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Register a new userAnalytic model of Regge trajectories
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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.
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Every conformal field theory (CFT) above two dimensions contains an infinite set of Regge trajectories of local operators which, at large spin, asymptote to double-twist composites with vanishing anomalous dimension. In two dimensions, due to the existence of local conformal symmetry, this and other central results of the conformal bootstrap do not apply. We incorporate exact stress tensor dynamics into the CFT$_2$ analytic bootstrap, and extract several implications for AdS$_3$ quantum gravity. Our main tool is the Virasoro fusion kernel, which we newly analyze and interpret in the bootstrap context. The contribution to double-twist data from the Virasoro vacuum module defines a Virasoro Mean Field Theory (VMFT), its spectrum includes a finite number of discrete Regge trajectories, whose dimensions obey a simple formula exact in the central charge $c$ and external operator dimensions. We then show that VMFT provides a baseline for large spin universality in two dimensions: in every unitary compact CFT$_2$ with $c > 1$ and a twist gap above the vacuum, the double-twist data approaches that of VMFT at large spin $ell$. Corrections to the large spin spectrum from individual non-vacuum primaries are exponentially small in $sqrt{ell}$ for fixed $c$. We analyze our results in various large $c$ limits. Further applications include a derivation of the late-time behavior of Virasoro blocks at generic $c$, a refined understanding and new derivation of heavy-light blocks, and the determination of the cross-channel limit of generic Virasoro blocks. We deduce non-perturbative results about the bound state spectrum and dynamics of quantum gravity in AdS$_3$.
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.
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 Mandelstam analyticity is analyzed and confronted with the experimental data on the spectrum of the $rho$ trajectory as well as those on the $pi^- pto pi^0 n$ charge-exchange reaction. The fitted trajectory deviates considerably from a linear one both in the space-like and time-like regions, matching nicely between the two.
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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