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Register a new userSelf-intersecting Regge trajectories in multi-channel scattering
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We present a simple direct method for calculating Regge trajectories for a multichannel scattering problem. The approach is applied to the case of two coupled Thomas-Fermi type potentials, used as a crude model for electron-atom scattering below the second excitation threshold. It is shown that non-adiabatic interaction may cause formation of loops in Regge trajectories. The accuracy of the method is tested by evaluating resonance contributions to elastic and inelastic integral cross sections.
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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.
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.
The collision of two atoms is an intrinsic multi-channel (MC) problem as becomes especially obvious in the presence of Feshbach resonances. Due to its complexity, however, single-channel (SC) approximations, which reproduce the long-range behavior of the open channel, are often applied in calculations. In this work the complete MC problem is solved numerically for the magnetic Feshbach resonances (MFRs) in collisions between generic ultracold 6Li and 87Rb atoms in the ground state and in the presence of a static magnetic field B. The obtained MC solutions are used to test various existing as well as presently developed SC approaches. It was found that many aspects even at short internuclear distances are qualitatively well reflected. This can be used to investigate molecular processes in the presence of an external trap or in many-body systems that can be feasibly treated only within the framework of the SC approximation. The applicability of various SC approximations is tested for a transition to the absolute vibrational ground state around an MFR. The conformance of the SC approaches is explained by the two-channel approximation for the MFR.
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.
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.
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