6 June KLH Electromagnetic Probes of Hot and Dense Matter1 The  Puzzle EM Probes of Hot and Dense Matter ECT, Trento, Italy 3-10 June 2005 Kevin Haglin St. Cloud State University Minnesota, USA

6 June KLH Electromagnetic Probes of Hot and Dense Matter2 Background – why is this a puzzle? Spectral properties for the  at  T > 0 Decay rate at finite temperature  decays allowed inside the fireball Yield estimates Progress assembling the puzzle pieces    J/J/ Learning outcomes, i.e. presentation outline

6 June KLH Electromagnetic Probes of Hot and Dense Matter3 K K     PLB 491, 59 (2000) T = 305 ± 15 MeV PLB 555, 147 (2003) T = 228 ± 10 MeV NA49:   K K +- NA50:  + -  45 fm/c   ̴  10 fm/c fireball ?!? Background:

6 June KLH Electromagnetic Probes of Hot and Dense Matter4 Model the degrees of freedom and the interactions with a three-flavor chiral Lagrangian † Nonlinear Sigma Model Where the pseudoscalar multiplet is

6 June KLH Electromagnetic Probes of Hot and Dense Matter5 The chiral covariant derivative introduces nonet of vector mesons i.e. vector mesons are dynamically generated.

6 June KLH Electromagnetic Probes of Hot and Dense Matter6  meson self energy The leading one-loop contributions      K K Two-loop contributions   K  K,, * + many others

6 June KLH Electromagnetic Probes of Hot and Dense Matter7  propagation, decay, scattering   K K one loop: decays two loop: scattering  K K     K K K * plus many others

6 June KLH Electromagnetic Probes of Hot and Dense Matter8 Four-point interactions are required to conserve the  current [gauge invariance]   K K  e.g.  + K   + K M = M + M + M ab c (a) (b) (c)

6 June KLH Electromagnetic Probes of Hot and Dense Matter9 Self-energy calculation to one-loop order where References: Gale & Kapusta, Nucl. Phys. B 357, 65 (1991) Haglin & Gale, Nucl. Phys. B 421 (1994)

6 June KLH Electromagnetic Probes of Hot and Dense Matter10 From the self energy to the propagator then, finally, the propagator is We make contact with observable decay rates

6 June KLH Electromagnetic Probes of Hot and Dense Matter11 One-loop thermal effects are quite small!

6 June KLH Electromagnetic Probes of Hot and Dense Matter12 Effective mass extraction at finite temperature (a pole in the propagator)  The effects are again quite small!

6 June KLH Electromagnetic Probes of Hot and Dense Matter13 Note: the real part of  cannot simply be absorbed into the definition of mass. Furthermore, the kaon and the  channel have competing influences.

6 June KLH Electromagnetic Probes of Hot and Dense Matter14 Two loops contribute to collision broadening of the  Particles contributing:    K K * b 1 References: K. Haglin, NPA 584, 719 (1995). L. Alvarez-Ruso and V. Koch, PRC 65, (2002).

6 June KLH Electromagnetic Probes of Hot and Dense Matter15  Finally, the  spectral function one loop two loop

6 June KLH Electromagnetic Probes of Hot and Dense Matter16  decay at T > 0 A. Weldon, Ann. Phys., 228, 43 (1993) f eq (2)(2) 3 

6 June KLH Electromagnetic Probes of Hot and Dense Matter17  decay at T > 0 (consistency check)  = 1.3 fm/c vacuum   

6 June KLH Electromagnetic Probes of Hot and Dense Matter18 higher order effects??  K      *   K   K K K * kaon spectral function picks up a finite width

6 June KLH Electromagnetic Probes of Hot and Dense Matter19 spectral properties of  and  (some of the) diagrams contributing to collision broadening           KK K * a 1 pionrho

6 June KLH Electromagnetic Probes of Hot and Dense Matter20 (in medium)  lifetime with in-medium daughters    K K where

6 June KLH Electromagnetic Probes of Hot and Dense Matter21 (leading) branching ratio and enhancement factor

6 June KLH Electromagnetic Probes of Hot and Dense Matter22 Symmetric Flow (Siemens-Rassmusen) [but generalized to include Bose-Einstein effects] Siemens and Rassmusen, PRL 42, 880 (1979). where KLH, nucl-th/ ; Laura Holt and KLH, J. Phys. G: Nucl. Part. Phys., 31, S245 (2005).

6 June KLH Electromagnetic Probes of Hot and Dense Matter23 We propose a scenario in which  Observable      occurs early (higher T, lower flow) Observable   K  occurs late (lower T, higher flow)

6 June KLH Electromagnetic Probes of Hot and Dense Matter24 Follow the evolution to estimate yields as functions of mass FWHM  20 MeV!

6 June KLH Electromagnetic Probes of Hot and Dense Matter25   KK is a surface effect, with T = 135 MeV and v = 0.6 FWHM = 4.4 MeV three-volume is a shell of thickness 1-2 fm free-space behavior!

6 June KLH Electromagnetic Probes of Hot and Dense Matter26 Summary & Conclusions   self energy was calculated with 1, 2 and 3-loop effects included   spectral function at finite temperature is modified significantly as compared with the vacuum  decay rate at finite temperature was estimated: with in-medium daughters it increased dramatically  decay lifetime of the  is shortened by the hadronic medium  m distributions for K K and   show different temperatures and different flow values  mass distributions for K K and    have different widths in the model by a factor of T -

6 June KLH Electromagnetic Probes of Hot and Dense Matter27 THE END This research has been supported in part by the National Science Foundation.