Transcript Slide 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
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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
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Motivation
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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
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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
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Many different theoretical approaches including
Lattice QCD still very much under development
cL
Lattice QCD
cm
‹qq›
(for mB=0 and
quenched approx.)
L
1.0
T/Tc
deconfinement
transition
1.0
T/Tc
chiral symmetry
restoration
two phase
transitions at the
same critical
temperature Tc
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> ?
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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]
 (770)
(782)
(1020)
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/c
2. continuous “regeneration” by 
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Low-mass dileptons + chiral symmetry
ALEPH data: Vacuum
At Tc: Chiral Restoration
• How is the degeneration of chiral partners realized ?
• In nuclear collisions, measure vectorm+m-, but axial vector?
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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
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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 
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Experimental set-up
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Standard way of measuring dimuons
muon trigger and tracking
magnetic field
target
beam
hadron absorber
Energy loss
Multiple scattering
Muon
Other
• Degraded dimuon mass resolution
• Cannot distinguish prompt dimuons from decay muons
or
?
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Measuring dimuons in NA60: concept
2.5 T dipole magnet
vertex tracker
magnetic field
beam
tracker
muon trigger and tracking
targets
hadron absorber
Matching in coordinate
and momentum space
• Origin of muons can be accurately determined
• Improved dimuon mass resolution
or
!
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Data Analysis
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Event sample: Indium-Indium
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
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Selection of primary vertex
The interaction vertex is identified
with better than 20 mm accuracy in
the transverse plane and 200 mm
along the beam axis.
(note the log scale)
Beam Tracker
sensors
windows
Present analysis (very conservative):
Select events with only one vertex in the target region,
i.e. eliminate all events with secondary interactions
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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
(c2) in slopes and inverse momenta. For each candidate a global fit
through the MS and VT is performed, to improve kinematics.
A certain fraction of muons is
matched to closest non-muon
tracks (fakes). Only events with
c2 < 3 are selected.
Fake matches are subtracted by
a mixed-events technique (CB)
and an overlay MC method (only
for signal pairs, see below)
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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
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Combinatorial Background from ,K→m decays
Agreement of data and mixed CB over several orders of magnitude
Accuracy of agreement ~1%
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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
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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%
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complete fake-match mass spectrum
agreement between overlay MC and
event mixing, in absolute level and in
shape, to within <5%
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Subtraction of combinatorial background and fakes
Net data sample:
360 000 events
Fakes / CB < 10 %



For the first time,  and 
peaks clearly visible in
dilepton channel ; even
μμ seen
Mass resolution:
23 MeV at the  position
Progress over CERES:
statistics: factor >1000
resolution: factor 2-3
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Associated track multiplicity distribution
Track multiplicity from VT tracks
for triggered dimuons for
opposite-sign pairs
combinatorial background
signal pairs
4 multiplicity windows:
Centrality bin
Peripheral
Semi-Peripheral
Semi-Central
Central
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multiplicity
〈dNch/dη〉3.8
4–28
17
28–92
63
92–160
133
> 160
193
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Signal and background in 4 multiplicity windows
S/B
2
1/3
1/8
1/11
Decrease of S/B with
centrality, as expected
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Phase space coverage in mass-pT plane
Final data after subtraction of
combinatorial background and
fake matches
MC
The acceptance of NA60 extends
(in contrast to NA38/50) all the way
down to small mass and small pT
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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
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Results
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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
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Comparison of hadron decay cocktail to data
all pT
log
Very good fit quality
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Comparison of hadron decay cocktail to data
pT < 0.5 GeV
The  region (small M, small pT)
is remarkably well described
→ the (lower) acceptance of NA60
in this region is well under control
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Comparison of hadron decay cocktail to data
0.5 < pT < 1 GeV
pT > 1 GeV
Again good agreement
between cocktail and data
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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
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Isolation of an excess
in the more central data
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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 pT data, but not yet used
Goal of the present analysis:
Find excess above cocktail (if it exists) without fits
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Conservative approach
Use particle yields so as to set a
lower limit to a possible excess
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Comparison of data to “conservative” cocktail
all pT
Cocktail definition:
see next slide
/ fixed to 1.2
●
data
-- sum of cocktail sources
including the 
Clear excess of data
above cocktail, rising
with centrality
But: how to recognize
the spectral shape
of the excess?
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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
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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.
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Excess spectra from difference: data - cocktail
all pT
No cocktail 
and no DD
subtracted
Clear excess above
the cocktail ,
centered at the
nominal  pole and
rising with centrality
Similar behaviour in
the other pT bins
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Excess spectra from difference data-cocktail
pT < 0.5 GeV
No cocktail 
and no DD
subtracted
Clear excess above
the cocktail ,
centered at the
nominal  pole and
rising with centrality
Similar behaviour in
the other pT bins
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Systematics
Illustration of sensitivity
 to correct subtraction of
combinatorial background
and fake matches;
 to variation of the  yield
Systematic errors of
continuum 0.4<M<0.6 and
0.8<M<1GeV 25%
Structure in  region
completely robust
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Comparison of excess
to model predictions
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Dilepton Rate in a strongly interacting medium
g*(q)
(T,mB)
dileptons produced by annihilation
of thermally excited particles:
μ+
μ-
+- in hadronic phase
qq in QGP phase
at SPS energies
+  - →*→μ+μdominant
hadron basis
photon selfenergy
spectral function
Vector-Dominance Model
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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
dN mm / dM  f ( M )  exp( M / T )   spectral function
Limitation:
Continuously varying values of temperature T and baryon
density B, (some control via multiplicity dependences)
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 spectral function in vacuum
Introduce  as gauge boson into free  + Lagrangian 
int
L

m  
2
1
= g m  (     )  g m     
2



m

 is dressed with free pions
vacuum spectral function
(like ALEPH data V(t→ 2nt ))
D (M ) = [M  (m )    (M )] 1
( 0)
2
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( 0) 2
( 0)
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 spectral function in hot and dense hadronic matter (I)
Dropping mass scenario
Brown/Rho et al., Hatsuda/Lee
explicit connection between hadron masses and chiral condensate
universal scaling law
 q q1/,2T  q q10/ 2 = (1  C
m* / m0 = q q1/,2T q q10/ 2

)(1  (T / Tcc ) 2 )
0
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continuous evolution of pole mass with T
and  ; broadening at fixed T, ignored
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 spectral function in hot and dense hadronic matter (II)
Hadronic many-body approach
hot matter
Rapp/Wambach et al., Weise et al.
hot and baryon-rich matter
B /0
0
0.1
0.7
2.6
D (M,q;mB,T)=[M2-m2- - B- M ]-1
 is dressed with:
hot pions  ,
baryons
 B (N,D ..)
mesons
 M (K,a1..)
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 “melts” in hot and dense matter
- pole position roughly unchanged
- broadening mostly through baryon interactions
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Final mass spectrum
continuous emission of thermal radiation
during life time of expanding fireball
therm
dN mm
dM
t fo
integration of rate equation over
space-time and momenta required
therm
dN
Md q
mm
=  dt VFB (t ) 
( M , q; T , mi )
4
4
q0 d xd q
t0
3
example: broadening scenario
B /0
0
0.1
0.7
2.6
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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
d 3 Ng *
dMdpT2 dy
decay the virtual photons g* into m+m- 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
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Acceptance filtering of theoretical prediction
all pT
Input (example):
thermal radiation
based on RW
spectral function
Output: spectral shape much distorted relative to
input, but somehow reminiscent of the spectral
function underlying the input; by chance?
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Understanding the spectral shape at the output
dN mm / dM  f ( M )  exp( M / T )   spectral function
all pT
Input:
thermal radiation
based on white
spectral function
Output:
white spectrum !
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>
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Comparison of data to RW, BR and Vacuum 
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)
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Comparison of data to RW, BR and Vacuum 
pT dependence
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same conclusions
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Controversy of Brown/Rho vs Rapp/Wambach
Could Brown/Rho scaling be saved by
• “fusion” of the two scenarios ?
• by change of the fireball parameters ?
Results of Rapp (8/2005):
(not propagated through
acceptance filter)
Neither fusion nor
parameter change
able to make BR
scaling unobservable
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Comparison of data to RW(2+4+QGP)
Predictions for In-In by Rapp et al. (11/2005) for 〈dNch/d〉 = 140
Vector-Axialvector Mixing: interaction with real ’s (Goldstone bosons).
Use only 4 and higher parts of the correlator PV in addition to 2
PV = (1   )  PV    P A
*
0
0
1  (T , m )
=
2  (Tc , m = 0)
Use
4, 6 …
and
3, 5… (+1) processes
from ALEPH data, mix them, time-reverse them and get m+m- yields
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Comparison of data to RW(2+4+QGP)
Predictions for In-In by Rapp et al. (11/2005) for 〈dNch/d〉 = 140
Now whole spectrum
reasonably well described,
even in absolute terms
(resulting from improved
fireball dynamics)
direct connection to IMR
results >1 GeV from NA60
The yield above 0.9 GeV
is sensitive to the degree
of vector-axialvector mixing
and therefore to chiral
symmetry restoration!
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Comparison of data to RR
Ruppert / Renk,
Phys.Rev.C (2005)
Spectral function only based
on hot pions, no baryon
interactions included (shape
similar RW)
D (M,q;T)=[M2-m2-  ]-1
broadening described
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continuum contributions, in
the spirit of quark-hadron
duality, also added (fills high
mass region analogous to
NA50 IMR description)
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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
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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 
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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
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The NA60 experiment
CERN
Heidelberg
~ 60 people
13 institutes
8 countries
Bern
Palaiseau
BNL
http://cern.ch/na60
Riken
Yerevan
Stony Brook
Torino
Lisbon
Clermont
Lyon
Cagliari
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
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