38,104 research outputs found
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 , 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
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