Use r as a probe for the restoration of chiral symmetry (Pisarski, 1982)

1. Prime goal Use r as a probe for the restoration of chiral symmetry (Pisarski, 1982) Principal difficulty : properties of r 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

2. General question of QCD Origin of the masses of light hadrons? • Expectation Mh~10-20 MeV approximate chiral SU(nf)L× SU(nf)R symmetry chiral doublets, degenerate in mass • Observed MN~1 GeV spontaneous chiral symmetry breaking <qq> ≠ 0 M ~ 0.77 GeV ≠ Ma1~ 1.2 GeV

3. Several theoretical approaches including lattice QCD still in development Lattice QCD(for mB=0 andquenched approx.) two phase transitions at the same critical temperature Tc cL - cm ‹qq› L 1.0 T/Tc 1.0 T/Tc 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 <qq> ?

4. 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 ,(,) Gtot [MeV] r (770) 150 (1.3fm/c) w(782) 8.6 (23fm/c) f(1020) 4.4 (44fm/c) in-medium radiation dominated by the  : • life time τ=1.3 fm/c << τcollision> 10 fm/c • continuous “regeneration” by 

5. CERES/NA45 at the CERN SPS Pioneering experiment, built 1989-1992 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 

6. Which processes populate the dimuon mass spectrum below 1 GeV?

7. Measuring the collision centrality The collision centrality can be measured via the charged particle multiplicity as measured by the pixel vertex telescope Track multiplicity of charged tracks for triggered dimuons for opposite-sign pairs combinatorial backgroundsignal pairs 4 multiplicity windows:

8. Comparison of hadron decay cocktail to peripheral data No (significant) in-medium effects are expected in peripheral collisions We can try to perform a fit with the hadron cocktail Very good description, also at low mass and pT where acceptance is smallest

9. Isolate possible excess by subtracting cocktail (without r) from the data How to fit in the presence of an unknown source?  Try to findexcess above cocktail(if it exists) without fit constraints • ωand  : fix yields such as to get, after subtraction, a smoothunderlying continuum •  : ()set upper limit, defined by “saturating” the measured yield in the mass region close to 0.2 GeV (lower limit for excess). () use yield measured for pT > 1.4 GeV/c

10. Evolution of the excess shape with centrality • No cocktail rand noDDsubtracted The evolution of the excess with centrality can be studied with precision with a rather fine binning in multiplicity data – cocktail (all pT) • Clear excessabove the cocktail ,centered at the nominal r poleand rising with centrality • Excess even more pronounced at low pT cocktail / =1.2

11. 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.

12. Systematics The largest source of systematic error comes from the subtraction of combinatorial and fake matches background. In principle there are other uncertainty sources as the form factors, but these are negligible compared to the background. Illustration of sensitivity to correct subtraction of combinatorial background and fake matches;to variation of the  yield The systematic errors of continuum 0.4<M<0.6 and 0.8<M<1GeV are 25% (at most) in the most central collisions The structure in  region looks rather robust

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

14. p p r r meson in vacuum Introduce r as gauge boson into free p+r Lagrangian  is dressed with free pions vacuum spectral function (like ALEPH data V(t→ 2pnt ))

15. Physics objective in heavy ion collisions Goal: Study properties of ther spectral function Im Drin 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 rB, (some control via multiplicity dependences)

16. r spectral function in hot and dense hadronic matter rB /r0 0 0.1 0.7 2.6 Hadronic many-body approachRapp/Wambach et al., Weise et al. hot matter hot and baryon-rich matter  is dressed with: hot pions Prpp ,baryonsPr B(N,D ..) mesonsPr M (K,a1..) • “melts” in hot and dense matter • - pole position roughly unchanged - broadening mostly through baryon interactions

17. r spectral function in hot and dense hadronic matter Dropping mass scenarioBrown/Rho et al., Hatsuda/Lee explicit connection between hadron masses and chiral condensate universal scaling law continuous evolution of pole mass with T and r ; broadening atfixed T,r ignored

18. Final mass spectrum rB /r0 0 0.1 0.7 2.6 continuous emission of thermal radiation during life time of expanding fireball integration of rate equation over space-time and momenta required example: broadening scenario

19. How to compare data with predictions? There are two possibilities, in principle: • correct data for acceptance in 3-dim. space M-pT-y and compare directly to predictions at the input • 2) use the predictions in the form • and generate Monte Carlo decays of the virtual photons g* into m+m- pairs, propagate these through the acceptance filter and compare results to uncorrected data at the output(done presently) • The conclusions on the agreement or disagreement between data and predictions in principle should be independent of whether comparison is done at input or output (provided you understand the effect of your detector on data well)

20. Acceptance filtering of theoretical prediction in NA60 rB /r0 0 0.1 0.7 2.6 Input (example): thermal radiation based on RW spectral function all pT Output:spectral shape much distorted relative to input, but somehow reminiscent of thespectral functionunderlying the input; by chance?

21. Comparison to the main models that appeared in the 90s Rapp-Wambach: hadronic model predicting strong broadening/no mass shift Brown/Rho scaling: dropping mass due to dropping of chiral condensate Predictions for In-In by Rapp et al (2003) for dNch/d = 140, covering all scenarios Theoretical yields normalized to data in mass interval < 0.9 GeV After acceptance filtering,data and predictions displayspectral functions, averaged over space-time and momenta Only broadening of (RW) observed, no mass shift (BR)

22. Brown-Rho vs Rapp-Wambach Modification od BR by change of the fireball parameters Van Hees and Rapp, hep-ph/0604269 even switching out all temperature effects does not lead to agreement between BR and the data

23. The role of baryons (Rapp-Hees) • Without baryons: • Not enough broadening • Lack of strength below the r peak

24. Semicentral collisions (Rapp-Hees) Something is missing at high pT. What?

25. The vacuum r contribution Ruppert-Renk At high pT there is an important contribution from the “vacuum r”: r decays at kinetic freeze-out We will see later why it is important at high pT (does not dominate the yield integrated in pT) Rapp-Hees

26. Intermediate summary In the last 2 years significative advance in understanding the in-medium effects on the r spectral function. The main result is: Hadronic many body approaches predict a broadening of the r without mass shift which is in fair agreement with data Models predicting a decrease of the r mass are ruled out data The main open question is: What is the connection to chiral symmetry?

27. The mass region above 1 GeV: vector-axial vector mixing Above 1 GeV we can have contributions from 4p processes. The spectral shape can be found for instance from e+e-4p or studying (ALEPH) t(2np)ν 2p, 4p, 6p … 3p, 5p… In addition, because of the pion “heat bath”, it is possible also to have processes in which an axial vector particle interacts with a pion, as pa1m+m-. This effectively introduces a mixing between vector and axial-vector states (at the correlator level). This mixing depends on the “amount” of chiral symmetry restoration

28. The mass region above 1 GeV: models vs data Ruppert / Renk, Phys.Rev.C (2005) Rapp/Hees Mass region above 1 GeV described dominantly in terms ofhadronic processes, 4 p … Mass region above 1 GeV described dominantly in terms ofpartonic processes,dominated byqqbar annihilation  Hadron-parton duality

29. s(e+e-→hadrons) in vacuum e+ e- p - p + rI =1 r 2p+4p+... pp e+ e- h1 h2 r+w+f KK q q _ qq … _ s ≥ sdual~(1.5GeV)2 : pQCD continuum s < sdual : Vector-Meson Dominance

30. Transverse momentum spectra In a static fireball at temperature T the differential particle momentum distribution is Lorentz invariant phase space element Assume a thermal Boltzmann shape  transverse mass spectra (integrated over rapidity) mT scaling: all particle spectra have the same T “slope”

31. The fireball produced in a heavy ion collision expands. The thermal energy is converted in mechanical work and collective motion (flow) develops. Due to the very high particle density at the center of the source, particles only get out to the side of the source  transverse direction = radial flow = energy of the particle in the local rest frame of fluid element boosted to the observer rest frame

32. The Cooper-Frye formula The number of particles that cross a closed surface can be written as When we count the particles produced in a collision we count for instance the number of particles across a surface for a long time  three dimensional space or hypersurface in space-time dSm Cooper-Frye formula

33. At kinetic freeze-out the stable hadrons stream free to the detector S can be taken as the last scattering surface Only the contributions from the narrow temperature window around kinetic freeze-out must be considered. With some mathematics one can show that Integrated over y Integrated over f Transverse flow-field Once the mass is fixed (the particle is specified), the function has only three parameters: vT, Tf and a normalization In principle they can be extracted with a two parameter fit to experimental distributions: Evaluate c2 for fixed vT and Tf Create a c2 map as a function of vT and Tf

34. Stable hadrons reflect the kinetic freeze-out conditions. Using exp(-mT/T) gives a T dependent on the momentum range  T from exponential fit (call Tslope) is not anymore the source temperature Tf. At high pT the spectra are still exponential with a common slope which reflects a freeze-out temperature blue-shifted by the flow transverse velocity vT: The pT spectra appear flattened at low pT and mT scaling is broken. The T slope becomes mass dependent (mT scaling is broken) In principle allows to separate the thermal from the collective motion

35. NA49/SPS results: Common flow velocity seen for very wideparticle species (Nucl.Phys A 715 61) Pion and deuteron are taken out from fit procedure (many pions come from resonance decays - deuterons are most likely produced with proton-neutron coalescence) However, spectra described are very well described with the thermal parameter extracted with other particles Common flow velocity in p,K,p and their anti-particles is seen at SPS and AGS energies Common flow velocities are seen also in RHIC Au-Au data (PHENIX and STAR)

36. Other effects of transverse flow: Peripheral collisions: shorter fireball lifetime  less time to develop flow (smaller vT) – earlier decoupling at higher Tf Central collisions: bigger fireball lifetime  more time to develop flow (larger vT) – later decoupling at smaller Tf Tf and vT are strongly anticorrelated: 1s contours n=1 • NA57 158 GeV • Centrality classes: • 0  40 to 53 % most central • 1  23 to 40 % most central • 2  11 to 23 % most central • 3  4.5 to 11 % most central • 4  4.5 % most central

37. f transverse momentum spectra Peripheral Central T slope extracted fitting f pT spectra are corrected for acceptance after background and side-window subtraction

38. T slope as a function of centrality 158 AGeV Central collisions Pb-Pb In-In Si-Si C-C pp Fit with exp(-mT/Tslope) vs centrality: increase of Tslope (indication of radial flow) NA60 (pT fit range 0-2.6 GeV) NA49 (pT fit range 0-1.6 GeV) NA50 (pT fit range 1.2-2.6 GeV) NA60 Preliminary NA50 and NA49 differerences (f puzzle): Decay channel (mm vs KK) pT fit range (high vs low) The In-In measurement of NA60follows the NA49 systematics

39. T slope, fit range dependence NA60 (pT fit range 1.2-2.6 GeV) NA49 (pT fit range 0-1.6 GeV) NA50 (pT fit range 1.2-2.6 GeV) NA60 (pT fit range 0.0-1.6 GeV) NA49 (pT fit range 0-1.6 GeV) NA50 (pT fit range 1.2-2.6 GeV) NA60 Preliminary NA60 Preliminary • Visible T dependence on the fit range • Low pT: Higher absolute values, steeper rise with centrality –agreement with NA49 • High pT: Lower absolute values, flatter rise with centrality –tendency towards NA50 but still some quantitative difference

40. Dimuon excess pT spectra Strategy of acceptance correction  reduce 3-dimensional acceptance correction in M-pT-y to 2-dimensional correction in M-pT, using measured y distribution as an input  use slices of m = 0.1 GeV and pT = 0.2 GeV  resum to three extended mass windows 0.4<M<0.6 GeV 0.6<M<0.9 GeV 1.0<M<1.4 GeV subtract charm from the data before acceptance correction (based on IMR results – we pospone this discussion)

41. Dimuon excess pT spectra for three centrality bins (spectra arbitrarily normalized) hardly any centrality dependence  integrate over centrality Significant mass dependence

42. r-like region mT spectrum (vs f) physics differences are better visible in mT- than in pT f: mT spectrum nearly pure exponential – Teff nearly independent of fit range with some hint of radial flow Excess: spectra show an increase (not flattening) at low mT What does it mean?

43. differentialfits to pT spectra, assuming locally 1-parameter mT scaling and using gliding windows of pT=0.8 GeV local slope Teff  slope Teff vs central pT of the 0.8 GeV moving window (very) soft slopes at at low pT hard slopes at high pT Why?

44. Consequences of continuum emission over the fireball life-time Important qualitative difference between f and dimuon excess f spectral slope: only contributions from the narrow temperature region around kinetic freeze-out important Excess dimuons: continuum emission during all the fireball lifetime – we see not only the emission at freeze-out! No flow: superposition from contributions of static fireballs at different T, weighted by the radiating volume In presence of flow: superposition from contributions at different T with different blue-shifts of T→ what we see in the spectra are effective pT dependent slopes Flow affects cold source emission, but not hot source emission → Softer slopes at low pTs correspond to early emission with small flow Harder slopes at high pTs corresponds to late emission with large flow

45. If this is correct, the higher the pT more evident the role of the vacuum r produced at kinetic freeze-out (but notice that it would dominate the spectrum only at very large pTs) If we look at the 0.4-0.6 mass region, where only a contribution from the in-medium r is seen, then we should see a lower slope This is qualitatively true

46. Reasonably accounted for by a theoretical model (Ruppert-Renk hep-ph/0612113) Is that all good then? Unfortunately not. the very low slopes at very low pT (<0.5 GeV/c) shown by the data are at the moment without explanation

47. The high mass continuum region (1<mmm<1.4 GeV) • The slopes of the high mass continuum region are smaller than the ones of the low mass continuum region (mmm<0.6 GeV) • Can we reconcile this with an hadronic source as 4p processes? • Shouldn’t 4p contribute all the way down to kinetic freeze-out? • then effect of flow is important and T slope cannot be so low if 4p is the dominant source This is a very much debated and very hot point But not yet a final answer agreed by everybody

48. The high mass continuum region (1<mmm<1.4 GeV)

49. Local slope vs mmm

50. The open charm and the intermediate mass region In all the discussions so far we assumed to know the charm yield and it was subtracted. But how do we know it? This brings us to discuss in more detail the intermediate mass region 1<mmm<2.5 GeV NA60 was mainly approved to assess the nature of an excess seen in the intermediate mass region above the expected yields of open charm and Drell-Yan This excess is the same we have been discussing above the f (interpreted either as an hadronic source or as a partonic source) Historically it was already noticed by previous experiments (HELIOS, NA38/50) but none of them was able to attribute it to a prompt source or to enhanced charm Only NA60 has clearly attributed it to a prompt source.