first measurement of the spectral function in high-energy nuclear collisions
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First measurement of the spectral function in high-energy nuclear collisions. Sanja Damjanovic NA60 Collaboration. Bielefeld, 13 December 2005. Outline. Motivation Experimental set-up Data analysis event selection combinatorial background - PowerPoint PPT PresentationTRANSCRIPT
S. Damjanovic, Bielefeld 13 December 2005 1
First measurement of the spectral function in high-energy nuclear collisions
Sanja Damjanovic NA60 Collaboration
Bielefeld, 13 December 2005
S. Damjanovic, Bielefeld 13 December 2005 2
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 2005 3
Motivation
S. Damjanovic, Bielefeld 13 December 2005 4
Prime goal
Use as a probe for the restoration of chiral symmetry (Pisarski, 1982)
Principal difficulty :
properties of in hot anddensematter 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 2005 5
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
General question of QCD
S. Damjanovic, Bielefeld 13 December 2005 6
‹qq›-
1.0 T/Tc
mL
L
1.0 T/Tc
Many different theoretical approaches including Lattice QCD still very much under development
Lattice QCD
(for B=0 andquenched approx.)
two phase transitions at the same critical temperature 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> ?
S. Damjanovic, Bielefeld 13 December 2005 7
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 << τcollision > 10 fm/c2. continuous “regeneration” by
S. Damjanovic, Bielefeld 13 December 2005 8
Low-mass dileptons + chiral symmetry
• How is the degeneration of chiral partners realized ?• In nuclear collisions, measure vector+-, but axial vector?
ALEPH data: VacuumAt Tc: Chiral Restoration
S. Damjanovic, Bielefeld 13 December 2005 9
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 2005 10
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
S. Damjanovic, Bielefeld 13 December 2005 11
Experimental set-up
S. Damjanovic, Bielefeld 13 December 2005 12
muon trigger and tracking
magnetic field
Standard way of measuring dimuons
• Degraded dimuon mass resolution• Cannot distinguish prompt dimuons from decay muons
MuonOther
Energy lossMultiple scattering
hadron absorber
target
beam
or
?
S. Damjanovic, Bielefeld 13 December 2005 13
2.5 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 trackermuon trigger and tracking
magnetic field
or
!
Measuring dimuons in NA60: concept
S. Damjanovic, Bielefeld 13 December 2005 14
Data Analysis
S. Damjanovic, Bielefeld 13 December 2005 15
5-week long run in Oct.–Nov. 2003
Indium beam of 158 GeV/nucleon ~ 4 × 1012 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 2005 16
Selection of primary vertex
Beam Trackersensors
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 2005 17
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 2005 18
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 2005 19
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 2005 20
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 2005 21
Fake-match background
example from overlay MC: the fake-match contribution localized in mass (and pT) 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 2005 22
Subtraction of combinatorial background and fakes
For the first time, and peaks clearly visible in dilepton channel ; even μμ seen
Net data sample: 360 000 events
Mass resolution:23 MeV at the position
Fakes / CB < 10 %
Progress over CERES: statistics: factor >1000resolution: factor 2-3
S. Damjanovic, Bielefeld 13 December 2005 23
Track multiplicity from VT tracks for triggered dimuons for
Centrality bin multiplicity ⟨dNch/dη⟩3.8
Peripheral 4–28 17
Semi-Peripheral
28–92 63
Semi-Central 92–160 133
Central > 160 193
Associated track multiplicity distribution
4 multiplicity windows:
opposite-sign pairs combinatorial background signal pairs
S. Damjanovic, Bielefeld 13 December 2005 24
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 2005 25
Phase space coverage in mass-pT 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 pT
MC
S. Damjanovic, Bielefeld 13 December 2005 26
Phase space coverage in y-pT plane
Examples from MC simulations
Optimal acceptance:
at high mass, high pT
<y> = 3.5
at low mass, low pT
<y> = 3.8
Shift of acceptance away from midrapidity not much different from CERES
S. Damjanovic, Bielefeld 13 December 2005 27
Results
S. Damjanovic, Bielefeld 13 December 2005 28
Understanding the Peripheral data
Fit hadron decay cocktail and DD to the data
5 free parameters to be fit:
DD, overall normalization
(0.12fixed)
Fit range: up to 1.4 GeV
S. Damjanovic, Bielefeld 13 December 2005 29
Comparison of hadron decay cocktail to data
all pT
Very good fit quality
log
S. Damjanovic, Bielefeld 13 December 2005 30
The region (small M, small pT)
is remarkably well described
Comparison of hadron decay cocktail to data
→ the (lower) acceptance of NA60
in this region is well under control
pT < 0.5 GeV
S. Damjanovic, Bielefeld 13 December 2005 31
Comparison of hadron decay cocktail to data
Again good agreement
between cocktail and data
0.5 < pT < 1 GeV
pT > 1 GeV
S. Damjanovic, Bielefeld 13 December 2005 32
Particle ratios from the cocktail fits
and nearly
independent of pT; 10% variation due to the
increase of at low pT (due to ππ annihilation, see later)General conclusion:
peripheral bin very well described in terms of known sources low M and low pT acceptance of NA60 under control
S. Damjanovic, Bielefeld 13 December 2005 33
Isolation of an excess in the more central data
S. Damjanovic, Bielefeld 13 December 2005 34
Understanding the cocktailfor 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 pT data, but not yet used
Goal of the present analysis:
Find excess above cocktail (if it exists) without fits
S. Damjanovic, Bielefeld 13 December 2005 35
Conservative approach
Use particle yields so as to set a lower limit to a possible excess
S. Damjanovic, Bielefeld 13 December 2005 36
● data
-- sum of cocktail sources
including the
Cocktail definition: see next slide
all pT
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 2005 37
Isolate possible excess by subtractingcocktail (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 2005 38
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 2005 39
Excess spectra from difference: data - cocktail
all pT
Clear excess above the cocktail , centered at the nominal pole and rising with centrality
Similar behaviour in the other pT bins
No cocktail and no DD subtracted
S. Damjanovic, Bielefeld 13 December 2005 40
Excess spectra from difference data-cocktail
No cocktail and no DD subtracted
pT < 0.5 GeV
Clear excess above the cocktail , centered at the nominal pole and rising with centrality
Similar behaviour in the other pT bins
S. Damjanovic, Bielefeld 13 December 2005 41
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 2005 42
Comparison of excess
to model predictions
S. Damjanovic, Bielefeld 13 December 2005 43
*(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 2005 44
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)
functionspectralTMMfdMdN )/exp()(/
S. Damjanovic, Bielefeld 13 December 2005 45
spectral function in vacuum
vacuum spectral function
2
21 g)(gintL
Introduce as gauge boson into free + Lagrangian
1)0(2)0(2)0( )]()([)( MmMMD
is dressed with free pions
(like ALEPH data V(→ 2
S. Damjanovic, Bielefeld 13 December 2005 46
spectral function in hot and dense hadronic matter (I)
Dropping mass scenario Brown/Rho et al., Hatsuda/Lee
universal scaling law
))/(1)(1( 2
0
2/10
2/1, cT TTCqqqq
2/10
2/1,
0* / qqqqmm T
explicit connection between hadron masses and chiral condensate
continuous evolution of pole mass with T and broadening atfixedignored
S. Damjanovic, Bielefeld 13 December 2005 47
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)=[M2-m2--B-M ]-1
B /0 0 0.1 0.7 2.6
hot and baryon-rich matter hot matter
is dressed with:
hot pions baryons(N,..) mesons (K,a1..)
“melts” in hot and dense matter
- pole position roughly unchanged - broadening mostly through baryon interactions
S. Damjanovic, Bielefeld 13 December 2005 48
Final mass spectrum
),;,()(44
0
3
0
i
therm
FB
therm
TqMqxdd
dN
q
qMdVd
dM
dN fo
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 /0 0 0.1 0.7 2.6
S. Damjanovic, Bielefeld 13 December 2005 49
How to compare data to predictions?
1) correct data for acceptance in 3-dim. space M-pT-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
dydMdp
Nd
T2
*3
S. Damjanovic, Bielefeld 13 December 2005 50
Acceptance filtering of theoretical prediction
all pT
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 2005 51
Output:
white spectrum !
Understanding the spectral shape at the output
By pure chance, for all pT and the slope of the pT spectra of the direct radiation, the NA60 acceptance roughly compensates for the phase-space factors and directly “measures” the <spectral function>
Input:
thermal radiation based on white spectral function
all pT functionspectralTMMfdMdN )/exp()(/
S. Damjanovic, Bielefeld 13 December 2005 52
Predictions for In-In by Rapp et al (2003) for ⟨dNch/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 2005 53
Comparison of data to RW, BR and Vacuum
pT dependence same conclusions
S. Damjanovic, Bielefeld 13 December 2005 54
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 2005 55
Predictions for In-In by Rapp et al. (11/2005) for ⟨dNch/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
)0,(
),(
2
1)1( 00*
cAVV T
T
Use 4, 6 … and 3, 5… (+1) processes from ALEPH data, mix them, time-reverse them and get +- yields
S. Damjanovic, Bielefeld 13 December 2005 56
Predictions for In-In by Rapp et al. (11/2005) for ⟨dNch/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 2005 57
Comparison of data to RR
D(M,q;T)=[M2-m2- ]-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 2005 58
Next steps of the analysis
• complete acceptance correction of the data in 3-dim. space M-pT-y
• determination of the (averaged) spectral functions in narrow bins of pT , 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 2005 59
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 2005 60
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 2005 61
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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,
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The NA60 experiment