We have calculated the D-meson spectral density at finite temperature within
a self-consistent coupled-channel approach that generates dynamically the
$\Lambda_c$ (2593) resonance. We find a small mass shift for the D-meson in
this hot and dense medium while the spectral density develops a sizeable width.
The reduced attraction felt by the D-meson in hot and dense matter together
with the large width observed have important consequences for the D-meson
production in the future CBM experiment at FAIR.Comment: 4 pages, 2 figures, to appear in the proceedings of 9th International
  Conference on Strangeness in Quark Matter (SQM2006), Los Angeles, USA, March
  26-31, 200

H Stöcker

J Schaffner-Bielich

L Tolós

Mishra A

Scomparin E

Weise W

English

arXiv

We have calculated the D-meson spectral density at finite temperature within a self-consistent coupled-channel approach that generates dynamically the Lambda_c (2593) resonance. We find a small mass shift for the D-meson in this hot and dense medium while the spectral density develops a sizeable width. The reduced attraction felt by the D-meson in hot and dense matter together with the large width observed have important consequences for the D-meson production in the future CBM experiment at FAIR

Tolós, Laura

Schaffner-Bielich, Jürgen

Stöcker, Horst

Hochschulschriftenserver - Universität Frankfurt am Main

arXiv:nucl-th/0605035 v1   16 May 2006Open-charm enhancement at FAIR?L Tol´ os1,2,3, J Schaﬀner-Bielich2 and H St¨ ocker2,31 Gesellschaft f¨ ur Schwerionenforschung, Planckstrasse 1, 64291 Darmstadt, Germany2 Institut f¨ ur Theoretische Physik, J.W. Goethe-Universit¨ at, Max-von-Laue 1, 60438Frankfurt (M), Germany3 FIAS, J.W. Goethe-Universit¨ at, Max-von-Laue 1, 60438 Frankfurt (M), GermanyAbstract. We have calculated the D-meson spectral density at ﬁnite temperaturewithin a self-consistent coupled-channel approach that generates dynamically the Λc(2593) resonance. We ﬁnd a small mass shift for the D-meson in this hot anddense medium while the spectral density develops a sizeable width. The reducedattraction felt by the D-meson in hot and dense matter together with the large widthobserved have important consequences for the D-meson production in the future CBMexperiment at FAIR.1. IntroductionThe future CBM experiment (Compressed Baryonic Matter) at the FAIR project(Facility for Antiproton and Ion Research) at GSI will explore matter in the region ofhigh-baryon densities and moderature temperatures [1]. Among others, it will addressthe in-medium modiﬁcations of open-charm mesons. The medium modiﬁcations of D-mesons have important consequences for J/Ψ suppression [2] as well as open-charmenhancement in nucleus-nucleus collisions [3]. The J/Ψ suppression can be understood inan hadronic environment due to inelastic comover scattering and, therefore, the mediummodiﬁcation of the D-mesons should modify the J/Ψ absorption. On the other hand, theNA50 Collaboration [3] has observed an enhancement of dimuons in Pb+Pb collisionswhich was tentatively attributed to an open-charm enhancement in A+A collisions byintroducting an attractive mass shift for D-mesons in the nuclear medium [4]. However,the latest results on dimuon production by NA60 [5] seem to disregard this possibility.Finally, the D-mesic nuclei, predicted by the quark-meson coupling (QMC) model [6]are the result of considering an attractive D-meson potential.Calculations based on the QMC model [6], QCD sum-rule (QSR) [7] and chiralmodels [8] obtain attractive mass shifts of -50 MeV to -200 MeV at nuclear mattersaturation density ρ0, although a second analysis using QSR predicted only a splittingof D+ and D− masses of 60 MeV at ρ0 [9]. In all these investigations, the D-mesonspectral density in dense matter is not studied. In our previous work [10], the D-mesonspectral density is obtained by including coupled-channel eﬀects as well as the dresssingof the intermediate propagators. Thus, the attractive potential felt by the D-meson isstrongly reduced or becomes slightly repulsive [10], which has been recently supportedby [11]. In this paper, ﬁnite temperature eﬀects are included in the determination ofOpen-charm enhancement at FAIR? 2the D-meson spectral density in order to adapt our calculation to the conditions ofdensity-temperature expected for the CBM experiment [1]. Our results indicate thatthe width of the D-meson is the only source of open-charm enhancement at FAIR [12].2. FormalismWe obtain the in-medium D-meson spectral density at ﬁnite temperature taking, asbare interaction, a separable potential which parameters, coupling constant and cutoﬀ,are determined by ﬁxing the position and the width of the Λc(2593) resonance (see [10]).Then, the in-medium DN interaction or G-matrix at ﬁnite temperature reads M1B1 | G(Ω,T) | M2B2  =  M1B1 | V | M2B2  +XM3B3 M1B1 | V | M3B3 FM3B3(T)Ω − EM3(T) − EB3(T) + iη M3B3 | G(Ω,T) | M2B2  , (1)where V is the separable potential and Ω is the starting energy. In this equation,Mi and Bi represent the possible mesons (D,π,η) and baryons (N,Λc,Σc), respectively.The function FM3B3(T) for the DN states stands for the Pauli operator, i.e QDN(T) =1 − n(kN,T), where n(kN,T) is the nucleon Fermi distribution at the correspondingtemperature. The function FM3B3(T) is 1 + n(kπ,T), with n(kπ,T) being the Bosedistribution of pions at a given temperature, for πΛc or πΣc states while it is unityfor the other intermediate states. Furthermore, the properties of the intermediatestates are also modiﬁed in the medium at ﬁnite temperature. For nucleons, we usea temperature-dependent Walecka-type σ −ω model with density-dependent scalar andvector coupling constants [13]. In the case of pions, the self-energy in nuclear matter atﬁnite temperature is obtained following the Appendix of [13].The D-meson potential at a given temperature is then calculated according toUD(kD,ED,T) =Zd3kN n(kN,T)  DN | GDN→DN(Ω = EN + ED,T) | DN  . (2)As for the case of T=0, this is a self-consistent problem for the D-meson potential,since the in-medium DN interaction depends on the D-meson single-particle energy,which in turn depends on the D-meson potential. After achieving self-consistencyfor the on-shell value UD(kD,ED,T), we obtain the self-energy ΠD(kD,ω,T) =2qm2D + k2D UD(kD,ω,T) and the corresponding spectral density isSD(kD,ω,T) = −1πIm1ω2 − m2D − k2D − 2qm2D + k2DUD(kD,ω,T). (3)3. Results and ConclusionIn the l.h.s. of Figure 1 the D-meson spectral density at zero momentum and T=120MeV is shown for diﬀerent densities and for Λ = 1 GeV and g2 = 13.4, which reproducethe position and width of the Λc(2593) resonance (see [10]). The temperature is chosenin accord with the expected temperatures at FAIR. The spectral density is displayed forOpen-charm enhancement at FAIR? 31500 1600 1700 1800 1900ω(MeV)012345S(k=0,ω) (GeV-2)ρ02ρ03ρ0ρ0 at T=01500 1600 1700 1800 1900 2000ω(MeV)178018001820184018601880Eqp(MeV)ρ02ρ03ρ00 20 40 60 80 100T(MeV)050100150200 Γ (MeV)0 20 40 60 80 100 120T(MeV)free D mass Figure 1. Left: D-meson spectral density at kD = 0 and T=120 MeV as a functionof energy for diﬀerent densities, together with the D-meson spectral density at kD = 0and T=0 MeV for ρ0 in the two approaches considered. Right: Quasiparticle energyand width of the D-meson spectral density at kD = 0 as a function of temperature fordiﬀerent densities and the two approaches considered.the two approaches considered: self-consistent calculation of the D-meson self-energyincluding the dressing of the nucleons in the intermediate states (left panel) and theself-consistent calculation including not only the dressing of nucleons but also the self-energy of pions (right panel). The spectral density at T=0 for nuclear matter saturationdensity, ρ0 = 0.17 fm−3, is also shown. Compared to the T=0 case, the quasiparticlepeak at ﬁnite temperature stays closer to its free position for the range of densitiesanalyzed (from ρ0 up to 3ρ0). This is due to the fact the Pauli blocking is reduced withincreasing temperature. Furthermore, structures present in the spectral distribution atT=0 due to the presence of the Λc(2593) resonance, as reported in [10], are washed out.However, the D-meson spectral density shows a sizeable width.Our self-consistent coupled-channel calculation is in stark contrast with previousworks based on the QMC model [6], QSR rules [7] or chiral eﬀective Lagrangians [8]which predict a strongly attractive D-nucleus potential. We ﬁnd that the coupled-channel eﬀects at zero temperature result in an important reduction of the in-mediummodiﬁcations and are responsible for the considerable width of the D-meson, whichwas not obtained in the previous mean-ﬁeld works. This eﬀect is independent of thein-medium properties of the intermediate states, as seen in l.h.s of Figure 1. Actually, arecent study of the D-meson spectral distribution at T=0 suggests a two-mode structurewith a repulsive main branch, due to the presence of a new resonance, the Σc(2620) [11].Finite temperatures eﬀects even make the quasiparticle peak get closer to the D-mesonfree mass and D-mesons only show a signiﬁcant width, as seen in the following.The r.h.s of Figure 1 shows the quasiparticle energy together with the width ofthe D-meson spectral density at zero momentum as a function of the temperature forthe previous densities and for the approaches considered before. For T=0 we observean attractive potential of -23 MeV for ρ0 and -76 MeV for 3ρ0 when D-mesons andOpen-charm enhancement at FAIR? 4nucleons are dressed in the intermediate states (upper left panel). For the full self-consistent calculation (upper right panel), the D-meson potential at T=0 lies between-5 MeV for ρ0 and -48 MeV for 3ρ0. For higher temperatures, the quasiparticle peakgets close to the D-meson free mass, so there is almost no mass shift expected at ﬁnitetemperature. On the other hand, the width of the spectral density depends weakly onthe temperature. At T=120 MeV the width increases from 52 MeV to 163 MeV for ρ0to 3ρ0 for the ﬁrst approach (lower left panel) and from 36 MeV at ρ0 to 107 MeV at3ρ0 for the second approach (lower right panel).Based on the previous mean-ﬁeld calculations which obtain a large D-meson massshift, an enhancement of open-charm in A+A collisions was predicted in order tounderstand the enhancement of ’intermediate-mass dileptons’ in Pb+Pb collisions atSPS energies [4]. According to our model, the inclusion of a considerable width of theD-meson in the medium (40-50 ρ/ρ0 for T=120 MeV) is the only source of enhanced in-medium D-meson production, as studied for kaons in [14]. As a consequence, an oﬀ-shelltransport theory to account for the D-meson production is needed. For that purpose,not only the D-meson spectral density but also in-medium D-meson cross sections arerequired. In our model, the cross sections at threshold are expected on the order of 1-20mb for the range of densities studied in both approaches.Mesons with charm content at beam energy close to threshold will be investigatedby the CBM experiment [1]. Our results indicate that the mass of the D-meson is notmodiﬁed but D-mesons show a considerable width in this hot and dense medium.AcknowledgmentsL.T. acknowledges ﬁnancial support from AvH Foundation and GSI.References[1] See http://www.gsi.de/fair/experiments/CBM[2] Gonin A et al. 1996 Nucl. Phys. A 610 404c–417c[3] Abreu M et al. 2000 Eur. Phys. J C 14 443–455[4] Cassing W, Bratkovskaya E L and Sibirtsev A 2001 Nucl. Phys. A 691 753–778[5] Scomparin E, Talk given at QM05 (Budapest, Hungary, 2005)[6] Tsushima K, Lu D H, Thomas A W, Saito K and Landau R H 1999 Phys. Rev. C 59 2824–2828;Sibirtsev A, Tsushima A and Thomas A W 1999 Eur. Phys. J. A 6 351–359[7] Hayashigaki A 2000 Phys. Lett. B 487 96–103[8] Mishra A, Bratkovskaya E L, Schaﬀner-Bielich J, Schramm S and St¨ ocker H 2004 Phys. Rev. C69 015202 1–11[9] Weise W 2001 Hirschegg ’01: Structure of Hadrons: 29th International Workshop on GrossProperties of Nuclei and Nuclear Excitations (Hirschegg 2001, Structure of hadrons), p. 249[10] Tol´ os L, Schaﬀner-Bielich J and Mishra A 2004 Phys. Rev. C 70 025203 1–10[11] Lutz M F M and Korpa C L 2006 Phys. Lett. B 633 43–48[12] Tol´ os L, Schaﬀner-Bielich J and St¨ ocker H 2006 Phys. Lett B 635 85–92[13] Tol´ os L, Ramos A and Polls A 2002 Phys. Rev. C 65 054907 1–10[14] Tol´ os L, Polls A, Ramos A and Schaﬀner-Bielich J 2003 Phys. Rev. C 68 024903 1–11

A and Polls A

Bratkovskaya E L and Sibirtsev A

Hayashigaki A

Hirschegg ’01: Structure of Hadrons:

Talk given at QM05

Open-charm enhancement at FAIR?

Tolós, L

Schaffner-Bielich, J

GSI Repository

Open-charm enhancement at FAIR

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Open-charm enhancement at FAIR?

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