Regge theory


Regge theory

In quantum physics, Regge theory is the study of the analytic properties of scattering as a function of angular momentum, where the angular momentum is not restricted to be an integer but is allowed to take any complex value. The nonrelativistic theory was developed by Tullio Regge in 1957.

The main result of the theory is that the scattering amplitude for potential scattering grows as a function of the cosine z of the scattering angle as a power which changes as the scattering energy changes::A(z) propto z^{l(E^2)}where l(E^2) is the noninteger value of the angular momentum of a would-be bound state with energy E. It is determined by solving the radial Schrödinger equation and it smoothly interpolates the energy of wavefunctions with different angular momentum but with the same radial excitation number. The trajectory function is a function of s=E^2 for relativistic generalization. l(s) is known as the Regge trajectory function, and when it is an integer, the particles form an actual bound state with this angular momentum. The asymptotic form applies when z much greater than one, which is not a physical limit in nonrelativistic scattering.

Shortly afterwards, Stanley Mandelstam noted that in relativity the purely formal limit of z large is near to a physical limit--- the limit of large t. Large t means large energy in the crossed channel, where one of the incoming particles has an energy momentum which makes it a very energetic outgoing antiparticle. This observation turned Regge theory from a mathematical curiosity into a physical theory: it demands that the function that determines the falloff rate of the scattering amplitude for particle-particle scattering at large energies is the same as the function which determines the bound state energies for a particle-antiparticle system as a function of angular momentum [ V. Gribov, "The Theory of Complex Angular Momentum"] .

The switch required swapping the Mandelstam variable s, which is the square of the energy, for t which is the squared momentum transfer, which for elastic soft collisions of identical particles is s times one minus the cosine of the scattering angle. The relation in the crossed channel becomes:A(z) propto s^{l(t)}

Which says that the amplitude has a different power law falloff as a function of energy at different corresponding angles, where corresponding angles are those which have the same value of t. It predicts that the function which determines the power law is the same function which interpolates the energies where the resonances will appear. The range of angles where scattering can be productively described by Regge theory shrinks into a narrow cone around the beam-line at large energies.

In 1960 Geoffrey Chew and Steven Frautschi conjectured from limited data that the strongly interacting particles had a very simple dependence of the squared-mass on the angular momentum: the particles fall into families where the Regge trajectory functions were straight lines: l(s)=ks with the same constant k for all the trajectories. The straight-line Regge trajectories were later understood as arising from massless endpoints on rotating relativistic strings. Since a Regge description implied that the particles were bound states, Chew and Frautschi concluded that none of the strongly interacting particles were elementary.

Experimentally, the near-beam behavior of scattering did fall off with angle as explained by Regge theory, leading many to accept that the particles in the strong interactions were composite. Much of the scattering was "diffractive", meaning that the particles hardly scatter at all--- staying close to the beam line after the collision. Vladimir Gribov noted that the Froissart bound combined with the assumption of maximum possible scattering implied that there was a Regge trajectory which would lead to logarithmically rising cross sections, a trajectory nowadays known as the Pomeron. He went on to formulate a quantitative perturbation theory for near beam line scattering dominated by multi-Pomeron exchange.

From the fundamental observation that hadrons are composite, there grew two points of view. Some correctly advocated that there were elementary particles, nowadays called quarks and gluons, which made a quantum field theory in which the hadrons were bound states. Others also correctly believed that it was possible to formulate a theory without elementary particles--- where all the particles were bound states lying on Regge trajectories and scatter self-consistently. This was called S-matrix theory.

The most successful S-matrix approach centered on the narrow-resonance approximation, the idea that there is a consistent expansion starting from stable particles on straight-line Regge trajectories. After many false starts, Dolen Horn and Schmidt understood a crucial property which led Gabriele Veneziano to formulate a self-consistent scattering amplitude, the first string theory. Mandelstam noted that the limit where the regge trajectories are straight is also the limit where the lifetime of the states is long.

As a fundamental theory of strong interactions at high energies, Regge theory enjoyed a period of interest in the 1960s, but it was largely succeeded by quantum chromodynamics. As a phenomenological theory, it is still an indispensable tool for understanding near-beam line scattering and scattering at very large energies. Modern research focuses both on the connection to perturbation theory and to string theory.

References

Further reading

* P.D.B. Collins, "An Introduction to Regge Theory and High-Energy Physics", Cambridge, England: Cambridge University Press, 1977, ISBN 0-521-21245-6
* R.J. Eden, "Regge poles and elementary particles", Rep. Prog. Phys. 34 995-1053 (1971).
* A.C. Irving, R.P. Worden, "Regge phenomenology", Phys.Rept. 34, 117-231 (1977).

ee also

*Pomeron
*S-matrix theory

External links

* [http://arxiv.org/abs/hep-ph/9608384 hep-ph/9608384 Regge Pole Model for Vector Meson Photoproduction at HERA]
* [http://arxiv.org/abs/hep-ph/0103011 hep-ph/0103011 Regge Poles in QCD]
* [http://arxiv.org/abs/hep-ph/0112242 hep-ph/0112242 A universal Regge pole model for all vector meson exclusive photoproduction by real and virtual photons]
* [http://arxiv.org/abs/hep-th/0410131 hep-th/0410131 Quantized tension: Stringy amplitudes with Regge poles and parton behavior]
* [http://arxiv.org/abs/hep-th/0409205 hep-th/0409205 Wilson Loop, Regge Trajectory and Hadron Masses in a Yang-Mills Theory from Semiclassical Strings]


Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Regge — may refer to* Tullio Regge (born 1931), Italian physicist, developer of Regge calculus and Regge theory * Regge calculus, formalism for producing simplicial approximations of spacetimes * Regge theory, study of the analytic properties of… …   Wikipedia

  • History of string theory — 1943 1958: S Matrix String theory is an outgrowth of a research program begun by Werner Heisenberg in 1943, picked up and advocated by many prominent theorists starting in the late 1950s and throughout the 1960s, which was discarded and… …   Wikipedia

  • Tullio Regge — (born July 11 1931 in Turin) is an Italian physicist.In 1957, Regge discovered a mathematical property of potential scattering in the Schrödinger equation that the scattering amplitude can be thought of as an analytic function of the angular… …   Wikipedia

  • Tullio Regge — Tullio Eugene Regge (* 11. Juli 1931 in Turin) ist ein italienischer Physiker, der vor allem in der theoretischen Elementarteilchenphysik arbeitete. Inhaltsverzeichnis 1 Leben 2 Werk 3 Veröffentlichungen …   Deutsch Wikipedia

  • String theory — This article is about the branch of theoretical physics. For other uses, see String theory (disambiguation). String theory …   Wikipedia

  • Non-critical string theory: Lorentz invariance — Usually non critical string theory is considered in frames of the approach proposed by Polyakov [1]. The other approach has been developed in [2] [3] [4]. It represents a universal method to maintain explicit Lorentz invariance in any quantum… …   Wikipedia

  • Редже, Туллио — Туллио Редже итал. Tullio Regge Дата рождения: 11 июля 1931(1931 07 11) (81 год) Место рождения: Турин, Италия …   Википедия

  • Stanley Mandelstam — (b. 1928, Johannesburg) is a South African born theoretical physicist. He introduced the relativistically invariant Mandelstam variables into particle physics in 1958 as a convenient coordinate system for formulating his double dispersion… …   Wikipedia

  • Pomeron — In physics, the pomeron is a Regge trajectory, a family of particles with increasing spin, postulated in 1961 to explain the slowly rising cross section of hadronic collisions at high energies. Contents 1 Overview 2 Odderon 3 String theory 4 …   Wikipedia

  • List of particles — This is a list of the different types of particles, known and hypothesized. For a chronological listing of subatomic particles by discovery date, see Timeline of particle discoveries. This is a list of the different types of particles found or… …   Wikipedia