First results on angular distributions of thermal dileptons in nuclear collisions

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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


2cossin

2cos2sincos1

cosd

dN 22

d


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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


2cossin

2cos2sincos1

cosd

dN 22

d


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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



2cos

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||d

dN


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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



2cos

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||d

dN


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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



2cos

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||d

dN

Method 3: Fix = 0 - analysis of the inclusive distributions in |cosθ| and

| | with 1-dim acceptance correction


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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

First results on angular distributions of thermal dileptons in nuclear collisions

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