Open charm mesons in a hot and dense medium1 L. Tolos 1, A. Ramos 2 and T. Mizutani 3 1 FIAS (University of Frankfurt) 2 Universitat de Barcelona 3 Virginia.

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Open charm mesons in a hot and dense medium1 L. Tolos 1, A. Ramos 2 and T. Mizutani 3 1 FIAS (University of Frankfurt) 2 Universitat de Barcelona 3 Virginia Polytechnic Institute and State University Phys. Rev. C77 (2008) FIAS June 25-27, 2008 Frankfurt, Germany

Open charm mesons in a hot and dense medium2 1. Motivation 2. Model: Self-consistent coupled-channel approach for DN scattering   c (2593) and  c (2800) are dynamically generated 3. Open-charm mesons in hot dense matter 4. Conclusions & Outlook Outline

Open charm mesons in a hot and dense medium3 Motivation I (experimental facts) 1. J/  suppression: it has been advocated as signature of QGP due to color screening T.Matsui and H. Satz, PLB 178 (1986) 416 NA50, NA60 Collaborations at CERN-SPS but there are alternative explanations in terms of conventional hadronic models:  “comover” scattering: N. Armesto, A. Capella, PLB430 (1998) 23 R. Vogt, Phys. Reports 310 (1999) 197. B.Zhang, C.M.Ko, B.A.Li, Z.W.Lin, S.Pal, PRC65 (2002) W. Cassing, E.L. Bratkovskaya, S. Juchem, NPA674 (2000) 249 O. Lynnyk,E.L. Bratkovskaya,W. Cassing, H.Stöcker, NPA786 (2007) 183  statistical hadronization model: A. Andronic, P. Braun-Munzinger, K. Redlich, J. Stachel. PLB571 (2003) 36; NPA789 (2007) 334; Phys. Lett. B659 (2008) Open-charm enhancement?: (due to medium modified properties of open charm mesons) NA50 Collaboration, M.C.Abreu et al., EPJ C14 (2000) 443 it would facilitate J/  suppression but … recently invalidated from an improved discrimination of muons (promt vs. semi-leptonic decays ) by the NA60 collaboration. R. Shahoyan, J.Phys.G34 (2005) S1029

Open charm mesons in a hot and dense medium4 To understand these issues it is imperative to have a realistic picture of the properties of charmonia and open charm mesons in a hot nuclear environment. This is especially important for the conditions of the heavy ion experiment, where both density (  ~1-2 fm -3 ) and temperature (T~100 MeV) are relevant parameters.

Open charm mesons in a hot and dense medium5 1. DN interaction: similar features as the thoroughly studied Kbar N interaction. In the charm sector we also find a subthreshold I=0 resonance, the  c (2593) (udc), that bears a strong resemblance to the  (1405) (uds). Motivation II (theoretical issues) May the  c (2593) be generated also dynamically, through a coupled-channel unitarized model? Is this model able to explain some of the newly observed charmed-baryon resonances at CLEO, Belle, BaBar?

Open charm mesons in a hot and dense medium6 2. Mean-field models:  predict the D +,D - mass shift QCD sum rule: The in-medium mass shift is propotional to the mass of the charmed quark (m c ) and the light meson q-qbar condensate: A. Hayashigashi, Phys. Let. B487, 96 (2000) P. Morath, W. Weise, S.H. Lee, 17 Autumn school on QCD, Lisbon 1999 (World Scientific, SIngapore, 2001) 2001 Quark Meson Coupling approach: Hadron interactions mediated by the exchange of scalar-isoscalar (  and vector (  and  ) medium modified mesons among the light constituent quarks. A.Sibirtsev, K.Tsushima, and A.W.Thomas, Eur. Phys. J. A6, 351 (1999) Nuclear Mean Field approach (NMFA):  model supplemented by chiral terms (of vector and scalar-isoscalar nature) A.Mishra, E.L. Brakovskaya, J. Schaffner-Bielich, S. Schramm, and H. Stoecker, PRC 70, (2004)

Open charm mesons in a hot and dense medium7 3. Spectral function models:  predict the full energy distribution of (dynamical approaches) the D + meson strength in a self- consistent coupled channel approach D self-energy with a SU(3) separable DN interaction with u, d, c content L. Tolós, J. Schaffner-Bielich, and A. Mishra, Phys. Rev.C 70, (2004) (T=0 MeV) L. Tolós, J. Schaffner-Bielich, and H. Stöcker, Phys. Lett. B635, 85 (2006) (finite T) D and Dbar self-energy with an improved SU(4) and chiral DN interaction J.Hofmann and M.F.M.Lutz, Nucl. Phys. A763, 90 (2005) M.F.M.Lutz, and C.L.Korpa, Phys. Lett. B 633,43 (2006) D self-energy using a revised SU(4) and chiral DN interaction, supplemented by an attractive scalar-isoscalar  DN T. Mizutani, A. Ramos, Phys. Rev. C74, (2006) HERE: we extend the model to Dbar mesons and implement finite T effects [see talk of J. Nieves for an extension of the model to SU(8)]

Open charm mesons in a hot and dense medium8 1.Transition potential V built from the meson-baryon Lagrangian at lowest order Model: V SU(4) symmetry broken by the use of physical masses. Coupled channels included in the DN sector (C=1, S=0):.

Open charm mesons in a hot and dense medium9 2. Unitarization: N/D method  equivalent to Bethe-Salpeter coupled-channel equations with on-shell amplitudes T ij = V ij + V il G l T lj = + The loop function G is regularized with a cut-off  [adjusted to reproduce  c (2593)] T. Mizutani, A. Ramos, Phys. Rev. C74, (2006) V is also supplemented by a scalar-isoscalar interaction (  DN term) (from QCDSR) Model A: Model B:

Open charm mesons in a hot and dense medium10 I=0 I=1 Free space DN amplitudes R. Mizuk et al. [Belle Collaboration] Phys.Rev.Lett.94, (2005)  c (2800),  ~60 MeV The model generates the I=0  c (2595) and another resonance in I=1 around the nominal  c (2800)!

Open charm mesons in a hot and dense medium11 Self-consistent coupled channels procedure T ij = V ij + V il G l T lj = + T ij (  ) = V ij + V il G l (  ) T lj (  ) = + Free space Medium Dressed D meson: =+ Pauli blocking and baryon dressing meson dressing

Open charm mesons in a hot and dense medium12 spectral density D-meson self-energy Loop function (depends on  and T)

Open charm mesons in a hot and dense medium13 DN amplitudes in hot dense matter (  =  0 )

Open charm mesons in a hot and dense medium14 D meson spectral in hot and dense matter (  =  0 )  N -1  N -1 quasiparticle peak MDMD MDMD

Open charm mesons in a hot and dense medium15 Evolution with density and temperature Similar trend to previous finite temperature results: LT, J. Schaffner-Bielich and H. Stoecker PLB 635 (2006) 85 =0=0  =2  0

Open charm mesons in a hot and dense medium16 D optical potentialDN interaction Free space: Medium (at T=0):

Open charm mesons in a hot and dense medium17 D and D meson potentials _

Open charm mesons in a hot and dense medium18 Conclusions & Outlook We have performed a self-consistent coupled-channel calculation of the D and D self-energies in symmetric nuclear matter at finite temperature taking, as bare interaction, the SU(4) TW contribution supplemented by a  DN term _ In hot dense matter,  c (2593) and  c (2800) stay close to their free position but develop a remarkable width The D meson spectral density shows a single pronounced peak at finite temperature that melts with increasing density Up to  0 the low-density theorem is a good approximation for the DN, where the repulsive I=1 component dominates Due to the distinct resonant structure of the interaction, temperature induces a stronger change in the properties of the D than the D meson _ _

Open charm mesons in a hot and dense medium19  J/  suppression  Open-charm enhancement  D-mesic nuclei Open questions? Looking forward to check these predictions with data from !