Conserved currents of the three-reggeon interaction
We consider an extension of Lipatov's conjecture about the deep relation between amplitudes in the high-energy limit of QCD and XXX Heisenberg chains with non-compact spins.
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arXiv subjects
R. Kirschner
Publications and source records attributed to R. Kirschner.
High-energy scattering in gauge theories and integrable spin chains
In the leading log approximation and at large $N_C$ the interaction of two fermionic and one gluonic reggeons is described by an integrable system corresponding to an open spin chain.
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Polarization in diffractive electroproduction of light vector mesons
We study in perturbative QCD the helicity ampltiudes of the process $γ^{*} p \to ρp $ at large virtualities $Q$ of the photon $γ^{*}$. We estimate all spin flip amplitudes taking into account an important effect of the scale behaviour of the gluon density. The transition of a transverse virtual photon to a longitudinal vector meson is not small at typical HERA conditions. This helicity non-conserving amplitude leads by interference to a measurable effect in the distribution of the angle between the electron scattering and the meson production planes.
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Small-x behaviour of the polarized structure function $F_3^γ(x,Q^2)$
We study the small-$x$ behaviour of the polarized photon structure function $F_3^{\ga}$, measuring the gluon transversity distribution, in the leading logarithmic approximation of perturbative QCD. There are two contributions, both arising from two-gluon exchange. The leading contribution to small-$x$ is related to the BFKL pomeron and behaves like $x^{-1-\om_2}$, $\om_2 = {\cal O}(\al_S)$. The other contribution includes in particular the ones summed by the DGLAP equation and behaves like $x^{1-\om_0^{(+)}}$, $\om_0^{(+)} = {\cal O}(\sqrt{\al_S})$.
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The BFKL Pomeron in 2+1 Dimensional QCD
We investigate the high-energy scattering in the spontaneously broken Yang - Mills gauge theory in 2+1 space--time dimensions and present the exact solution of the leading $\ln s$ BFKL equation. The solution is constructed in terms of special functions using the earlier results of two of us (L.N.L. and L.S.). The analytic properties of the $t$-channel partial wave as functions of the angular momentum and momentum transfer have been studied. We find in the angular momentum plane: (i) a Regge pole whose trajectory has an intercept larger than 1 and (ii) a fixed cut with the rightmost singularity located at $j=1$. The massive Yang - Mills theory can be considered as a theoretical model for the (non-perturbative) Pomeron. We study the main structure and property of the solution including the Pomeron trajectory at momentum transfer different from zero. The relation to the results of M. Li and C-I. Tan for the massless case is discussed.
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Next-to-leading gluonic reggeons in the high-energy effective action
We study the next-to-leading gluon exchange in the high-energy scattering that contributes to the amplitude to order $s^0$ up to logarithmic corrections. Similar to the leading gluon exchange these contribution can be described in terms of reggeon exchanges. There are several gluonic reggeons at the next-to-leading level. Some of them transfer parity or gauge group representation different from the leading gluonic reggeon. Unlike the leading one they are sensitive to the helicity and transverse momenta of the scattering partons. We extend the high-energy effective action and derive from the action of gluodynamics the terms describing the next-to-leading reggeons and their interaction in the multi-Regge approximation.
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Gluonic reggeons
Contributions from gluon interactions, which are non-leading in high-energy semi-hard processes, are studied and represented in terms of reggeon exchanges. Unlike the leading gluonic reggeon, related to the BFKL pomeron, the non-leading reggeons are sensitive to the spin and transverse momentum distributions of scattering partons. There are several gluonic reggeons with poles in the vicinity of angular momentum $j=0$ contributing to the perturbative Regge asymptotics of QCD. We extend the high-energy effective action including sub-leading terms which describe these reggeons and their interactions with scattering quarks and gluons in the multi-Regge approximation.
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Polarized parton distributions and non-leading reggeons
The small $x$ behaviour of polarized parton distributions is related to non-leading reggeons in the framework of the high-energy effective action. Double-logarithmic contributions to the reggeon interaction beyond the ones included in the GLAP equation are encountered in all polarized parton distributions. The transversity distributions of quarks and gluons behave similar at small $x$. Contribution to the spin workshop at DESY-Zeuthen, September 1997.
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Diffractive meson production from virtual photons with odd charge-parity exchange
We calculate the cross section of diffractive charge-parity C=+1 neutral meson production in virtual photon proton collision at high energies. Due to the opposite C-parities of photon and meson M (M = eta_C, pi^0, a_2) this process probes the t-channel C=-1 odderon exchange which is described here as noninteracting three-gluon exchange. Estimates for the cross section of the inelastic diffractive process gamma^* p -> eta_C X_p are presented. The total cross section of diffractive η_C meson photoproduction is found to be 47 pb. The cross sections for the diffractive production of light mesons (pi^0, a_2) in γ^* p collisions are of the same order if the photon virtuality Q^2 is m^2_C.
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Small $x$ behaviour of the chirally-odd parton distribution $h_1(x,Q^2)$
The small $x$ behaviour of the structure function $h_1(x,Q^2)$ is studied within the leading logarithmic approximation of perturbative QCD. There are two contributions relevant at small $x$. The leading one behaves like $(\frac{1}{x})^0$ i.e. it is just a constant in this limit. The second contribution, suppressed by one power of $x$, includes the terms summed by the GLAP equation. Thus for $h_1(x,Q^2)$ the GLAP asymptotics and Regge asymptotics are completely different, making $h_1(x,Q^2)$ quite an interesting quantity for the study of small $x$ physics.
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Perturbative Regge asymptotics in the case of non-vacuum exchange
Some results on the perturbative Regge asymptotics are reviewed. The concepts of the reggeon interaction approach and the double logarithmic approximation are outlined. Contribution to the Zeuthen Workshop on QCD and QED at higher order, Rheinsberg, April 1996.
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t-channel Approach to Reggeon Interactions in QCD
Starting from the multi-Regge effective action for high-energy scattering in QCD a $t$-channel approach can be developed which is similar to the approach by White based on general Regge arguments. The BFKL kernel of reggeized gluon interaction, contributions to the $2 \rightarrow 4 $ reggeized gluon vertex function and the one-loop correction to the BFKL kernel are considered. The conditions are discussed under which this approach can provide a simple estimante of the next-to-leading logarithmic corrections to the BFKL perturbative pomeron intercept.
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Effective Action for High-Energy Scattering in Gravity
The multi-Regge effective action is derived directly from the linearized gravity action. After excluding the redundant field components we separate the fields into momentum modes and integrate over modes which correspond neither to the kinematics of scattering nor to the one of exchanged particles. The effective vertices of scattering and of particle production are obtained as sums of the contributions from the triple and quartic interaction terms and the fields in the effective action are defined in terms of the two physical components of the metric fluctuation.
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Low x Physics and Perturbative Regge Asymptotics
Deep-inelastic scattering at small x is a new field of QCD phenomenology which HERA experiments started to explore. The data show the feature expected by the perturbative Regge asymptotics. We describe the parton picture of structure function evolution both for increasing $Q^2$ and for decreasing $x$ and discuss the leading logarithmic approximation of QCD on which this picture is based. The steep rise of the parton density towards smaller $x$ gets saturated by parton recombination. An essential improvement of the leading logarithmic approximation has to be worked out in order to satisfy the unitarity conditions and in this way to describe the parton recombination in perturbative QCD. We review some ideas of the perturbative Regge asymptotics and some recent theoretical results about multi-reggeon exchange in QCD. Talk at the Tennessee Intern. Symposium on Rad. Corrections, prepared for the proceedings.
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Reggeon Interactions in Perturbative QCD
We study the pairwise interaction of reggeized gluons and quarks in the Regge limit of perturbative QCD. The interactions are represented as integral kernels in the transverse momentum space and as operators in the impact parameter space. We observe conformal symmetry and holomorphic factorization in all cases.
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Regge Asymptotics of Scattering with Flavour Exchange in QCD
The contribution to the perturbative Regge asymptotics of the exchange of two reggeized fermions with opposite helicity is investigated. The methods of conformal symmetry known for the case of gluon exchange are extended to this case where double-logarithmic contributions dominate the asymptotics. The Regge trajectories at large momentum transfer are calculated.
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Symmetry Properties of the Effective Action for High-Energy Scattering in QCD
We study the effective action describing high-energy scattering processes in the multi-Regge limit of QCD, which should provide the starting point for a new attempt to overcome the limitations of the leading logarithmic and the eikonal approximations. The action can be obtained via simple graphical rules or by integrating in the QCD functional integral over momentum modes of gluon and quark fields that do not appear explicitely as scattering or exchanged particles in the considered processes. The supersymmetry is used to obtain the terms in the action involving quarks fields from the pure gluonic ones. We observe a Weizsäcker - Williams type relations between terms describing scattering and production of particles.
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Effective Action for Multi-Regge Processes in QCD
We construct the effective Lagrangian describing QCD in the multi-Regge kinematics. It is obtained from the original QCD Lagrangian by eliminating modes of gluon and quark fields not appearing in this underlying kinematics.
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