arXiv subjects

R. Kirschner

Publications and source records attributed to R. Kirschner.

At least 37 records · Page 2Linked to original sources

arXiv2008

Iterative construction of $U_q (s\ell (n+1)) $ representations and Lax matrix factorisation

The construction of a generic representation of $g\ell(n+1)$ or of the trigonomentric deformation of its enveloping algebra known as algebraic induction is conveniently formulated in term of Lax matrices. The Lax matrix of the constructed representation factorises into parts determined by the Lax matrix of a generic representation of the algebra with reduced rank and others appearing in the factorised expression of the Lax matrix of the special Jordan-Schwinger representation.

hep-th↗

arXiv2007

Yang-Baxter R operators and parameter permutations

We present an uniform construction of the solution to the Yang- Baxter equation with the symmetry algebra $s\ell(2)$ and its deformations: the q-deformation and the elliptic deformation or Sklyanin algebra. The R-operator acting in the tensor product of two representations of the symmetry algebra with arbitrary spins $\ell_1$ and $\ell_2$ is built in terms of products of three basic operators $\mathcal{S}_1, \mathcal{S}_2,\mathcal{S}_3$ which are constructed explicitly. They have the simple meaning of representing elementary permutations of the symmetric group $\mathfrak{S}_4$, the permutation group of the four parameters entering the RLL-relation.

hep-th↗

arXiv2005

Baxter Q-operators of the XXZ chain and R-matrix factorization

We construct Baxter operators as generalized transfer matrices being traces of products of generic $R$ matrices. The latter are shown to factorize into simpler operators allowing for explicit expressions in terms of functions of a Weyl pair of basic operators. These explicit expressions are the basis for explicit expression for Baxter Q-operators and for investigating their properties.

hep-th↗

arXiv2005

Symmetric reggeon interaction in perturbative QCD

Integral kernels describing the pair interaction of reggeized gluons and quarks are reconstructed in terms of conformal symmetric 4-point functions in the transverse plane of impact parameters.

hep-ph↗

arXiv2004

Diffractive large transferred momentum photoproduction of vector mesons

The large $t$ behaviour of the helicity amplitudes of diffractive photoproduction is estimated relying on models of the photon and meson light-cone wave functions and on the double-logarithmic approximation to the exchanged gluon interaction. The role of large-size colour dipole contributions to the photon-meson transition impact factor is discussed.

hep-ph↗

arXiv2004

Parton interaction in super Yang Mills theory

We apply the effective action scheme to the leading parton interactions in ${\cal N} = 1$ supersymmetric gauge theory. The effective interaction in the Bjorken asymptotics at one loop is written in terms of parton superfield vertices explicitely symmetric with respect to superconformal transformations.

hep-th↗

arXiv2003

Universal R operator with Jordanian deformation of conformal symmetry

The Jordanian deformation of $sl(2)$ bi-algebra structure is studied in view of physical applications to breaking of conformal symmetry in the high energy asymptotics of scattering. Representations are formulated in terms of polynomials, generators in terms of differential operators. The deformed $R$ operator with generic representations is analyzed in spectral and integral forms.

nlin.SI↗

arXiv2003

Parton interactions in the Bjorken aymptotics

We demonstrate the effective action scheme for the leading parton interactions and discuss the symmetry properties. The interaction kernels are particular cases of conformal symmetric two-particle kernels. There is a direct relation to the conformal symmetric rational solution of the Yang-Baxter equation.

hep-ph↗

arXiv2003

Electroproduction of vector mesons - factorization of end-point contributions

The end-point contributions in the quark longitudinal momentum fraction of the virtual photon ($γ^*$) to vector meson ($V$) impact factor to the diffractive electroproduction amplitude can be factorized in terms of a generalized parton evolution of the target parton distribution. The result is used to model the helicity amplitudes $γ^* p \to V p$ in terms of small $x$ generalized parton distributions.

hep-ph↗

arXiv2002

Universal R operator with deformed conformal symmetry

We study the general solution of the Yang-Baxter equation with deformed $sl(2)$ symmetry. The universal R operator acting on tensor products of arbitrary representations is obtained in spectral decomposition and in integral forms. The results for eigenvalues, eigenfunctions and integral kernel appear as deformations of the ones in the rational case. They provide a basis for the construction of integrable quantum systems generalizing the XXZ spin models to the case of arbitrary not necessarily finite-dimensional representations on the sites.

nlin.SI↗

arXiv2001

Parton interactions in the Bjorken limit of QCD

We consider the Bjorken limit in the framework of the effective action approach and discuss its similarities to the Regge limit. The proposed effective action allows for a rather simple calculation of the known evolution kernels. We represent the result in terms of two-parton interaction operators involving gluon and quark operators depending on light-ray position and helicity and analyze their symmetry properties.

hep-ph↗

arXiv2001

Direct J/Psi hadroproduction in k_\perp-factorization and the color octet mechanism

The hadroproduction of direct J/Psi in the framework of the k_\perp-factorization approach is studied. The color-singlet contribution is essentially larger than in the collinear approach but is still an order of magnitude below the data. The deficit may be well described by the color octet contribution with the value of the matrix element <0|O^{J/Ψ}_8(^3S_1)|0> substantially decreased in comparison with the fits in the collinear factorization. This should lead to a reduction of the large transverse polarization, predicted in the collinear approach.

hep-ph↗

arXiv2001

Towards a solution of the charmonium production controversy: k_t-factorization versus color octet mechanism

The cross section of χ_{cJ} hadroproduction is calculated in the k_t-factorization approach. We find a significant contribution of the χ_{c1} state due to non-applicability of the Landau-Yang theorem because of off-shell gluons. The results are in agreement with data and, in contrast to the collinear factorization, show a dominance of the color singlet part and a strong suppression of the color octet contribution. Our results could therefore lead to a solution of the longstanding controversy between the color singlet model and the color octet mechanism.

hep-ph↗

arXiv2001

Universal R-matrix as integral operator

We derive the integral operator form for the general rational solution of the Yang-Baxter equation with $s\ell(2|1)$ symmetry. Considering the defining relations for the kernel of the R-operator as a system of second order differential equations we observe remarkable reduction to a system of simple first order equations. The obtained kernel of R-operator has a very simple structure. To illustrate all this in the simplest situation we treat also the $s\ell(2)$ case.

nlin.SI↗

arXiv2000

Light vector meson photoproduction at large t

We have studied in perturbative QCD all independent helicity amplitudes describing the photoproduction of light vector mesons at large $t$. We found a new hard production mechanism which is related to the possibility for a real photon to fluctuate into a massless $q\bar q$ pair in a chiral-odd spin configuration. Each helicity amplitude is given as a sum of a usual chiral-even contribution (when the helicities of quark and antiquark are antiparallel) and this additional chiral-odd part (where the helicities of quark and antiquark are parallel). The chiral-odd contribution is large, it leads to a dominance of the non spin-flip amplitude in a very broad region of intermediately high $|t|$. All amplitudes are expressed in terms of short distance asymptotics of the light-cone wave functions of vector meson (photon). We demonstrate that for each helicity amplitude there exists a soft non-factorizable contribution. We give arguments that for dominant non spin-flip helicity amplitude the relative contribution of the soft nonfactorizable interactions is numerically not large.

hep-ph↗

arXiv2000

Heavy quark production as sensitive test for an improved description of high energy hadron collisions

QCD dynamics at small quark and gluon momentum fractions or large total energy, which plays a major role for HERA, the Tevatron, RHIC and LHC physics, is still poorly understood. For one of the simplest processes, namely bottom-antibottom production, next-to-leading-order perturbation theory fails. We show that the combination of two recently developed theoretical concepts, the k_perp-factorization and the next-to-leading-logarithmic-approximation BFKL vertex, gives perfect agreement with data. One can therefore hope that these concepts provide a valuable foundation for the description of other high energy processes.

hep-ph↗

arXiv2000

Heisenberg spin chains based on sl(2|1) symmetry

We find solutions of the Yang-Baxter equation acting on tensor product of arbitrary representations of the superalgebra sl(2|1). Based on these solutions we construct the local Hamiltonians for integrable homogeneous periodic chains and open chains.

nlin.SI↗

arXiv1999

The gluon field of a fast moving nucleus and the effective langrangian for QCD at high energy

Starting from the effective lagrangian for QCD at high energy we calculate the lowest perturbative contributions to the potential of a relativistic nucleus and compare our results to those derived by Kovchegov (see Y.V. Kovchegov, Phys. Rev. {\bf D55}, 5445 (1997)). The results differ already at order g^3 which can be traced to the fact that the meaning of the underlying gluon fields is different. (The effective gluon field we use is a gauge invariant object.) Both approaches should therefore be seen as alternatives, the relative merits of which have to be judged by their phenomenological success.

hep-ph↗