S. Damjanovic, Bielefeld 13 December First measurement of the  spectral function in high-energy nuclear collisions Sanja Damjanovic NA60 Collaboration Bielefeld, 13 December 2005

S. Damjanovic, Bielefeld 13 December Outline  Motivation  Experimental set-up  Data analysis event selection combinatorial background fake matches  Understanding the peripheral data  Isolation of an excess in the more central data  Comparison of the excess to model predictions  Conclusions

S. Damjanovic, Bielefeld 13 December Motivation

S. Damjanovic, Bielefeld 13 December Prime goal Use  as a probe for the restoration of chiral symmetry ( Pisarski, 1982 ) Principal difficulty : properties of  in hot and  dense  matter unknown (related to the mechanism of mass generation) properties of hot and dense medium unknown (general goal of studying nuclear collisions)  coupled problem of two unknowns: need to learn on both

S. Damjanovic, Bielefeld 13 December Origin of the masses of light hadrons?  Expectation M h ~10-20 MeV approximate chiral SU(n f ) L × SU(n f ) R symmetry chiral doublets, degenerate in mass  Observed M N ~1 GeV spontaneous chiral symmetry breaking  ≠ 0 M  ~ 0.77 GeV ≠ M a1 ~ 1.2 GeV General question of QCD

S. Damjanovic, Bielefeld 13 December ‹qq› T/T c mm LL L Many different theoretical approaches including Lattice QCD still very much under development Lattice QCD (for  B =0 and quenched approx.) two phase transitions at the same critical temperature T c deconfinement chiral symmetry transition restoration hadron spectral functions on the lattice only now under study explicit connection between spectral properties of hadrons (masses,widths) and the value of the chiral condensate ?

S. Damjanovic, Bielefeld 13 December High Energy Nuclear Collisions Principal experimental approach: measure lepton pairs (e+e- or μ+μ-) no final state interactions; continuous emission during the whole space-time evolution of the collision system dominant component at low invariant masses: thermal radiation, mediated by the vector mesons ,( ,  )  tot [MeV]  (770) 150 (1.3fm/c)  8.6 (23fm/c)  4.4 (44fm/c) in-medium radiation dominated by the  : 1. life time τ =1.3 fm/c 10 fm/c 2. continuous “regeneration” by 

S. Damjanovic, Bielefeld 13 December Low-mass dileptons + chiral symmetry How is the degeneration of chiral partners realized ? In nuclear collisions, measure vector   +  -, but axial vector? ALEPH data: Vacuum At T c : Chiral Restoration

S. Damjanovic, Bielefeld 13 December In-medium changes of the  properties (relative to vacuum) Selected theoretical references mass of  width of  Pisarski 1982 Leutwyler et al 1990 ( ,N) Brown/Rho 1991 ff Hatsuda/Lee 1992 Dominguez et. al1993 Pisarski 1995 Rapp 1996 ff very confusing, experimental data crucial

S. Damjanovic, Bielefeld 13 December CERES/NA45 at the CERN SPS Pioneering experiment, built results on p-Be/Au, S-Au and Pb-Au first measurement of strong excess radiation above meson decays; vacuum-  excluded resolution and statistical accuracy insufficient to determine the in-medium spectral properties of the 

S. Damjanovic, Bielefeld 13 December Experimental set-up

S. Damjanovic, Bielefeld 13 December muon trigger and tracking magnetic field Standard way of measuring dimuons Degraded dimuon mass resolution Cannot distinguish prompt dimuons from decay muons Muon Other Energy loss Multiple scattering hadron absorber target beam or ?

S. Damjanovic, Bielefeld 13 December T dipole magnet hadron absorber Origin of muons can be accurately determined Improved dimuon mass resolution Matching in coordinate and momentum space targets beam tracker vertex tracker muon trigger and tracking magnetic field or ! Measuring dimuons in NA60: concept

S. Damjanovic, Bielefeld 13 December Data Analysis

S. Damjanovic, Bielefeld 13 December week long run in Oct.–Nov Indium beam of 158 GeV/nucleon ~ 4 × ions delivered in total ~ 230 million dimuon triggers on tape present analysis: ~1/2 of total data Event sample: Indium-Indium

S. Damjanovic, Bielefeld 13 December Selection of primary vertex Beam Tracker sensors windows The interaction vertex is identified with better than 20  m accuracy in the transverse plane and 200  m along the beam axis. (note the log scale) Present analysis (very conservative): Select events with only one vertex in the target region, i.e. eliminate all events with secondary interactions

S. Damjanovic, Bielefeld 13 December A certain fraction of muons is matched to closest non-muon tracks (fakes). Only events with  2 < 3 are selected. Fake matches are subtracted by a mixed-events technique (CB) and an overlay MC method (only for signal pairs, see below) Muon track matching Matching between the muons in the Muon Spectrometer (MS) and the tracks in the Vertex Telescope (VT) is done using the weighted distance (  2 ) in slopes and inverse momenta. For each candidate a global fit through the MS and VT is performed, to improve kinematics.

S. Damjanovic, Bielefeld 13 December Determination of Combinatorial Background Basic method: Event mixing takes account of charge asymmetry correlations between the two muons, induced by magnetic field sextant subdivision trigger conditions

S. Damjanovic, Bielefeld 13 December Combinatorial Background from ,K→  decays Agreement of data and mixed CB over several orders of magnitude Accuracy of agreement ~1%

S. Damjanovic, Bielefeld 13 December Fake Matches Fake matches of the combinatorial background are automatically subtracted as part of the mixed-events technique for the combinatorial background Fake matches of the signal pairs (<10% of CB) are obtained in two different ways: Overlay MC : Superimpose MC signal dimuons onto real events. Reconstruct and flag fake matches. Choose MC input such as to reproduce the data. Event mixing : More complicated, but less sensitive to systematics

S. Damjanovic, Bielefeld 13 December Fake-match background example from overlay MC: the  fake-match contribution localized in mass (and p T ) space:   = 23 MeV,  fake = 110 MeV; fake prob. 22% complete fake-match mass spectrum agreement between overlay MC and event mixing, in absolute level and in shape, to within <5%

S. Damjanovic, Bielefeld 13 December Subtraction of combinatorial background and fakes For the first time,  and  peaks clearly visible in dilepton channel ; even  μμ seen Net data sample: events Mass resolution: 23 MeV at the  position Fakes / CB < 10 %   Progress over CERES: statistics: factor >1000 resolution: factor 2-3

S. Damjanovic, Bielefeld 13 December Track multiplicity from VT tracks for triggered dimuons for Centrality binmultiplicity 〈 dN ch /dη 〉 3.8 Peripheral 4–28 17 Semi-Peripheral 28–92 63 Semi-Central 92– Central > Associated track multiplicity distribution 4 multiplicity windows: opposite-sign pairs combinatorial background signal pairs

S. Damjanovic, Bielefeld 13 December Signal and background in 4 multiplicity windows S/B 2 1/3 1/8 1/11 Decrease of S/B with centrality, as expected

S. Damjanovic, Bielefeld 13 December Phase space coverage in mass-p T plane Final data after subtraction of combinatorial background and fake matches The acceptance of NA60 extends (in contrast to NA38/50) all the way down to small mass and small p T MC

S. Damjanovic, Bielefeld 13 December Phase space coverage in y-p T plane Examples from MC simulations Optimal acceptance: at high mass, high p T = 3.5 at low mass, low p T = 3.8 Shift of acceptance away from midrapidity not much different from CERES

S. Damjanovic, Bielefeld 13 December Results

S. Damjanovic, Bielefeld 13 December Understanding the Peripheral data Fit hadron decay cocktail and DD to the data 5 free parameters to be fit:   DD, overall normalization (  0.12  fixed) Fit range: up to 1.4 GeV

S. Damjanovic, Bielefeld 13 December Comparison of hadron decay cocktail to data all p T Very good fit quality log

S. Damjanovic, Bielefeld 13 December The  region (small M, small p T ) is remarkably well described Comparison of hadron decay cocktail to data → the (lower) acceptance of NA60 in this region is well under control p T < 0.5 GeV

S. Damjanovic, Bielefeld 13 December Comparison of hadron decay cocktail to data Again good agreement between cocktail and data 0.5 < p T < 1 GeV p T > 1 GeV

S. Damjanovic, Bielefeld 13 December Particle ratios from the cocktail fits  and  nearly independent of p T ; 10% variation due to the  increase of  at low p T (due to ππ annihilation, see later) General conclusion:  peripheral bin very well described in terms of known sources  low M and low p T acceptance of NA60 under control

S. Damjanovic, Bielefeld 13 December Isolation of an excess in the more central data

S. Damjanovic, Bielefeld 13 December Understanding the cocktail for the more central data Need to fix the contributions from the hadron decay cocktail Cocktail parameters from peripheral data? How to fit in the presence of an unknown source?  Nearly understood from high p T data, but not yet used Goal of the present analysis: Find excess above cocktail (if it exists) without fits

S. Damjanovic, Bielefeld 13 December Conservative approach Use particle yields so as to set a lower limit to a possible excess

S. Damjanovic, Bielefeld 13 December ● data -- sum of cocktail sources including the  Cocktail definition: see next slide all p T Comparison of data to “conservative” cocktail Clear excess of data above cocktail, rising with centrality  fixed to 1.2 But: how to recognize the spectral shape of the excess?

S. Damjanovic, Bielefeld 13 December Isolate possible excess by subtracting cocktail (without  ) from the data   set upper limit, defined by “saturating” the measured yield in the mass region close to 0.2 GeV  leads to a lower limit for the excess at very low mass  and  : fix yields such as to get, after subtraction, a smooth underlying continuum difference spectrum robust to mistakes even at the 10% level; consequences highly localized

S. Damjanovic, Bielefeld 13 December Sensitivity of the difference procedure Change yields of ,  and  by +10%:  enormous sensitivity, on the level of 1-2%, to mistakes in the particle yields. The difference spectrum is robust to mistakes even on the 10% level, since the consequences of such mistakes are highly localized.

S. Damjanovic, Bielefeld 13 December Excess spectra from difference: data - cocktail all p T Clear excess above the cocktail , centered at the nominal  pole and rising with centrality Similar behaviour in the other p T bins No cocktail  and no DD subtracted

S. Damjanovic, Bielefeld 13 December Excess spectra from difference data-cocktail No cocktail  and no DD subtracted p T < 0.5 GeV Clear excess above the cocktail , centered at the nominal  pole and rising with centrality Similar behaviour in the other p T bins

S. Damjanovic, Bielefeld 13 December Systematics Systematic errors of continuum 0.4<M<0.6 and 0.8<M<1GeV 25% Illustration of sensitivity  to correct subtraction of combinatorial background and fake matches;  to variation of the  yield Structure in  region completely robust

S. Damjanovic, Bielefeld 13 December Comparison of excess to model predictions

S. Damjanovic, Bielefeld 13 December  * (q) (T,  B ) μ + μ - Dilepton Rate in a strongly interacting medium dileptons produced by annihilation of thermally excited particles:  +  - in hadronic phase qq in QGP phase photon selfenergy at SPS energies  +  - →  *→μ + μ - dominant Vector-Dominance Model hadron basis spectral function

S. Damjanovic, Bielefeld 13 December Physics objective Goal: Study properties of the rho spectral function Im D  in a hot and dense medium Procedure: Spectral function accessible through rate equation, integrated over space-time and momenta Limitation: Continuously varying values of temperature T and baryon density  B, (some control via multiplicity dependences)

S. Damjanovic, Bielefeld 13 December  spectral function in vacuum  vacuum spectral function   Introduce  as gauge boson into free  +  Lagrangian   is dressed with free pions (like ALEPH data V(  → 2   

S. Damjanovic, Bielefeld 13 December  spectral function in hot and dense hadronic matter (I) Dropping mass scenario Brown/Rho et al., Hatsuda/Lee universal scaling law explicit connection between hadron masses and chiral condensate continuous evolution of pole mass with T and  broadening at  fixed  ignored

S. Damjanovic, Bielefeld 13 December  spectral function in hot and dense hadronic matter (II) Hadronic many-body approach Rapp/Wambach et al., Weise et al. D  (M,q;  B,T)=[M 2 -m  2 -   -   B -   M ] -1  B /  hot and baryon-rich matter hot matter  is dressed with: hot pions    baryons   (N, ..) mesons   (K,a 1..)  “melts” in hot and dense matter - pole position roughly unchanged - broadening mostly through baryon interactions

S. Damjanovic, Bielefeld 13 December Final mass spectrum integration of rate equation over space-time and momenta required continuous emission of thermal radiation during life time of expanding fireball example: broadening scenario  B / 

S. Damjanovic, Bielefeld 13 December How to compare data to predictions? 1)correct data for acceptance in 3-dim. space M-p T -y and compare directly to predictions at the input (to be done in the future) 2) use predictions in the form decay the virtual photons  * into  +  - pairs, propagate these through the NA60 acceptance filter and compare results to uncorrected data at the output (done presently)  conclusions as to agreement or disagreement of data and predictions are independent of whether comparison is done at input or output

S. Damjanovic, Bielefeld 13 December Acceptance filtering of theoretical prediction all p T Output: spectral shape much distorted relative to input, but somehow reminiscent of the spectral function underlying the input; by chance? Input (example): thermal radiation based on RW spectral function

S. Damjanovic, Bielefeld 13 December Output: white spectrum ! Understanding the spectral shape at the output By pure chance, for all p T and the slope of the p T spectra of the direct radiation, the NA60 acceptance roughly compensates for the phase-space factors and directly “measures” the Input: thermal radiation based on white spectral function all p T

S. Damjanovic, Bielefeld 13 December Predictions for In-In by Rapp et al (2003) for 〈 dN ch /d  〉 = 140, covering all scenarios Theoretical yields, folded with acceptance of NA60 and normalized to data in mass interval < 0.9 GeV Only broadening of  ( RW) observed, no mass shift (BR) Comparison of data to RW, BR and Vacuum 

S. Damjanovic, Bielefeld 13 December Comparison of data to RW, BR and Vacuum  p T dependence same conclusions

S. Damjanovic, Bielefeld 13 December Could Brown/Rho scaling be saved by “fusion” of the two scenarios ? by change of the fireball parameters ? Controversy of Brown/Rho vs Rapp/Wambach Results of Rapp (8/2005): (not propagated through acceptance filter) Neither fusion nor parameter change able to make BR scaling unobservable

S. Damjanovic, Bielefeld 13 December Predictions for In-In by Rapp et al. (11/2005) for 〈 dN ch /d  〉 = 140 Comparison of data to RW(2  +4  +QGP) Vector-Axialvector Mixing:  interaction with real  ’ s (Goldstone bosons). Use only 4  and higher parts of the correlator  V in addition to 2  Use 4 , 6  … and 3 , 5  … (+1  ) processes from ALEPH data, mix them, time-reverse them and get  +  - yields

S. Damjanovic, Bielefeld 13 December Predictions for In-In by Rapp et al. (11/2005) for 〈 dN ch /d  〉 = 140 Comparison of data to RW(2  +4  +QGP) The yield above 0.9 GeV is sensitive to the degree of vector-axialvector mixing and therefore to chiral symmetry restoration! Now whole spectrum reasonably well described, even in absolute terms (resulting from improved fireball dynamics) direct connection to IMR results >1 GeV from NA60

S. Damjanovic, Bielefeld 13 December Comparison of data to RR D  (M,q;T)=[M 2 -m  2 -   ] -1 Ruppert / Renk, Phys.Rev.C (2005) Spectral function only based on hot pions, no baryon interactions included (shape similar RW) continuum contributions, in the spirit of quark-hadron duality, also added (fills high mass region analogous to NA50 IMR description) broadening described

S. Damjanovic, Bielefeld 13 December Next steps of the analysis complete acceptance correction of the data in 3-dim. space M-p T -y determination of the (averaged) spectral functions in narrow bins of p T, correcting for the (averaged) phase space factors; also insight into temperature and radial flow; improve shape analysis is it possible to extract dispersion relation E(p) for the  (common in condensed-matter physics)? does the  also “melt”? increase statistics by factor > 2 for all these points

S. Damjanovic, Bielefeld 13 December Conclusions (I) : data pion annihilation seems to be a major contribution to the lepton pair excess in heavy-ion collisions at SPS energies no significant mass shift of the intermediate  only broadening of the intermediate 

S. Damjanovic, Bielefeld 13 December Conclusions (II) : interpretation all models predicting strong mass shifts of the intermediate   including Brown/Rho scaling, are not confirmed by the data models predicting strong broadening roughly verified; unclear whether broadening due to T or baryon density theoretical investigation on an explicit connection between broadening and the chiral condensate clearly required

S. Damjanovic, Bielefeld 13 December Lisbon CERN Bern Torino Yerevan Cagliari Lyon Clermont Riken Stony Brook Palaiseau Heidelberg BNL ~ 60 people 13 institutes 8 countries R. Arnaldi, R. Averbeck, K. Banicz, K. Borer, J. Buytaert, J. Castor, B. Chaurand, W. Chen, B. Cheynis, C. Cicalò, A. Colla, P. Cortese, S. Damjanović, A. David, A. de Falco, N. de Marco, A. Devaux, A. Drees, L. Ducroux, H. En’yo, A. Ferretti, M. Floris, P. Force, A. Grigorian, J.Y. Grossiord, N. Guettet, A. Guichard, H. Gulkanian, J. Heuser, M. Keil, L. Kluberg, Z. Li, C. Lourenço, J. Lozano, F. Manso, P. Martins, A. Masoni, A. Neves, H. Ohnishi, C. Oppedisano, P. Parracho, P. Pillot, G. Puddu, E. Radermacher, P. Ramalhete, P. Rosinsky, E. Scomparin, J. Seixas, S. Serci, R. Shahoyan, P. Sonderegger, H.J. Specht, R. Tieulent, E. Tveiten, G. Usai, H. Vardanyan, R. Veenhof and H. Wöhri The NA60 experiment