first results on angular distributions of thermal dileptons in nuclear collisions
DESCRIPTION
First results on angular distributions of thermal dileptons in nuclear collisions. G. Usai – INFN and University of Cagliari (Italy) QM09 -Knoxville. Summary of previous results on thermal dileptons. Phys. Rev. Lett. 96 (2006) 162302. - PowerPoint PPT PresentationTRANSCRIPT
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First results on angular distributions of thermal dileptons in nuclear collisions
G. Usai – INFN and University of Cagliari (Italy)QM09 -Knoxville
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• Invariant mass region M<1 GeV: thermal dilepton production largely mediated by the broad vector meson ρ
via →→→ annihilation. Hadronic nature supported by the rise of radial flow up to M=1 GeV
• M>1 GeV: sudden fall of radial flow of thermal dimuons occurs , naturally explained as a transition to a qualitatively different source, i.e.
mostly partonic radiation, qq→→μμ
Summary of previous results on thermal dileptons
Phys. Rev. Lett. 96 (2006) 162302
Phys. Rev. Lett. 100 (2008) 022302
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Is the radiation thermal?
Features of thermal radiation:
- Plack-like exponential shape of mass spectra (for flat spectral function)
- mT scaling of transverse momentum spectra
- Absence of any polarization in angular distributions (this talk)
- Agreement between data and thermal models in yields and spectral shapes
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Excess mass spectrum up to 2.5 GeV
thermal (M<1 GeV)
&&
thermal qq (M >1 GeV) suggested dominant by Teff vs M (supported by R/R, D/Z)
also multipion processes (H/R)
All known sources (hadro-cocktail, open charm, DY) subtracted
Acceptance corrected spectrum (pT>0.2 GeV)
Absolute normalization → comparison to theory in absolute terms!
Planck-like mass spectrum; falling exponentially
Agreement with theoretical models up to 2.5 GeV!
Eur. Phys. J. C 59 (2009) 607
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General formalism for the description of an angular distribution
dσ/dcosθ d is the differential decay angular distribution in the rest
frame of the virtual photon * with respect to a suitably chosen axis
are structure functions related to helicity structure functions and the spin density matrix elements of the virtual photon
Angular distributions
2cossin
2cos2sincos1
cos d
dσ1 22
d
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Analysis in the mass region M<1 GeV:
excess dileptons produced from annihilation of pions
The answer is no!
Even for annihilation of spinless particles, like annihilation, the structure function parameters can have any value λ, μ, ν ǂ 0
for collinear pions along z axis = -1 longitudinal polarization of the virtual photon
However, a completely random orientation of annihilating pions in 3 dimensions would lead to = 0
However, pions are spinless:
Don’t we expect to find a trivial result for λ, μ and ν?
What can we learn from angular distributions?
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Collins Soper (CS) frame
θ is the angle between the positive muon pμ+ and the z-axis.
The z axis is the bisector between pproj and - ptarget
Reference frame
2cossin
2cos2sincos1
cos d
dσ1 22
d
ϕ
pprojectile ptarget
z axis CS
pµ+
yx
Viewed from dimuonrest frame
Choice of the frame non relevant: once all measured, can be re-computed in any other frame with a simple transformation (Z. Phys. C31, 513 (1986))
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Results on centrality integrated data
with pT>0.6 GeV for:
Excess dileptons in 2 mass windows:
0.4<M<0.6 GeV (~17600 pairs) 0.6<M<0.9 GeV (~36000 pairs)
Vector mesons ω and (~73000 pairs)
Angular distributions in the low mass region
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Steps followed for each of the [m x n] bins:
1) Combinatorial background subtraction
2) Assessment of fake matches
3) Isolation of excess by subtraction of the known sources
4) Acceptance correction in 2-dim cosθ- space or in 1-dim projections
Analysis steps
Analysis done in cosθ - space with
different binnings in [dN/dcosθd]m x n to study the systematics
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Combinatorial background reduced for pT>0.6 GeV: B/S ~ 2-3Systematic errors due to subtraction of combinatorial background ~2-3%
Combinatorial background subtraction
Example: 0.0<IcosθI<0.1 and
4 bins in IcosI
checked in all other bins
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Assessment of fake matches
Overlay Monte Carlo:
Monte Carlo muons superimposed to real events and reconstructed
Fake matches are tagged and the relative fraction of correct matched muons is evaluated
Systematic errors due to subtraction of fakes <1%
hadron absorber
muon trigger and tracking
targetfake
correctHadron absorber
Muon spectrometer
Fake match: muon matched to a wrong track in the vertex telescope
Can be important in high multiplicity events (negligible in pA or peripheral AA)
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Systematic uncertainties: 4-6% - up to 10-15% in some low-populated
cosθ - bins →main source of systematic errors
However, measurement still dominated by statistical errors
Subtraction of known sources
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Acceptance projections in IcosθI and II
Acceptance correction
1-dim correction: full range in cosθ and used
2-dim correction: 0.7<||<2.4 (-0 .75<cos<0.75) applied to exclude regions with very low acceptance
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Final results on acceptance corrected |cos||cos| d
dN
d
Acceptance corrected decay angular distributions
mesonExcess 0.6<M<0.9 GeV
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Three methods
Method 1: Analysis of the 2-dim distribution cosθ-cosrestricted to 6x6 matrix
2cossin
2cos2sincos1
cosd
dN 22
d
Determination of the structure coefficients I
Fit with function to extract all 3 structure parameters
-0.6<cosθ<0.6 (bin width 0.2) -
0 .75<cos<0.75 (bin width 0.25)
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Method 2: Project 2-dim decay angular distribution over polar or azimuth angle
2cos1| cos|d
dN
2cos
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||d
dNFit over polarangle
Fit over azimuth angle
Determination of the structure coefficients II
Method 3: Analysis of the inclusive distributions in |cosθ| and || with a 1-dim acceptance correction
|cosθ|<0.8 (bin width 0.1) |
cos<0.75 (bin width 0.25)
|cosθ|<0.8 (bin width 0.1)
0<II<(bin width 0.3)
Analysis of projections: fixed to value found from method 1
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Results: = -0.19 ± 0.12 = 0.03 ± 0.15μ = 0.05 ± 0.03
Method 1: 2-dim fit to data with
2cossin
2cos2sincos1
cosd
dN 22
d
Structure coefficients ,: excess 0.6<M<0.9 GeV
All parameters zero within errors
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Structure coefficients ,: excess 0.4<M<0.6 GeV
Results = -0.13 ± 0.27 = 0.12 ± 0.30μ = -0.04 ± 0.10
Method 1: 2-dim fit to data with
2cossin
2cos2sincos1
cosd
dN 22
d
All parameters zero within errors
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Structure coefficients ,: ω and ɸ mesons
Results for the ω = -0.10 ± 0.10 = 0.05 ± 0.11μ = -0.05 ± 0.02
Results for the = -0.07 ± 0.09 = -0.10 ± 0.08μ = 0.04 ± 0.02
Method 1: 2-dim fit to data with
2cossin
2cos2sincos1
cosd
dN 22
d
All parameters zero within errors
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Method 2: Fix = 0 and project the decay angular distribution over polar or azimuth angles
2cos1 |cos|d
dNA
Polar angular distributions: excess
Uniform polar distributions : no polarization for the excess in the ρ like region 0.6<M<0.9 GeV and in the region 0.4<M<0.6 GeV
=-0.13±0.12 (= 0.05±0.15)
=-0.10±0.24 (=0.11 ±0.30)
excess
(0.6<M<0.9 GeV)
excess
(0.4<M<0.6 GeV)
Fit function for azimuth angle
Fit function for polar angle
2cos
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||d
dN
Submitted to PRL, arXiv:0812.3100
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Polar angular distributions: and
Uniform polar distributions : no polarization also for ω and
=-0.12±0.09 (=-0.06±0.10)
=-0.13±0.08 (=-0.09±0.08)
meson
meson
Method 2: Fix = 0 and project the decay angular distribution over polar or azimuth angles
2cos1 |cos|d
dNA
Fit function for azimuth angle
Fit function for polar angle
2cos
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||d
dN
Submitted to PRL, arXiv:0812.3100
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Method 3: Fix = 0 - analysis of the inclusive distributions in |cosθ| and
| | with 1-dim acceptance correction
Azimuth angular distributions: excess
Uniform azimuth distributions for the excess in the ρ like region 0.6<M<0.9 GeV and in the region 0.4<M<0.6 GeV
=0.00±0.12 (=-0.15±0.09)
excess
(0.6<M<0.9 GeV)
=0.10±0.18 (=-0.09±0.16)
excess
(0.4<M<0.6 GeV)
2cos1 |cos|d
dNA
Fit function for azimuth angle
Fit function for polar angle
2cos
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||d
dN
Submitted to PRL, arXiv:0812.3100
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Azimuth angular distributions: and
Uniform azimuth distributions also for ω and
=-0.02±0.08 (=-0.12±0.06)
=-0.06±0.06 (=--0.05±0.06)
meson
meson
2cos1 |cos|d
dNA
Fit function for azimuth angle
Fit function for polar angle
2cos
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||d
dN
Method 3: Fix = 0 - analysis of the inclusive distributions in |cosθ| and
| | with 1-dim acceptance correction
Submitted to PRL, arXiv:0812.3100
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excess 0.6<M<0.9 GeV λ ν μmethod 1 -0.19 +- 0.12 0.03 +- 0.15 0.05 +- 0.03
method 2 -0.13 +- 0.12 0.05 +- 0.15
method 3 -0.15 +- 0.09 0.00 +- 0.12
excess 0.4<M<0.6 GeV λ ν μmethod 1 -0.13 +- 0.27 0.12 +- 0.30 -0.04 +- 0.10
method 2 -0.10 +- 0.24 0.11 +- 0.30
method 3 -0.09 +- 0.16 0.10 +- 0.18
ω meson λ ν μmethod 1 -0.10 +- 0.10 -0.05 +0 0.11 -0.05 +- 0.02
method 2 -0.12 +- 0.09 -0.06 +- 0.10
method 3 -0.12 +- 0.06 -0.02 +- 0.08
meson λ ν μmethod 1 -0.07 +- 0.09 -0.10 +- 0.08 0.04 +- 0.02
method 2 -0.13 +- 0.08 -0.09 +- 0.08
method 3 -0.05 +- 0.06 -0.06 +- 0.06
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Comparison of results from different methods
Choice of the frame non relevant: once all measured, can be re-computed in any other frame with a simple transformation (Z. Phys. C31, 513 (1986))
→ re-computed in Gottfried-Jackson frame
zero also in Gottfried-Jackson frame
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Absence of any polarization:
Fully consistent with the interpretation of the observed excess as thermal radiation
Necessary but not sufficient condition
Put together with other features: Planck-like shape of mass spectra, temperature systematics, agreement of data with thermal models
Thermal interpretation more plausible than ever before
Summary
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M>1 GeV: sudden fall of radial flow of thermal dimuons occurs , naturally explained as a transition to a qualitatively different source, i.e.
mostly partonic radiation, qq→→μμ
Pure in-medium part
HADRONIC source alone (2pi+4pi+a1pi)(in HYDRO and other models of fireball expansion) continuous rise of Teff with mass, no way to get a discontinuity at M=1 GeV like at any other mass value
Uncertainty in fraction of QGP, 50%, 60%, 80%, …. But a strong contribution of partonic source is needed to get a discontinuity in Teff at M=1GeV, HADRONIC source ALONE CANNOT do that