arXiv subjects
Publications and source records attributed to A. I. Karanikas.
A theoretical framework is presented to treat hadronic observables within analytic perturbative QCD beyond the leading order of the coupling and for more than one single large momentum scale. The approach generalizes and extends the pioneering work of Shirkov and Solovtsov on an analytic strong running coupling. Some applications to hadronic observables at the partonic level are also discussed.
The validity of the Bianchi identity, which is intimately connected with the zig zag symmetry, is established, for piecewise continuous contours, in the context of Polakov's gauge field-string connection in the large 'tHooft coupling limit, according to which the chromoelectric `string' propagates in five dimensions with its ends attached on a Wilson loop in four dimensions. An explicit check in the wavy line approximation is presented.
Adopting as working assumption that the conformal group O(4,2) of Minkowski space, being the largest symmetry group which respects its light cone structure, is the appropriate global symmetry underlying the description of relativistic systems, it is shown that AdS$_5$ uniquely emerges as the space on the boundary of which a corresponding relativistic field system should be accommodated. The basic mathematical tools employed for establishing this result are (a) Cartan's theory of spinors and (b) group contraction methods. Extending our considerations to supersymmetry it is demostrated how an $N$=1 SUSY YM field system can emerge as a broken version of an $N$=4 SUSY YM field system. An especially important feature of the presentation is the `unearthing' of seminal, independent from each other, works of I. Segal and of S. Fubini which give a purely field theoretical perspective on the intimate relation between conformally invariant relativistic field theories and AdS$_5$ including, in particular, the warping phenomenon.
The one-loop vacuum energy is explicitly computed for a class of perturbative string vacua where supersymmetry is spontaneously broken by a T-duality invariant asymmetric Scherk-Schwarz deformation. The low-lying spectrum is tachyon-free for any value of the compactification radii and thus no Hagedorn-like phase-transition takes place. Indeed, the induced effective potential is free of divergence, and has a global anti de Sitter minimum where geometric moduli are naturally stabilised.
Demanding the analyticity of hadronic observables (calculated in terms of power series of the running coupling) as a {\it whole}, we show that they are free of the Landau singularity. Employing resummation and dispersion-relation techniques, we compute in a unifying way power corrections to two different hard-scattering functions in perturbative QCD: the electromagnetic pion form factor to leading order and the inclusive cross section of the Drell-Yan process. In the second case, the leading nonperturbative power correction in $bΛ_{\rm QCD}$ gives rise to a Sudakov-like exponential factor in the impact parameter space which provides enhancement rather than suppression.
A numerical program is presented which facilitates a computation pertaining to the full set of one-gluon loop diagrams (including ghost loop contributions), with M attached external gluon lines in all possible ways. The feasibility of such a task rests on a suitably defined master formula, which is expressed in terms of a set of Grassmann and a set of Feynman parameters. The program carries out the Grassmann integration and performs the Lorentz trace on the involved functions, expressing the result as a compact sum of parametric integrals. The computation is based on tracing the structure of the final result, thus avoiding all intermediate unnecessary calculations and directly writing the output. Similar terms entering the final result are grouped together. The running time of the program demonstrates its effectiveness, especially for large M.
Different ``analytization'' procedures for the factorized pion form factor are discussed in comparison with the standard QCD perturbation theory at NLO. It is argued that demanding the analyticity of the exclusive amplitude as a \emph{whole}, entails insensitivity of the results on all scheme and scale-setting parameters, including the factorization scale. This enables us to develop an approach of optimized perturbation theory within the MS-bar scheme and to generalize the Analytic Perturbation Theory to non-integer (fractional) powers of the strong running coupling in the complex Q^2 plane
The removal of unphysical singularities in the perturbatively calculable part of the pion form factor--a classic example of a three-point function in QCD--is discussed. Different ``analytization'' procedures in the sense of Shirkov and Solovtsov re examined in comparison with standard QCD perturbation theory. We show that demanding the analyticity of the partonic amplitude as a \emph{whole}, as proposed before by Karanikas and Stefanis, one can make infrared finite not only the strong running coupling and its powers, but also cure potentially large logarithms (that first appear at next-to-leading order) containing the factorization scale and modifying the discontinuity across the cut along the negative real axis. The scheme used here generalizes the Analytic Perturbation Theory of Shirkov and Solovtsov to non-integer powers of the strong coupling and diminishes the dependence of QCD hadronic quantities on all perturbative scheme and scale-setting parameters, including the factorization scale.
Within the framework of the Fock-Feynman-Schwinger (equivalently, worldline) casting of QCD a four-point process, mediated by a closed quark loop, is studied in the Sudakov kinematical region, first perturbatively and subsequently with the inclusion of non-perturbative contributions through the use of the stochastic vacuum model. Deformations of the, first order, perturbative results are determined. Finally, the resummation of the leading logarithmic terms is performed and physical implications of the result are discussed.
Implications stemming from the inclusion of non-perturbative, confinining effects, as contained in the Stochastic Vacuum Model of Dosch and Simonov, are considered in the context of a, hypothetical, quark-quark `scattering process' in the Regge kinematical region. In a computation wherein the non-perturbative input enters as a correction to established perturbative results, a careful treatment of infrared divergencies is shown to imply the presence of an effective propagator associated with the existence of a linear term in the static potential. An equivalent statement is to say that the modified gluonic propagator receives contribution from a tachyonic ghost state, an occurence which is fully consistent with earlier such suggestions made in the context of low energy QCD phenomenology.
A numerical program is presented which facilitates the computation of the full set of one-gluon loop diagrams (including ghost loop contributions), with M attached external gluon lines in all possible ways. The feasibility of such a task rests on a suitably defined master formula, which is expressed in terms of a set of Grassmann and a set of Feynman parameters, the number of which increases with M. An important component of the numerical program is an algorithm for computing multi-Grassmann variable integrals. The cases M=2, 3, 4, which are the only ones having divergent terms, are fully worked out. A complete agreement with known, analytic results pertaining to the divergent terms is attained.
The applicability of the space-time formulation of the gluonic sector of QCD in terms of the Polyakov worldline path integral, via the use of the background field gauge fixing method, is extended to multi-gluon loop configurations. Relevant master formulas are derived for the computation of effective action terms.
We employ the Polyakov world-line path-integral version of QCD to identify and resum at leading perturbative order enhanced radiative gluon contributions to the Drell-Yan type ($q\bar{q}$ pair annihilation) cross-sections. We emphasize that this is the first time that world-line techniques are applied to cross-section calculations.
The Polyakov world-line path integral describing the propagation of gluon field quanta is constructed by employing the background gauge fixing method and is subsequently applied to analytically compute the divergent terms of the one (gluonic) loop effective action to fourth order in perturbation theory. The merits of the proposed approach is that, to a given order, it reduces to performing two integrations, one over a set of Grassmann and one over a set of Feynman-type parameters through which one manages to accomodate all Feynman diagrams entering the computation at once.
By remaining strictly within the confines of QCD, i.e., {\it without} invoking the parton model or any other exogenous element, we identify and resum perturbatively to leading order, along with a correction term, enhanced radiative gluon contributions to the Drell-Yan type ($q\bar{q}$ pair annihilation) and deep-inelastic-scattering type ($eq\to eq+X$) cross-sections. The key feature of the adopted approach is the recasting of QCD in terms of a space-time mode of description, which employs a path-integral formulation of field theories, as originally implied in works of Fock, Feynman and Schwinger.
A theoretical scheme which relates multiparticle states generated in ultrarelativistic nuclear collisions to a QCD phase transition is considered in the framework of the universality class provided by the 3-D Ising model. Two different evolution scenarios for the QGP system are examined. The statistical mechanics of the critical state is accounted for in terms of (critical) cluster formation consistent with suitably cast effective action functionals, one for each considered type of expansion. Fractal properties associated with these clusters, characterizing the density fluctuations near the QCD critical point, are determined. Monte-Carlo simulations are employed to generate events, pertaining to the total system, which correspond to signals associated with unconventional sources of pion production.
Polyakov's spin factor enters as a weight in the path-integral description of particle-like modes propagating in Euclidean space-times, accounting for particle spin. The Fock-Feynman-Schwinger path integral applied to QCD accomodates Polyakov's spin factor in a natural manner while, at the same time, it identifies Wilson line (loop) operators as sole agents of interaction dynamics among matter and gauge field quanta. A direct application of such a separation between spin content and dynamics is the emergence of master expressions for the perturbative series involving either open or closed fermionic lines which provide new, comprehensive approaches to perturbative QCD.
We consider a four-point process, associated with a wide-angle elastic scattering of two off-mass-shell spin-1/2 matter particles, in a non-abelian gauge theory. On the basis of a worldline approach, which reverts the functional to a path-integral description of the system, we factorize an eikonal (``soft'') subsector of the full theory and calculate the Sudakov-like suppression factor for the four-point function as a whole, once we have extracted the associated anomalous dimensions and taken into account the renormalization-group controlled evolution.