First measurement of the spectral function in high-energy nuclear collisions

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


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


Motivation


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


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


‹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> ?


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


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


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


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


Experimental set-up


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

?


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


Data Analysis


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


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


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.


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


Combinatorial Background from ,K→ decays

Agreement of data and mixed CB over several orders of magnitude

Accuracy of agreement ~1%


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


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%


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


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


Signal and background in 4 multiplicity windows

S/B

2 1/3

1/8 1/11

Decrease of S/B with centrality, as expected


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


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


Results


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


Comparison of hadron decay cocktail to data

all pT

Very good fit quality

log


The region (small M, small pT)

is remarkably well described


→ the (lower) acceptance of NA60

in this region is well under control

pT < 0.5 GeV



Again good agreement

between cocktail and data

0.5 < pT < 1 GeV

pT > 1 GeV


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


Isolation of an excess in the more central data


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


Conservative approach

Use particle yields so as to set a lower limit to a possible excess


● 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?


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


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.


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


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


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


Comparison of excess

to model predictions


*(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


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()(/


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


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


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


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


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


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


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()(/


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


Comparison of data to RW, BR and Vacuum

pT dependence same conclusions


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


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


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


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


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


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


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


http://cern.ch/na60

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~ 60 people13 institutes8 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

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First measurement of the spectral function in high-energy nuclear collisions