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Register a new userGlueballs as the Ithaca of meson spectroscopy
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Felipe J. Llanes-Estrada
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This compact review about gluonium focuses on a slate of theoretical efforts; among the many standing works, I have selected several that are meant to assist in the identification, among ordinary mesons, of the few Yang-Mills glueball configurations that populate the energy region below 3 GeV. This includes $J/psi$ radiative and vector-meson decays, studies of scalar meson mixing, of high-energy cross sections via the Pomeron and the odderon, glueball decays, etc. The weight of accumulated evidence seems to support the $f_0(1710)$ as having a large (and the largest) glueball component among the scalars, although no single observable by itself is conclusive. Further tests would be welcome, such as exclusive $f_J$ production at asymptotically high $s$ and $t$. No clear experimental candidates for the pseudoscalar or tensor glueball stand out yet, and continuing investigations trying to sort them out will certainly teach us much more about mesons.
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The graviton solutions for the glueball spectrum of ref. cite{Rinaldi:2017wdn} interpreted in a different manner lead to very interesting results which we describe in this comment.
The bottom-up approach of the AdS/CFT correspondence leads to the study of field equations in an $AdS_5$ background and from their solutions to the determination of the hadronic mass spectrum. We extend the study to the equations of $AdS_5$ gravitons and determine from them the glueball spectrum. We propose an original presentation of the results which facilitates the comparison of the various models with the spectrum obtained by lattice QCD. This comparison allows to draw some phenomenological conclusions.
We study two- and three-gluon glueballs of $C=+$ using the method of QCD sum rules. We systematically construct their interpolating currents, and find that all the spin-1 currents of $C=+$ vanish. This suggests that the ground-state spin-1 glueballs of $C=+$ do not exist within the relativistic framework. We calculate masses of the two-gluon glueballs with $J^{PC} = 0^{pm+}/2^{pm+}$ and the three-gluon glueballs with $J^{PC} = 0^{pm+}/2^{pm+}$. We propose to search for the $J^{PC} = 0^{-+}/2^{-pm}/3^{pm-}$ three-gluon glueballs in their three-meson decay channels in future BESIII, GlueX, LHC, and PANDA experiments.
Many hadronic states observed since 2003, especially for the positive-parity charm-strange states $D_{s0}^ast (2317)$ and $D_{s1}(2460)$, do not conform with the conventional quark model expectations and raise various puzzles in charm meson spectroscopy. We demonstrate that those puzzles find a natural solution thanks to the recent development of chiral effective theory and Lattice simulations. The existence of the $D_{s0}^ast (2317)$ and $D_{s1}(2460)$ are attributed to the nonperturbative dynamics of Goldstone bosons scattering off $D$ and $D^ast$ mesons. It indicates that the lowest positive parity nonstrange scalar charm mesons, the $D_0^ast(2400)$ in the Review of Particel Physics, should be replaced by two states. The well constructed amplitudes are fully in line with the high quality data on the decays $B^-to D^+pi^-pi^-$ and $D_s^0to bar{D}^0K^-pi^+$. This implies that the lowest positve-parity states are dynamically generated rather than conventional quark-antiquark states. This pattern has also been established for the scalar and axial-vector mesons made from light quarks ($u$, $d$ and $s$ quarks).
We test the validity of the QCD sum rules applied to the meson $Z^+(4430)$, by considering a diquark-antidiquark type of current with $J^{P}=0^{-}$ and with $J^{P}=1^{-}$. We find that, with the studied currents, it is possible to find an acceptable Borel window. In such a Borel window we have simultaneously a good OPE convergence and a pole contribution which is bigger than the continuum contribution. We get $m_Z=(4.52pm0.09)GeV$ and $m_Z=(4.84pm0.14)GeV$ for the currents with $J^{P}=0^{-}$ and $J^{P}=1^{-}$ respectively. We conclude that the QCD sum rules results favors $J^{P}=0^{-}$ quantum numbers for the $Z^+(4430)$ meson.
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