Gribov's Reggeon Calculus Research Articles

Euler-Lagrange equations for the Gribov reggeon calculus in QCD and in gravity

The theory of the high energy scattering in QCD and gravity is based on the reggeization of gluons and gravitons, respectively. We discuss the corresponding effective actions for reggeized particle interactions. The Euler-Lagrange equations in these theories are constructed with a variational approach for the effective actions and by using their invariance under the gauge and general coordinate transformations.

Nuclear suppression at RHIC and LHC in Glauber–Gribov approach

The approach to problem of nuclear shadowing based on Gribov Reggeon calculus is presented. Here the total cross section of hA interaction is found in a parameter-free description, employing the new data on the gluon density of the Pomeron, measured with high precision at HERA, as input. The model is then applied for calculation of J/ψ production in dAu collisions at top RHIC energy. It is shown that the theoretical estimates are in a very good agreement with the PHENIX data, and further predictions for the J/ψ suppression in pPb collisions at energies of LHC are made.

Nuclear structure functions at small x from inelastic shadowing and diffraction

Nuclear structure functions at small x and small or moderate $Q^2$ are studied using the relation with diffraction on nucleons which arises from Gribov's Reggeon Calculus. A reasonable description of experimental data is obtained with no fitted parameters. A comparison with other models and predictions for future lepton-ion colliders are provided. Consequences for the reduction of multiplicities in nucleus-nucleus collisions at energies of RHIC and LHC are examined.

Normalization of the triple-Pomeron coupling

Various papers on the Gribov Reggeon calculus use various normalization conventions for the triple-Pomeron coupling constant. These normalizations are compared, and some errors are corrected.

Pion-nucleon charge-exchange polarization by gribov reggeon calculus and the derivative rule

Polarization measurements in u + p + u ~ indicate the presence of a relative phase between the nonflip and the flip helicity amplitudes. Corrections to the single Reggeon exchange can, in principle, generate such a relative phase. These corrections are cuts in the complex j-plane whose strength can be calculated by means of the absorption model. This model (1) describes the polarization data for very small momentum transfers but for larger values it fails entirely giving a tremendous negative peak where the experimental data are consistent with zero. The polarization obtained from the absorption model changes sign at t -~ _~ 0.20 (GeV/c) 2 as a direct consequence of the fact that the relative phase between the absorption cut and the pole of the nonfiip helicity amplitude reaches 180 ~ I t is an inevitable feature of the tradit ional absorption model tha t this relative phase can never be much larger than 180 ~ at t = 0 (GeV/c) 2. Since the cut rotates very slowly in comparison with the pole, any modification of the model has to considerably increase the starting point of the cut. The phase-modified absorption model (2) is the most extreme version of a successful modification. This model pushes the cut right into the fourth quadrant by multiplying the nourotat ing part of the cut by a factor of i and therefore absorbs the imaginary part of the amplitude total ly at the expense of the real part. The zero of the imaginary part of the helicity nonflip amplitude has to occur before the zero of the real part of this amplitude. Unless the cut is modified, the relative positions of these zeros are interchanged and the amplitude therefore rotates incorrectly in a counterclockwise manner around the origin of the Argand diagram (3). In order to achieve the needed modification in a less arbitrary way, one can do the traditional absorption model convolution, but with a pomeron which has a real and a more detailed structure (4).

Inclusive central region in perturbative Reggeon calculus

The single-particle inclusive cross section and the correlation function are studied in the perturbative approach to Gribov's Reggeon calculus, evaluating the leading contributions to both functions. The large energy rise of the inclusive cross section appears as a consequence of the Pomeron having an intercept larger than 1. The same set of parameters which describes correctly the cross-section data and the triple-Regge region also describes the inclusive data in the central region.

High-energy average charged multiplicities from nuclei in a Regge-calculus model

Lehman and Winbow have used a Gribov Reggeon-calculus approach to derive expressions for average charge multiplicities in high-energy scattering off nuclei. They find the multiplicity to be n = bY + f (A), where b is independent of A. It is shown that a reasonable modification of their model yields n = b'A$sup 1$/$sup 3$Y + g (A), where b' is known. It is found that this expression agrees with experimental data on dn/dY (where Y = lns) better than that of Lehman and Winbow, and agrees as well as the energy flux model of Gottfried. (AIP)

Reggeon cuts in a multiparticle unitary model: (II). Four-particle case

We investigate the reggeon cuts in a model with four-particle unitarity in the t-channel. The model, which was previously discussed by McCoy and Wu, is derived from ø 3 theory. Our analysis of asymptotic behaviour uses momentum-space techniques. We investigate carefully the integral equation for the partial-wave amplitude and use it to exhibit the origin of the various reggeon cuts, which turn out to satisfy discontinuity formulae consistent with Gribov's reggeon calculus. We suggest that there is a four-particle Regge pole to the right of all the cuts.

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.

The n-loop expansion of the Reggeon calculus

We apply the technique known in solid state physics as the n-loop expansion to calculate the critical indices of the φ 3 Gribov Reggeon calculus directly in two transverse dimensions. Infrared pathologies of the massless theory require the calculation to be done in the infinite momentum limit of the massive theory. For n = 1 the results are close to those of the ε-expansion in O(ε). For n = 2 the β function has no zero, analogously to the case in solid state physics. Use of a Padé approximant for β yields σ tot ≈ (1 n s) 0.27 at infinity, close to the O(ε 2) result.

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

The Regge-eikonal model in φ 3 field theory is studied within the framework of Gribov's reggeon calculus. A condition is derived that indicates what sort of multireggeon exchange diagrams are important for large energies, and it is shown that the eikonal form is valid only in the weak-coupling limit, i.e., when the inner coupling constant of the reggeons goes to zero: g 2 ∼ 1/ln s. The breakdown of the eikonal approximation outside of this limit is shown to be an effect of inelastic intermediate states.

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

A previous study of the Regge-eikonal model in φ 3 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 φ 3: 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.

A new interpretation of the absorption mechanism for high energy scattering

We propose a new s-channel absorption mechanism for high energy processes. A possible small dimensionless physical quantity naturally emerges. Consequently, the proposed s-channel equation can accommodate, at present energies, an elastic amplitude dominated by a simple factorizable bare pomeron pole, as in the t-channel perturbative expansion of the Gribov's Reggeon calculus in the strong coupling limit.

The origin of a high-energy scale in the Pomeron calculus

The Gribov-Reggeon calculus, whose perturbative expansion is expected to converge at low energy, is known to give rise to critical phenomena at ultra-high energies. The aim of this paper is to investigate the transition between these two regimes and to determine the scale with which this transition happens. This is done by solving exactly the renormalization group equation in a model theory. The propagator shows a singularity whose position determines the scale in question. The dynamical origin of this scale — whose evaluation situates it beyond present machine energies — is discussed, and so the dual relation between the perturbative and the critical expansions.

Asymptotic behaviour of multiplicities in models with interacting pomerons

Using renormalization group techniques, the asymptotic behaviour of 〈 n P 〉 in models with strong coupling pomeron interactions is found to be ln s P(1+ γ) . In the Gribov reggeon calculus γ=η(η= lim ln σ T (s) ln ln s ) , in an absorptive model γ=− η. The values of 〈n P〉 〈n〉 P are calculated pertubatively. The Gribov model results are shown to be consistent with positivity requirements, and in suprisingly good agreement with experimental values at present energies.

Are constant asymptotic total cross sections ruled out by high-energy measurements?

It is a common belief that the conventional contributions of the Pomeron pole and the two-Pomeron cut in the Gribov Reggeon calculus cannot give enough rise of the $pp$ total cross section at CERN ISR energies. However, we find from a detailed analysis of $\frac{d\ensuremath{\sigma}}{dt}$ at small $t$ that one can, in fact, get a reasonable rise of the $pp$ total cross section at CERN ISR energies. The ${K}^{+}p$ total cross sections are also fitted; however, their consistency with $\frac{d\ensuremath{\sigma}}{dt}$ has to be checked out when the data are available.

Reggeon calculus as a low-order perturbation theory for the Pomeron

We review the foundations of the Gribov Reggeon calculus with an emphasis on the relationship between the energy-plane and $J$-plane descriptions of the diagrams of the calculus. The question of the "large-rapidity-gap cutoff" for the Pomeron and the problem of signature are treated in more detail than in the traditional approach to the calculus. Except for some slight differences, the main results agree with Gribov's original formulation. We advocate the use of the Reggeon calculus as a refinement on the contemporary "two-component" model for the Pomeron and collect some formulas useful for phenomenological applications.

An improvement of Gribov's reggeon calculus

We derive an expression for Regge cuts and the associated enhancement of Regge poles, following Gribov' s derivation of the reggeon calculus, but refraining from making an approximation made by Gribov. We show that Gribov's loop integrand should be multiplied by A(t_ tl, t2))/'+1-~1 --a2 F(-~)l~(/'+2--Ctl--a2)

Threshold singularities and Gribov's Reggeon calculus

Within the framework of Gribov's Reggeon calculus we study the influence of the two-pion threshold on the Pomeron trajectory. We point out that in order to obtain a physically meaningful result, it is important to know which Reggeon-Reggeon-particle-particle partial-wave amplitudes can be taken to be constants.

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.