low and intermediate mass dimuons in na60

1

Low and intermediate mass dimuons in NA60

G. Usai – INFN and University of Cagliari (Italy)

2

spontaneous chiral symmetry breaking <qq> ≠ 0

General question of QCD

Origin of the masses of light hadrons?

mGGDiL aa

QCD 4

1 MeV50, dum

Expectation: approximate chiral SU(nf)L x SU(nf)R symmetry chiral doublets, degenerate in mass, with

MeV2010 hadronM

However, we observe

GeV 2.1GeV 77.0

GeV 1

1

a

N

MM

M

3

‹qq›-

1.0 T/Tc

mL

L

1.0 T/Tc

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> ?

Several theoretical approaches including lattice QCD still in development

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

4

tot [MeV]

(770) 150 (1.3fm/c)

8.6 (23fm/c)

4.4 (44fm/c)

In-medium radiation dominated by the :

1. life time =1.3 fm/c << collision > 10 fm/c2. continuous “regeneration” by

main difficulty:

Properties of in hot and dense matter unknown (related to the mechanism of mass generation)

Properties of hot and dense medium unknow (general goal of studying nuclear collisions)

Why focus (mainly) on the ?

5

MuonOther

hadron absorber

muon trigger and tracking

target

beam

magnetic field

Standard dimuon detection: NA50, PHENIX, ALICE, …

Thick hadron absorber to reject hadronic background

Trigger system based on fast detectors to select muon candidates (1 in 10-4 PbPb collisions at SPS energy)

Muon tracks reconstructed by a spectrometer (tracking detectors+magnetic field)

Extrapolate muon tracks back to the target taking into account multiple scattering and energy loss, but … - poor reconstruction of interaction vertex (z 10 cm)

- poor mass resolution (80 MeV at the )

6

2.5 T dipole magnet

hadron absorber

• Origin of muons can be accurately determined• Improved dimuon mass resolution

targets

beam tracker

vertex trackermuon trigger and tracking

magnetic field

MuonOther

or!

Measuring dimuons in heavy ion collisions – the NA60 case

Matching of muon tracks

7

DIPOLE MAGNET2.5 T

HADRON ABSORBER

TARGETS

~40 cm

1 cm

12 tracking points with good acceptance8 “small” 4-chip planes, plus8 “big” 8-chip planes (4 tracking stations)

~ 3% X0 per plane750 µm Si read-out chip300 µm Si sensorceramic hybrid

800’000 R/O channels - 96 pixel assemblies

The NA60 pixel vertex detector

8

Resolution ~ 10 - 20 m in the transverse plane

Beam Trackersensors

windows

z ~ 200 m along the beam directionGood vertex identification with 4 tracks

X

Y

Extremely clean target identification (Log scale!)

Vertexing

9

The dimuon invariant mass resolution has two components

Multiple scattering in the hadron absorber dominates the resolution for low momentum muons

The variance ϑs of the angle distribution is proportional to 1/p

At high momenta the resolution is dominated by the tracking accuracy (p/p proportional to p)

Contributions to dimuon mass resolution

rad

2ms

/MeV15

X

d

p

c

at m ~ 3 GeV the resolution is

dominated by this componentTrack matching not so important

at m ~ 1 GeV track matching

is very effective to increase the momentum resolution

10

The muon spectrometer and the pixel telescope determine the track parameters in two reference planes z1 and z2.

A choice of the track parameters at each plane is

Muon track matching

1211

12)1(

2

/ ,'

)(

ppDDDCC

pppT

rr

r

rr

r

rr

rrrr

Pp

dz

dyp

dz

dxp

ypxp

1

,,

,

,5

,4,3

,2,1

p1,r and its covariance matrix are propagated to z2

Muon spectrometer Pixel telescope

1p )1(

2p

2p

1z 2z

Absorber

Measured points Measured points

11

joint least square ansatz

Contributions to multiple scattering between z1 and z2 are added to C’1

muon spectrometer surface z1

hadron absorber

muon spectrometer track parameters propagated to pixel telescope surface

pixel telescope surface z2

weigthed mean

muon spectrometer track parameters with errors

pixel telescope track parameters with errors

21

2)1(

21)1(

2

112

1)1(2,2 pCpCCCp fit

M(p2,fit) distributed as a 2 with 5 dof)()(

)()()()1(

2,21)1(

2)1(

2,2

2,21

22,2,2

ppCpp

ppCpppM

fitT

fit

fitT

fitfit

12

M(p2,fit) distributed as a 2 with 5 degrees of freedom

The pixel telescope improves drastically the angular resolution:

~10 mrad (muon spectrometer only) ~1 mrad (adding pixel telescope)

The momentum resolution is comparable in the two detectors. However, the use of the momentum information in a high multiplicity environment is fundamental to achieve the matching

the pixel telescope must be a spectrometer

13

6500 A

4000 A

dN

/dM

(

Eve

nt s

/ 50

MeV

)

(80% of collected statistics)

• Opposite-sign dimuon mass distributions before quality cuts• No muon track matching(two magnet settings)

(100% of collected statistics)

Improvement in mass resolution

Vertex selection andmuon track matching

M() 80 MeV

M(J/) 100 MeV

M() 20 MeV

(1020)

(1020)

Drastic improvement in mass resolution: Narrow vector mesons clearly resolved

But still sitting on a large unphysical background

M(J/) 70 MeV

14

Problems with the matching: fake matchesFake match: muon matched to a wrong track in the vertex telescope

Can be important in high multiplicity events (negligible in pA or peripheral AA)

hadron absorber

muon trigger and tracking

targetfake

correctHadron absorber

Muon spectrometer

Simple technique: the match with the smallest 2 is retained. But is it correct or fake?

Fake matches can be studied and subtracted using an overlay Monte Carlo:

- Monte Carlo muons are superimposed to real events (in the vertex telescope)

- Reconstructed as real events, fake matches can be tagged and the fraction relative ....to correct matched muons is then evaluated

15

The Monte Carlo provides also the kinematic distribution (mass, pT, ...) of the fake matches

Here is the example for the meson

The fake-match contribution appears localized in mass (and pT) space as a broad peak

correct matches: = 23 MeV

wrong matches: fake = 110 MeV

16

Background sources (dimuons)Main source of background: (uncorrelated) decays of and K

the hadron absorber should be as close as possible to the interaction point

If we have N pions, the average number which decays within 1m is ~10-3N

!

),( er

rPr

PPAN

PAeAPAN

PAeAPAN

22

22

2

1

2

1),2(

2

1

2

1),2(

ePP

ePP

),1(

),1(

number of detected muon pairs is

A++ (A--) acceptance for a like sign muon pair

A+- acceptance for a opposite sign muon pair

We have the probabilities ( )

AA

ANNN 2

17

NNN 2

In NA50 acceptance was independent of charge

In NA60 acceptance is different for + and – Cuts to equalize it (“image” cut in NA50) impossible

Event Mixing:

Define a pool of + and - tracks out of a sample of like sign events (++ and --) .

Pick + and - from these like sign pools corresponding to different events.

The + and - are picked in a fraction which reflects the probabilities to detect them in the experimental apparatus

NN

NP

NN

NP ,

Combine them to form artificial pairs of all sign combinations.

If N++(mixed) and N--(mixed) reproduce the corresponding data samples N++ and N--, then N+-(mixed) should give the combinatiorial background of the +- sample.

18

Estimated estimated through the comparison of N++/--(mixed) to N++/--(real)

In NA60 the accuracy is ~1% all over the dimuon mass range. Is that good or bad? It depends on the signal to background ratio ...

Accuracy of background subtraction

19

The signal to background ratio depends on the matching 2 cut.

Tight cut: more precise matching – helps to reject tracks not precisely connected to primary vertex

1%

The worst case happens in the continuum region around the where the bkg/signal can reach ~25 in the most central collisions

signal/signal ~ 25% in low mass continuum region at most

In more peripheral collisions signal/signal is much better

signal

bkg

bkgsignalbkgsignal

20

The quest of the correct background normalization

CLAS experiment: photoproduction of vector mesons off nuclei

e+e- combinatorial background determined by event mixing

Background normalization found directly from fit: best fit prefers meson with mass shift (in medium effect)

Background normalization following prescription for P+ P-: best fit prefers meson with no in medium effect

21

The final mass spectra (m<2GeV/c2)

• Fakes/CB < 10 %

Red distribution: final spectrum after getting rid of fake and combinatorial background.

The net data sample consists of 420000 events! ( 50% of total statistics)

For the first time and peaks are clearly visible in dilepton channel (23 MeV/c2 mass resolution at the

is also visible

22

Phase phase coverage (mass-pT)

The dimuon kinematics can be specified by (m,y,pT,cosϑ)

The probability that a dimuon with certain kinematic values is detected depends on:

Thickness of the muon filter, position of the target relative to the detecting elements, magnetic fields (both in the muon spectrometer and in the vertex telescope), ...

Drop with no vertex magnet

The dipole magnetic field in the vertex region improves significantly the acceptance for low mass and low pT

opposite sign dimuons

without field

A(%

)

with 2.5 T field

A(%

)

Monte-Carlo

0.20<M<0.45

0.45<M<0.70

NA60

NA38

0.45<M<0.70

23

Phase phase coverage (y-pT)

A fixed target experiment usually covers the forward rapidity emisphere.

NA60 (and its predecessors) are optimized to cover the range 3-4 in the lab system (the target rapidity is zero, the beam rapidity is 6) corresponding to 0-1 in the CMS system

Example of phase space coverage for a few processes (Monte Carlo)

Dimuon rapidity coverage in the lab frame:• roughly between 3.3 and 4.3 for low masses• between 3 and 4 for the J/ dimuons

(mid rapidity is at 2.9)

24

Track multiplicity of charged tracks for triggered dimuons for

Centrality bin multiplicity <dNch/dη>3.8

Peripheral 4–28 17

SemiPeripheral 28–92 63

Semi-Central 92–160 133

Central > 160 193

4 multiplicity windows:

opposite-sign pairs combinatorial background signal pairs

Measuring the collision centralityThe collision centrality can be measured via the charged particle multiplicity as measured by the pixel vertex telescope

25

Which processes populate the dimuon mass spectrum below 1 GeV?

26

Dalitz decay:

(q2)

(k)

- p2

+ p1

(q2)

(q2)

(k)

- p2

+ p1

)(

)()(61)(

220

2

20

220

2

2

22

*

qmq

m

qmq

q

qdg

egqF VVP

Anomaly in the form-factor: VMD predicts a (significantly) smaller value

Vector meson dominance:

27

Dalitz decay:

)()(

681)(

220

2

2

2

22

* qmq

q

qeg

dqF

Vector meson dominance

Previous data (Landsberg et al.) fitted with a pole formula:

2222* /)( qqF

Dalitz form factor

22*

3

2

2

2

22/1

2

2

22)(1

21

41

3

2qF

m

q

q

m

q

m

qdq

d

,(q2)

(k)

- p2

+ p1

(q2)

(q2)

(k)

- p2

+ p1

28

• ω and : fix yields such as to get, after subtraction, a smooth underlying 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

Isolate possible excess by subtracting cocktail (without ) from the data

How to fit in the presence of an unknown source?

Try to find excess above cocktail (if it exists) without fit constraints

29

• Clear excess above the cocktail , centered at the nominal pole and rising with centrality

• Excess even more pronounced at low pT

•No cocktail and no DD subtracted

data – cocktail(all pT)

cocktail / =1.2

The evolution of the excess with centrality can be studied with precision with a rather fine binning in multiplicity

Evolution of the excess shape with centrality

30

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.

Sensitivity of the difference procedure

31

The systematic errors of continuum 0.4<M<0.6 and 0.8<M<1GeV are 25% (at most) in the most central collisions

Illustration of sensitivity to correct subtraction of combinatorial background and fake matches; to variation of the yield

The structure in region looks rather robust

SystematicsThe 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.

32

Evolution of the excess shape as a function of centralityQuantify the peak and the broad symmetric continuum with a mass interval C around the peak (0.64 <M<0.84 GeV) and two equal side bins L, U

peak/

continuum/

peak/continuum

continuum = 3/2(L+U) peak = C-1/2(L+U)

Peak/cocktail drops by a factor 2 from peripheral to central:

the peak seen is not the cocktail

nontrivial changes of all three variables at dNch/dy>100 ?

Fine analysis in 12 centrality bins

33

Free pions Lagrangian

-and electromagnetic interactions in vacuum

*2* mL

Free Lagrangian (vector meson)

2

2

1

4

1mL

self interactions are neglected

- and e.m. interactions introduced via gauge couplings

ieAigD g = g = pion- coupling constant

Direct coupling

F

g

eL

2

1

0 The couples only to conserved currents, so that

34

If g = g electromagnetic field equations

g

mJ em

2

The hadronic part of the electromagnetic current is then proportional to the meson field

2m

g

eF The meson is the only hadronic source of the

electromagnetic field

What does it mean?

Hadron matter couples to a qqbar pair which propagates as a vector meson which then materializes as a photon

All QCD complexity, gluon self interactions and confinement are incorporated in the physical vector meson which forms the intermediate state

Hadron medium

VMD

q

q

+

-

35

The free field describes a “bare” meson which we can interpret as the qqbar component of the physical meson.

The bare propagator is given by

20

20

22

0 )(

m

qqg

mq

iqD

The self-energy

+=1PI

)( 2q

However, is strong coupled to pions

the physical meson appears as a broad resonance.

properties accounted for by the second order self-energy diagrams

2int

2

1)( ggL

36

Without loss of generality

The dressed propagator

where

The full (dressed) propagator comes from an infinite sum of diagrams with self-energy insertions

)(3

1)(

),()(

22

22

2

qq

qq

qqgq

This infinite series can be easily summed ...

“polarization scalar”

1PI 1PI 1PI

)()(

220

22

qmq

igqD

The field is always coupled to conserved currents (qJ = 0) and so the terms

proportional to qq can be dropped

37

According to the optical theorem

)())()(( 2qqqM

general expression of the decay width

In this specific case the final state is (dominantly) . Thus we come to the result

2)(

2

1)(Im fMdM f

2

22 )(Im)(

q

qq

)(

1)(

2222

2

qqimqqD

mass dependent width

1PI

= scattering

The imaginary part of

)( 22 qq

38

The real part of

Determines the mass shift due to the self-energy:

0

24

42

102

)'(

')'(Im)(

iqsq

dssqqccq

00)0( 02 cq

Needed to keep the photon massless

0)(Re122

22

mq

qdq

dZ

Fixes c1

m0 can be fixed from the comparison to the

measured elastic cross section

The mass shift induced by the self-energy is small

%50

0

m

mm GeVs

I=1 P wave phase shift

♦ Frogatt and Petersen

1 [d

egre

es]

GeVm 81.00

0)(Re 220

2 mmm

Regularization. Cut-off or dispersion relations

39

vacuum spectral function

2

21 g)(gintL

1)0(2)0(2)0( )]()([)( MmMMD

is dressed with free pions

(like ALEPH data V(→ 2

40

*(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

41

Study the properties of the spectral function Im Din a hot and dense medium

Physics objective in heavy ion collisions

42

Hadronic many-body approach Rapp/Wambach et al., Weise et al.

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

spectral function in hot and dense hadronic matter

1222 ),;(

MBB mqTqD

43

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

44

),;,()(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

Final mass spectrum

45

Thus, the spectral function accessible through rate equation, integrated over space-time and momenta

Limitation:Continuously varying values of temperature T and baryon density B,

functionspectralTMMfdMdN )/exp()(/

46

dydMdp

Nd

T2

*3

Comparison of predictions to data

Two possibilities, in principle:

1) Use the prediction for

Generate Monte Carlo events of * decays into muon pairs

Propagate through the acceptance filter and compare to uncorrected data

Done presently for invariant mass (work in progress for acceptance correction)

2) Correct the data for acceptance in 3-dim space M-pT-y and compare them directly to predictions

Done for pT distributions

47

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

Acceptance filtering of theoretical prediction in NA60

B /0 0 0.1 0.7 2.6

all pT

48

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

Only broadening of (RW) observed, no mass shift (BR)

Rapp-Wambach: hadronic model predicting strong broadening/no mass shift

Brown/Rho scaling: dropping mass due to dropping of chiral condensate

After acceptance filtering, data and predictions display spectral functions, averaged over space-time and momenta

Comparison to the main models that appeared in the 90s

49

Without baryons:• Not enough broadening• Lack of strength below the peak

Improved model:• Fireball dynamics• 4 processes• spectrum described in absolute terms

Comparison to the main models that appeared in the 90s

50

Something is missing at high pT. What?

Semicentral collisions: low vs high pT

Rapp-Hees Rapp-Hees

51

The vacuum (and other) contributions

At high pT there is an important

contribution from the “vacuum ”:

decays at kinetic freeze-out

Additional contribution:

Primordial (Rapp-Hees)

Rapp-Hees

Ruppert-Renk

52

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 a1+-.

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

The mass region above 1 GeV: vector-axial vector mixingAbove 1 GeV we can have contributions from 4processes. The spectral shape can be found for instance from e+e-4 or studying (ALEPH) (2n)ν

3, 5…2, 4, 6 …

53

Mass region above 1 GeV described dominantly in terms of hadronic processes, 4 …

Hadron-parton duality

The mass region above 1 GeV: models vs data

Rapp/Hees Ruppert / Renk, Phys.Rev.C (2005)

Mass region above 1 GeV described dominantly in terms of partonic processes, dominated by qqbar annihilation

54

(e+e-→hadrons) in vacuum

)s(Im em)s(DIm

gm

V,, V

V

22

s,d,u

Sqc

)s()e(N

s

1

122

e+

e-

h1

h2…

s ≥ sdual~(1.5GeV)2 :

pQCD continuum

s < sdual :

Vector-Meson Dominance

q

q_

qq_

24

KK

e+

e-

55

Disentangling the signal sources in the IMR

The dileptons from charm decay can be identified by tagging their production point with respect to the primary interaction vertex

•Identify the typical offset of D-meson decay (~100 µm)

•Need a very good vertexing accuracy (~20-30 µm, in the transverse plane)

D0

K-

+

e

D0

100m

56

Offsets:δX, δY between the vertex and the track impact point in the transverse plane at Zvertex

Resolution depends on track momentum:

use offset weighted by the covariance matrices of the vertex and of the muon track:

Measuring the muon offset

For dimuons

2/)2( 11212

xyyyxx VyxVyVx

2/)( 22

21

57

dN/d

Δ

Procedure: Fix the prompt contribution to the expected DY yield and see if the offset distribution can be described with enhanced Charm

Answer: No, Charm can’t fill the small offset region…

more prompts are needed

New alignment

Is the excess enhanced charm?

58

Procedure: Leave both contributions free and see if we can describe the offset distribution for 1.2 < Mµµ < 2.7

Answer: The best fit requires 2.6 times more prompts than the expected Drell-Yan yield

dN/d

Δ

New alignment

How many prompts are needed?

59

Transverse momentum spectra

60

Spectra from a static fireball

In a static fireball at temperature T the differential particle momentum distribution is

)(3

Efpd

dNE

Lorentz invariant phase space element

dyddppE

pdTT

3

Assume a thermal Boltzmann shape

ymT

E TyeCmCEeEf coshcosh)(

transverse mass spectra (integrated over rapidity)

Tm

TT

Tedmm

dN / mT scaling: all particle spectra have the same T “slope”

61

An expanding fireball

Thermalized matter starts to expand because of the pressure gradient with respect to the surrounding vacuum.

A collective motion (flow) develops.

Flow velocity of a volume element of thermalized matter in a spacetime point x

0

0 ,

P

P

EPpP ii

Sum all the particles 3-momenta and energies

The ratio gives the collective velocity

for completely random thermal motions 0

62

Fluid 4-velocity

= radial flow field

))(),(,1)(()( xxxxu LT

z

xy

Tv

T

Superimposed tranverse expansion Superimposed tranverse expansion

)(1

1)(

2 xx

Bjorken scalingBjorken scaling: At very high energies the physics of : At very high energies the physics of secondary particle production should be the same as secondary particle production should be the same as described in different frames moving along the z axis. described in different frames moving along the z axis.

t

zL longitudinal flow field

transverse flow

63

-

+

Excess dimuons: continuum emission during all the fireball lifetime (4-dim volume) – we see not only the emission at freeze-out!

Since the is strongly coupled to the pions,the thermal pT is boosted by flow in the lab frame

In fluid local rest framethermal pT

Dimuon emission

64

Example of hydrodynamic evolution (specific for In-In – Dusling et al.)

vT =

0.1

vT =

0.2 vT

= 0

.3

v T =

0.4

v T =

0.5

Monotonic decrease of T from: early times to late timesmedium center to edge

Monotonic increase of vT from: early times to late timesmedium center to edge

emission of dileptons sensing- Large T and small vT at early times- Large VT and small T at later time

T– vT anticorrelation

Potentially could permits to distinguish between hadronic and partonic nature

65

Dilepton transverse momentum spectra

Obtained integrating dR/dq4 over fireball space-time history xqdd

dNxd

qd

dN44

44

Superposition of spectra at different T weighted by

- Thermal factor exp(-E/T) (pu = dilepton energy in local fluid rest frame)

- Invariant mass shape of spectral function- Volume increase

In addition, resonance decays determine an overpopulation of pions Non zero chemical potential (T)

Fugacity exp((T)/T)

Trdddxd24

00

q

MdMdq

dyddqqq

qdTT

0

3

max

0 0 44

2

02

r

TT xddq

dNdrdrdddy

dqMdMq

dN f

),,,,(Im/))((

3244xTqMe

Mxqdd

dNBem

TTup

66

Hadron pT spectra

When the temperature of a fluid element drops below a certain value Tf , the mean free path exceeds the dimesions of the system

Thermal equilibrium is broken and particles stream out free to the detectors

The isotherm T(r,t)=Tf defines a 3-dim hypersurface in the space-time last-scattering surface

Total number of particles crossing Total number of particles crossing sum over d sum over d33

3

3

)(

dj

j

d

x 3-dim hypersurface divide in infinitesimal elements d3

outward-pointing 4-vector perpendicular to (x)

number of particles passing through d3

E

pdppxfddjN ii

3

3),(

)2(

1

current of particles through x

j

67

Transverse flow-field

T

pI

T

mKrdrm

dmdym

dN TR

TT

TT

i sinh

cosh 00 1

Integrated over Integrated over y

R

rvr fT )(tanh)( ,

1

Once the mass is fixed (the particle is specified), the function has only three parameters: vT, Tf and a normalization

With some mathematics one can show thatWith some mathematics one can show that

Cooper-Frye formula

3

33),(

)2(

1dppxf

ddpdyp

dN

pd

dNE i

TT

ii

68

Common flow velocity in ,K,p and their anti-particles is seen at SPS and AGS energies

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 velocities are seen also in RHIC Au-Au data (PHENIX and STAR)

69

1 contours n=1

NA57NA57 158 GeV 158 GeV

Centrality classes:Centrality classes:

0 0 40 to 53 % most central 40 to 53 % most central

1 1 23 to 40 % most central 23 to 40 % most central

2 2 11 to 23 % most central 11 to 23 % most central

3 3 4.5 to 11 % most central 4.5 to 11 % most central

4 4 4.5 % most central 4.5 % most central

Tf – vT,f anticorrelation as a function of centrality

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

Extracted with a two parameter fit to experimental distributions: Evaluate 2 for fixed vT and Tf Create a 2 map as a function of vT and Tf

Tf and vT,f are strongly anticorrelated

70

Stable hadrons reflect the kinetic freeze-out conditions.

Fitting with 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:

iTT

Tfslope mp

v

vTT

1

1

At low pT, the pT spectra appear flattened and mT scaling is broken. The T slope becomes mass dependent (mT scaling is broken)

iTTifslopei mpvmTT 2

1 2

,In principle allows to separate the thermal from the collective motion

Effect of radial flow on hadron pT spectra

71

158 AGeV Central collisions

Pb-Pb

In-In

Si-Si

C-C

pp

2

, Tifslopei vmTT

Notice that for mi 0 we should see Ti,slope Tf However, Ti,slope 170 MeV, while we know that Tf ~ 110-120 MeV for central Pb-Pb collisions the linear approximation fails for mi 0

Mass ordering of hadronic slopes

Flattening of spectra at low pT resulting in higher Teff

Pions: softening at very low pT because of resonance decays

72

pT spectra are corrected for acceptance after background and side-window subtraction

T slope extracted fitting

Peripheral

Central

transverse momentum spectra

73

158 AGeV Central collisions

Pb-Pb

In-In

Si-Si

C-C

pp

The In-In measurement of NA60follows the NA49 systematics

NA60 (pT fit range 0-2.6 GeV)

NA50 and NA49 differerences ( puzzle):Decay channel ( vs KK)pT fit range (high vs low)

NA49 (pT fit range 0-1.6 GeV) NA50 (pT fit range 1.2-2.6 GeV)

NA60 Preliminary

T slope as a function of centrality

Fit with exp(-mT/Tslope) vs centrality: increase of Tslope (indication of radial flow)

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Dimuon excess pT spectra

Divide the pT interval 0-2 GeV/c in 200 MeV bins

For each pT bin consider the mass projection and determine the excess yield with the local subtraction procedure

pT spectrum of the excess

Make this for 3 different mass windows

75

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

Strategy of acceptance correction

subtract charm from the data before acceptance correction (based on IMR results – we pospone this discussion)

76

hardly any centrality dependence integrate over centrality

(spectra arbitrarily normalized)

Dimuon excess pT spectra for three centrality bins

77

significant mass dependence (also vs. mT, see below )

possible origin:

different physics sources

radial flow

p-dependence of in-medium spectral function

(arbitrarily normalized at pT=1GeV)

Centrality integrated excess pT spectra

78

: 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 very low mT reminiscent of pions

Why?

Centrality integrated mT spectra

physics differences are better visible in mT- than in pT

79

at high pT, rho like region hardest, high-mass region softest !

differential fits to pT

spectra, assuming locally 1-parameter mT scaling and using gliding windows of pT=0.8 GeV local slope Teff

Mass dependence of pT/mT spectra

80

pT spectrum of at low pT much flatter (higher Teff)

acceptance of inbetweenthat of the twomass windows

enhanced yield at low pT not due to incorrect acceptance

Systematics: acceptance correction

81

mT spectrum of nearly pure exponential

Teff of nearly independent of fit range

Different behaviour of excess not due to incorrect acceptance

82

peripheral 1%semiperipheral 0.8% semicentral 0.6%central 0.8%

corresponding fraction of CB for the four centrality bins

Uncertainty in combinatorial bkg subtractionEstimated estimated through the comparison of N++/--(mixed) to N++/--(real)

83

enhanced yield at low-pT seen at all centralities, including the peripheral bin

estimate of errors at low pT, due to subtraction of combinatorial background: peripheral 1%semiperipheral 10% semicentral 20%central 25%

84

evolution of Teff vs m: , ,

Linear rise – the seems to flow less

Fit the spectra in the range 0.4-1.8 GeV/c

85

evolution of excess Teff vs macross the low and

intermediate mass

Linear rise also for excess quite reminiscent of radial flow of a hadronic source!

But excess Teff higher than hadron Teff. Why?

Fit the spectra in the range 0.4-1.8 GeV/c

87

evolution of excess Teff vs macross the low and

intermediate mass

Mass window 0.6-0.9:

The peak Teff gets to 300 MeV!

The continuum Teff drops to ~ 230 MeV

88

evolution of excess Teff vs macross the low and

intermediate mass

Sudden drop at ~ 1 GeV

For M>1 GeV Teff is roughly constant

Seemingly non flow?

89

evolution of excess Teff vs macross the low and

intermediate massSummary:

In the region where 2 processes are dominant (up to 1 GeV) there is strong evidence for radial flow of dileptons.

What is the explanation for the drop?

If the rise is truly due to flow:

- the lack of flow above 1 GeV could be naturally related to emission in an early stage partonic processes

- If the region above 1 GeV is dominated by hadronic sources, shouldn’t Teff keep rising? How is the drop explained in that case?