A.I. Karanikas

Analyticity and power corrections in hard-scattering hadronic functions

Abstract Demanding the analyticity of hadronic observables (calculated in terms of power series of the running coupling) as a 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 QCD gives rise to a Sudakov-like exponential factor in the impact parameter space which provides enhancement rather than suppression.

Analyticity properties of three-point functions in QCD beyond leading order

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 are examined in comparison with standard QCD perturbation theory. We show that demanding the analyticity of the partonic amplitude as a 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 noninteger 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.

Wilson lines in transverse-momentum dependent parton distribution functions with spin degrees of freedom

Abstract We propose a new framework for transverse-momentum dependent parton distribution functions, based on a generalized conception of gauge invariance which includes into the Wilson lines the Pauli term ∼ F μ ν [ γ μ , γ ν ] . We discuss the relevance of this nonminimal term for unintegrated parton distribution functions, pertaining to spinning particles, and analyze its influence on their renormalization-group properties. It is shown that while the Pauli term preserves the probabilistic interpretation of twist-two distributions—unpolarized and polarized—it gives rise to additional pole contributions to those of twist-three. The anomalous dimension induced this way is a matrix, calling for a careful analysis of evolution effects. Moreover, it turns out that the crosstalk between the Pauli term and the longitudinal and the transverse parts of the gauge fields, accompanying the fermions, induces a constant, but process-dependent, phase which is the same for leading and subleading distribution functions. We include Feynman rules for the calculation with gauge links containing the Pauli term and comment on the phenomenological implications of our approach.

Worldline approach to Sudakov-type form factors in non-Abelian gauge theories

We calculate Sudakov-type form factors for isolated spin-12 particles (fermions) entering non-Abelian gauge-field systems. We consider both the on- and the off-mass-shell case using a methodology which rests on a worldline casting of field theories. The simplicity and utility of our approach derives from the fact that we are in a position to make, a priori, a more transparent separation (factorization), with respect to a given scale, between short- and long-distance physics than diagramatic methods.

World-line techniques for resumming gluon radiative corrections at the cross-section level

Abstract. 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 (

Zig zag symmetry in AdS/CFT duality

q\bar{q}

Coherent state path integrals in the continuum

pair annihilation) cross-sections. We emphasize that this is the first time that world-line techniques are applied to cross-section calculations.

Perturbative computation of the gluonic effective action via Polyakov’s world-line path integral

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 ’t Hooft 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.

Worldline approach to forward and fixed angle fermion-fermion scattering in Yang-Mills theories at high energies

We discuss the time-continuous path integration in the coherent states basis in a way that is free from inconsistencies. Employing this notion we reproduce known and exact results working directly in the continuum. Such a formalism can set the basis to develop perturbative and non-perturbative approximations already known in the quantum field theory community. These techniques can be proven useful in a great variety of problems where bosonic Hamiltonians are used.

Study of the phase structure of Abelian field theories through non-lattice, non-perturbative 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 are 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 accommodate all Feynman diagrams entering the computation at once.