November 9, 2018 19:7 WSPC/INSTRUCTION FILE DPeressounko-
ggHBT-T
International Journal of Modern Physics E
c© World Scientific Publishing Company
Bose-Einstein correlations of direct photons in Au+Au collisions at
sNN = 200 GeV
D. Peressounko for the PHENIX collaboration∗
RRC ”Kurchatov Institute”, Kurchatov sq.1,
Moscow, 123182, Russia
peressou@rcf.rhic.bnl.gov
Received (received date)
Revised (revised date)
The current status of the analysis of direct photon Bose-Einstein correlations in Au+Au
collisions at
sNN = 200 GeV done by the PHENIX collaboration is summarized. All
possible sources of distortion of the two-photon correlation function are discussed and
methods to control them in the PHENIX experiment are presented.
1. Introduction
Photons have an extremely long mean free path length and escape from the hot
matter without rescattering. By measuring their Bose-Einstein (or Hanbury-Brown
Twiss, HBT) correlations one can extract the space-time dimensions of the hottest
central part of the collision1,2,3,4,5 in contrast to hadron HBT correlations which
measure the size of the system at the moment of its freeze-out. Moreover, photons
emitted at different stages of the collision dominate in different ranges of trans-
verse momentum6, therefore measuring photon correlation radii at various average
transverse momenta (KT ) one can scan the space-time dimensions of the system at
various times and thus trace the evolution of the hot matter.
Photons emitted directly by the hot matter – direct photons – constitute only a
small fraction of the total photon yield while the dominant contribution comes from
decays of the final state hadrons, mainly π0 → 2γ and η → 2γ mesons. Fortunately,
the lifetime of these hadrons is extremely large and the width of the Bose-Einstein
correlations between the decay photons is of the order of a few eV and cannot
obscure the direct photon correlations. This feature can be used to extract the direct
photon yield3: assuming that direct photons are emitted incoherently, the photon
correlation strength parameter can be related to the proportion of direct photons as
λ = 1/2(Ndirγ /N
2. This approach is probably the only way to experimentally
measure direct photon yield at very small pT . Presently, the only experiment to
∗For the full list of the PHENIX collaboration and acknowledgments, see9.
http://arxiv.org/abs/0704.0852v1
November 9, 2018 19:7 WSPC/INSTRUCTION FILE DPeressounko-
ggHBT-T
2 D. Peressounko
have measured direct photon Bose-Einstein correlations in ultrarelativistic heavy
ion collisions is WA987. An invariant correlation radius was extracted and the direct
photon yield was measured in Pb+Pb collisions at
sNN = 17 GeV.
Since the strength of the direct photon Bose-Einstein correlation is typically a
few tenths of a percent, it is important to exclude all background contributions
which could distort the photon correlation function. These contributions can be
classified as following: apparatus effects (close clusters interference – attraction of
close clusters in the calorimeter during reconstruction) and correlations caused by
real particles. The latter in turn can be divided into contribution due to ”splitting”
of particles – processes like antineutron annihilation in the calorimeter and photon
conversion on detector material in front of the calorimeter; contamination by corre-
lated hadrons (e.g. Bose-Einstein-correlated π±); background correlations of decay
photons. In this paper we consider all of these contributions in detail and describe
how to control for them in the PHENIX experiment.
2. Analysis
This analysis is based on the data taken by PHENIX in Run3 (d+Au) and Run4
(Au+Au). The total collected statistics is ≈ 3 billion d+Au events and ≈ 900 M
Au+Au events. Details of the PHENIX configuration in these runs can be found in
references 8 and 9, respectively.
2.1. Apparatus effects
Since correlation functions are rapidly rising functions at small relative momenta
any small distortion of the relative momentum for real pairs, because of errors in
reconstruction of close clusters in the calorimeter (”cluster attraction”) for example,
can lead to the appearance of a fake bump in the correlation function.
To explore the influence of cluster interference in the calorimeter EMCAL, we
construct a set of correlation functions by applying different cuts on the minimal
distance between photon clusters in EMCAL. To quantify the difference between
these correlation functions we fit them with a Gaussian and compare the extracted
correlation parameters. We find that for correlation functions that include clusters
with small relative distances there is strong dependence on minimal distance cut,
but for distance cuts above 24 cm (4-5 modules) the correlation parameters are
independent of the relative distance cut. This implies that with this distance cut
the apparatus effects are sufficiently small.
2.2. Photon conversion, n̄ annihilation, and similar backgrounds
The next class of possible backgrounds are processes in which one real particle
produces several clusters in the calorimeter close to each other. These are processes
like n̄ annihilation in the calorimeter producing several separated clusters, or photon
conversion in front of calorimeter, or residual correlations between photons that
November 9, 2018 19:7 WSPC/INSTRUCTION FILE DPeressounko-
ggHBT-T
Bose-Einstein correlations of direct photons in Au+Au collisions 3
 (GeV)
0 0.05 0.1 0.15 0.2 0.25 0.3
C Min.Bias, Au+Au
Min.Bias, d+Au, scaled
Fig. 1. Two-photon correlation function measured in d+Au collisions at
sNN = 200 GeV scaled
to reproduce the height of the π0 peak in Au+Au collisions compared to the same correlation
function measured in Au+Au collisions at
sNN = 200 GeV. Absolute vertical scale is omitted
in this technical plot.
belong to different π0 in decays like η → 3π0 → 6γ. The common feature of this
type of process is that their strength is proportional to the number of particles per
event and not to the square of the number of particles, as would be the case for
Bose-Einstein correlations.
To estimate the upper limit on these contributions, we compare two-photon
correlation functions, calculated in d+Au and Au+Au collisions. For the moment
we assume, that all correlations at small relative momenta seen in d+Au collisions
are due to the background effects under consideration. Then we scale the correlation
function obtained in d+Au collisions with the number of π0 (that is we reproduce
the height of the π0 peak in Au+Au collisions):
Cscaled2 = 1−
hAu+Auπ
hd+Auπ
(C2 − 1). (1)
The result of this operation is shown in Fig. 1. We find that the scaled d+Au
correlation function lies well below (close to unity) the correlation function calcu-
lated for Au+Au collisions at small relative momenta. From this we conclude that
the contribution from effects with strength proportional to the first power of the
number of particles is negligible in Au+Au collisions.
2.3. Charged and neutral hadron contamination
Another possible source of distortion of the photon correlation function is a contam-
ination by (correlated) hadrons. Although we use rather strict identification criteria
November 9, 2018 19:7 WSPC/INSTRUCTION FILE DPeressounko-
ggHBT-T
4 D. Peressounko
for photons there still may be some admixture of correlated hadrons contributing
to the region of small relative momenta.
 (GeV)
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
C Converted + EMCAL
EMCAL + EMCAL
Fig. 2. Comparison of two-photon correlation functions measured in Au+Au collisions at
sNN =
200 GeV by two different methods: both photons are registered in the EMCAL (closed) and one
photon is registered in EMCAL while the other is reconstructed through its external conversion
(open). Absolute vertical scale is omitted in this technical plot.
To exclude this possibility, we construct the two-photon correlation function
using one photon registered in the calorimeter EMCAL and reconstructing the sec-
ond photon from its conversion into an e+e− pair on the material of the beam
pipe. The photon sample, constructed using external conversions is completely free
from hadron contamination, so comparison of the standard correlation function
with the pure one allows to estimate the contribution from non-photon contami-
nation. This comparison is shown in Fig. 2. We find that the correlation function
constructed with the more pure photon sample demonstrates a slightly larger cor-
relation strength. This demonstrates that the observed correlation is indeed a pho-
ton correlation, while hadron contamination in the photon sample just increases
combinatorial background and reduces the correlation strength. In addition, this
comparison shows that we have properly excluded the region of cluster interference.
Due to deflection by the magnetic field the electrons of the e+e− conversion pair
hit the calorimeter far from the location of the pair photon used in the correlation
function and thus effects related to the interference of close clusters are absent.
2.4. Photon residual correlations
The last possible source of the distortion of the photon correlation function are
residual correlations between photons. We have already demonstrated that the con-
November 9, 2018 19:7 WSPC/INSTRUCTION FILE DPeressounko-
ggHBT-T
Bose-Einstein correlations of direct photons in Au+Au collisions 5
tributions of residual correlations between photons in decays like η → 3π0 → 6γ,
with strength proportional to Npart and not N
part is negligible in Au+Au collisions.
Below we consider other effects, which may cause photon correlations. These are
collective flow (and jet-like correlations) and correlations between photons, origi-
nated from decays of Bose-Einstein correlated mesons. Collective (elliptic) flow as
well as jet-like correlations are long-range effects, resulting in correlations at relative
angles much larger than under consideration here (for example, the opening angle of
a photon pair with 20 MeV mass and KT = 500 MeV is ∼ 5 degrees). Monte-Carlo
simulations demonstrate that flow and jet-like contribution are indeed negligible.
 (GeV)
0 0.05 0.1 0.15 0.2 0.25 0.3
C Min.Bias Au+Au, Data
 HBT resid.corr., Sim.0π
Fig. 3. Comparison of two-photon correlation functions measured in Au+Au collisions at
sNN =
200 GeV with Monte-Carlo simulations of the contribution of residual correlations due to decays
of Bose-Einstein-correlated neutral pions. Absolute vertical scale is omitted in this technical plot.
Potentially, the most serious distortion of the photon correlation function are
residual correlations between decay photons of HBT-correlated π0s. Monte-Carlo
simulations show that this contribution is not negligible, but has a rather specific
shape (see Fig. 3), so that it does not distort the photon correlation function at
small Qinv. This result can be explained as follows. Let us consider two π
0s with
zero relative momentum. The distribution of decay photons is isotropic in their rest
frame, and the probability to find a collinear photon pair (Qinv = 0) is suppressed
due to phase space reasons. The photon pair mass distribution has a maximum at
2/3mπ, not at zero. After convoluting with the pion correlation function we find
a step-like two-photon correlation function3. On the other hand, if one artificially
chooses photons with momentum along the direction of the parent π0 (e.g. by
looking at photon pairs at very large KT ), then the shape of the decay photon
correlation function will reproduce the shape of the parent π0 correlation. This
November 9, 2018 19:7 WSPC/INSTRUCTION FILE DPeressounko-
ggHBT-T
6 D. Peressounko
probably explains the different shape of the residual correlations due to decays of
HBT-correlated π0 found in10.
3. Conclusions
We have presented the current status of analysis of direct photon Bose-Einstein
correlations in the PHENIX experiment. We are able to measure the two-photon
correlation function with a precision sufficient to extract the direct photon corre-
lations. Correlation measurements in which one of the photon pair has converted
to an e+e− pair have been used to provide an important cross-check. We have
demonstrated that all known backgrounds are under control. The extraction of the
correlation parameters of direct photon pairs is in progress.
References
1. A.N. Makhlin, JETP Lett. 46:55 (1987); A.N. Makhlin, Sov.J.Nucl.Phys.
49:151,(1989).
2. D.K. Srivastava, J. Kapusta, Phys.Rev. C48:1335 (1993); D.K. Srivastava, C. Gale,
Phys.Lett. B319:407 (1993); D.K. Srivastava, Phys.Rev. D49:4523 (1994); D.K. Srivas-
tava, J. Kapusta, Phys.Rev. C50:505 (1994). D.K. Srivastava, Phys.Rev. C71:034905
(2005); S. Bass, B. Muller, D.K. Srivastava, Phys.Rev. Lett. 93:162301 (2004).
3. D. Peressounko, Phys.Rev. C67:014905 (2003).
4. J. Alam et al., Phys.Rev. C67:054902 (2003); J. Alam et al., Phys.Rev. C70:054901
(2004).
5. T. Renk, Phys.Rev. C71:064905 (2005); hep-ph/0408218.
6. D. d’Enterria and D.Peressounko, Eur.Phys.J.C46:451 (2006).
7. M.M. Aggarwal et al., Phys.Rev.Lett. 93:022301 (2004).
8. S.S.Adler et al., (PHENIX collaboration), Phys.Rev.Lett. 98:012002.
9. S.Bathe et al., (PHENIX collaboration), Nucl.Phys. A774:731 (2006).
10. D.Das et al., nucl-ex/0511055.
http://arxiv.org/abs/hep-ph/0408218
http://arxiv.org/abs/nucl-ex/0511055
	Introduction
	Analysis
	Apparatus effects
	Photon conversion,  annihilation, and similar backgrounds
	Charged and neutral hadron contamination
	Photon residual correlations
	Conclusions

  The current status of the analysis of direct photon Bose-Einstein
correlations in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV done by the PHENIX
collaboration is summarized. All possible sources of distortion of the
two-photon correlation function are discussed and methods to control them in
the PHENIX experiment are presented.

Introduction
Photons have an extremely long mean free path length and escape from the hot
matter without rescattering. By measuring their Bose-Einstein (or Hanbury-Brown
Twiss, HBT) correlations one can extract the space-time dimensions of the hottest
central part of the collision1,2,3,4,5 in contrast to hadron HBT correlations which
measure the size of the system at the moment of its freeze-out. Moreover, photons
emitted at different stages of the collision dominate in different ranges of trans-
verse momentum6, therefore measuring photon correlation radii at various average
transverse momenta (KT ) one can scan the space-time dimensions of the system at
various times and thus trace the evolution of the hot matter.
Photons emitted directly by the hot matter – direct photons – constitute only a
small fraction of the total photon yield while the dominant contribution comes from
decays of the final state hadrons, mainly π0 → 2γ and η → 2γ mesons. Fortunately,
the lifetime of these hadrons is extremely large and the width of the Bose-Einstein
correlations between the decay photons is of the order of a few eV and cannot
obscure the direct photon correlations. This feature can be used to extract the direct
photon yield3: assuming that direct photons are emitted incoherently, the photon
correlation strength parameter can be related to the proportion of direct photons as
λ = 1/2(Ndirγ /N
2. This approach is probably the only way to experimentally
measure direct photon yield at very small pT . Presently, the only experiment to
∗For the full list of the PHENIX collaboration and acknowledgments, see9.
http://arxiv.org/abs/0704.0852v1
November 9, 2018 19:7 WSPC/INSTRUCTION FILE DPeressounko-
ggHBT-T
2 D. Peressounko
have measured direct photon Bose-Einstein correlations in ultrarelativistic heavy
ion collisions is WA987. An invariant correlation radius was extracted and the direct
photon yield was measured in Pb+Pb collisions at
sNN = 17 GeV.
Since the strength of the direct photon Bose-Einstein correlation is typically a
few tenths of a percent, it is important to exclude all background contributions
which could distort the photon correlation function. These contributions can be
classified as following: apparatus effects (close clusters interference – attraction of
close clusters in the calorimeter during reconstruction) and correlations caused by
real particles. The latter in turn can be divided into contribution due to ”splitting”
of particles – processes like antineutron annihilation in the calorimeter and photon
conversion on detector material in front of the calorimeter; contamination by corre-
lated hadrons (e.g. Bose-Einstein-correlated π±); background correlations of decay
photons. In this paper we consider all of these contributions in detail and describe
how to control for them in the PHENIX experiment.
2. Analysis
This analysis is based on the data taken by PHENIX in Run3 (d+Au) and Run4
(Au+Au). The total collected statistics is ≈ 3 billion d+Au events and ≈ 900 M
Au+Au events. Details of the PHENIX configuration in these runs can be found in
references 8 and 9, respectively.
2.1. Apparatus effects
Since correlation functions are rapidly rising functions at small relative momenta
any small distortion of the relative momentum for real pairs, because of errors in
reconstruction of close clusters in the calorimeter (”cluster attraction”) for example,
can lead to the appearance of a fake bump in the correlation function.
To explore the influence of cluster interference in the calorimeter EMCAL, we
construct a set of correlation functions by applying different cuts on the minimal
distance between photon clusters in EMCAL. To quantify the difference between
these correlation functions we fit them with a Gaussian and compare the extracted
correlation parameters. We find that for correlation functions that include clusters
with small relative distances there is strong dependence on minimal distance cut,
but for distance cuts above 24 cm (4-5 modules) the correlation parameters are
independent of the relative distance cut. This implies that with this distance cut
the apparatus effects are sufficiently small.
2.2. Photon conversion, n̄ annihilation, and similar backgrounds
The next class of possible backgrounds are processes in which one real particle
produces several clusters in the calorimeter close to each other. These are processes
like n̄ annihilation in the calorimeter producing several separated clusters, or photon
conversion in front of calorimeter, or residual correlations between photons that
November 9, 2018 19:7 WSPC/INSTRUCTION FILE DPeressounko-
ggHBT-T
Bose-Einstein correlations of direct photons in Au+Au collisions 3
 (GeV)
0 0.05 0.1 0.15 0.2 0.25 0.3
C Min.Bias, Au+Au
Min.Bias, d+Au, scaled
Fig. 1. Two-photon correlation function measured in d+Au collisions at
sNN = 200 GeV scaled
to reproduce the height of the π0 peak in Au+Au collisions compared to the same correlation
function measured in Au+Au collisions at
sNN = 200 GeV. Absolute vertical scale is omitted
in this technical plot.
belong to different π0 in decays like η → 3π0 → 6γ. The common feature of this
type of process is that their strength is proportional to the number of particles per
event and not to the square of the number of particles, as would be the case for
Bose-Einstein correlations.
To estimate the upper limit on these contributions, we compare two-photon
correlation functions, calculated in d+Au and Au+Au collisions. For the moment
we assume, that all correlations at small relative momenta seen in d+Au collisions
are due to the background effects under consideration. Then we scale the correlation
function obtained in d+Au collisions with the number of π0 (that is we reproduce
the height of the π0 peak in Au+Au collisions):
Cscaled2 = 1−
hAu+Auπ
hd+Auπ
(C2 − 1). (1)
The result of this operation is shown in Fig. 1. We find that the scaled d+Au
correlation function lies well below (close to unity) the correlation function calcu-
lated for Au+Au collisions at small relative momenta. From this we conclude that
the contribution from effects with strength proportional to the first power of the
number of particles is negligible in Au+Au collisions.
2.3. Charged and neutral hadron contamination
Another possible source of distortion of the photon correlation function is a contam-
ination by (correlated) hadrons. Although we use rather strict identification criteria
November 9, 2018 19:7 WSPC/INSTRUCTION FILE DPeressounko-
ggHBT-T
4 D. Peressounko
for photons there still may be some admixture of correlated hadrons contributing
to the region of small relative momenta.
 (GeV)
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
C Converted + EMCAL
EMCAL + EMCAL
Fig. 2. Comparison of two-photon correlation functions measured in Au+Au collisions at
sNN =
200 GeV by two different methods: both photons are registered in the EMCAL (closed) and one
photon is registered in EMCAL while the other is reconstructed through its external conversion
(open). Absolute vertical scale is omitted in this technical plot.
To exclude this possibility, we construct the two-photon correlation function
using one photon registered in the calorimeter EMCAL and reconstructing the sec-
ond photon from its conversion into an e+e− pair on the material of the beam
pipe. The photon sample, constructed using external conversions is completely free
from hadron contamination, so comparison of the standard correlation function
with the pure one allows to estimate the contribution from non-photon contami-
nation. This comparison is shown in Fig. 2. We find that the correlation function
constructed with the more pure photon sample demonstrates a slightly larger cor-
relation strength. This demonstrates that the observed correlation is indeed a pho-
ton correlation, while hadron contamination in the photon sample just increases
combinatorial background and reduces the correlation strength. In addition, this
comparison shows that we have properly excluded the region of cluster interference.
Due to deflection by the magnetic field the electrons of the e+e− conversion pair
hit the calorimeter far from the location of the pair photon used in the correlation
function and thus effects related to the interference of close clusters are absent.
2.4. Photon residual correlations
The last possible source of the distortion of the photon correlation function are
residual correlations between photons. We have already demonstrated that the con-
November 9, 2018 19:7 WSPC/INSTRUCTION FILE DPeressounko-
ggHBT-T
Bose-Einstein correlations of direct photons in Au+Au collisions 5
tributions of residual correlations between photons in decays like η → 3π0 → 6γ,
with strength proportional to Npart and not N
part is negligible in Au+Au collisions.
Below we consider other effects, which may cause photon correlations. These are
collective flow (and jet-like correlations) and correlations between photons, origi-
nated from decays of Bose-Einstein correlated mesons. Collective (elliptic) flow as
well as jet-like correlations are long-range effects, resulting in correlations at relative
angles much larger than under consideration here (for example, the opening angle of
a photon pair with 20 MeV mass and KT = 500 MeV is ∼ 5 degrees). Monte-Carlo
simulations demonstrate that flow and jet-like contribution are indeed negligible.
 (GeV)
0 0.05 0.1 0.15 0.2 0.25 0.3
C Min.Bias Au+Au, Data
 HBT resid.corr., Sim.0π
Fig. 3. Comparison of two-photon correlation functions measured in Au+Au collisions at
sNN =
200 GeV with Monte-Carlo simulations of the contribution of residual correlations due to decays
of Bose-Einstein-correlated neutral pions. Absolute vertical scale is omitted in this technical plot.
Potentially, the most serious distortion of the photon correlation function are
residual correlations between decay photons of HBT-correlated π0s. Monte-Carlo
simulations show that this contribution is not negligible, but has a rather specific
shape (see Fig. 3), so that it does not distort the photon correlation function at
small Qinv. This result can be explained as follows. Let us consider two π
0s with
zero relative momentum. The distribution of decay photons is isotropic in their rest
frame, and the probability to find a collinear photon pair (Qinv = 0) is suppressed
due to phase space reasons. The photon pair mass distribution has a maximum at
2/3mπ, not at zero. After convoluting with the pion correlation function we find
a step-like two-photon correlation function3. On the other hand, if one artificially
chooses photons with momentum along the direction of the parent π0 (e.g. by
looking at photon pairs at very large KT ), then the shape of the decay photon
correlation function will reproduce the shape of the parent π0 correlation. This
November 9, 2018 19:7 WSPC/INSTRUCTION FILE DPeressounko-
ggHBT-T
6 D. Peressounko
probably explains the different shape of the residual correlations due to decays of
HBT-correlated π0 found in10.
3. Conclusions
We have presented the current status of analysis of direct photon Bose-Einstein
correlations in the PHENIX experiment. We are able to measure the two-photon
correlation function with a precision sufficient to extract the direct photon corre-
lations. Correlation measurements in which one of the photon pair has converted
to an e+e− pair have been used to provide an important cross-check. We have
demonstrated that all known backgrounds are under control. The extraction of the
correlation parameters of direct photon pairs is in progress.
References
1. A.N. Makhlin, JETP Lett. 46:55 (1987); A.N. Makhlin, Sov.J.Nucl.Phys.
49:151,(1989).
2. D.K. Srivastava, J. Kapusta, Phys.Rev. C48:1335 (1993); D.K. Srivastava, C. Gale,
Phys.Lett. B319:407 (1993); D.K. Srivastava, Phys.Rev. D49:4523 (1994); D.K. Srivas-
tava, J. Kapusta, Phys.Rev. C50:505 (1994). D.K. Srivastava, Phys.Rev. C71:034905
(2005); S. Bass, B. Muller, D.K. Srivastava, Phys.Rev. Lett. 93:162301 (2004).
3. D. Peressounko, Phys.Rev. C67:014905 (2003).
4. J. Alam et al., Phys.Rev. C67:054902 (2003); J. Alam et al., Phys.Rev. C70:054901
(2004).
5. T. Renk, Phys.Rev. C71:064905 (2005); hep-ph/0408218.
6. D. d’Enterria and D.Peressounko, Eur.Phys.J.C46:451 (2006).
7. M.M. Aggarwal et al., Phys.Rev.Lett. 93:022301 (2004).
8. S.S.Adler et al., (PHENIX collaboration), Phys.Rev.Lett. 98:012002.
9. S.Bathe et al., (PHENIX collaboration), Nucl.Phys. A774:731 (2006).
10. D.Das et al., nucl-ex/0511055.
http://arxiv.org/abs/hep-ph/0408218
http://arxiv.org/abs/nucl-ex/0511055
	Introduction
	Analysis
	Apparatus effects
	Photon conversion,  annihilation, and similar backgrounds
	Charged and neutral hadron contamination
	Photon residual correlations
	Conclusions
