Regge Cuts Research Articles

Regge Cuts in QCD

Regge Cuts in QCD

Disentangling the Regge Cut and Regge Pole in Perturbative QCD.

The high-energy limit of gauge-theory amplitudes features both a Regge pole and Regge cuts. We show how to disentangle these, and hence how to determine the Regge trajectory beyond two loops. While the nonplanar part of multiple Reggeon t-channel exchange forms a Regge cut, the planar part contributes to the pole along with the single Reggeon. With this, we find that the infrared singularities of the trajectory are given by the cusp anomalous dimension. By matching to recent QCD results, we determine the quark and gluon impact factors to two loops and the Regge trajectory to three loops.

Scattering amplitudes in the Regge limit and the soft anomalous dimension through four loops

Using rapidity evolution equations we study two-to-two gauge-theory scattering amplitudes in the Regge limit. We carry out explicit computations at next-to-next-to-leading logarithmic accuracy through four loops and present new results for both infrared-singular and finite contributions to the amplitude. New techniques are devised in order to derive the colour structure stemming from three-Reggeon exchange diagrams in terms of commutators of channel operators, obtaining results that are valid for any gauge group, and apply to scattered particles in any colour representation. We also elucidate the separation between contributions to the Regge cut and Regge pole in the real part of the amplitude to all loop orders. We show that planar contributions due to multiple-Reggeon exchange diagrams can be factorised as a Regge pole along with the single-Reggeon exchange, and when this is done, the singular part of the gluon Regge trajectory is directly determined by the cusp anomalous dimension. We explicitly compute the Regge cut component of the amplitude through four loops and show that it is non-planar. From a different perspective, the new results provide important information on soft singularities in general kinematics beyond the planar limit: by comparing the computed corrections to the general form of the four-loop soft anomalous dimension we derive powerful constraints on its kinematic dependence, opening the way for a bootstrap-based determination.

Heptagon functions and seven-gluon amplitudes in multi-Regge kinematics

We compute all 2 → 5 gluon scattering amplitudes in planar mathcal{N} = 4 super-Yang-Mills theory in the multi-Regge limit that is sensitive to the non-trivial (“long”) Regge cut. We provide the amplitudes through four loops and to all logarithmic accuracy at leading power, in terms of single-valued multiple polylogarithms of two variables. To obtain these results, we leverage the function-level results for the amplitudes in the Steinmann cluster bootstrap. To high powers in the series expansion in the two variables, our results agree with the recently conjectured all-order central emission vertex used in the Fourier-Mellin representation of amplitudes in multi-Regge kinematics. Our results therefore provide a resummation of the Fourier-Mellin residues into single-valued polylogarithms, and constitute an important cross-check between the bootstrap approach and the all-orders multi-Regge proposal.

Logarithmic Regge pole

This work presents the subtraction procedure and the Regge cut in the logarithmic Regge pole approach. The subtraction mechanism leads to the same asymptotic behavior as previously obtained in the non-subtraction case. The Regge cut, in contrast, introduces a clear role to the non-leading contributions for the asymptotic behavior of the total cross-section. From these results, some simple parameterization is introduced to fit the experimental data for the proton-proton and antiproton-proton total cross-section above some minimum value up to the cosmic-ray. The fit parameters obtained are used to present predictions for the -parameter as well as to the elastic slope at high energies.

BFKL Equation: Status and Problems

The BFKL equation was derived for description of high energy behaviour of scattering amplitudes in non-Abelian gauge theories. Now it is widely known and used in quantum chromodynamics in the leading and next-to-leading logarithmic approximations. Its derivation is based on the pole Regge form of amplitudes with gluon exchanges in cross channels. In higher approximations this form is violated by contributions of Regge cuts, which complicates the derivation of the equation in the BFKL approach.

Higher-Order Contributions to QCD Amplitudes in Regge Kinematics (Scientific Summary)

The famous Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation was derived using the hypothesis that amplitudes of non-abelian gauge theories with the adjoint representation of the gauge group in cross-channels are given by the Reggeized gauge boson contributions. The hypothesis is true in the leading logarithmic approximation, wherein the equation was originally derived, and in the next-to-leading one. However, in the next-to-next-to-leading logarithmic approximation this is not so, since in this approximation the Regge cuts begin to contribute. Calculations of their contributions to elastic scattering amplitudes in quantum chromodynamics and their role in derivation of the BFKL equation are discussed.

Regge Cuts and NNLLA BFKL

In the leading and next-to-leading logarithmic approximations, QCD amplitudes with gluon quantum numbers in cross-channels and negative signature have the pole form corresponding to a reggeized gluon. The famous BFKL equation was derived using this form. In the next-to-next-to-leading approximation (NNLLA), the pole form is violated by contributions of Regge cuts. We discuss these contributions and their impact on the derivation of the BFKL equation in the NNLLA.

BFKL Equation and Regge Cuts

The BFKL equation is based on the gluon yReggeization. In the leading and next-to-leading logarithmic approximations it is derived using the pole Regge form of QCD amplitudes with gluon quantum numbers in cross-channels and negative signature. This form is violated in the next-to-next-to-leading approximation. In two and three loops the observed violation can be explained by the presence of the three-Reggeon cut. Contributions of this cut to elastic scattering amplitudes up to four loops is discussed.

Features of ω photoproduction off nucleon target at forward angles: dominance of π exchange with Regge cuts and scaling of differential cross-sections

We investigate the photoproduction of ω off a nucleon target by using a Reggeized model where π(135) + σ(500) + f1(1285) + f2(1270) + pomeron exchanges are included in the t-channel for the reaction at forward angles. The reaction mechanism at low energy is featured by the dominance of the π exchange with the absorptive cuts introduced to modulate the pion contribution to both γp → ωp and reactions. The necessity of σ exchange is illustrated in the analysis of the cross-section from natural parity exchanges. Cross-sections for the differential, total, and spin density matrix with parity and beam polarization asymmetries are reproduced and compared with existing data on . Scaled differential cross-sections of Jefferson Lab data on are investigated at the production angle θ = 90° with the nonlinear trajectories for a saturation. Differential and total cross-sections for the reaction are analyzed to compare with recent experimental data at the CBELSA/TAPS Collaboration. An application of the reaction is presented to demonstrate the significance of the π exchange in the total and differential cross-sections.

Features of forward πN scattering from a Reggeized model

Charge exchange process ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}n$ and elastic scatterings ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}p$ are investigated within the Regge framework where the relativistic Born amplitude is Reggeized for the $t$-channel meson exchange. The charge exchange cross section is featured by single $\ensuremath{\rho}$ exchange. Additional corrections by Regge cuts, $\ensuremath{\rho}\text{\ensuremath{-}}{f}_{2}$ and $\ensuremath{\rho}$-Pomeron, agree with differential cross sections, and a new trajectory for the ${\ensuremath{\rho}}^{\ensuremath{'}}(1450)$ exchange is attempted to reproduce polarization data. For the description of elastic scattering data up to pion momentum ${P}_{\mathrm{Lab}}\ensuremath{\approx}250$ GeV/c, Pomeron exchange of the Donnachie-Landshoff type is newly constructed and applied in this work. Elastic cross section data are well reproduced with the dominance of ${f}_{2}$ and Pomeron exchanges in intermediate and high energies. Analysis of nucleon resonances is presented to test the validity of the present Regge framework below $W\ensuremath{\le}2$ GeV.

Regge phenomenology in π0 and η photoproduction

The $\gamma N \to \pi^0 N$ and $\gamma N \to \eta N$ reactions at photon beam energies above 4 GeV are investigated within Regge models. The models include $t$-channel exchanges of vector ($\rho$ and $\omega$) and axial vector ($b_1$ and $h_1$) mesons. Moreover, Regge cuts of $\rho{\mathbb P}$, $\rho f_2$, $\omega{\mathbb P}$, and $\omega f_2$ are investigated. A good description of differential cross sections and polarization observables at photon beam energies from 4 to 15 GeV can be achieved.

Photoproduction ofa0(980)andf0(980)

There is no generally accepted view of the structure of the light-quark non-strange scalar mesons. A variety of models have been proposed that encompass $qq\bar{q}\bar{q}$, molecular, $q\bar{q}$ and glueball states in various combinations. Previously we considered scalar-meson photoproduction in a simple Regge-pole model and showed that it was experimentally viable. Recent data on the photoproduction of $a_0(980)$ and $f_0(980)$ confirm this. We extend our model to incorporate Regge cuts, based on our knowledge of $\pi^0$ photoproduction. The theoretical predictions are compared to the $a_0(980)$ and $f_0(980)$ photoproduction data.

Photoproduction ofηandη′ mesons with EtaMAID

The unitary isobar model EtaMAID has been updated with an extended list of nucleon resonances, fitted to recent and new data for differential cross sections and polarization observables. The nonresonant background is described by Regge trajectories of ω,ρ and a 1 , b 1 mesons and in addition Regge cuts, where vector and axial vector mesons are exchanged together with Pomeron and f 2 mesons.

Analytic structure of then=7scattering amplitude inN=4SYM theory in multi-Regge kinematics: Conformal Regge cut contribution

In this second part of our investigation of the analytic structure of the $2\to5$ scattering amplitude in the planar limit of $\mathcal{N}=4$ SYM in multi-Regge kinematics we compute, in all kinematic regions, the Regge cut contributions in leading order. The results are infrared finite and conformally invariant.

Heptagon amplitude in the multi-Regge regime

As we have shown in previous work, the high energy limit of scattering amplitudes in N=4 supersymmetric Yang-Mills theory corresponds to the infrared limit of the 1-dimensional quantum integrable system that solves minimal area problems in AdS5. This insight can be developed into a systematic algorithm to compute the strong coupling limit of amplitudes in the multi-Regge regime through the solution of auxiliary Bethe Ansatz equations. We apply this procedure to compute the scattering amplitude for n=7 external gluons in different multi-Regge regions at infinite 't Hooft coupling. Our formulas are remarkably consistent with the expected form of 7-gluon Regge cut contributions in perturbative gauge theory. A full description of the general algorithm and a derivation of results will be given in a forthcoming paper.

Analytic structure of then=7scattering amplitude inN=4SYM theory in the multi-Regge kinematics: Conformal Regge pole contribution

We investigate the analytic structure of the $2\to5$ scattering amplitude in the planar limit of $\mathcal{N}=4$ SYM in multi-Regge kinematics in all physical regions. We demonstrate the close connection between Regge pole and Regge cut contributions: in a selected class of kinematic regions (Mandelstam regions) the usual factorizing Regge pole formula develops unphysical singularities which have to be absorbed and compensated by Regge cut contributions. This leads, in the corrections to the BDS formula, to conformal invariant 'renormalized' Regge pole expressions in the remainder function. We compute these renormalized Regge poles for the $2\to5$ scattering amplitude.

Multi-Regge limit of the n-gluon bubble ansatz

Abstract We investigate n-gluon scattering amplitudes in the multi-Regge region of $ \mathcal{N}=4 $ supersymmetric Yang-Mills theory at strong coupling. Through a careful analysis of the thermodynamic bubble ansatz (TBA) for surfaces in AdS 5 with n-g(lu)on boundary conditions we demonstrate that the multi-Regge limit probes the large volume regime of the TBA. In reaching the multi-Regge regime we encounter wall-crossing in the TBA for all n > 6. Our results imply that, in this limit, amplitudes at strong coupling can be calculated through an auxiliary system of algebraic Bethe ansatz equations. Their solutions are expected to determine the strong coupling analogue of Regge cut contributions to the amplitude.

Single transverse spin asymmetry of forward neutrons

We calculate the single transverse spin asymmetry $A_N(t)$, for inclusive neutron production in $pp$ collisions at forward rapidities relative to the polarized proton in the energy range of RHIC. Absorptive corrections to the pion pole generate a relative phase between the spin-flip and non-flip amplitudes, leading to a transverse spin asymmetry which is found to be far too small to explain the magnitude of $A_N$ observed in the PHENIX experiment. A larger contribution, which does not vanish at high energies, comes from the interference of pion and $a_1$-Reggeon exchanges. The unnatural parity of $a_1$ guarantees a substantial phase shift, although the magnitude is strongly suppressed by the smallness of diffractive $\pi p\to a_1 p$ cross section. We replace the Regge $a_1$ pole by the Regge cut corresponding to the $\pi\rho$ exchange in the $1^+S$ state. The production of such a state, which we treat as an effective pole $a$, forms a narrow peak in the $3\pi$ invariant mass distribution in diffractive $\pi p$ interactions . The cross section is large, so one can assume that this state saturates the spectral function of the axial current and we can determine its coupling to nucleons via the PCAC Goldberger-Treiman relation and the second Weinberg sum rule. The numerical results of the parameter-free calculation of $A_N$ are in excellent agreement with the PHENIX data.

IR divergences and Regge limits of subleading-color contributions to the four-gluon amplitude in 𝒩 = 4 SYM theory

We derive a compact all-loop-order expression for the IR-divergent part of the N=4 SYM four-gluon amplitude, which includes both planar and all subleading-color contributions, based on the assumption that the higher-loop soft anomalous dimension matrices are proportional to the one-loop soft anomalous dimension matrix, as has been recently conjectured. We also consider the Regge limit of the four-gluon amplitude, and we present evidence that the leading logarithmic growth of the subleading-color amplitudes is less severe than that of the planar amplitudes. We examine possible 1/N^2 corrections to the gluon Regge trajectory, previously obtained in the planar limit from the BDS ansatz. The double-trace amplitudes have Regge behavior as well, with a nonsense-choosing Regge trajectory and a Regge cut which first emerges at three loops.