Isoscalar Mesons Research Articles

Δ(1232) effects in density-dependent relativistic Hartree-Fock theory and neutron stars

The density-dependent relativistic Hartree-Fock (DDRHF) theory is extended to include $\Delta$-isobars for the study of dense nuclear matter and neutron stars. To this end, we solve the Rarita-Schwinger equation for spin-3/2 particle. Both the direct and exchange terms of the $\Delta$-isobars' self-energies are evaluated in details. In comparison with the relativistic mean field theory (Hartree approximation), a weaker parameter dependence is found for DDRHF. An early appearance of $\Delta$-isobars is recognized at $\rho_B\sim0.27$fm$^{-3}$, comparable with that of hyperons. Also, we find that the $\Delta$-isobars' softening of the equation of state is found to be mainly due to the reduced Fock contributions from the coupling of the isoscalar mesons, while the pion contributions are found negligibly small. We finally conclude that with typical parameter sets, neutron stars with $\Delta$-isobars in their interiors could be as heavy as the two massive pulsars whose masses are precisely measured, with slightly smaller radii than normal neutron stars.

Hot and dense matter beyond relativistic mean field theory

Properties of hot and dense matter are calculated in the framework of quantum hadro-dynamics by including contributions from two-loop (TL) diagrams arising from the exchange of iso-scalar and iso-vector mesons between nucleons. Our extension of mean-field theory (MFT) employs the same five density-independent coupling strengths which are calibrated using the empirical properties at the equilibrium density of iso-spin symmetric matter. Results of calculations from the MFT and TL approximations are compared for conditions of density, temperature, and proton fraction encountered in astrophysics applications involving compact objects. The TL results for the equation of state (EOS) of cold pure neutron matter at sub- and near-nuclear densities agree well with those of modern quantum Monte Carlo and effective field-theoretical approaches. Although the high-density EOS in the TL approximation for neutron-star matter is substantially softer than its MFT counterpart, it is able to support a $2M_\odot$ neutron star required by recent precise determinations. In addition, radii of $1.4M_\odot$ stars are smaller by $\sim 1$ km than obtained in MFT. In contrast to MFT, the TL results also give a better account of the single-particle or optical potentials extracted from analyses of medium-energy proton-nucleus and heavy-ion experiments. In degenerate conditions, the thermal variables are well reproduced by results of Landau's Fermi-Liquid theory in which density-dependent effective masses feature prominently. The ratio of the thermal components of pressure and energy density expressed as $\Gamma_{th}=1+(P_{th}/\epsilon_{th})$, often used in astrophysical simulations, exhibits a stronger dependence on density than on proton fraction and temperature in both MFT and TL calculations. The prominent peak of $\Gamma_{th}$ at supra-nuclear density found in MFT is, however, suppressed in TL calculations.

Localization of the glueball and possible decuplets of tensor mesons

We continue the study of flavor aspects of strong interaction. The answer to the question of glueball existence is probably a necessary step in this investigation. The existence of the glueball implies the existence of the decuplets. The model we consider requires that the mass of meson decuplet dominated by the glueball is enclosed between the masses of the ideal nonet N and S states.This description is applied to the two sets of the tensor mesons. One of them comprises the well-known particles that are attributed to the widely known nonet 2++. We argue that they belong to a decuplet if there exists the isoscalar tensor meson having the mass obeying the condition on the gluebal-dominated meson; the meson f2(1430) could be a candidate. Another set includes a large number of mesons lying in the 2 GeV region. This set is used to test the ability of the model to select particles belonging to the decuplet.

Measurement of central exclusiveπ+π−production inpp¯collisions ats=0.9and 1.96 TeV at CDF

We measure exclusive $\pi^+\pi^-$ production in proton-antiproton collisions at center-of-mass energies $\sqrt{s}$ = 0.9 and 1.96 TeV in the Collider Detector at Fermilab. We select events with two oppositely charged particles, assumed to be pions, with pseudorapidity $|\eta| < 1.3$ and with no other particles detected in $|\eta| < 5.9$. We require the $\pi^+\pi^-$ system to have rapidity $|y|<$ 1.0. The production mechanism of these events is expected to be dominated by double pomeron exchange, which constrains the quantum numbers of the central state. The data are potentially valuable for isoscalar meson spectroscopy and for understanding the pomeron in a region of transition between nonperturbative and perturbative quantum chromodynamics. The data extend up to dipion mass $M(\pi^+\pi^-)$ = 5000 MeV/$c^2$ and show resonance structures attributed to $f_0$ and $f_2(1270)$ mesons. From the $\pi^+\pi^-$ and $K^+K^-$ spectra, we place upper limits on exclusive $\chi_{c0}(3415)$ production.

Spin alignment and violation of the OZI rule in exclusive ω and ϕ production in pp collisions

Exclusive production of the isoscalar vector mesons ω and ϕ is measured with a 190 GeV/c proton beam impinging on a liquid hydrogen target. Cross section ratios are determined in three intervals of the Feynman variable xF of the fast proton. A significant violation of the OZI rule is found, confirming earlier findings. Its kinematic dependence on xF and on the invariant mass MpV of the system formed by fast proton pfast and vector meson V is discussed in terms of diffractive production of pfastV resonances in competition with central production. The measurement of the spin density matrix element ρ00 of the vector mesons in different selected reference frames provides another handle to distinguish the contributions of these two major reaction types. Again, dependences of the alignment on xF and on MpV are found. Most of the observations can be traced back to the existence of several excited baryon states contributing to ω production which are absent in the case of the ϕ meson. Removing the low-mass MpV resonant region, the OZI rule is found to be violated by a factor of eight, independently of xF.

DISPERSION THEORY METHODS FOR TRANSITION FORM FACTORS

Dispersion-theoretical analyses of transition form factors are stepping stones to a model-independent determination of the light-by-light scattering contribution to (g - 2)μ. We extend a calculation of the conversion decays of the lightest isoscalar vector mesons, ω/ϕ → π0ℓ+ℓ-, that builds on a previous dispersive analysis of the ω/ϕ → 3π partial-wave amplitudes and the pion vector form factor as its sole ingredients. We construct a good parametrization of e+e- → 3π that, together with information on the anomalous process γπ → ππ, allows us to obtain a description of the π0 transition form factor measured in e+e- → π0γ.

Toward the excited isoscalar meson spectrum from lattice QCD

We report on the extraction of an excited spectrum of isoscalar mesons using lattice QCD. Calculations on several lattice volumes are performed with a range of light quark masses corresponding to pion masses down to about 400 MeV. The distillation method enables us to evaluate the required disconnected contributions with high statistical precision for a large number of meson interpolating fields. We find relatively little mixing between light and strange in most JPC channels; one notable exception is the pseudoscalar sector where the approximate SU(3)F octet, singlet structure of the {\eta}, {\eta}' is reproduced. We extract exotic JPC states, identified as hybrid mesons in which an excited gluonic field is coupled to a color-octet qqbar pair, along with non-exotic hybrid mesons embedded in a qqbar-like spectrum.

Dispersive analysis of ω→3π and ϕ→3π decays

We study the three-pion decays of the lightest isoscalar vector mesons, omega and phi, in a dispersive framework that allows for a consistent description of final-state interactions between all three pions. Our results are solely dependent on the phenomenological input for the pion-pion P-wave scattering phase shift. We predict the Dalitz plot distributions for both decays and compare our findings to recent measurements of the phi --> 3pi Dalitz plot by the KLOE and CMD-2 collaborations. Dalitz plot parameters for future precision measurements of omega --> 3pi are predicted. We also calculate the pi-pi P-wave inelasticity contribution from omega-pi intermediate states.

Decay constants and form factors of s-wave and p-wave mesons in the covariant light-front quark model

We reanalyze the decay constants of s-wave and p-wave mesons and the D, B → M form factors, where M represents a pseudoscalar meson, a vector meson, a scalar meson or an axial vector meson within a covariant light-front quark model. The parameter β for wavefunctions of most of s-wave mesons and that of a few axial-vector mesons are fixed with the latest experimental information, wherever available or using the lattice calculations. The treatment of masses and mixing angles for strange axial vector mesons is improved for the purpose. We extend our analysis to determine the form factors appearing in the Ds, Bs → M transitions, and to the isoscalar final state mesons. Numerical results of the form factors for transitions between a heavy pseudoscalar meson and an s-wave or a p-wave light meson and their momentum dependence are presented in detail. Further, their sensitivity to uncertainties of the β parameters of the initial as well as the final mesons is investigated. Some experimental measurements of the charmed and bottom meson decays are employed to compare the decay constants and transition form factors obtained in this and other works.

Revisiting axial-vector meson mixing

Various phenomenological studies indicate that the mixing angle θK1 of K1A and K1B, the strange partners of the axial-vector mesons a1(1260) and b1(1235), respectively, lies in the vicinity of 35° or 55°, but whether this angle is larger or smaller than 45° still remains controversial. When the f1(1285)–f1(1420) mixing angle θP13 and the h1(1170)–h1(1380) mixing angle θP11 are determined from the mass relations, they depend on the masses of K1A and K1B, which in turn depend on the mixing angle θK1. We show that the approximate decoupling of the light qq¯ state from the heavier ss¯ state, which is empirically valid for vector, tensor and 3−− mesons, when applied to isoscalar axial-vector mesons, will enable us to discriminate different solutions of θP13 and θP11 and pick up θK1∼35°. Indeed, for θK1∼55°, the predicted θP11 disagrees sharply with the recent lattice calculation and the implied large ss¯ content of h1(1170) and qq¯ component of h1(1380) cannot explain the observation of their strong decays. We conclude that θK1 is smaller than 45°.

Relativistic description of finite nuclei based on realisticNNinteractions

A set of relativistic mean-field models is constructed, which includes the Hartree and Hartree-Fock (HF) approximations accounting for the exchange of isoscalar and isovector mesons as well as the pion. Density-dependent coupling functions are determined to reproduce the components of the nucleon self-energy at the Fermi surface, obtained within the Dirac-Brueckner-HF (DBHF) approach by using a realistic nucleon-nucleon interaction. It is investigated to which extent the various mean-field models can reproduce the DBHF results for the momentum dependence of the self-energies and the total energy of infinite matter. Also, the mean-field models are used to evaluate the bulk properties of spherical closed-shell nuclei. We find that the HF model, which allows for the exchange of $\ensuremath{\sigma},\phantom{\rule{0.28em}{0ex}}\ensuremath{\omega},\phantom{\rule{0.28em}{0ex}}\ensuremath{\rho}$, and $\ensuremath{\delta}$ mesons and pions, yields the best reproduction of the DBHF results in infinite matter and also provides a good description of the properties of finite nuclei without any adjustment of parameters.

Isoscalar meson spectroscopy from lattice QCD

We extract to high statistical precision an excited spectrum of single-particle isoscalar mesons using lattice QCD, including states of high spin and, for the first time, light exotic JPC isoscalars. The use of a novel quark field construction has enabled us to overcome the long-standing challenge of efficiently including quark-annihilation contributions. Hidden-flavor mixing angles are extracted and while most states are found to be close to ideally flavor mixed, there are examples of large mixing in the pseudoscalar and axial sectors in line with experiment. The exotic JPC isoscalar states appear at a mass scale comparable to the exotic isovector states.

Where is the pseudoscalar glueball?

The pseudoscalar mesons π(1300), K(1460), η(1295), η(1405) and η(1475) are assumed to form the meson decuplet which includes the glueball as the basis state supplementing the standard SU(3)F nonet of light states (q = u, d, s). The decuplet is investigated by using the algebraic approach based on the hypothesis of vanishing exotic commutators of SU(3)F ‘charges’ and their time derivatives. This leads to a system of master equations determining: (a) octet contents of the physical isoscalar mesons, (b) the mass formula relating all masses of the decuplet and (c) the mass ordering rule. The states of the physical isoscalar mesons η(1295), η(1405), η(1475) are expressed as superpositions of the ‘ideal’ (N and S) states and the glueball G one. The ‘mixing matrix’ realizing transformation from the unphysical states to the physical ones follows from the octet contents and is totally expressed by the decuplet meson masses. Among four one-parameter families of the resulting mixing matrices (multitude of the solutions arising from bad quality of data on the π(1300) and K(1460) meson masses) there is a family attributing the glueball-dominated composition to the η(1405) meson. The pseudoscalar decuplet is similar in some respects to the scalar one: both are composed of the excited states and G; the mass ordering of their N, S, G—dominated isoscalars is the same. Contrary to the lattice QCD and other predictions, the mass of the pseudoscalar pure glueball state is smaller than the scalar one.

Applications of two-body Dirac equations to the meson spectrum with three versus two covariant interactions, SU(3) mixing, and comparison to a quasipotential approach

In a previous paper Crater and Van Alstine applied the Two Body Dirac equations of constraint dynamics to the meson quark-antiquark bound states using a relativistic extention of the Adler-Piran potential and compared their spectral results to those from other approaches, ones which also considered meson spectroscopy as a whole and not in parts. In this paper we explore in more detail the differences and similarities in an important subset of those approaches, the quasipotential approach. In the earlier paper, the transformation properties of the quark-antiquark potentials were limited to a scalar and an electromagnetic-like four vector, with the former accounting for the confining aspects of the overall potential, and the latter the short range portion. A part of that work consisted of developing a way in which the static Adler-Piran potential was apportioned between those two different types of potentials in addition to covariantization. Here we make a change in this apportionment that leads to a substantial improvement in the resultant spectroscopy by including a time-like confining vector potential over and above the scalar confining one and the electromagnetic-like vector potential. Our fit includes 19 more mesons than the earlier results and we modify the scalar portion of the potential in such a way that allows this formalism to account for the isoscalar mesons {\eta} and {\eta}' not included in the previous work. Continuing the comparisons made in the previous paper with other approaches to meson spectroscopy we examine in this paper the quasipotential approach of Ebert, Faustov, and Galkin for a comparison with our formalism and spectral results.

Gluonium nature of the [formula omitted] from its coupling to [formula omitted

We extract the K+K− couplings of the isoscalar scalar mesons σ/f0(600) and f0(980) from ππ→ππ/KK¯ scatterings. We find respectively about 0.6(2) and 2.0(3) for the ratios of the K+K− over π+π− couplings of the σ and f0(980), which we compare with some other determinations. The (relative) strong coupling of the σ→K¯K, together with its tiny “direct”γγ and its large hadronic widths, are in favour of a large gluonium/glueball component of the σ-meson, as predicted by QCD spectral sum rules (QSSR) ⊕ some low-energy theorems (LET). These properties then suggest that the σ can be (up to some mixing) a scalar meson associated to the U(1)V conformal anomaly like the η′-meson to the U(1)A anomaly.

The [formula omitted] splitting in constituent quark models

In this Letter we present a solution to describe simultaneously the light isoscalar and isovector vector mesons in constituent quark models. In Ref. [J. Vijande, F. Fernández, A. Valcarce, J. Phys. G 31 (2005) 481] the qq¯ spectrum was studied in a generalized constituent quark model constrained by the NN phenomenology and the baryon spectrum. An overall good fit to the available experimental data was obtained. A major problem of this description was the relative position of the vector ω and ρ mesons. The present results improve the description of the isoscalar meson spectroscopy. They should serve as a step forward in distinguishing conventional quark model mesons from exotic states.

Selected Topics on Hadronic B Decays from BaBar

Recent measurements of branching fractions and decay-rate asymmetries in charmless hadronic B decays at the BaBar experiment are presented. The selected topics include Dalitz plot analyses of B → K + π − π and signal searches in B → P P and PV, where isoscalar mesons are involved, and in B → b 1 P ; P and V denote a pseudoscalar and vector meson, respectively. Several measurements in charmless hadronic B decays have indicated possible deviations from the theoretical predictions within the Standard Model. The measurements presented would contribute to searching for and resolving such puzzles.

Radiative decays with scalar mesons and in Resonance Chiral Theory

The phi(1020) radiative decays form a good playground for study of the low-lying a0(980) and f0(980) scalar mesons. The complicated interplay of kaon loop mechanism, isoscalar meson mixing and momentum dependence of the effective couplings manifests itself in the invariant mass distributions in the phi(1020) -> pi0 pi0 gamma and pi eta gamma spectra. These distributions are fitted in framework of Resonance Chiral Theory.

An identity on SU(2) invariants

We prove an identity (equation (1) below) among SU(2) 6j and 9j symbols that generalizes the Biedenharn–Elliott sum rule. We prove the result using diagrammatic techniques (briefly reviewed here), and then provide an algebraic proof. This identity is useful for studying meson–baryon scattering in which an extra isoscalar meson is produced.

Comparison of isoscalar vector meson production cross sections in proton–proton collisions

Abstract The reaction p p → p p ω was investigated with the TOF spectrometer, which is an external experiment at the accelerator COSY (Forschungszentrum Julich, Germany). Total as well as differential cross sections were determined at an excess energy of 93 MeV ( p beam = 2950 MeV / c ). Using the total cross section of ( 9.0 ± 0.7 ± 1.1 ) μb for the reaction p p → p p ω determined here and existing data for the reaction p p → p p ϕ , the ratio R ϕ / ω = σ ϕ / σ ω turns out to be significantly larger than expected by the Okubo–Zweig–Iizuka (OZI) rule. The uncertainty of this ratio is considerably smaller than in previous determinations. The differential distributions show that the ω production is still dominated by S-wave production at this excess energy, however higher partial waves clearly contribute. A comparison of the measured angular distributions for ω production to published distributions for ϕ production at 83 MeV shows that the data are consistent with an identical production mechanism for both vector mesons.