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Register a new userMasses of J^PC =1^-+ exotic quarkonia in a Bethe-Salpeter-equation approach
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We investigate the properties of mesons with the exotic J^PC = 1^-+ quantum numbers. Starting out from the light-quark domain, where the pi_1 states are used as references, we predict the masses of analogous quarkonia for cbar{c} and bbar{b} configurations. We employ a covariant Dyson-Schwinger-Bethe-Salpeter-equation approach with a rainbow-ladder truncated model of quantum chromodynamics.
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Using a well-established effective interaction in a rainbow-ladder truncation model of QCD, we fix the remaining model parameter to the bottomonium ground-state spectrum in a covariant Bethe-Salpeter equation approach and find surprisingly good agreement with the available experimental data including the 2^{--} Upsilon(1D) state. Furthermore, we investigate the consequences of such a fit for charmonium and light-quark ground states.
We use the Laplace/Borel sum rules (LSR) and the finite energy/local duality sum rules (FESR) to investigate the non-strange $udbar ubar d$ and hidden-strange $usbar ubar s$ tetraquark states with exotic quantum numbers $J^{PC}=0^{+-}$ . We systematically construct all eight possible tetraquark currents in this channel without covariant derivative operator. Our analyses show that the $udbar ubar d$ systems have good behaviour of sum rule stability and expansion series convergence in both the LSR and FESR analyses, while the LSR for the $usbar ubar s$ states do not associate with convergent OPE series in the stability regions and only the FESR can provide valid results. We give the mass predictions $1.43pm0.09$ GeV and $1.54pm0.12$ GeV for the $udbar ubar d$ and $usbar ubar s$ tetraquark states, respectively. Our results indicate that the $0^{+-}$ isovector $usbar ubar s$ tetraquark may only decay via weak interaction mechanism, e.g. $X_{usbar{u}bar{s}}to Kpipi$, since its strong decays are forbidden by kinematics and the symmetry constraints on the exotic quantum numbers. It is predicted to be very narrow, if it does exist. The $0^{+-}$ isoscalar $usbar ubar s$ tetraquark is also predicted to be not very wide because its dominate decay mode $X_{usbar{u}bar{s}}tophipipi$ is in $P$-wave.
The off-mass shell scattering amplitude, satisfying the Bethe-Salpeter equation for spinless particles in Minkowski space with the ladder kernel, is computed for the first time.
Mesons with quantum numbers $J^{PC}=1^{-+}$ cannot be represented as simple quark-antiquark pairs. We explore hybrid configurations in the light meson sector comprising a quark, an antiquark and an excited gluon, studying the properties of such states in a phenomenological model inspired by the gauge/gravity correspondence. The computed mass, compared to the experimental mass of the $1^{-+}$ candidates $pi_1(1400)$, $pi_1(1600)$ and $pi_1(2015)$, favous $pi_1(1400)$ as the lightest hybrid state. An interesting result concerns the stability of hybrid mesons at finite temperature: they disappear from the spectral function (i.e. they melt) at a lower temperature with respect to other states, light vector and scalar mesons, and scalar glueballs.
We study the possible bound states of the $D_1D$ system in the Bethe-Salpeter (BS) formalism in the ladder and instantaneous approximations. By solving the BS equation numerically with the kernel containing one-particle exchange diagrams and introducing three different form factors (monopole, dipole, and exponential form factors) at the vertices, we investigate whether the isoscalar and isovector $D_1D$ bound states may exist, respectively. We find that $Y(4260)$ could be accommodated as a $D_1D$ molecule, whereas the interpretation of $Z_2^+(4250)$ as a $D_1D$ molecule is disfavored. The bottom analog of $Y(4260)$ may exist but that of $Z_2^+(4250)$ does not.
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