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Register a new userScalar mesons and the fragmented glueball
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Authors
Eberhard Klempt
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The center-of-gravity rule is tested for heavy and light-quark mesons. In the heavy-meson sector, the rule is excellently satisfied. In the light-quark sector, the rule suggests that the $a_0(980)$ could be the spin-partner of $a_2(1320)$, $a_1(1260)$, and $b_1(1235)$; $f_0(500)$ the spin-partner of $f_2(1270)$, $f_1(1285)$, and $h_1(1170)$; and $f_0(980)$ the spin-partner of $f_2(1525)$, $f_1(1420)$, and $h_1(1415)$. From the decay and the production of light scalar mesons we find a consistent mixing angle $theta^{rm s}=(14pm4)^circ$. We conclude that $f_0(980)$ is likely octet-like in SU(3) with a slightly larger $sbar s$ content and $f_0(500)$ is SU(3) singlet-like with a larger $nbar n$ component. The $a_0(1450)$, $K^*_0(1430)$, $f_0(1500)$ and $f_0(1370)$ are suggested as nonet of radial excitations. The scalar glueball is discussed as part of the wave function of scalar isoscalar mesons and not as additional intruder. It seems not to cause supernumerosity.
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A coupled-channel analysis has been performed to identify the spectrum of scalar mesons. The data include BESIII data on radiative $J/psi$ decays into $pi^0pi^0$,$K_SK_S$, $etaeta$, and $omegaphi$, 15 Dalitz plots from $bar pN$ annihilation at rest at LEAR, the CERN-Munich multipoles for $pipi$ elastic scattering, the $S$-wave from BNL data on $pipi$ scattering into $K_SK_S$, from GAMS data on $pipito pi^0pi^0, etaeta$, and $etaeta$, and NA48/2 data on low-mass $pipi$ interactions from $K^pmtopipi e^pm u$ decays. The analysis reveals the existence of ten scalar isoscalar resonances. The resonances can be grouped into two classes: resonances with a large SU(3) singlet component and those with a large octet component. The production of isoscalar resonances with a large octet component should be suppressed in radiative $J/psi$ decays. However, in a limited mass range centered at 1900,MeV, these mesons are produced abundantly. Mainly-singlet scalar resonances are produced over the full mass range but with larger intensity at 1900,MeV. The total scalar isoscalar yield in radiative decays into scalar mesons shows a clear peak which is interpreted as the scalar glueball of lowest mass.
We study the decays of the pseudotensor mesons $[ pi_{2}(1670) , K_{2}(1770) , eta_{2}(1645) , eta_{2}(1870) ]$ interpreted as the ground-state nonet of $1^1 D_{2}$ $bar{q}q$ states using interaction Lagrangians which couple them to pseudoscalar, vector, and tensor mesons. While the decays of $pi_2 (1670)$ and $K_2 (1770)$ can be well described, the decays of the isoscalar states $eta_2 (1645)$ and $eta_2 (1870)$ can be brought in agreement with experimental data only if the mixing angle between nonstrange and strange states is surprisingly large (about $-42^circ$, similar to the mixing in the pseudoscalar sector, in which the chiral anomaly is active). Such a large mixing angle is however at odd with all other conventional quark-antiquark nonets: if confirmed, a deeper study of its origin will be needed in the future. Moreover, the $bar{q}q$ assignment of pseudotensor states predicts that the ratio $[ eta_2 (1870) rightarrow a_2 (1320) pi]/[eta_2 (1870) rightarrow f_2 (1270) eta]$ is about $23.5$. This value is in agreement with Barberis et al., ($20.4 pm 6.6$), but disagrees with the recent reanalysis of Anisovich et al., ($1.7 pm 0.4$). Future experimental studies are necessary to understand this puzzle. If Anisovichs value shall be confirmed, a simple nonet of pseudoscalar mesons cannot be able to describe data (different assignments and/or additional state, such as an hybrid state, will be needed). In the end, we also evaluate the decays of a pseudoscalar glueball into the aforementioned conventional $bar{q}q$ states: a sizable decay into $K^ast_2 (1430) K$ and $a_2 (1230) pi$ together with a vanishing decay into pseudoscalar-vector pairs [such as $rho(770) pi$ and $K^ast (892) K$] are expected. This information can be helpful in future studies of glueballs at the ongoing BESIII and at the future PANDA experiments.
It is shown that the scalar mesons $sigma$, $f_0(980)$ and $a_0(980)$ as $t$-channel exchanges quantitatively solve the problem of diamagnetism and give an explanation of the large missing part of the electric polarizability $alpha$ showing up when only the pion cloud is taken into account. The electric polarizability of the proton $alpha_p$ confirms a two-photon width of the $sigma$ meson of $Gamma_{sigmagammagamma}=(2.58pm 0.26)$ keV.
We discuss the effect of the instanton induced, six-fermion effective Lagrangian on the decays of the lightest scalar mesons in the diquark--antidiquark picture. This addition allows for a remarkably good description of light scalar meson decays. The same effective Lagrangian produces a mixing of the lightest scalars with the positive parity q-qbar states. Comparing with previous work where the q-qbar mesons are identified with the nonet at 1200-1700 MeV, we find that the mixing required to fit the mass spectrum is in good agreement with the instanton coupling obtained from light scalar decays. A coherent picture of scalar mesons as a mixture of tetraquark states (dominating in the lightest mesons) and heavy q-qbar states (dominating in the heavier mesons) emerges.
Within the framework of covariant confined quark model, we compute the transition form factors of $D$ and $D_s$ mesons decaying to light scalar mesons $f_0(980)$ and $a_0(980)$. The transition form factors are then utilized to compute the semileptonic branching fractions. We study the channels namely, $D_{(s)}^+ to f_0(980) ell^+ u_ell$ and $D to a_0(980) ell^+ u_ell$ for $ell = e$ and $mu$. For computation of semileptonic branching fractions, we consider the $a_0(980)$ meson to be the conventional quark-antiquark structure and the $f_0(980)$ meson as the admixture of $sbar{s}$ and light quark-antiquark pairs. Our findings are found to support the recent BESIII data.
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