Project B.5: Hadrons in Nuclear Matter

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1 Project B.5: Hadrons in Nuclear Matter Janus Weil, Murat Kaskulov, Ulrich Mosel Institut für Theoretische Physik, JLU Giessen Arbeitstreffen SFB/TR 16 Bochum,

2 Outline introduction/motivation the GiBUU transport model off-shell transport photoproduction of omega mesons on nuclei (CB/TAPS) dileptons (CLAS/g7, HADES) summary

3 Motivation: Hadrons in Medium how do vector mesons behave inside a hadronic medium? major prediction: mass shift (partial) restoration of chiral symmetry in medium Brown/Rho (eff. Lagrang. approach): m V (ρ 0)/m V 0.8 Hatsuda/Lee (using QCD sum rules, neglecting width): m V (ρ)/m V 1 α(ρ/ρ 0 ), α 0.16 ± 0.06 mass shift V-N potential bound states?

4 Motivation II other effects: collisional broadening, resonance structures,... collisional broadening (LDA): Γ coll = ρ < v rel σ VN > absorption extended sum-rule analysis by Leupold/Peters/Mosel, including finite width (NPA 628, 1998) coupling to resonances can introduce additional structures in the spectral function (Post, 2003)

5 The GiBUU Transport Model semi-classical hadronic transport model unified framework for various types of reactions (pa, πa, γa, ea, νa, AA) and observables modular and well-documented Fortran code collaborative effort, SVN-based multi-user environment publicly available releases (open source)

6 The BUU equation BUU equation describes time evolution of phase space density f i ( r, t, p, µ) for each particle species i (i = N,, π, ρ,...): ( t + ( p H i ) r ( r H i ) p ) fi ( r, t, p, µ) = I coll [f i, f j,...] collision term I coll : depends on all f i coupled-channel problem decays and scattering processes (2- and 3-body) low energy: resonance model high energy: string model (PYTHIA) Hamiltonian H i : hadronic mean fields and potentials off-shell potential model includes 61 baryons and 21 mesons solve numerically via test-particle method: f = δ( r r i )δ(p p i ) i

7 In-Medium Effects Mass Shifts incorporated as simple scalar potential Collisional Broadening in medium: Γ tot = Γ vac + Γ coll Γ coll = ρ v rel σ VN (low density approx. in lab frame) contributing processes: VN πn, ππn, R,... in practice: use Γ coll = const. (from transparency measurements) Off-Shell Transport density-dependent spectral functions need to be handled consistently smooth transition from in-medium to vacuum distribution

8 Off-Shell Transport off-shell EOM for test particles [Cassing/Juchem (NPA 665, 2000), Leupold (NPA 672, 2000)]: r i = p i + 1 E i 2E i p i = 1 2E i χ i = m2 i M 2 Γ i [ Γ i Re(Σ i ) + χ i p i p i ] [ r i Re(Σ i ) + χ i Γ i r i = const., ], incorporate density-dependent self energies Σ i, Γ i Im(Σ i ) Hamiltonian formulation: H i = M 2 + χ i Γi + p i 2 + Re(Σ i ) major difference to BUU model used by Mühlich (which relied on an old recipe by Effenberger)

9 The CB/TAPS detector γa ωx π 0 γx 3γX Bremsstrahlung photon beam (tagged), E γ = GeV one setup at ELSA (Bonn), one at MAMI (Mainz) measure photon triples demand that two make up a π 0 reconstruct ω mass mass resolution 25MeV

10 CB/TAPS: early results Trnka et al., PRL 94, 2005: m ω = 722 MeV Γ ω = 55 MeV Kotulla et al., PRL 100, 2008: T A = 12 σ(γa ωx ) A σ(γ 12 C ωx ) Γ coll. = MeV

11 MC simulation results Kaskulov/Oset, EPJ A31 (2007): CB/TAPS only weakly sensitive to in-medium effects (at full energy range of GeV) but: rather sensitive to background subtraction

12 CB/TAPS: background channels main brackground channels: π 0 π 0 4γ (missing 1 γ) π 0 η 4γ (missing 1 γ) nπ 0 π + misidentified as 3γ + p S. Friedrich: describe background via GiBUU simulation take complete GiBUU output, feed through GEANT detector simulation

13 Photoproduction of ω mesons σ γn VN = 1 16πk cm s s mn m π dµ M γn VN ( s) 2 A V (µ, ρ)p cm (µ) 9 γ N ω N in 40 Ca nucleus (no FSI) σ/a [µb] SAPHIR data vac. 1 FM + PB + coll. broad. + 16% mass shift E γ [GeV]

14 ω Excitation Function measure total ω production cross section via π 0 γ final states as a function of E γ (including FSI/absorption) curves: GiBUU simulations, data: B. Lemmer data disfavor mass shift scenario

15 π 0 γ Spectrum: BUU simulations by P. Mühlich γ + 40 Ca, E γ = GeV large low-mass tail γ + 40 Ca, E γ = GeV almost to effects K. Gallmeister, P. Mühlich et al., Prog. Part. Nucl. Phys. 61 (2008)

16 recent simulations with GiBUU γ+nb, E γ = MeV γ+nb, E γ = MeV dσ/m πγ [normalized to max.] a) vac. SF CB CB + shift 16% shift shift (ρ=const.) dσ/m πγ [normalized to max.] b) vac. SF CB CB + shift 16% shift shift (ρ=const.) M πγ [MeV/c 2 ] M πγ [MeV/c 2 ] recent simulations show: effects do increase at threshold but: Mühlich tails not reproduced soon to be published [arxiv: ]

17 π 0 γ Mass Spectrum: Comparison to Data γ+nb, E γ = MeV; M. Nanova, J.W. et al. [arxiv: ] dσ/m πγ [normalized to max.] vac. SF CB CB + shift 16% shift data M πγ [MeV/c 2 ] statistics not sufficient to distinguish different scenarios!

18 Reasons for weak sensitivity 1 long ω decay length [few decays in medium] 2 strong broadening/absorption [smearing of in-medium peak] 3 nuclear density profile [very few decays at full density] 10 8 decay position of ω π 0 γ [γ+nb, E γ = GeV] vac. SF [ r<5fm: 15.7 % ] 16% shift [ r<5fm: 27.3 % ] ρ=const [ r<6fm: 39.1 % ] dn/dr ρ [fm -3 ] radius r [fm]

19 Dileptons from HADES HADES: in-medium physics with protons and heavy ions pp, pa, AA e + e X e.g. pp@3.5gev (base line for pnb@3.5gev) open issue: time-like N- transition form factor cross checks: dilepton p T spectra and pion spectra medium effects in p+nb, Ar+KCl? dσ/dm ee [µb/gev] dσ/dp t dσ/dy HADES: p GeV (GiBUU simulation) data (A. Rustamov) GiBUU total ρ e + e - ω e + e - φ e + e - ω π 0 e + e - π 0 e + e - γ η e + e - γ Ne + e dilepton mass m ee [GeV] low mass bin (m<150mev)? transverse momentum p t [GeV] middle mass bin (150<m<550) data GiBUU total ρ e + e - ω e + e - φ e + e - ω π 0 e + e - π 0 e + e - γ η e + e - γ Ne + e - high mass bin (m>550mev) rapidity y

20 JLab: CLAS/g7 new results on transparency ratio (preliminary) problems with background subtraction (Bethe-Heitler? ρ-ω mixing?) to be resolved... M. Wood et al. [arxiv: ]

21 Summary 1 VM properties in cold nuclear matter: a challenging problem! 2 GiBUU: a valuable tool to study in-medium physics 3 CB/TAPS: present data inconclusive 4 perspectives: improve statistics on π 0 γ line shape, measure omega excitation function