Construction of a crossing - symmetric, Regge behaved amplitude for linearly rising trajectories
CERN1
01 Jan 1968-Nuovo Cimento Della Societa Italiana Di Fisica A-nuclei Particles and Fields (Springer Berlin Heidelberg)-Vol. 57, Iss: 1, pp 190-197
About: This article is published in Nuovo Cimento Della Societa Italiana Di Fisica A-nuclei Particles and Fields.The article was published on 1968-01-01 and is currently open access. It has received 1346 citations till now. The article focuses on the topics: Crossing & Veneziano amplitude.
Citations
More filters
TL;DR: In this article, the authors present explicit models for a symmetry breakdown in the cases of the Weyl (or homothetic) group, the SL(4, R), or the GL(4-R) covering subgroup.
1,474 citations
TL;DR: In this article, the authors derive a formula which expresses any closed string tree amplitude in terms of a sum of the products of appropriate open string tree amplitudes, which is applicable to the heterotic string as well as to the closed bosonic string and type II superstrings.
1,330 citations
TL;DR: In this paper, the authors studied the high-energy behavior of string scattering amplitudes to all orders in perturbation theory, with the aim of exploring the short distance structure of string theory.
1,228 citations
TL;DR: In this article, the large energy, fixed-angle, behavior of string scattering amplitudes is considered to arbitrary order in perturbation theory, and it is shown that the path integal over surfaces is dominated, in this limit, by a saddle point.
771 citations
TL;DR: In this paper, recent progress made towards the understanding of closed bosonic and fermionic string perturbation theory, formulated in a Lorentz-covariant way on Euclidean space-time, is devoted to recent progress.
Abstract: This paper is devoted to recent progress made towards the understanding of closed bosonic and fermionic string perturbation theory, formulated in a Lorentz-covariant way on Euclidean space-time. Special emphasis is put on the fundamental role of Riemann surfaces and supersurfaces. The differential and complex geometry of their moduli space is developed as needed. New results for the superstring presented here include the supergeometric construction of amplitudes, their chiral and superholomorphic splitting and a global formulation of supermoduli space and amplitudes.
721 citations
References
More filters
TL;DR: In this article, the Pomeranchuk trajectory is mostly built from the nonresonating background at low energies, which explains the constancy of the total cross-sections and predicts many interesting relations which are experimentally satisfied.
Abstract: While "ordinary" Regge trajectories can be bootstrapped using the resonance approximation to finite-energy sum rules, we suggest that the Pomeranchuk trajectory is mostly built from the nonresonating background at low energies. This hypothesis (a) explains the constancy of $\mathrm{KN}$ and $\mathrm{NN}$ total cross-sections (in contrast to $\overline{K}N$ and $\overline{N}N$ over a wide energy range; (b) predicts many other interesting relations which are experimentally satisfied; and (c) leads to no obvious inconsistencies.
313 citations
TL;DR: In this article, the sum rules for strong interactions are derived from analyticity and high energy bounds for the scattering amplitudes of particles endowed with spin, which are strongly suggested by unitarity.
162 citations
TL;DR: In this paper, a charge exchange scattering with helicity flip is analyzed in the direct channel, which produces resonance circles on the Argand diagram corresponding to the prominent experimental ${N}^{*}$ resonances.
Abstract: The $\ensuremath{\rho}$ Regge amplitude for $\ensuremath{\pi}N$ charge-exchange scattering with helicity flip is partial-wave analyzed in the direct channel. This produces resonance circles on the Argand diagram corresponding to the prominent experimental ${N}^{*}$ resonances.
122 citations
53 citations
TL;DR: In this article, the sum rules as a function of momentum transfer were studied for natural-parity trajectories, and a set of residue functions were found to be self-consistent and such that the Regge and resonance sides of the equations are almost equal in a large region of $t$.
Abstract: In this paper we study the reactions $\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\omega}({1}^{\ensuremath{-}})$, $\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\pi}{A}_{2}({2}^{+})$, and $\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\pi}{\ensuremath{\omega}}_{3}({3}^{\ensuremath{-}})$ as a bootstrap system for natural-parity trajectories We start from the solution of our previous work that gave, among other results, expressions for the trajectory and residue functions as well as mass formulas, in agreement with experiment Here we study in detail the sum rules as a function of momentum transfer $t$ We find a set of residue functions $\ensuremath{\beta}(t)$ that are self-consistent and such that the Regge and resonance sides of the equations are almost equal in a large region of $t$ We study also a step-by-step approximation that, at each stage, enlarges the region where the equations are valid We find, however, that the leading Regge trajectories, even if infinitely rising, cannot bootstrap themselves We outline two possible (not incompatible) ways of implementing the bootstrap The first way demands an optimized choice of the cutoff parameter and considers the whole family of reactions $\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\pi}{X}_{J}$ (${X}_{J}$ being a normal-parity state of spin $J$) Our results for $J\ensuremath{\le}3$ show that this is a definite possibility The second way is to consider a whole family (parent and daughters) as participating in the bootstrap We find this possibility also attractive, and as a consequence we find that daughters must be parallel to the parent, for linear trajectories The properties of our parametrization are also discussed\char22{}in particular, the Khuri paradox and the coupling of high-spin resonances to the system We also compare our results with experiment whenever possible Our ${A}_{2}$ trajectory, for instance, follows the Gell-Mann mechanism, and the exponential $t$ dependence of our residue functions is perfectly consistent with the one found in recent phenomenological fits to inelastic reactions
32 citations