Ap\'ery Polynomials and the multivariate Saddle Point Method

The Ap\'ery polynomials and in particular their asymptotic behavior play an essential role in the understanding of the irrationality of \zeta(3). In this paper, we present a method to study the asymptotic behavior of the sequence of the Ap\'ery polynomials ((B_{n})_{n=1}^{\infty}) in the whole complex plane as (n\rightarrow \infty). The proofs are based on a multivariate version of the complex saddle point method. Moreover, the asymptotic zero distributions for the polynomials ((B_{n})_{n=1}^{\infty}) and for some transformed Ap\'ery polynomials are derived by means of the theory of logarithmic potentials with external fields, establishing a characterization as the unique solution of a weighted equilibrium problem. The method applied is a general one, so that the treatment can serve as a model for the study of objects related to the Ap\'ery polynomials.Comment: 19 page

Rapidity dependence of HBT correlation radii in non-boost invariant models

Hanbury-Brown Twiss (HBT) correlation measurements provide valuable information about the phase space distribution of matter in ultrarelativistic heavy-ion collisions. The rapidity dependence of HBT radii arises from a nontrivial interplay between longitudinal and transverse expansion and the time dependence of the freeze-out pattern. For a non-accelerating longitudinal expansion the dependence primarily arises from the amount of radiating matter per unit rapidity $dN/d\eta$, but for a scenario with strong longitudinal acceleration additional complications occur. In this paper I explore schematically what type of dependence can be expected for RHIC conditions under different model assumptions for the dynamics of spacetime expansion and freeze-out.Comment: Talk at the Workshop on Particle Correlations and Femtoscopy, Kromeriz, Czech Republic, August 15-17, 200

The Phenomenology of Elastic Energy Loss

The unexpectedly strong suppression of high p_T heavy-quarks in heavy-ion collisions has given rise to the idea that partons propagating through a medium in addition to energy loss by induced radiation also undergo substantial energy loss due to elastic collisions. However, the precise magnitude of this elastic energy loss component is highly controversial. While it is for a parton inside a medium surprisingly difficult to define the difference between elastic and radiative processes rigorously, the main phenomenological difference is in the dependence of energy loss on in-medium pathlength: in a constant medium radiative energy loss is expected to grow quadratically with pathlength, elastic energy loss linearly. In this paper, we investigate a class of energy loss models with such a linear pathlength dependence and demonstrate that they are incompatible with measured data on hard hadronic back-to-back correlations where a substantial variation of pathlength is probed. This indicates that any elastic energy loss component has to be small.Comment: 7 pages, 3 figure