low and intermediate mass dimuons in na60
DESCRIPTION
Low and intermediate mass dimuons in NA60. G. Usai – INFN and University of Cagliari (Italy). General question of QCD. Origin of the masses of light hadrons?. spontaneous chiral symmetry breaking ≠ 0. - PowerPoint PPT PresentationTRANSCRIPT
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
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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
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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
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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
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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
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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
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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
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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
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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.
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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
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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
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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
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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
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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
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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)
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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
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• 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
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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
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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
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
)(
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
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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
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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
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pT spectra are corrected for acceptance after background and side-window subtraction
T slope extracted fitting
Peripheral
Central
transverse momentum spectra
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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
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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)
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hardly any centrality dependence integrate over centrality
(spectra arbitrarily normalized)
Dimuon excess pT spectra for three centrality bins
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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
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: 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
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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
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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
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mT spectrum of nearly pure exponential
Teff of nearly independent of fit range
Different behaviour of excess not due to incorrect acceptance
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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)
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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%
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evolution of Teff vs m: , ,
Linear rise – the seems to flow less
Fit the spectra in the range 0.4-1.8 GeV/c
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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
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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
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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?
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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?