Triple Pomeron Vertex Research Articles

Pomeron fan diagrams in perturbative QCD

Within QCD reggeon field theory we study the formation of two subsequent triple pomeron vertices in the process P→PP→PPP. We make use of an earlier investigation [1] of the six-reggeon amplitude in deep inelastic scattering and show that in the large-Nc limit pomeron fan diagrams emerge with the same triple pomeron vertex in all places. We thus confirm the BK-equation, but we also find additional terms related to the reggeization of the gluon, and we discuss their potential significance. Our analysis also includes the general pomeron → two odderon vertex: a particular version of this vertex has been included into earlier generalizations the BK equation.

QCD unitarity constraints on Reggeon Field Theory

We point out that the $s$-channel unitarity of QCD imposes meaningful constraints on a possible form of the QCD Reggeon Field Theory. We show that neither the BFKL nor JIMWLK nor Braun's Hamiltonian satisfy the said constraints. In a toy, zero transverse dimensional case we construct a model that satisfies the analogous constraint and show that at infinite energy it indeed tends to a "black disk limit" as opposed to the model with triple Pomeron vertex only, routinely used as a toy model in the literature.

Pomeron interaction in the perturbative QCD

Formation of the triple pomeron vertices in processes P→PP→PPP and PP→P→PP is studied in the BFKL-Bartels approach. It is demonstarted that successive splittings of the pomeron indeed generate the standard triple pomeron vertex in agreement with the dipole approach. In contrast, in the process PP→P→PP the improper part of the vertex is found missing. Significance of this result is discussed in the framework of the theory of interacting pomerons.

QCD Reggeon calculus from KLWMIJ/JIMWLK evolution: vertices, reggeization and all

We show explicitly how the high energy QCD evolution generated by the KLWMIJ Hamiltonian can be cast in the form of the QCD Reggeon Field Theory. We show how to reduce the KLWMIJ Hamitonian to physical color singlet degrees of freedom. We suggest a natural way of defining the Pomeron and other Reggeons in the framework of the KLWMIJ evolution and derive the QCD Reggeon Field Theory Hamiltonian which includes several lowest Reggeon operators. This Hamiltonian generates evolution equations for all Reggeons in the case of dilute-dense scattering, including the nonlinear Balitsky-Kovchegov equation for the Pomeron. We also find explicit expressions for the Reggeon conjugate operators in terms of QCD operators, and derive their evolution equations. This provides a natural and unambiguous framework for reggeization procedure introduced in [4, 5]. The Bartels triple Pomeron vertex is inherited directly from the RFT Hamiltonian. For simplicity in the bulk of the paper we work in the large N c limit.

Scattering amplitude and pomeron loops in perturbative QCD at large [formula omitted

The amplitude for the collision of two hadrons with the lowest order pomeron loop is calculated. Numerical calculations show that the loop contribution to the amplitude begins to dominate the single-pomeron exchange at rapidities 8–10. Full dependence of the triple-pomeron vertex on intermediate conformal weights is taken into account.

Uncovering the triple ℙomeron vertex from Wilson line formalism

We compute the triple pomeron vertex from the Wilson line formalism, including both planar and non-planar contributions, and get perfect agreement with the result obtained in the Extended Generalized Logarithmic Approximation based on reggeon calculus.

The possibility that the triple-Pomeron coupling vanishes at q t =0

We study the case when the triple-Pomeron vertex is assumed to have a vectorial form, that is, the amplitude of high-mass diffractive dissociation vanishes as $V \propto \vec q_t \cdot \vec e$ as $q_t \to 0$. We find that the available data in the triple-Reggeon region may be well described in such a `weak' coupling scenario, providing that absorptive effects are taken into account. We compare this weak (vector) coupling scenario with the strong and weak (scalar) coupling scenarios. Corresponding predictions are presented for an LHC energy of 14 TeV.

The effective action and the triple Pomeron vertex

We study integrations over light-cone momenta in the gauge invariant effective action of high energy QCD. A regularization mechanism which allows for the evaluation of the longitudinal integrations is presented. After a rederivation of the reggeized gluon and the BFKL-equation from the effective action, we study the 1-3 and 2-4 reggeized gluon transition vertex of QCD Reggeon field theory and discuss their connection with the usual triple Pomeron vertex of perturbative QCD.

The triple Pomeron vertex in large-NcQCD and the pair-of-pants topology

We investigate the high energy behavior of QCD for different surface topologies of color graphs. After a brief review of the planar limit (bootstrap and gluon reggeization) and of the cylinder topology (BFKL) we investigate the 3 ? 3 scattering in the triple Regge limit which belongs to the pair-of-pants topology. We re-derive the triple Pomeron vertex function and show that it belongs to a specific set of graphs in color space which we identify as the analogue of the Mandelstam diagram.

The topology of the triple Pomeron vertex in [formula omitted] SYM

We investigate, within N=4 SYM, the high energy behavior in the triple Regge limit of a six point correlator of R-currents. Using the leading logarithmic approximation, we sum all diagrams whose color lines fit onto the surface of a sphere. We find three distinct classes of graphs, and one of them contains the triple Pomeron vertex known from QCD. We present results which, within the AdS/CFT correspondence, can be compared with scattering amplitudes in the dual string theory.

Pomeron loops in the perturbative QCD with large N c

The lowest order pomeron loop is calculated for the leading conformal weight with full dependence of the triple-pomeron vertex on intermediate conformal weights. The loop is found to be convergent. Its contribution to the pomeron Green function begins to dominate already at rapidities 10–15. The pomeron pole renormalization is found to be quite small due to a rapid fall of the triple-pomeron vertex with rising conformal weights.

Diffractive dissociation re-visited for predictions at the LHC

We describe the formalism, and present the results, for a triple-Regge analysis of the available pp and p\bar{p} high-energy data which explicitly accounts for absorptive corrections. In particular, we allow for the gap survival probability, S^2, in single proton diffractive dissociation. Since for pp scattering the value of S^2 is rather small, the triple-Pomeron vertex obtained in this analysis is larger than that obtained in the old analyses where the suppression caused by the absorptive corrections was implicitly included in an effective vertex. We show that the bare triple-Pomeron coupling that we extract from the pp and p\bar{p} data is consistent with that obtained in a description of the gamma p -> J/psi + Y HERA data. The analyses of the data prefer a zero slope, corresponding to the small size of the bare vertex, giving the hope of a smooth matching to the perturbative QCD treatment of the triple-Pomeron coupling.

Survival probability for diffractive Higgs production in high density QCD

In this paper, the contribution of hard processes described by BFKL pomeron exchange is taken into account by calculating the first enhanced diagram. The survival probability is estimated, using the ratio of the first enhanced diagram and the single pomeron amplitude, taking into account all essential pomeron loop diagrams in the toy model of Mueller. The triple pomeron vertex is calculated explicitly in the momentum representation. This calculation is used for estimating the survival probability, and it turns out that the survival probability is small, at 0.4%. Hard pomeron rescattering processes contribute substantially to the survival probability.

Baryon scattering at high energies: wave function, impact factor, and gluon radiation

The scattering of a baryon consisting of three massive quarks is investigated in the high energy limit of perturbative QCD. A model of a relativistic proton-like wave function, dependent on valence quark longitudinal and transverse momenta and on quark helicities, is proposed, and we derive the baryon impact factors for two, three and four t-channel gluons. We find that the baryonic impact factor can be written as a sum of three pieces: in the first one a subsystem consisting of two of the three quarks behaves very much like the quark-antiquark pair in gamma* scattering, whereas the third quark acts as a spectator. The second term belongs to the odderon, whereas in the third (C-even) piece all three quarks participate in the scattering. This term is new and has no analogue in gamma* scattering. We also study the small x evolution of gluon radiation for each of these three terms. The first term follows the same pattern of gluon radiation as the gamma*-initiated quark-antiquark dipole, and, in particular, it contains the BFKL evolution followed by the 2-->4 transition vertex (triple Pomeron vertex). The odderon-term is described by the standard BKP evolution, and the baryon couples to both known odderon solutions, the Janik-Wosiek solution and the BLV solution. Finally, the t-channel evolution of the third term starts with a three reggeized gluon state which then, via a new 3-->4 transition vertex, couples to the four gluon (two-Pomeron) state. We briefly discuss a few consequences of these findings, in particular the pattern of unitarization of high energy baryon scattering amplitudes.

Soft diffraction at the LHC: a partonic interpretation

We present a ‘new generation’ model for high energy proton–proton ‘soft’ interactions. It allows for a full set of multipomeron vertices as well as for including multichannel eikonal scattering. It describes the behaviour of the proton–proton total, σtot, and elastic, dσel/dt, cross sections together with those for low- and high-mass proton dissociation. Although the model contains a comprehensive set of multipomeron diagrams, it has a simple partonic interpretation. Including the more complicated multipomeron vertices reduces the absorptive effects as compared to the predictions in which only the triple-pomeron vertex is considered. Tuning the model to describe the available ‘soft’ data in the CERN ISR–tevatron energy range, we predict the total, elastic, single- and double-diffractive dissociation cross sections at the LHC energy. An inescapable consequence of including multichannel eikonal and multipomeron effects is that the total cross section is expected to be lower than before: indeed, we find σtot≃ 90 mb at the LHC energy. We also present differential forms of the cross sections. In addition, we calculate soft diffractive central production.

A momentum space analysis of the triple pomeron vertex in pQCD

We study the properties of the momentum space triple pomeron vertex in perturbative QCD. Particular attention is given to the collinear limit where the transverse momenta on one side of the vertex are much larger than on the other side. We also comment on the kernels in the non-linear evolution equations.

Solving effective field theory of interacting QCD pomerons in the semiclassical approximation

Effective field theory of Balitsky, Fadin, Kuraev, and Lipatov (BFKL) pomerons interacting by QCD triple pomeron vertices is investigated. Classical equations of motion for the effective pomeron fields are presented being a minimal extension of the Balitsky-Kovchegov equation that incorporates both merging and splitting of the pomerons and that is self-dual. The equations are solved for symmetric boundary conditions. The solutions provide the dominant contribution to the scattering amplitudes in the semiclassical approximation. We find that for rapidities of the scattering larger than a critical value ${Y}_{c}$ at least two classical solutions exist. Curiously, for each of the two classical solutions with the lowest action the symmetry between the projectile and the target is found to be spontaneously broken, being however preserved for the complete set of classical solutions. The solving configurations at rapidities $Y>{Y}_{c}$ consist of a Gribov field being strongly suppressed even at very large gluon momenta and the complementary Gribov field that converges at high $Y$ to a solution of the Balitsky-Kovchegov equation. Interpretation of the results is given and possible consequences are shortly discussed.

The extraction of the bare triple-pomeron vertex; a crucial ingredient for diffraction

Abstract The triple-pomeron coupling lies at the heart of the predictions for high energy diffractive processes. We explain why the existing determinations, which use single-particle inclusive hadronic data a + b → a + Y , underestimate the value of the bare coupling, due to the neglect of soft rescattering which populates the rapidity gaps. We describe how data for the process γ + p → J / ψ + Y can be used to give a much more reliable estimate of the bare coupling. We use the existing, fragmentary, J / ψ data from HERA to show that the triple-pomeron coupling is probably about 3 times larger than the previous determinations. We emphasize the importance of an explicit measurement of the mass spectrum of the Y system which accompanies J / ψ production at HERA. The consequences for ultra high energy cosmic ray showers are mentioned.

On the inclusive gluon jet production from the triple pomeron vertex in the perturbative QCD

Single and double inclusive cross-sections for gluon jet production from within the triple pomeron vertex are studied in the reggeized gluon technique in the QCD with Nc→∞. It is shown that to satisfy the AGK rules the vertex has to be fully symmetric in all four reggeized gluons which form the two final pomerons. The single inclusive cross-sections are found for different cuttings of the triple pomeron vertex. They sum to the expression obtained by Kovchegov and Tuchin in the color dipole picture. The found double inclusive cross-sections satisfy the AGK rules.

Möbius Representation for Reggeized Gluons

It is shown that the BFKL equation is invariant under a gauge-type transformation. As a result one can impose on the Pomeron wave function Ψ ( ρ → 1 , ρ → 2 ) the colour transparency condition Ψ ( ρ → , ρ → ) = 0 valid for functions in the Mobius representation. The triple Pomeron vertex in the multi-colour QCD at this representation is equivalent to the integral kernel in the Balitiski-Kovchegov (BK) equation. As a result, the BK equation for the dipole density is obtained from the nonlinear equation for the sum of fan diagrams.