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Register a new userDispersive calculation of complex Regge trajectories for the lightest $f_2$ resonances
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We apply a recently developed dispersive formalism to calculate the Regge trajectories of the $f_2(1270)$ and $f_2(1525)$ mesons. Trajectories are calculated, not fitted to a family of resonances. Assuming that these spin-2 resonances can be treated in the elastic approximation the only input are the pole position and residue of the resonances. In both cases, the predicted Regge trajectories are almost real and linear, with slopes in agreement with the universal value of order 1 GeV$^{-2}$.
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Maximally complex Regge trajectories are introduced for which both Re $alpha(s)$ and Im $alpha(s)$ grow as $s^{1-epsilon}$ ($epsilon$ small and positive). Our expression reduces to the standard real linear form as the imaginary part (proportional to $epsilon$) goes to zero. A scaling formula for the total widths emerges: $Gamma_{TOT}/Mto$ constant for large M, in very good agreement with data for mesons and baryons. The unitarity corrections also enhance the space-like slopes from their time-like values, thereby resolving an old problem with the $rho$ trajectory in $pi N$ charge exchange. Finally, the unitarily enhanced intercept, $alpha_{rho}approx 0.525$, olinebreak is in good accord with the Donnachie-Landshoff total cross section analysis.
A model for a Regge trajectory compatible with the threshold behavior required by unitarity and asymptotics in agreement with analyticity constraints is given in explicit form. The model is confronted in the time-like region with widths and masses of the mesonic resonances and, in the space-like region, the $rho$ trajectory is compared with predictions derived from $pi-N$ charge-exchange reaction. Breaking of the exchange degeneracy is studied in the model and its effect on both the masses and widths is determined.
We discuss some problems concerning the application of perturbative QCD to high energy soft processes. We show that summing the contributions of the lowest twist operators for non-singlet $t$-channel leads to a Regge-like amplitude. Singlet case is also discussed.
Understanding the nature of charge carriers in doped Mott insulators holds the key to unravelling puzzling properties of strongly correlated electron systems, including cuprate superconductors. Several theoretical models suggested that dopants can be understood as bound states of partons, the analogues of quarks in high-energy physics. However, direct signatures of spinon-chargon bound states are lacking, both in experiment and theory. Here we numerically identify long-lived rotational resonances at low doping, which directly reveal the microscopic structure of spinon-chargon bound states. Similar to Regge trajectories reflecting the quark structure of mesons, we establish a linear dependence of the rotational energy on the super-exchange coupling. Rotational excitations are strongly suppressed in standard angle-resolved photo-emission (ARPES) spectra, but we propose a multi-photon rotational extension of ARPES where they have strong spectral weight. Our findings suggest that multi-photon spectroscopy experiments should provide new insights into emergent universal features of strongly correlated electron systems.
Based on previous studies that support the vector-vector molecular structure of the $f_2(1270)$, $f_2(1525)$, $bar{K}^{*,0}_2(1430)$, $f_0(1370)$ and $f_0(1710)$ resonances, we make predictions for $psi (2S)$ decay into $omega(phi) f_2(1270)$, $omega(phi) f_2(1525)$, $K^{*0}(892) bar{K}^{*,0}_2(1430)$ and radiative decay of $Upsilon (1S),Upsilon (2S), psi (2S)$ into $gamma f_2(1270)$, $gamma f_2(1525)$, $gamma f_0(1370)$, $gamma f_0(1710)$. Agreement with experimental data is found for three available ratios, without using free parameters, and predictions are done for other cases.
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