Eta Decay Research Articles

Measurement of tau _text {L} using the {B} _s^0 rightarrow J/psi eta decay mode

Using a proton–proton collision data sample collected by the LHCb detector and corresponding to an integrated luminosity of 5.7~text {fb}^{-1}, the lifetime of the light {{B} ^0_{s}} mass eigenstate, tau _{L}, is measured using the B^0_s rightarrow J/psi eta decay mode to be τL=1.445±0.016(stat)±0.008(syst)ps.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \ au _{\ ext {L}} = 1.445 \\pm 0.016 \ ext {(stat)} \\pm 0.008 \ ext {(syst)} \\,\ ext {ps}. \\end{aligned}$$\\end{document}A combination of this result with a previous LHCb analysis using an independent dataset corresponding to 3 fb^{-1} of integrated luminosity gives τL=1.452±0.014±0.007±0.002ps,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \ au _{\ ext {L}} = 1.452 \\pm 0.014 \\pm 0.007 \\pm 0.002 \\,\ ext {ps}, \\end{aligned}$$\\end{document}where the first uncertainty is statistical, the second due to the uncorrelated part of the systematic uncertainty and the third due to the correlated part of the systematic uncertainty.

A theoretical analysis of the semileptonic decays eta ^{(prime )}rightarrow pi ^0l^+l^- and eta ^prime rightarrow eta l^+l^-

A complete theoretical analysis of the C- conserving semileptonic decays eta ^{(prime )}rightarrow pi ^0l^+l^- and eta ^prime rightarrow eta l^+l^- (l=e or mu ) is carried out within the framework of the Vector Meson Dominance (VMD) model. An existing phenomenological model is used to parametrise the VMD coupling constants and the associated numerical values are obtained from an optimisation fit to Vrightarrow Pgamma and Prightarrow Vgamma radiative decays (V=rho ^0, omega , phi and P=pi ^0, eta , eta ^{prime }). The decay widths and dilepton energy spectra for the two eta rightarrow pi ^0l^+l^- processes obtained using this approach are compared and found to be in good agreement with other results available in the published literature. Theoretical predictions for the four eta ^{prime }rightarrow pi ^0l^+l^- and eta ^prime rightarrow eta l^+l^- decay widths and dilepton energy spectra are calculated and presented for the first time in this work.

Resonant a_0(980) state in triangle rescattering D_s^+rightarrow pi ^+pi ^0eta decays

We study the D_s^+rightarrow pi ^+(a_0(980)^0rightarrow )pi ^0eta , pi ^0(a_0(980)^+rightarrow )pi ^+eta decays, which have been recently measured by the BESIII collaboration. We propose that D_s^+rightarrow pi ^{+(0)}(a_0(980)^{0(+)}rightarrow )pi ^{0(+)}eta receives the contributions from the triangle rescattering processes, where M^0 and rho ^+ in D_s^+rightarrow M^0 rho ^+, by exchanging pi ^{0(+)}, are formed as a_0(980)^{0(+)} and pi ^{+(0)}, respectively, with M^0=(eta ,eta '). Accordingly, we calculate that mathcal{B}(D_s^+rightarrow a_0(980)^{0(+)}pi ^{+(0)})= (1.7pm 0.2pm 0.1)times 10^{-2} and mathcal{B}(D_s^+rightarrow pi ^{+(0)}(a_0(980)^{0(+)}rightarrow )pi ^{0(+)}eta ) =(1.4pm 0.1pm 0.1)times 10^{-2}, being consistent with the data.

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.

Dispersive analysis of eta rightarrow 3 pi

The dispersive analysis of the decay eta rightarrow 3pi is reviewed and thoroughly updated with the aim of determining the quark mass ratio Q^2=(m_s^2-m_{ud}^2)/(m_d^2-m_u^2). With the number of subtractions we are using, the effects generated by the final state interaction are dominated by low energy pi pi scattering. Since the corresponding phase shifts are now accurately known, causality and unitarity determine the decay amplitude within small uncertainties – except for the values of the subtraction constants. Our determination of these constants relies on the Dalitz plot distribution of the charged channel, which is now measured with good accuracy. The theoretical constraints that follow from the fact that the particles involved in the transition represent Nambu–Goldstone bosons of a hidden approximate symmetry play an equally important role. The ensuing predictions for the Dalitz plot distribution of the neutral channel and for the branching ratio varGamma _{eta rightarrow 3pi ^0}/ varGamma _{eta rightarrow pi ^+pi ^-pi ^0} are in very good agreement with experiment. Relying on a known low-energy theorem that relates the meson masses to the masses of the three lightest quarks, our analysis leads to Q=22.1(7), where the error covers all of the uncertainties encountered in the course of the calculation: experimental uncertainties in decay rates and Dalitz plot distributions, noise in the input used for the phase shifts, as well as theoretical uncertainties in the constraints imposed by chiral symmetry and in the evaluation of isospin breaking effects. Our result indicates that the current algebra formulae for the meson masses only receive small corrections from higher orders of the chiral expansion, but not all of the recent lattice results are consistent with this conclusion.

Analytic representations of mK , FK , mη , and Fη in two loop SU(3) chiral perturbation theory

In this work, we consider expressions for the masses and decay constants of the pseudoscalar mesons in $SU(3)$ chiral perturbation theory. These involve sunset diagrams and their derivatives evaluated at $p^2=m_P^2$ ($P=\pi, K, \eta$). Recalling that there are three mass scales in this theory, $m_\pi$, $m_K$ and $m_\eta$, there are instances when the finite part of the sunset diagrams do not admit an expression in terms of elementary functions, and have therefore been evaluated numerically in the past. In a recent publication, an expansion in the external momentum was performed to obtain approximate analytic expressions for $m_\pi$ and $F_\pi$, the pion mass and decay constant. We provide fully analytic exact expressions for $m_K$ and $m_\eta$, the kaon and eta masses, and $F_K$ and $F_\eta$, the kaon and eta decay constants. These expressions, calculated using Mellin-Barnes methods, are in the form of double series in terms of two mass ratios. A numerical analysis of the results to evaluate the relative size of contributions coming from loops, chiral logarithms as well as phenomenological low-energy constants is presented. We also present a set of approximate analytic expressions for $m_K$, $F_K$, $m_\eta$ and $F_\eta$ that facilitate comparisons with lattice results. Finally, we show how exact analytic expressions for $m_\pi$ and $F_\pi$ may be obtained, the latter having been used in conjunction with the results for $F_K$ to produce a recently published analytic representation of $F_K/F_\pi$.

Probing a new strongly interacting sector via composite diboson resonances

Diphoton resonance was a crucial discovery mode for the 125 GeV SM Higgs boson at the LHC. This mode or the more general diboson modes may also play an important role in probing for new physics beyond the SM. In this paper, we consider the possibility that a diphoton resonance is due to a composite (pseudo)scalar boson, whose constituents are either new hyperquarks Q or scalar hyperquarks tilde{Q} confined by a new hypercolor force at a confinement scale Lambda_h. Assuming the mass m_Q (or m_{tilde Q}) >> Lambda_h, a diphoton resonance could be interpreted as either a Q bar{Q} state eta_Q with J^{PC} = 0^{-+} or a tilde{Q} tilde{Q}^dagger state eta_{tilde Q} with J^{PC}=0^{++}. For the Q bar{Q} scenario, there will be a spin-triplet partner psi_Q which is slightly heavier than eta_Q due to the hyperfine interactions mediated by hypercolor gluon exchange; while for the tilde{Q} tilde{Q}^dagger scenario, the spin-triplet partner chi_{tilde Q} arises from higher radial excitation with nonzero orbital angular momentum. We consider productions and decays of eta_Q, eta_{tilde Q}, psi_Q, and chi_{tilde Q} at the LHC using the NRQCD factorization approach. We discuss how to test these scenarios by using the DY process and the forward dijet azimuthal angular distributions to determine the J^{PC} quantum number of the diphoton resonance. Constraints on the parameter space can be obtained by interpreting some of the small diphoton excesses reported by the LHC as the composite scalar or pseudoscalar of the model. Another important test of the model is the presence of a nearby hypercolor-singlet but color-octet state like the eta^8_Q or eta^8_{tilde Q}, which can also be constrained by dijet or monojet+monophoton data. Both possibilities of a large or small width of the resonance can be accommodated, depending on whether the hyper-glueball states are kinematically allowed in the final state or not.

The branching ratio omega rightarrow pi ^+pi ^- revisited

We analyze the most recent data for the pion vector form factor in the timelike region, employing a model-independent approach based on dispersion theory. We confirm earlier observations about the inconsistency of different modern high-precision data sets. Excluding the BaBar data, we find an updated value for the isospin-violating branching ratio {mathscr {B}}(omega rightarrow pi ^+pi ^-) = (1.46pm 0.08) times 10^{-2}. As a side result, we also extract an improved value for the pion vector or charge radius, sqrt{langle r_V^2rangle } = 0.6603(5)(4),text {fm}, where the first uncertainty is statistical as derived from the fit, while the second estimates the possible size of nonuniversal radiative corrections. In addition, we demonstrate that modern high-quality data for the decay eta 'rightarrow pi ^+pi ^-gamma will allow for an even improved determination of the transition strength omega rightarrow pi ^+pi ^-.

The strong decays of X(3940) and X(4160)

The new mesons X(3940) and X(4160) have been found by Belle Collaboration in the processes e^+e^-rightarrow J/psi D^{(*)}{bar{D}}^{(*)}. Considering X(3940) and X(4160) as eta _c(3S) and eta _c(4S) states, the two-body open charm OZI-allowed strong decay of eta _c(3S) and eta _c(4S) are studied by the improved Bethe–Salpeter method combined with the ^3P_0 model. The strong decay width of eta _c(3S) is Gamma _{eta _c(3S)}=(33.5^{+18.4}_{-15.3}) MeV, which is close to the result of X(3940); therefore, eta _c(3S) is a good candidate of X(3940). The strong decay width of eta _c(4S) is Gamma _{eta _c(4S)}=(69.9^{+22.4}_{-21.1}) MeV, considering the errors of the results, it is close to the lower limit of X(4160). But the ratio of the decay width frac{Gamma (D{bar{D}}^*)}{Gamma (D^*{bar{D}}^*)} of eta _c(4S) is larger than the experimental data of X(4160). According to the above analysis, eta _c(4S) is not the candidate of X(4160), and more investigations of X(4160) is needed.

On the structure of anomalous composite Higgs models

We describe the anomaly structure of a composite Higgs model in which the SO(5) / SO(4) coset structure of the minimal model is extended by an additional, non-linearly realised U(1)_{eta }. In addition, we show that the effective Lagrangian admits a term that, like the Wess–Zumino–Witten term in the chiral Lagrangian for QCD, is not invariant under the non-linearly realised symmetries, but rather changes by a total derivative. This term is unlike the Wess–Zumino–Witten term in that it does not arise from anomalies. If present, it may give rise to the rare decay eta rightarrow h W^+ W^-Z. The phenomenology of the singlet in this model differs from that in a model based on SO(6) / SO(5), in that couplings to both gluons and photons, arising via anomalies, are present. We show that while some tuning is needed to accommodate flavour and electroweak precision constraints, the model is no worse than the minimal model in this regard.

Convergence properties of eta rightarrow 3pi decays in chiral perturbation theory

The convergence of the decay widths and some of the Dalitz plot parameters of the decay eta rightarrow 3pi seems problematic in low energy QCD. In the framework of resummed chiral perturbation theory, we explore the question of compatibility of experimental data with a reasonable convergence of a carefully defined chiral series. By treating the uncertainties in the higher orders statistically, we numerically generate a large set of theoretical predictions, which are then confronted with experimental information. In the case of the decay widths, the experimental values can be reconstructed for a reasonable range of the free parameters and thus no tension is observed, in spite of what some of the traditional calculations suggest. The Dalitz plot parameters a and d can be described very well too. When the parameters b and alpha are concerned, we find a mild tension for the whole range of the free parameters, at less than 2sigma C.L. This can be interpreted in two ways – either some of the higher order corrections are indeed unexpectedly large or there is a specific configuration of the remainders, which is, however, not completely improbable.

New measurement of the rare decayη→π0γγwith the Crystal Ball/TAPS detectors at the Mainz Microtron

A new measurement of the rare, doubly radiative decay eta->pi^0 gamma gamma was conducted with the Crystal Ball and TAPS multiphoton spectrometers together with the photon tagging facility at the Mainz Microtron MAMI. New data on the dependence of the partial decay width, Gamma(eta->pi^0 gamma gamma), on the two-photon invariant mass squared, m^2(gamma gamma), as well as a new, more precise value for the decay width, Gamma(eta->pi^0 gamma gamma) = (0.33+/-0.03_tot) eV, are based on analysis of 1.2 x 10^3 eta->pi^0 gamma gamma decays from a total of 6 x 10^7 eta mesons produced in the gamma p -> eta p reaction. The present results for dGamma(eta->pi^0 gamma gamma)/dm^2(gamma gamma) are in good agreement with previous measurements and recent theoretical calculations for this dependence.

New determination of theηtransition form factor in the Dalitz decayη→e+e−γwith the Crystal Ball/TAPS detectors at the Mainz Microtron

The Dalitz decay eta -> e^+ e^- gamma has been measured in the gamma p -> eta p reaction with the Crystal Ball and TAPS multiphoton spectrometers, together with the photon tagging facility at the Mainz Microtron MAMI. The experimental statistic used in this work is one order of magnitude greater than in any previous measurement of eta -> e^+ e^- gamma. The value obtained for the slope parameter 1/Lambda^2 of the eta transition form factor, 1/Lambda^2 = (1.95 +/- 0.15_stat +/- 0.10_syst) [1/GeV^2], is in good agreement with recent measurements conducted in eta -> e^+ e^- gamma and eta -> mu^+ mu^- gamma decays, as well as with recent form-factor calculations. The uncertainty obtained in the value of 1/Lambda^2 is lower compared to results from previous measurements of the eta -> e^+ e^- gamma decay.

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.

Comment on “Determination of light quark masses fromη→3π0”

In the commented paper [PRD 78, 034032 (2008); arXiv:0803.2956] Deandrea et al. claim that they provide a model-independent determination of the quantity $B_0(m_d-m_u)$ based on the analysis of the decay of eta to three neutral pions that takes the strong-interaction correction as an unknown parameter. In the following we show that the two constraints presented there as independent equations are in fact two approximations of a single constraint connecting together $B_0(m_d-m_u)$ with the strong-interaction correction to the $\eta\to3\pi^0$ decay amplitude. Thus, without some additional information on the latter (such as its correct value at least at one kinematic point) it does not lead to any determination of $B_0(m_d-m_u)$ and the numerical values presented there should not be taken seriously. We have also found that the numerical result for the studied quantity obtained in the commented paper is just an accidental number stemming from some numerical errors that had occurred in the computations presented there.

First study ofηc(1S),η(1760)andX(1835)production viaη′π+π−final states in two-photon collisions

The invariant mass spectrum of the \eta' \pi^+ \pi^- final state produced in two-photon collisions is obtained using a 673 fb^{-1} data sample collected in the vicinity of the \Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy e^+e^- collider. We observe a clear signal of the \eta_c and measure its mass and width to be M(\eta_c)=(2982.7 +- 1.8(stat) +- 2.2(syst) +- 0.3(model)) MeV/c^2 and \Gamma(\eta_c) = (37.8^{+5.8}_{-5.3}(stat) +- 2.8(syst) +- 1.4(model)) MeV/c^2. The third error is an uncertainty due to possible interference between the \eta_c and a non-resonant component. We also report the first evidence for \eta(1760) decay to \eta' \pi^+ \pi^-; we find two solutions for its parameters, depending on the inclusion or not of the X(1835), whose existence is of marginal significance in our data. From a fit to the mass spectrum using coherent X(1835) and \eta(1760) resonant amplitudes, we set a 90% confidence level upper limit on the product \Gamma_{\gamma\gamma} \BR (\eta' \pi^+ \pi^-) for the X(1835).

Anomalous decays ofη′ andηinto four pions

We report about the calculation of the branching ratios of the yet unmeasured eta' decays into four pions, based on a combination of chiral perturbation theory and vector-meson dominance [1]. The decays eta' -> 2(pi^+pi^-) and eta' -> pi^+pi^-2pi^0 are P-wave dominated and can largely be thought to proceed via two rho resonances. Branching fractions of (1.0 +- 0.3) x 10^-4 and (2.4 +- 0.7) x 10^-4, respectively, are calculated which are not much lower than the current experimental upper limits. The decays eta' -> 4pi^0 and eta -> 4pi^0, in contrast, are D-wave driven [2] as long as conservation of CP symmetry is assumed, and are significantly further suppressed. Any experimental evidence for the decay eta -> 4pi^0 could almost certainly be interpreted as a signal of CP violation. The CP-violating amplitudes for eta', eta -> 4pi^0, induced by the QCD theta-term, are given as well.

Search forCPandPviolating pseudoscalar decays intoππ

Using a sample of $(225.2\pm 2.8)\times 10^6$ $J/\psi$ events collected with the Beijing Spectrometer (BESIII) at the Beijing Electron-Positron Collider, CP and $P$ violating decays of $\eta$, $\eta'$ and $\etac$ into $\pi^+\pi^-$ and $\pi^0 \pi^0$ are searched for in $\jpsi$ radiative decays. No significant $\eta$, $\eta'$ or $\etac$ signal is observed, and 90% confidence level upper limits of $\BR(\eta \to \pi^+\pi^-)<3.9\times 10^{-4}$, $\BR(\eta' \to \pi^+\pi^-)<5.5\times 10^{-5}$, $\BR(\etac \to \pi^+\pi^-)<1.3\times 10^{-4}$, $\BR(\eta \to \pi^0 \pi^0)<6.9\times 10^{-4}$, $\BR(\eta' \to \pi^0 \pi^0)<4.5\times 10^{-4}$ and $\BR(\etac \to \pi^0 \pi^0)<4.2\times 10^{-5}$ are obtained.

Chiral dynamics predictions for η′ → ηππ

The hadronic decays eta' -> eta pi pi are studied in the frameworks of large-Nc Chiral Perturbation Theory, at lowest and next-to-leading orders, and Resonance Chiral Theory in the leading 1/Nc approximation. Higher order effects such as pi-pi final state interactions are taken into account through a detailed unitarization procedure. The inclusion of finite-width effects in the case of RChT is also discussed. The Dalitz plot distribution and the differential branching ratio are computed in both approaches. The predicted Dalitz plot parameters obtained from the different treatments are compared with the most recent measured values. We find that the eta' -> eta pi pi branching ratios are easily understood, while the Dalitz plot parameters require the inclusion of pi-pi loops in order to achieve a reasonable agreement. Our final predictions agree with the experimental measurements. We hope our results to be of relevance for present and future experimental analyses of these decays.

ETA-NUCLEON COUPLING CONSTANT IN QCD WITHSU(3)SYMMETRY BREAKING

We study the ηNN coupling constant using the method of QCD sum rules starting from the vacuum-to-eta correlation function of the interpolating fields of two nucleons. The matrix element of this correlation has been taken with respect to nucleon spinors to avoid unwanted pole contribution. The SU(3) -flavor symmetry breaking effects have been accounted for via the η-mass, s-quark mass and eta decay constant to leading order. Out of the four sum rules obtained by taking the ratios of the two sum rules in conjunction with the two sum rules in nucleon mass, three are found to give mutually consistent results. We find the SU(3) breaking effects significant, as large as 50% of the SU(3) symmetric part.