We perform an Amplitude Analysis of the world published data on $γγ\toπ^+π^-$ and $π^0π^0$. These are dominated in statistics by the recently published results from Belle on the charged pion channel. Nevertheless, having only limited angular information, a range of solutions remain possible. We present two solutions with $Γ(f_0(980)\toγγ) = 0.42$ and 0.10 keV, and $Γ(f_2(1270)\toγγ) = 3.14 \pm 0.20$ and $3.82 \pm 0.30$ keV, respectively: the former being the solution favoured by $χ^2$, the latter at the edge of acceptability. Models of the structure of the $f_0(980)$ predict two photon widths to be between 0.2 and 0.6 keV, depending on its composition as mainly ${\bar K}K$, ${\bar s}s$ or ${\bar{qq}}qq$. Presently available data cannot yet distinguish unambiguously between these predictions. However, we show how forthcoming results on $γγ\toπ^0π^0$ can not only discriminate between, but also refine, these classes of partial wave solutions.
In the article of V.V. Anisovich et al., Yad. Fiz. 63, 1489 (2000), the K-matrix solutions for the wave IJ^{PC}=00^{++} were obtained in the mass region 450 - 1900 MeV where four resonances f0(980), f0(1300), f0(1500), f0(1750) and the broad state f0(1530^{+90}_{-250}) are located. Based on these solutions, we determine partial widths for scalar-isoscalar states decaying into the channels pi-pi, K-anti K, eta-eta, eta-eta', pi-pi-pi-pi and corresponding decay couplings.
This study revisits the issue of the extraction of estimates for the masses and for the partial decay widths to two pions of the scalar-isoscalar $I^G\,(J^{PC}) = 0^+\,(0^{++})$ and vector-isovector $I^G\,(J^{PC}) = 1^+\,(1^{--})$ mesons below $2$ GeV, from the data contained in the recent compilation by the Particle Data Group.
A coupled-channel analysis of BESIII data on radiative $J/ψ$ decays into $ππ$, $K\bar K$, $ηη$ and $ωϕ$ has been performed. The partial-wave amplitude is constrained by a large number of further data. The analysis finds ten isoscalar scalar mesons. Their masses, widths and decay modes are determined. The scalar mesons are interpreted as mainly SU(3)-singlet and mainly octet states. Octet isoscalar scalar states are observed with significant yields only in the 1500-2100\,MeV mass region. Singlet scalar mesons are produced over a wide mass range but their yield peaks in the same mass region. The…
We investigate the hadronic two-body decay modes of the scalar-isoscalar $f_0(1370)$, $f_0(1500)$ and $f_0(1710)$ states as resulting from the mixture of the lowest lying scalar glueball with the isoscalar states of the ground state $^3P_0$ $Q\bar Q$ nonet. In the decay analysis we take into account the direct coupling of the quarkonia and glueball components of the $f_0$ states to the quarkonia components of the two-meson final state with the decay dynamics inspired by the strong coupling limit of QCD. We calculate partial decay widths for the $f_0$ states in the proposed three-state mixing s…
The gluonic widths of four leading glueball candidates are determined from their production in radiative quarkonium decays, allowing quantitative estimation of their glue content. Lattice predictions for the scalar and tensor channels seem to be in reasonable agareement with present data (allowing for mixing with $q \bar{q}$ states). However there is a glueball-like-state in the pseudoscalar spectrum whose mass is considerably lower than expected from lattice estimates.
We investigate the determination of the pole associated to $σ$ from $ππ$ scattering data below the $K\bar{K}$ threshold, including the new precise data from $K_{e4}$ decay reported recently by the NA48/2 Collaboration. Using a large class of analytic parametrizations based on expansions in powers of conformal variables, we obtain for the mass and width of $σ$ values which are consistent with those calculated recently using ChPT and Roy equations, but have larger theoretical uncertainties.
Peculiarities of obtaining parameters for broad multi-channel resonances from data are discussed analyzing the experimental data on processes $ππ\toππ,K\bar{K}$ in the $I^GJ^{PC}=0^+0^{++}$ channel in a model-independent approach based on analyticity and unitarity and using an uniformization procedure. We show that it is possible to obtain a good description of the $ππ$ scattering data from the threshold to 1.89 GeV with parameters of resonances cited in the PDG tables as preferred. However, in this case, first, representation of the $ππ$ background is unsatisfactory; second, the data on the c…
On the basis of data on the decay D^+_s -> pi^+ pi^+ pi^-, which goes dominantly via the transition D_s -> pi^+ s anti-s, we evaluate the 1^3P_0 s anti-s components in the scalar-isoscalar resonances f0(980), f0(1300), f0(1500) and broad state f0(1200-1600)$. The data point to a large s anti-s component in the f0(980): 40% < s anti-s < 70%. Nearly 30% of the 1^3P_0 s anti-s component flows to the mass region 1300-1500 MeV being shared by f0(1300), f0(1500) and broad state f0(1200-1600): the interference of these states results in a peak near 1400 MeV with the width around 200 MeV.
We develop tools to determine the gluonic content of a resonance of known mass, width and $J^{PC}$ from its branching fraction in radiative quarkonium decays and production cross section in $γγ$ collisions. We test the procedures by applying them to known $q\bar{q}$ mesons, then analyze four leading glueball candidates. We identify inconsistencies in data for $J/ψ\to γf_0(1500)$ and $J/ψ\to γf_J(1710)$ whose resolution can quantify their glueball status.When $Γ(f_0(1500) \to γγ)$ and $Γ(f_J(1710) \to γγ)$ are known, the $n\bar{n}, s\bar{s},gg$ mixing angles can be determined. The enigmatic sit…
We demonstrate that near the threshold, the pi pi scattering amplitude contains a pole with the quantum numbers of the vacuum - commonly referred to as the sigma - and determine its mass and width within small uncertainties. Our derivation does not involve models or parametrizations, but relies on a straightforward calculation based on the Roy equation for the isoscalar S-wave.
We use a non-perturbative approach which combines coupled channel Lippmann-Schwinger equations with meson-meson potentials provided by the lowest order chiral Lagrangian. By means of one parameter, a cut off in the momentum of the loop integrals, which results of the order of 1 GeV, we obtain singularities in the S-wave amplitudes corresponding to the sigma, f_0 and a_0 resonances. The ππ--> ππ, ππ--> K bar(K) phase shifts and inelasticities in the T=0 scalar channel are well reproduced as well as the π^0 eta and K bar(K) mass distributions in the T=1 channel. Furthermore, the total and partia…
We use a nonperturbative approach which combines coupled channel Lippmann Schwinger equations with meson-meson potentials provided by the lowest order chiral Lagrangians. By means of one parameter, a cut off in the momentum of the loop integrals, which results of the order of 1 GeV, we obtain singularities in the S-wave amplitudes corresponding to the σ,f_0 and a_0 resonances. The ππ-->ππ, ππ-->K\bar{K} phase shifts and inelasticities in the T=0 scalar channel are well reproduced as well as the π^-ηand K^-K^0 mass distributions in the T=1 channel. Furthermore, the total and partial decay width…
We discuss gamma gamma partial widths of pseudoscalar/isoscalar mesons eta(M) in the mass region M = 1000-1500 MeV. The transition amplitudes eta(1295) -> gamma gamma and eta(1440) -> gamma gamma are studied within an assumption that the decaying mesons are the members of the first radial excitation nonet 2^1S_0 q\bar q. The calculations show that partial widths being of the order of 0.1 keV are dominantly due to the n\bar n meson component while the contribution of the s\bar s component is small.
We study the decays of the $J^{PC}=1^{-+}$ hybrid nonet using a Lagrangian invariant under the flavor symmetry, parity reversal, and charge conjugation. We use the available experimental data, the lattice predictions, and the flavor constraints to evaluate the coupling strengths of the $π_1(1600)$ to various two-body mesonic states. Using these coupling constants, we estimate the partial widths of the two-body decays of the hybrid pion, kaon and the isoscalars. We find that the hybrid kaon can be nearly as broad as the $π_1(1600)$. Quite remarkably, we find also that the light isoscalar must b…
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 a…
The analysis of the vector isoscalar excitations in the energy range between 1 and 2 GeV of the $e^+e^-$ annihilation is presented for the final states $π^+π^-π^0$, $ωπ^+π^-$, $K^+K^-$, $K^0_SK^\pmπ^\mp$ and $K^{\ast0}K^-π^++ c.c$. The effects of both the resonance mixing and the successive opening of multiparticle channels, with the energy dependent partial widths, are taken into account. The work extends our previous analysis hep-ph/9609216 of the vector isovector excitations and is aimed to compare the existing data with the predictions of the $q\bar q$ model. It is shown that this hypothes…
Radiative decays of the isoscalar $S$-wave $D\bar D$ molecule
College of Physics and Engineering, Qufu Normal University（曲阜师范大学物理工程学院）；Instituto de Física Corpuscular (centro mixto CSIC-UV)（粒子物理与辐射物理研究所（CSIC-UV联合中心））
Inspired by the recent discovery of a doubly charmed tetraquark state $T_{cc}^+$ by the LHCb Collaboration, we employ the effective Lagrangian approach to investigate the decay width of $T_{cc}^{+}\to D^{+} D^{0}π^{0}/D^{0} D^{0}π^{+}$ and $T_{cc}^{+}\to D^{0}D^{+}γ$ with the assumption that $T_{cc}^{+}$ is an isoscalar $DD^{\ast}$ molecule. We show that both the $T_{cc}\to D Dπ$ and $T_{cc}\to DDγ$ modes contribute to the decay width of $T_{cc}$, with the former being dominant. The resulting total decay width of about $Γ=63$ keV is smaller than the experimental decay width obtained from the B…
Possibility of an axial vector isoscalar tetraquark with $ud\bar{s}\bar{s}$ is discussed. If the pentaquark $Θ^+(1540)$ has the $(qq)_{\bar{3}}(qq)_{\bar{3}}\bar{q}$ configuration, the isoscalar $ud\bar{s}\bar{s}$($\vartheta^+$-meson) state with $J^P=1^+$ is expected to exist in the mass region lower than or close to the mass of $Θ^+(1540)$. Within a flux-tube quark model, a possible resonant state of $ud\bar{s}\bar{s}(J^{P}=1^{+})$ is suggested to appear around 1.4 GeV with the width ${\cal{O}}(20\sim 50)$ MeV. We propose that the $\vartheta^+$-meson is a good candidate for the tetraquark sea…
We use a nonpertubative approach which combines coupled channel Lippmann Schwinger equations with meson-meson potentials provided by the lowest order chiral Lagrangian. By means of one parameter, a cut off in the momentum of the loop integrals, which results of the order of 1 GeV, we obtain singularities in the S-wave amplitudes corresponding to the $σ$, f_0 and a_0 resonances. The $ππ\to ππ, ππ\to K \bar{K}$ phase shifts and inelasticities in the T = 0 scalar channel are well reproduced as well as the $π^0 η$ and $K \bar{K}$ mass distributions in the T = 1 channel. Furthermore, the total and …
Based on the previous and recent fits of multiple data on the reactions of e^+e^- annihilation, tau lepton decay, and the reaction K^-p -> pi^+pi^- Lambda, the magnitude of the branching ratios and total widths of the isovector rho', rho'', and the isoscalar omega', omega'' resonances are calculated. Some topics on the spectroscopy of the rho(1450) and omega(1420) states are discussed.
We have studied the meson-baryon $S-$wave interaction, using coupled channels, in the isoscalar hidden-charm strange sector and $J^P = 1/2^-,3/2^-$ and $5/2^-$. We impose constraints of heavy quark spin symmetry in the interaction and obtain the non vanishing matrix elements from an extension of the local hidden gauge approach to the charm sector. The ultraviolet divergences are renormalized using the same meson-baryon-loops regulator previously employed in the non-strange hidden charm sector, where a good reproduction of the properties of the newly discovered pentaquark states is obtained. We…
We investigate heavy quark symmetries for heavy meson hadronic molecules, and explore the consequences of assuming the X(3872) and $Z_b(10610)$ as an isoscalar $D\bar D^*$ and an isovector $B\bar B^*$ hadronic molecules, respectively. The symmetry allows to predict new hadronic molecules, in particular we find an isoscalar $1^{++}$ $B\bar B^*$ bound state with a mass about 10580 MeV and the isovector charmonium partners of the $Z_b(10610)$ and the $Z_b(10650)$ states. Next, we study the $X(3872) \to D^0 \bar D^0π^0$ three body decay. This decay mode is more sensitive to the long-distance struc…
An overview of the GW SAID and ITEP groups effort to analyze pion photoproduction on the neutron-target will be given. The disentanglement the isoscalar and isovector EM couplings of N* and Delta* resonances does require compatible data on both proton and neutron targets. The final-state interaction plays a critical role in the state-of-the-art analysis in extraction of the gamma n --> pi N data from the deuteron target experiments. It is important component of the current JLab, MAMI-C, SPring-8, ELSA, and ELPH programs
The lowest-lying resonance in the QCD spectrum is the $0^{++}$ isoscalar $σ$ meson, also known as the $f_0(500)$. We augment SU(2) chiral perturbation theory ($χ$PT) by including the $σ$ meson as an additional explicit degree of freedom, as proposed by Soto, Talavera, and Tarrús and others. In this effective field theory, denoted $χ$PT$_S$, the $σ$ meson's well-established mass and decay width are not sufficient to properly renormalize its self energy. At $\mathcal{O}(p^4)$ another low-energy constant appears in the dressed $σ$-meson propagator; we adjust it so that the isoscalar pion-pion sca…
Strong decay widths of S- and P-wave singly- and doubly-heavy charm and bottom baryons
ELTE Eötvös Loránd University（厄特沃什·罗兰大学）；MTA–ELTE Lendület “Momentum” Strongly Interacting Matter Research Group（马塔-厄特沃什·罗兰大学雷内勒特“动量”强相互作用物质研究组）；Universidad Nacional Autónoma de México（墨西哥国立自治大学）
We present the results of the current analysis of the partial wave IJ^{PC}=00^{++} based on the available data for meson spectra (pi-pi, K\bar K, eta-eta, eta-eta', pi-pi-pi-pi). In the framework of the K-matrix approach, the analytical amplitude has been restored in the mass region 280 MeV< \sqrt s <1900 MeV. The following scalar-isoscalar states are seen: comparatively narrow resonances f_0(980), f_0(1300), f_0(1500), f_0(1750) and the broad state f_0(1200-1600). The positions of the amplitude poles (masses and total widths of the resonances) are determined as well as pole residues (partial …
Based on the assignment of the first radial excitation states of the isoscalar pseudoscalars for $η(1295)$ and $η(1405/1475)$, we investigate their three-body and four-body decay contributions to the total widths. In agreement with our previous studies we find that the triangle singularity (TS) mechanism arising from the intermediate $K^*\bar{K}$ rescatterings by exchanging a kaon or pion plays a crucial role in both $K\bar{K}π$ and $ηππ$ channels. For the $η_X$ ($η_X$ stands for $η(1295)$ and $η(1405/1475)$) decays into $K\bar{K}π$, we find that although the transition $η_X\to K^*\bar{K}+c.c.…
We have systematically investigated the mass spectrum and rearrangement decay properties of the exotic tetraquark states with four different flavors using a color-magnetic interaction model. Their masses are estimated by assuming that the $X(4140)$ is a $cs\bar{c}\bar{s}$ tetraquark state and their decay widths are obtained by assuming that the Hamiltonian for decay is a constant. According to the adopted method, we find that the most stable states are probably the isoscalar $bs\bar{u}\bar{d}$ and $cs\bar{u}\bar{d}$ with $J^P=0^+$ and $1^+$. The width for most unstable tetraquarks is about ten…
We use our latest dispersive analysis of pion-pion scattering data and the very recent Kl4 experimental results to obtain the mass, width and couplings of the two lightest scalar-isoscalar resonances. These parameters are defined from their associated poles in the complex plane. The analytic continuation to the complex plane is made in a model independent way by means of once and twice subtracted dispersion relations for the partial waves, without any other theoretical assumption. We find the f0(600) pole at (457^{+14}_{-13})-i(279^{+11}_{-7}) MeV and that of the f0(980) at (996\pm7)-i(25^{+10…
We present the first full-fledged study of the flavor-exotic isoscalar $T_{bb}^-\equiv b b \bar u \bar d$ tetraquark with spin and parity $J^P=1^+$. We report accurate solutions of the four-body problem in a quark model, characterizing the structure of the state as a function of the ratio $M_Q/m_q$ of the heavy to light quark masses. For such a standard constituent model, $T_{bb}^-$ lies approximately 150 MeV below the strong decay threshold $B^-\bar {B^*}^{0}$ and 105 MeV below the electromagnetic decay threshold $B^- \bar B^0 γ$. We evaluate the lifetime of $T_{bb}^-$, identifying the promis…
We perform a theoretical study based on dispersion relations of the reaction γγ\to π^0π^0 emphasizing the low energy region. We discuss how the f_0(980) signal emerges in γγ\to ππwithin the dispersive approach and how this fixes to a large extent the phase of the isoscalar S-wave γγ\to ππamplitude above the K\bar{K} threshold. This allows us to make sharper predictions for the cross section at lower energies and our results could then be used to distinguish between different ππisoscalar S-wave parameterizations with the advent of new precise data on γγ\toπ^0π^0. We compare our dispersive appro…
We perform a high statistics calculation of disconnected fermion loops on Graphics Processing Units for a range of nucleon matrix elements extracted using lattice QCD. The isoscalar electromagnetic and axial vector form factors, the sigma-terms and the momentum fraction and helicity are among the quantities we evaluate. We compare the disconnected contributions to the connected ones and give the physical implications on nucleon observables that probe its structure.
