Propagation of spectral functions and dilepton production at SIS energies
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ELEMENTARY PARTICLES AND FIELDS Theory
Propagation of Spectral Functions and Dilepton Production at SIS Energies* 2)*** 1)**** ¨ ´ enyi ´ Gy. Wolf1)** , B. Kampfer , and M. Zet
Received March 31, 2011
Abstract—The time evolution of vector meson spectral functions is studied within a BUU-type transport model. Applications focus on ρ and ω mesons being important pieces for the interpretation of the dielectron invariant mass spectrum. Since the evolution of the spectral functions is driven by the local density, the inmedium modifications turn out to compete, in this approach, with the known vacuum contributions. DOI: 10.1134/S1063778812060336
1. INTRODUCTION Dielectrons serve as direct probes of dense nuclear matter stages during the course of heavy-ion collisions. The superposition of various sources, however, requires a deconvolution of the spectra by means of models. Of essential interest are the contributions of the light vector mesons ρ and ω. The spectral functions of both mesons are expected to be modified in a strongly interacting environment. Measurements with HADES [1, 2] start to explore systematically the dilepton production at beam energies in the fewA GeV region. In our transport model the time evolution of single-particle distribution functions of various hadrons is evaluated within the framework of a kinetic theory. The ρ meson is already a broad resonance in vacuum, while the ω meson may acquire a noticeable width in nuclear matter [3]. Therefore, one has to propagate properly the spectral functions of the ρ and ω mesons. This is the main goal of our paper. 2. OFF-SHELL TRANSPORT OF BROAD RESONANCES Recently theoretical progress has been made in describing the in-medium properties of particles starting from the Kadanoff–Baym equations for the Green functions of particles. Applying first-order gradient expansion after a Wigner transformation [4, ∗
The text was submitted by the authors in English. KFKI RMKI, Budapest, Hungary. 2) Forschungszentrum Dresden-Rossendorf, Institut Strahlenphysik, Dresden, Germany. ** E-mail: [email protected] *** E-mail: [email protected] **** E-mail: [email protected] 1)
¨ fur
5] one arrives at a transport equation for the retarded Green function. In the medium, particles acquire a self-energy Σ(x, p) which depends on position and momentum as well as the local properties of the surrounding medium. Their properties are described by the spectral function being the imaginary part of the retarded propagator
=
A(p) = −2ImGret (x, p) ˆ p) Γ(x,
(1)
ˆ p)2 (E 2 − p2 − m20 − ReΣret (x, p))2 + 14 Γ(x,
,
ˆ are related via where the resonance widths Γ and Γ ret ˆ Γ(x, p) = −2ImΣ ≈ 2m0 Γ, and m0 is the vacuum pole mass of the respective particle. To solve numerically the Kadanoff–Baym equations one may exploit the test-particle ansatz for the retarded Green function [4, 5]. This function can be interpreted as a product of particle number density multiplied with the spectral function A. The relativistic version of the equation of motion has been derived in [4]: 1 1 dx = 2p + ∇p
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