Eta Pi Research Articles

Chiral nonet mixing in pi eta scattering

The generalized linear sigma model for mixing among two- and four-quark components of scalar (and pseudoscalar) mesons below and above 1 GeV is applied to the pi eta channel in which the isovector scalars a_0(980) and a_0(1450) are probed. In the leading order, the model parameters have been previously fixed by various low-energy experimental data, and then applied to pi pi and pi K channels in which the properties of the light and broad sigma and kappa mesons are extracted in agreement with estimates reported in the literature. With the same parameters fixed in the leading order, in the present work the prediction of the model for the pi eta scattering amplitude in the elastic region is given and unitarized with the K-matrix method. The poles of the unitarized scattering amplitude, which determine the mass and decay width of a_0(980) and a_0(1450) are computed. It is found that the model predicts an isovector scalar state below 1 GeV, with mass 984 ± 6 MeV and decay width 108 ± 30 MeV which is a clear signal for the a_0(980). The a_0 pole extracted in this work, further supports the plausibility of the mixing patterns for scalar mesons predicted by this model according to which there is a significant underlying mixing among scalars below and above 1 GeV, with those below 1 GeV being generally of four-quark nature while those above 1 GeV being overall closer to quark–antiquark states. Predictions for various scattering lengths as well as for properties of a_0(1450) are also presented.

Two dynamical generated a_0 resonances by interactions between vector mesons

We study dynamically generated a_0 resonances by interactions between vector mesons including their coupling to channels of pseudoscalar mesons within coupled-channel approach. Both vector and pseudoscalar mesons are considered as t-channel exchanged mesons for calculating interactions between vector mesons. Analogous to a_0(980) as a K{bar{K}}-pi eta dynamically generated state, there is an a_0(1710) as a coupled channel dynamically generated state near K^*bar{K}^* threshold. The channels involved are rho phi ,K^*bar{K}^*,rho omega , Kbar{K},pi eta . This a_0 mainly decays to rho omega , pi eta and Kbar{K}. This pole is much tied to the coupled channel effect. If we turn off either rho phi or K^*bar{K}^*, the pole disappears. In addition, it is found that a_0(1450) may also be dynamically generated by rho omega interactions due to pi and eta exchange.

Investigation of the lightest hybrid meson candidate with a coupled-channel analysis of {{bar{p}}p}-, pi ^- p- and {pi pi }-Data

A sophisticated coupled-channel analysis is presented that combines different processes: the channels {pi ^0pi ^0eta }, {pi ^0eta eta } and {K^+K^-pi ^0} from {{bar{p}}p} annihilations, the P- and D-wave amplitudes of the pi eta and pi eta ^prime systems produced in pi ^-p scattering, and data from {pi pi }-scattering reactions. Hence our analysis combines the data sets used in two independent previous analyses published by the Crystal Barrel experiment and by the JPAC group. Based on the new insights from these studies, this paper aims at a better understanding of the spin-exotic pi _1 resonances in the light-meson sector. By utilizing the K-matrix approach and realizing the analyticity via Chew-Mandelstam functions the amplitude of the spin-exotic wave can be well described by a single pi _1 pole for both systems, pi eta and pi eta ^prime . The mass and the width of the pi _1-pole are measured to be (1623 , pm , 47 , ^{+24}_{-75}), mathrm {MeV/}c^2 and (455 , pm 88 , ^{+144}_{-175}), mathrm {MeV}.

Study of the D_s^+rightarrow a_0(980) rho and a_0(980) omega decays

We study D_{s}^{+}rightarrow rho ^{0(+)}a^{+(0)}_{0}, D_{s}^{+}rightarrow omega a^{+}_{0}, and the resonant D_{s}^{+}rightarrow rho a_0, a_{0}rightarrow eta pi (KK) decays. In the final state interaction, where D_s^+rightarrow (eta ^{(prime )}pi ^+,K^+{{bar{K}}}^0) are followed by the (eta ^{(prime )}pi ^+,K^+{{bar{K}}}^0) to rho ^{0(+)}a^{+(0)}_{0} rescatterings, we predict mathcal{B}(D_{s}^{+}rightarrow rho ^{0(+)}a^{+(0)}_{0})=(3.0pm 0.3pm 1.0)times 10^{-3}. Due to the cancellation of the rescattering effects and the suppressed short-distance W annihilation contribution, we expect that {{mathcal {B}}}(D_{s}^{+}rightarrow omega a^{+}_{0}) simeq mathcal{B}(D_s^+rightarrow pi ^+pi ^0)<3.4times 10^{-4}. In our calculation, {{mathcal {B}}}(D_{s}^{+}rightarrow rho ^{0}(a^{+}_{0}rightarrow )eta pi ^{+}) =(1.6^{+0.2}_{-0.3}pm 0.6)times 10^{-3} agrees with the data, whereas {{mathcal {B}}}(D_{s}^{+}rightarrow rho ^{+}(a^{0}_{0}rightarrow )K^+K^-) is 10 times smaller than the observation, which requires a careful examination.

Revisiting gamma ^*rightarrow gamma pi ^0eta near the phi (1020) using analyticity and the left-cut structure

Amplitudes of the form gamma ^*(q^2)rightarrow gamma P_1P_2 appear as sub-processes in the computation of the muon g-2. We test a proposed theoretical modelling against very precise experimental measurements by the KLOE collaboration at q^2=m^2_phi . Starting from an exact, parameter-free dispersive representation for the S-wave satisfying QCD asymptotic constraints and Low’s soft photon theorem we derive, in an effective theory spirit, a two-channel Omnès integral representation which involves two subtraction parameters. The discontinuities along the left-hand cuts which, for timelike virtualities, extend both on the real axis and into the complex plane are saturated by the contributions from the light vector mesons. In the case of P_1P_2=pi eta , we show that a very good fit of the KLOE data can be achieved with two real parameters, using a T-matrix previously determined from gamma gamma scattering data. This indicates a good compatibility between the two data sets and confirms the validity of the T-matrix. The resulting amplitude is also found to be compatible with the chiral soft pion theorem. Applications to the I=1 scalar form factors and to the a_0(980) resonance complex pole are presented.

Chiral dynamics and S-wave contributions in {bar{B}}^0/D^0 rightarrow pi ^{pm }eta l^{mp } nu decays

In this work, we analyze the semi-leptonic decays bar{B}^0/D^0 rightarrow (a_0(980)^{pm }rightarrow pi ^{pm }eta ) l^{mp } nu within light-cone sum rules. The two and three-body light-cone distribution amplitudes (LCDAs) of the B meson and the only available two-body LCDA of the D meson are used. To include the finite-width effect of the a_0(980), we use a scalar form factor to describe the final-state interaction between the pi eta mesons, which was previously calculated within unitarized Chiral Perturbation Theory. The result for the decay branching fraction of the D^0 decay is in good agreement with that measured by the BESIII Collaboration, while the branching fraction of the {bar{B}}^0 decay can be tested in future experiments.

Study of the process e^+e^- rightarrow eta pi ^0gamma in the energy range sqrt{s} = {1.05-2.00} GeV with the SND detector

The process e^+e^-rightarrow eta pi ^0gamma is studied in the center-of-mass energy range 1.05–2.00 GeV using data with an integrated luminosity of 94.5 hbox {pb}^{-1} collected by the SND detector at the VEPP-2000 e^{+}e^{-} collider. The e^+e^-rightarrow eta pi ^0gamma cross section is measured for the first time. It is shown that the dominant mechanism of this reaction is the transition through the omega eta intermediate state. The measured cross section of the subprocess e^+e^-rightarrow omega eta rightarrow eta pi ^0gamma is consistent with previous measurements in the e^+e^-rightarrow pi ^+pi ^-pi ^0eta mode. It is found, with a significance of 5.6sigma , that the process e^+e^-rightarrow eta pi ^0gamma is not completely described by hadronic vector-pseudoscalar intermediate states. The cross section of this missing contribution, which can originate from radiation processes, e. g. e^+e^-rightarrow a_{0}(1450)gamma , is measured. It is found to be 15–20 pb in the wide energy range from 1.3 to 1.9 GeV.

QCD sum rule studies on the s s {bar{s}} {bar{s}} tetraquark states of J^{PC} = 0^{-+}

We apply the method of QCD sum rules to study the s s {bar{s}} {bar{s}} tetraquark states of J^{PC} = 0^{-+}. We construct all the relevant s s {bar{s}} {bar{s}} tetraquark currents, and find that there are only two independent ones. We use them to further construct two weakly-correlated mixed currents. One of them leads to reliable QCD sum rule results and the mass is extracted to be 2.51^{+0.15}_{-0.12} GeV, suggesting that the X(2370) or the X(2500) can be explained as the ss{bar{s}}{bar{s}} tetraquark state of J^{PC} = 0^{-+}. To verify this interpretation, we propose to further study the pi pi /K {bar{K}} invariant mass spectra of the J/psi rightarrow gamma pi pi eta ^prime /gamma K {bar{K}} eta ^prime decays in BESIII to examine whether there exists the f_0(980) resonance.

The pi eta interaction and a_0 resonances in photon\u2013photon scattering

We revisit the information on the two lightest a_0 resonances and S-wave pi eta scattering that can be extracted from photon–photon scattering experiments. For this purpose we construct a model for the S-wave photon–photon amplitudes which satisfies analyticity properties, two-channel unitarity and obeys the soft photon as well as the soft pion constraints. The underlying I=1 hadronic T-matrix involves six phenomenological parameters and is able to account for two resonances below 1.5 GeV. We perform a combined fit of the gamma gamma rightarrow pi eta and gamma gamma rightarrow K_SK_S high statistics experimental data from the Belle collaboration. Minimisation of the chi ^2 is found to have two distinct solutions with approximately equal chi ^2. One of these exhibits a light and narrow excited a_0 resonance analogous to the one found in the Belle analysis. This however requires a peculiar coincidence between the J=0 and J=2 resonance effects which is likely to be unphysical. In both solutions the a_0(980) resonance appears as a pole on the second Riemann sheet. The location of this pole in the physical solution is determined to be m-ivarGamma /2=1000.7^{+12.9}_{-0.7} -i,36.6^{+12.7}_{-2.6} MeV. The solutions are also compared to experimental data in the kinematical region of the decay eta rightarrow pi ^0gamma gamma . In this region an isospin violating contribution associated with {pi ^+}{pi ^-} rescattering must be added for which we provide a dispersive evaluation.

Determination of the Pole Position of the Lightest Hybrid Meson Candidate.

Mapping states with explicit gluonic degrees of freedom in the light sector is a challenge, and has led to controversies in the past. In particular, the experiments have reported two different hybrid candidates with spin-exotic signature, π_{1}(1400) and π_{1}(1600), which couple separately to ηπ and η^{'}π. This picture is not compatible with recent Lattice QCD estimates for hybrid states, nor with most phenomenological models. We consider the recent partial wave analysis of the η^{(')}π system by the COMPASS Collaboration. We fit the extracted intensities and phases with a coupled-channel amplitude that enforces the unitarity and analyticity of the S matrix. We provide a robust extraction of a single exotic π_{1} resonant pole, with mass and width 1564±24±86 and 492±54±102 MeV, which couples to both η^{(')}π channels. We find no evidence for a second exotic state. We also provide the resonance parameters of the a_{2}(1320) and a_{2}^{'}(1700).

Measurement of ηc(1S) , ηc(2S) , and nonresonant η′π+π− production via two-photon collisions

We report the measurement of gamma gamma to eta_c(1S), eta_c(2S) to eta' pi+ pi- with eta' decays to gamma rho and eta pi+ pi- using 941 fb^{-1} of data collected with the Belle detector at the KEKB asymmetric-energy e+e- collider. The eta_c(1S) mass and width are measured to be M = [2984.6\pm0.7 (stat.)\pm2.2 (syst.)] MeV/c^{2} and \Gamma = [30.8^{+2.3}_{-2.2}~(stat.) \pm 2.5~(syst.)] MeV, respectively. First observation of eta_c(2S) to eta' pi+ pi- with a significance of 5.5sigma including systematic error is obtained, and the eta_c(2S) mass is measured to be M = [3635.1\pm3.7~(stat.)\pm2.9~(syst.)] MeV/c^{2}. The products of the two-photon decay width and branching fraction (B) of decays to eta'pi+ pi- are determined to be \Gamma_{gamma gamma}B = [65.4\pm2.6~(stat.)\pm6.9~(syst.)] eV for eta_c(1S) and [5.6^{+1.2}_{-1.1}~(stat.)\pm1.1~(syst.)] eV for eta_c(2S). A new decay mode for the eta_c(1S) to eta'f_0(2080) with f_0(2080) to pi+ pi- is observed with a statistical significance of 20sigma. The f_0(2080) mass and width are determined to be M = [2083^{+63}_{-66}~(stat.)\pm 32~(syst.)] MeV/c^{2} and \Gamma = [178^{+60}_{-178}~(stat.) \pm 55~(syst.)] MeV. The cross sections for gamma gamma to eta' pi+ pi- and eta'f_{2}(1270) are measured for the first time.

Eta ^{prime }rightarrow eta pi pi decays in unitarized resonance chiral theory

We study the hadronic eta ^{prime }rightarrow eta pi pi decays within the framework of U(3)_{L}otimes U(3)_{R} Chiral Perturbation Theory including resonance states and the complete one-loop corrections. The amplitude is projected in partial waves and unitarized by means of the N / D method resumming both the important S- and D-wave pi pi and the subleading S-wave pi eta final-state interactions. The participating scalar multiplet mass and coupling strengths are determined from fits to the Dalitz plot experimental data recently released by the A2 collaboration. As a byproduct of our analysis, the associated Dalitz-plot slope parameters are found to be a=-,0.072(7)_{mathrm{stat}}(8)_{mathrm{syst}},,b=-,0.052(1)_{mathrm{stat}}(2)_{mathrm{syst}}, d=-,0.051(8)_{mathrm{stat}}(6)_{mathrm{syst}}, which lie in the ballpark of the current experimental and theoretical determinations.

Measurements of absolute branching fractions for D mesons decays into two pseudoscalar mesons

Using a data sample of $e^+e^-$ collision data with an integrated luminosity of 2.93 fb$^{-1}$ taken at the center-of-mass energy $\sqrt s= 3.773$~GeV with the BESIII detector operating at the BEPCII storage rings, we measure the absolute branching fractions of the two-body hadronic decays $D^+\to \pi^+\pi^0$, $K^+ \pi^0$, $\pi^+ \eta$, $K^+\eta$, $\pi^+\eta^\prime$, $K^+\eta^\prime$, $K_S^0 \pi^+$, $K_S^0 K^+$, and $D^0\to \pi^+ \pi^-$, $K^+ K^-$, $K^\mp \pi^\pm$, $K_S^0 \pi^0$, $K_S^0 \eta$, $K_S^0 \eta^\prime$. Our results are consistent with previous measurements within uncertainties. Among them, the branching fractions for $D^+\to\pi^+\pi^0$, $K^+\pi^0$, $\pi^+\eta$, $\pi^+\eta^\prime$, $K_S^0 \pi^+$, $K_S^0 K^+$ and $D^0 \to K_S^0 \pi^0$, $K_S^0 \eta$, $K_S^0 \eta^\prime$ are determined with improved precision compared to the world average values.

Extended chiral Khuri\u2013Treiman formalism for eta rightarrow 3pi and the role of the a_0(980), f_0(980) resonances

Recent experiments on eta rightarrow 3pi decays have provided an extremely precise knowledge of the amplitudes across the Dalitz region which represent stringent constraints on theoretical descriptions. We reconsider an approach in which the low-energy chiral expansion is assumed to be optimally convergent in an unphysical region surrounding the Adler zero, and the amplitude in the physical region is uniquely deduced by an analyticity-based extrapolation using the Khuri–Treiman dispersive formalism. We present an extension of the usual formalism which implements the leading inelastic effects from the Kbar{K} channel in the final-state pi pi interaction as well as in the initial-state eta pi interaction. The constructed amplitude has an enlarged region of validity and accounts in a realistic way for the influence of the two light scalar resonances f_0(980) and a_0(980) in the dispersive integrals. It is shown that the effect of these resonances in the low-energy region of the eta rightarrow 3pi decay is not negligible, in particular for the 3pi ^0 mode, and improves the description of the energy variation across the Dalitz plot. Some remarks are made on the scale dependence and the value of the double quark mass ratio Q.

Dispersion relations for eta 'rightarrow eta pi pi

We present a dispersive analysis of the decay amplitude for eta 'rightarrow eta pi pi that is based on the fundamental principles of analyticity and unitarity. In this framework, final-state interactions are fully taken into account. Our dispersive representation relies only on input for the {pi pi } and {pi }eta scattering phase shifts. Isospin symmetry allows us to describe both the charged and neutral decay channel in terms of the same function. The dispersion relation contains subtraction constants that cannot be fixed by unitarity. We determine these parameters by a fit to Dalitz-plot data from the VES and BES-III experiments. We study the prediction of a low-energy theorem and compare the dispersive fit to variants of chiral perturbation theory.

Possible signatures for tetraquarks from the decays of a_0(980), a_0(1450)

Based on the recent proposal for the tetraquarks with the mixing scheme, we investigate fall-apart decays of a_0(980), a_0(1450) into two lowest-lying mesons. This mixing scheme suggests that a_0(980) and a_0(1450) are the tetraquarks with the mixtures of two spin configurations of diquark and antidiquark. Due to the relative sign differences in the mixtures, the couplings of fall-apart decays into two mesons are strongly enhanced for a_0(980) but suppressed for a_0(1450). We report that this expectation is supported by their experimental decays. In particular, the ratios of the associated partial decay widths, which depend on some kinematical factors and the couplings, are found to be around Gamma [a_0(980)rightarrow pi eta ]/Gamma [a_0(1450)rightarrow pi eta ] = 2.51-2.54, Gamma [a_0(980)rightarrow Kbar{K}]/Gamma [a_0(1450)rightarrow Kbar{K}] = 0.52-0.89, which seems to agree with the experimental ratios reasonably well. This agreement can be interpreted as the tetraquark signatures for a_0(980), a_0(1450).

Form factors of the isovector scalar current and the [Formula: see text] scattering phase shifts.

A model for S-wave eta pi scattering is proposed which could be realistic in an energy range from threshold up to above 1 GeV, where inelasticity is dominated by the K{bar{K}} channel. The T-matrix, satisfying two-channel unitarity, is given in a form which matches the chiral expansion results at order p^4 exactly for the eta pi rightarrow eta pi , eta pi rightarrow K{bar{K}} amplitudes and approximately for K{bar{K}}rightarrow K{bar{K}}. It contains six phenomenological parameters. Asymptotic conditions are imposed which ensure a minimal solution of the Muskhelishvili–Omnès problem, thus allowing one to compute the eta pi and K{bar{K}} form factor matrix elements of the I=1 scalar current from the T-matrix. The phenomenological parameters are determined such as to reproduce the experimental properties of the a_0(980), a_0(1450) resonances, as well as the chiral results of the eta pi and K{bar{K}} scalar radii, which are predicted to be remarkably small at O(p^4). This T-matrix model could be used for a unified treatment of the eta pi final-state interaction problem in processes such as eta 'rightarrow eta pi pi , phi rightarrow eta pi gamma , or the eta pi initial-state interaction in eta rightarrow 3pi .

Lambda Pi Eta: The Founding and Evolution of Communication's Undergraduate Honor Society from a Systems Perspective

From a systems standpoint, Lambda Pi Eta is an influential subsystem within the Communication discipline. The input–throughput–output teaching-learning dialectic arguably achieves maximum potential at the point where the student is positioned. The evolution of the Arkansas Alpha LPH chapter into an accredited national honor society, documented in the words of the founding student and professor, illustrate key concepts of systems thinking, sense-making, and “learning organizations.” Envisioning the student-scholar, the honor society, NCA and its institutional members, and their interconnected partners as a transformative “super-system” fosters appreciation of the active role students play in networked realms of 21st century communication and education.

Analysis of theη′photoproduction off the proton and preliminary beam asymmetry results at the GRAAL experiment

Differential and total cross section measurements on eta' photoproduction were published by the CLAS Collaboration (M. Dugger et al., Phys. Rev. Lett. 96, 062001 (2006) and M. Williams et al., Phys.Rev.C80, 045213 (2009)) for center-of-mass energies from near the threshold up to 2.84 GeV, and by the CB-ELSA-TAPS Collaboration (V. Crede et al., Phys. Rev. C80, 055202 (2009)) up to 2.36 GeV and also making a precise threshold scan of the differential cross section in the 1446 -1527.4 MeV gamma beam energy range. However, the wide information about reaction cross sections are not sufficient to understand the role of resonances involved in the process. Different theoretical works stressed the importance to have also polarization observables in order to solve the ambiguity in the choice of the parameters used in their models. We present the analysis of the eta' photoproduction off the proton, identifying the meson via the gamma gamma, pi(0)pi(0)eta, and pi(+)pi(-)eta decay modes by using the GRAAL apparatus; and we show the preliminary GRAAL results on the beam asymmetry Sigma from the threshold (1.446 GeV) up to 1.5 GeV.

Effective multiquark interactions with explicit breaking of chiral symmetry

In a long distance Lagrangian approach to the low lying meson phenomenology we present and discuss the most general spin zero multi-quark interaction vertices of non-derivative type which include a set of effective interactions proportional to the current quark masses, breaking explicitely the chiral SU(3)_L X SU(3)_R and U_A(1) symmetries. These vertices are of the sameorder in Nc counting as the 't Hooft flavor determinant interaction and the 8 quark interactions which extend the original leading in Nc four quark interaction Lagrangian of Nambu and Jona-Lasinio. The Nc assignements match the counting rules based on arguments set by the scale of spontaneous chiral symmetry breaking. With path integral bosonization techniques which take appropriately into account the quark mass differences we derive the mesonic Lagrangian up to 3-point mesonic vertices. We demonstrate that explicit symmetry breaking effects in interactions are essential to obtain the correct empirical ordering and magnitude of the splitting of certain states such as m_K < m_eta for the pseudoscalars and m{kappa(800)} < m{a0(980)} m{f0(980)} in the scalar sector, and achieve total agreement with the empirical low lying meson mass spectra. With all parameters of the model fixed by the spectra we analyze further a bulk of two body decays at tree level of the bosonic Lagrangian: the strong decays of the scalars sigma->pi pi, f0->pi pi, kappa->pi K, a0(980)->pi eta, as well as the two photon decays of a0, f0 and sigma mesons and the anomalous decays of the pseudoscalars {pi,eta,eta'}-> 2 photons. Our results for the strong decays are within the current expectations and the pseudoscalar radiative decays are in very good agreement with data. The radiative decays of the scalars are smaller than the observed values for the f0 and the sigma, but reasonable for the a0. A detailed discussion accompanies all the results.