{-}\to Σ^{-}γ) weak decays in dispersion theory tree order. We also summarize the recent chiral perturbation theory (ChPT) version of the eight independent B (\to) (B^{\prime}π) weak (ΔI) = 1/2 amplitudes containing considerably more than eight low-energy weak constants in one-loop order.
We study the $J/ψ\to \bar{p}ηp$ and $J/ψ\to \bar{p}K^+Λ$ reactions with a unitary chiral approach. We find that the unitary chiral approach, which generates the $N^*(1535)$ dynamically, can describe the data reasonably well, particularly the ratio of the integrated cross sections. This study provides further support for the unitary chiral description of the $N^*(1535)$. We also discuss some subtle differences between the coupling constants determined from the unitary chiral approach and those determined from phenomenological studies.
We revisit two-color, two-flavor chiral perturbation theory at finite isospin and baryon density. We investigate the phase diagram obtained varying the isospin and the baryon chemical potentials, focusing on the phase transition occurring when the two chemical potentials are equal and exceed the pion mass (which is degenerate with the diquark mass). In this case, there is a change in the order parameter of the theory that does not lend itself to the standard picture of first order transitions. We explore this phase transition both within a Ginzburg-Landau framework valid in a limited parameter…
The self-energy of an eta in a nuclear medium is calculated in a chiral unitary model, and applied to eta states in nuclei. Our calculation predicts an attractive eta nucleus optical potential which can accommodate many eta bound states in different nuclei.
We study the structure of dynamically generated bound states in the chiral unitary approach. The compositeness of a bound state is defined through the wavefunction renormalization constant in the nonrelativistic field theory. We apply this argument to the chiral unitary approach and derive the relation between compositeness of the bound state and the subtraction constant of the loop integral. The compositeness condition is fairly compatible with the natural renormalization scheme, previously introduced in a different context.
We calculate the magnetic moments of the N(1535) resonance using the chiral unitary model, where the resonance is dynamically generated in the scatterings of the lowest-lying mesons and baryons. We obtain the magnetic moments of the resonance as +1.1 and -0.25 for p(1535) and n(1535), respectively, in units of the nuclear magneton. We discuss the origin of these numbers within the chiral unitary model, then we compare the present results with those of the quark model and the chiral doublet model. The possibility to observe the magnetic moments in experiments is also investigated.
We examine flavor SU(3) breaking effects on meson-baryon scattering amplitudes in the chiral unitary model. It turns out that the SU(3) breaking, which appears in the leading quark mass term in the chiral expansion, can not explain the channel dependence of the subtraction parameters of the model, which are crucial to reproduce the observed scattering amplitudes and resonance properties.
In the anomaly equation for the singlet axial current the chiral limit of the quark mass term does not vanish but comprises contribution from fermion zero modes whose integral exactly cancels the topological charge arising from the Adler-Bell-Jackiw anomaly. This signals chiral symmetry and opens a window for restoring the status of Goldstone boson for the singlet $η^\prime$ without having to invoke the large $N_c$ limit in the underlying QCD. We construct the anomaly term in the effective action that incorporates the chiral symmetry property and yet accounts for the excess mass of $η^\prime$ …
