Reggeon field with non-vanishing vacuum expectation value

It is argued that if the vacuum expectation value of the reggeon field does not vanish, the solution of the reggeon calculus corresponds to the leading singularity of intercept one. The physical interpretation of the reggeon field theory with unstable vacuum is discussed.     

Reggeon field theory on a lattice: A formulation

The principle of universality is taken from statistical mechanics and applied to the reggeon field theory. Following a pedagogical review of the implications of universality for the reggeon calculus, a lattice formulation of the reggeon field theory is presented and discussed. Scaling laws for the thermodynamic quantities of such systems are described and relations among critical indices are derived. These relations enable high-energy scattering behaviour to be calculated using lattice methods.     

A topological expansion for high-energy hadronic collisions: (I). General properties and connection with the reggeon calculus

In this and in a companion paper a “topological expansion” for high-energy hadronic processes is proposed and discussed. In this first paper the general properties of the expansion and its connection with Gribov's reggeon calculus are presented. The topological expansion is first defined mathematically for a large class of theories and is shown to be equivalent to a “large N expansion” in some theories which include planar dual models and non-Abelian gauge theories. Next, the definition of the bare parameters is given in terms of graphs on a sphere. The bare pomeron pole and its couplings are thus introduced. The (inclusive) form of s-channel unitarity and its consequences fo the above couplings are recalled. It is then shown how the expansion in the number of “handles” of the graph can be related to Gribov's reggeon calculus and how, with the aid of discontinuity equations in the J-plane, scaling solutions can be obtained and critical indices can be computed to yield known results. Our main new results, including the study of s-channel discontinuities and of positivity constraints as well as the definition of a new fireball expansion, and the discussion of the relevance of this theory at finite (present) energies are presented in the second paper.     

Exploiting the equivalence of reggeon field theory in zero transverse dimensions and reaction–diffusion processes

The reggeon field theory in zero transverse dimensions is investigated. Two versions of the theory are considered: one that allows for at most triple pomeron interactions and the other that embodies an additional 2→2 quartic reggeon coupling. The behavior of the scattering amplitude at asymptotic rapidities is obtained in both cases. In an s-channel picture of the high energy scattering both models can be viewed as reaction–diffusion processes. We derive known results in reggeon field theory rather easily using the reaction–diffusion formalism. We find that some results which are surprising from the reggeon field theory point of view turn out to have a simple interpretation from the reaction–diffusion point of view.     

The content of unitarity constraints on a pomeron pole of intercept one

We present a consistent picture of a pomeron pole with intercept one, together with its cuts, which evades the decoupling arguments. We use the reggeon cut discontinuity formulae to introduce Gribov's reggeon calculus as an exact solution of multiparticle t-channel unitarity. We show how, within the calculus, two-pomeron iterations of a singular kernel can be responsible for the zero in the triple-pomeron vertex. Using the concept of a bare pomeron pole as a multiperipheral production process which is subsequently renormalised by other effects, we apply the reggeon calculus analysis to inclusive cross sections. We find that the inclusive sum rule decoupling arguments are avoided because of the addition of enhanced absorptive corrections to the conventional Regge pole contributions. However, we show that in this picture the combined pole and two-pomeron cut contribution to the total cross section factories to order (ln s)^?2.We also show that, when the correct helicity structure of the pomeron is taken into account, the s-channel unitarity condition for pomeron scattering amplitudes does not lead to any serious decouplings.     

Phase transitions and the high temperature expansion for the reggeon calculus

We study a recently proposed lattice version of the reggeon field theory. First a simple one-dimensional system possessing many of the features of the reggeon calculus (Ising model in an imaginary magnetic field) is solved. Surprisingly, the system is found to undergo a phase transition at a non-zero critical temperature, which, although of first order obeys the universality and scaling laws previously postulated for the reggeon calculus. Returning to the full lattice theory, the machinery for performing a high temperature expansion is set up, and initial calculations carried out to order T^?3. In this order, best estimates for the critical indices η and v in the asymptotic elastic amplitude A(s,t) ～ is (ln s)^ηf(t(lns)^v) yield $\text{η = 0 (}\text{1}\text{2}\text{～ 1), v = 0(1}\text{1}\text{2}\text{～ 2)}$. Check on the method, including comparisons with known Ising model results, are also discussed.     

Problems with spontaneous breakdown in reggeon field theories

We prove a theorem which states that if a reggeon field theory undergoes spontaneous breakdown as a result of the pomeron intercept being above one, then the shifted Lagrangian must in general develop terms which are non-canonical from the point of view of reggeon Lagrangians. We discuss the interpretation of these terms and point out some of the problems associated with them.     

An SU(2) symmetric reggeon field theory with a negative mass

An SU(2) invariant reggeon field theory (RFT) containing three reggeon multiplets, one of which has a negative mass, is studied in the classical approximation with zero transverse dimensions. We explain how to introduce a continuous symmetry into RFT and explore under what restrictions our model has stable classical solutions. We find the the same ambiguity of having two different types of solutions as in supercritical pomeron theory. One of them is shown to lead to a constant total cross section and decreasing cross sections for quantum number exchanges.     

Is reggen field theory rendered obsolete byqcd?

We affirm the power of the eikonal approximation in reggeon field theory (rft) and point out its merit as contrasted with renormalization group method for calculating reggeon self-energy correction due to pomeron exchanges. Relative merits ofrft andqcd in appropriate momentum regions of hadronic interactions are also examined to suggest a negative answer to the title.     

Reggeon quantum mechanics: Effect of four-reggeon couplings

We study reggeon quantum mechanics when four-reggeon couplings are present as well as the conventional three-reggeon coupling. We show that as the reggeon intercept is increased an infinite number of states pass through energy zero. We give the values of the intercepts at which states pass through zero, construct the states explicitly, and tell how fast their energy changes with intercept. We show that these higher states do not interfere with the construction of spin models. However, no spin model is possible if the one-reggeon ? three-reggeon coupling is non-zero.     

Existence of a phase transition in reggeon field theory in two transverse dimensions

We show that a reggeon field theory, in the physical number of dimensions, with a linear bare trajectory and a constant triple-pomeron coupling, undergoes a phase transition as the bare pomeron intercept is increased through a certain critical value.     

Flavouring the Gribov process

The exchange of flavour carrying trajectories is studied in the non-covariant parton interpretation of reggeon field theory. While pomeron exchange is described by wee partondensities, i.e. diagonal elements of the density matrix of a fast hadron, meson exchange is described by density matrix elements which are diagonal in parton number but off-diagonal in flavour. The reggeon field theory “hamiltonian” describes a markoffian evolution of this block-diagonal density matrix during a boost. This interpretation is possible both if there are two distinctf and ? trajectories and in case of ? identity. The meson trajectories are superpositions of odd and even signature trajectories.     

Three gluon integral equation and odd C singlet Regge singularities in QCD

The integral equation for a three gluon system in the odd C colour singlet channel is derived utilising reggeon calculus based on QCD. This equation is shown to be free from infrared divergences. It generates a fixed branch point near j = 1 as the singularity.     

Reggeon calculus at collider energies

The phenomenology of the perturbative reggeon calculus at collider energies is studied. It is found that the graphs which were neglected at ISR energies are still negligeable at \(\sqrt s = 540 GeV\) . The pertubative series for the total cross section still converges reasonably fast. The values of the different parameters which describe rightly the data up to ISR energies give rise to a total cross section of around 60 mb at \(\sqrt s = 540 GeV\) . For these values, the corresponding low mass and high mass eikonal series converges much more slowly. The non perturbative reggeon calculus gives rise to a total cross section less than 60 mb.     

An exact solution to reggeon calculus

By choosing a suitable but unconventional bare pomeron propagator and bare triple-pomeron coupling the Dyson equations of reggeon calculus are shown to reduce to algebraic equations for the various coupling constants. The resulting pomeron, which is identical to the input pomeron is the familiar black or gray disk.     

Nonequilibrium critical poisoning in a single-species model

A simple model is introduced, which exhibits a poisining transition similar to that observed in studies of catalyc surface reactions. Steady-state behavior and critical exponents are determined via series expansion and Monte Carlo simulations. The relation between catalytic surface models and reggeon field theory is examined.     

A field-theoretic study of the Regge-eikonal model. II

A previous study of the Regge-eikonal model in φ³ is extended to QED. First we define a reggeon amplitude that is built up by tower diagrams, and then study multiregge exchange by use of Gribov's reggeon calculus. The situation is essentially the same as in φ³: The eikonal approximation is the true high-energy and weak coupling limit (s → ∞, α ln s = fixed), but it breaks down outside of the weak-coupling limit. This confirms that the eikonal approximation as a model for Regge-cuts is not justifiable by field-theoretic arguments because of the neglect of inelastic intermediate states.     

Magnitude of Regge cut contributions in the triple-Regge region

Starting from the reggeon calculus, the various possibilities of absorptive pomeron cut corrections in the triple-Regge region are considered. For the case of pp → pX, we estimate their importance at present day energies. We conclude that at highest ISR energies, pomeron cuts of the eikonal type are not enough, and enhanced diagrams with at least one additional triple-pomeron coupling need be included.     

Loops in the reggeon model for <Emphasis Type="Italic">hA</Emphasis> scattering

The contribution of the simplest loops is studied in the local reggeon field theory with a supercritical pomeron in nuclear matter. It is shown that the latter transforms the supercritical pomeron into a subcritical one. Renormalization of the intercept and difficulties related to the fact that the renormalised intercept is complex are discussed. Numerical results with the conventional parameters are reported.     

f-pole corrections to the critical parameters of the pomeron

A reggeon field theory with two vacuum quantum numbers Regge poles, the pomeron and the f-reggeon is presented. In such a theory only one stable fixed point appears which is sensibly different from that governing a RFT with the pomeron alone. This fact is responsible for the modifications of the critical parameters of the pomeron. In particular, the intercept of the bare pomeron increases and approaches the phenomenological value.