Kos: A Potential Signature for
Quark-Gluon Plasma
Summer Research Experience for Undergraduates 2002
Iowa State University
Beau Meredith, Greenville College
Mentored by Dr. Craig Ogilvie
Abstract
The purpose of this project was to analyze a potential signature for quark-gluon plasma. The signature
analyzed was the Kos. The analysis was done using various mathematical and computation tools.
Experimental data from the PHENIX detector at RHIC was taken and used to form a pure and background
signal for the Kos at different pT bins. The number of Kos was extracted from the pure signal by means of
subtracting the scaled background signal. A Monte Carlo was run for the Kos, and reconstruction efficiency
as a function of pT was created. A pT spectrum was then created for low pT. The spectrum did not
incorporate the higher pT due to a lack of accuracy in attaining the number of Kos. The spectrum needs to
be completed for high pT (> 2.0 GeV/c) before the Kos can be tested to see whether or not it is a potential
signature of quark-gluon plasma.
I. Introduction
Physicists working at the Relativistic Heavy Ion Collider (RHIC) in Brookhaven, NY are
searching for a new state of matter. This state of matter, known as quark-gluon plasma (QGP), is theorized
to exist at very high pressures and temperatures (above 1 trillion degrees). QGP is thought to be produced
in the energetic central Au-Au collisions at RHIC. In these densely energetic but microscopic collisions,
two gold ions are accelerated up to 99.95% the speed of light. “Physicists believe that RHIC collisions
will compress and heat the gold nuclei so much that their individual protons and neutrons will overlap,
creating an enormously energetic area where, for a brief time, a relatively large number of free quarks and
gluons can exist. This is the quark-gluon plasma,” [2]. The free quarks and gluons referred to by the
previous text are in a state in which quarks and gluons no longer bond to form hadronic matter. These
bonds have been broken and are replaced by a conglomerate bonding of quarks and gluons in a plasma-like
state.
Fig. 1: A Representation of QGP [2]
Quark-gluon plasma is thought to be the state that matter existed in 10 millionths of a second after
the big bang. If physicists at RHIC could show that QGP does exist, it would be a big advance in both
nuclear physics and cosmology. The way in which signatures, or plausible indications, of QGP can be
found involve a colored interaction between partons (quarks, gluons, and anti-quarks) and QGP. As the
QGP is forming a rare collision between incoming partons can take place. The hard-partons that are
scattered are predicted by the quantum chromodynamic theory to lose energy as they travel through the
plasma. The partons then hadronize to form protons, neutrons, pions, kaons, etc. (hadrons). Because of the
parton energy loss, the resulting hadrons have less energy than would be predicted in a cold nuclear
collision where QGP was not formed. The PHENIX group, a collaboration of physicists working with the
PHENIX detector at RHIC, is trying to show that this energy loss does occur in hadrons emitted from the
collision. A way to measure the energy loss is to look at the number of high momentum particles emitted
from the collision. If QGP is truly formed in the Au-Au collision, there should be fewer high momentum
particles than would be expected in the cold nuclear collision. So, a potential signature of quark-gluon
plasma is suppression in the number of high momentum particles emitted from the collision. A specific
component of the momentum, the transverse momentum (pT), measures the momentum perpendicular to the
collision axis. This means that before the collision takes place, there is no pT. Hence all pT of the particles
is produced by the collision of the two gold ions. Because it is produced totally from the collision, pT is
more sensitive to small changes in energy and is a much better indicator for the suppression of high
momentum particles. Therefore, the signature of QGP is the suppression in the number of high transverse
momentum particles emitted from the collision. The actual method used to test this suppression is
comparing pT spectra.
The specific potential signature analyzed in this research was the neutral kaon with a short lifetime
o
(K s). The goal of the research was to analyze the pT spectrum of the Kos and see whether or not
suppression in high pT particles takes place. The lifetime of the Kos, 0.8923 x 10-10 seconds, is too short to
make any hits on the PHENIX detector. The Kos must be identified in PHENIX by its two daughter pions
(π). The Kos decays into two oppositely charged pions 68% of the time [1].
For pion identification in PHENIX, the PHENIX detector tracks the pion paths. The PHENIX
detector is comprised of two arms that subtend a total solid angle of ~ 1 S.R. The setup of the detector is
shown below in Fig. 2-A from the perspective of a gold ion moving toward its collision point.
Fig. 2: The PHENIX detector [3]
Fig. 2-A: A head on view of PHENIX with
Fig. 2-B: An angled view of the actual
the chambers labeled
PHENIX detector
A pion must travel through the drift chamber, three pad chambers, and reach the PbSc
electromagnetic calorimeter to be registered as a particle track, or path in PHENIX. This process of
identification leads to three clear difficulties in identifying the Kos.
1.
Not all pions from the Kos will be registered as tracks (due to both solid angle limitations and
tracking problems)
2.
There is no clear indication of which two pions correspond to the decay of a specific Kos
3.
The pions registered as tracks are not all from Kos (from other particles such as rho)
The research done in this project involved solving these three difficulties and then trying to create a
transverse momentum spectrum for the Kos. The data was collected by PHENIX during the fall 01/winter
02 in the second run of RHIC. There were 1,3041,984 collisions processed in this data set.
II. Analysis
The invariant mass of a Kos is found by the formula
________________________
minv =√ m12 + m22 + 2(E1E2 + p1●p2)
where mi, pi ,and Ei are the corresponding invariant mass, total vector momentum, and kinetic energy of a
pion in a π+/π− pair. To identify the Kos from the pion tracks, the invariant mass of every possible π+/π−
combination from the same collision is calculated. The invariant mass is then plotted on a histogram called
the pure signal. This histogram should contain both a background signal of random π+/π− correlations and
a Gaussian shape of true π+/π− correlations. The true π+/π− correlations are from π+/π− pairs that actually
decay from a Kos. The Gaussian shape, or Kos peak, comes from the combining of π+/π− pairs that are truly
daughter particles of a Kos. They should all have an invariant mass within certain limits of the Gaussian
shape. The reason the distribution takes a Gaussian shape is the measurement error in calculating the track
of a particle. The reason the background consists of random correlations is that these particular
π+/π− pairings did not come from the same Kos. There should be no real relationship between them. A
pure signal histogram is shown below.
Fig. 3: Pure Signal for pT 1.0-1.2 GeV/c
Frequency
(units of 102
Counts)
Invariant Mass (GeV/c2)
The pure signal is composed both of the background signal and Kos peak. The peak extraction is
achieved by subtracting out the background signal. The background signal contains random correlations of
π+/π− pairs. To produce these correlations without the Kos peak, a π+ and π− from different collisions are
paired together in the invariant mass calculation. These mixed event π+/π− pairs should have no
correlation since the two pions could not possibly have come from the same Kos. Thus a mixed background
signal is produced that has no Kos peak. The extraction of the Kos peak is begun by scaling the mixed
background signal to the size of the background signal contained within the pure signal. The mixed
background signal is then subtracted from the pure signal and a Kos peak should result. A mixed
background signal histogram is shown below.
Fig. 4: Mixed Signal for pT 1.0-1.2 GeV/c
Frequency
(units of 102
Counts)
Invariant Mass (GeV/c2)
The preceding two signals were from a Kos group with pT between 1.0-1.2 GeV/c. The extraction
of the Kos peak was done in 0.2 GeV/c pT bins. There were 20 bins ranging from 0.0-4.0 GeV/c used. The
scaling of the mixed background signal was done so as to create an equal area to the background signal
residing in the pure signal. The scaling was done by integrating along a fixed range on both of the
histograms and taking the ratio of the two results. The range of integrations should contain no true
correlations to produce a proper scale factor. Two difficulties that have yet to be totally solved arose from
this process.
1.
There are correlations from the π+/π− pairs besides the Kos
2.
The scale factor is flawed because there are π+/π− correlations within the integration range
The result from the preceding mentioned scaling and subtraction involving 1.0-1.2 GeV/c bin is shown on
the next page.
Fig. 5: Kos peak for pT 1.0-1.2 GeV/c
F re q u e n c y
( c o u n ts )
Invariant Mass (GeV/c2)
There are two main correlations shown in this histogram. The larger one is believed to be an e+/epeak resulting from a misidentification of pions. The smaller peak centered at ~ 0.5 GeV/c2 is the Kos peak.
The invariant mass of a Kos is .4977 GeV/c2, so the peak center is very acceptable. The small dip in
between the two peaks is thought to contain some Kos counts. This is why counts are extracted on a
background. The peak was extracted by using a linear fit in between the minimum in the dip and 0.6
GeV/c2. The number of Kos is the counts contained within the bounds of the peak and the line connecting
the dip to 0.6 GeV/c2. This line is shown in Figure 6. This process was done for all pT bins from 0.8-1.6
GeV/c. The peak extraction process was not applicable for all pT because the larger peak began to meld
into the Kos peak at high pT (pT > 2 GeV/c). This made it impossible to gain a final pT spectrum at high pT.
The number of Kos reconstructed per pT bin in PHENIX was attained in the preceding fashion.
This is not the total number of the Kos that were emitted from the collisions. The total is found by
incorporating a particle simulation Monte Carlo to find the reconstruction efficiency. The PISA Event
Generator simulates the actual detection process done by PHENIX. Almost 275,000 single Kos were
thrown with varying momenta and directions at the simulated detectors. The successful tracks produced by
the pions used the same criteria as in the actual detector. The invariant mass of the π+/π− pairs deemed to
have successful tracks for both members in the pair was plotted on a histogram. The result is the following
Gaussian shape:
Fig. 5: PISA Simulation Kos peak for pT 0.5-6.0 GeV/c
F re q u e n c y
( c o u n ts )
Invariant Mass (GeV/c2)
The Kos peak is distinctly visible without a background. Most of the Kos counts are contained
within an invariant mass range of 0.3-0.6 GeV/c2. Because of this, 0.6 GeV/c2 was used in the upper limit
in the Kos count extraction. This simulated reconstruction data leads to a relationship between pT and the
efficiency of reconstruction in PHENIX. A plot of reconstruction efficiency vs. pT is shown below. A
smooth efficiency function was fit to the data.
Fig. 6: Efficiency vs. pT
Efficiency
pT (GeV/c)
The error bars in the efficiency plot use a Poisson error approximation. The error is proportional to the
square root of the number of Kos reconstructed.
Using both the reconstruction efficiency function and number of Kos per pT group reconstructed, an
experimental pT spectrum was created. A pT spectrum is simply the number of Kos emitted per collision at a
certain pT divided by that pT. The formula used in calculating the pT spectrum was
1 x NR /(2πpT x BF x Eff x NE)
where NR is the number reconstructed, BF is a bin factor related to the size of the histogram bin and the
rapidity range, Eff is the reconstruction efficiency of the PHENIX detector, and NE is the number of events
or collisions produced in PHENIX. The data associated with this function is archived at Iowa State
University.
A plot of the pT spectrum vs. pT is shown below.
Fig 7: pT Spectrum
PT Spectrum
pT (GeV/c)
The pT spectrum above is only for pT between 0.7-1.5 GeV/c. It does not encompass the whole pT spectrum
due to a lack of accuracy in the extraction of the Kos peak at high pT. The uncertainties in the pT spectrum
are very high, due to the inaccuracy in the extraction of the Kos peak and the uncertainty in the efficiency
function. The error in extraction was produced by extracting the counts with three different scale factors.
The scale factors arose from an integration of the signals within a fixed range. This range was varied in
three ways and the three resulting number of counts were averaged and produced a sample standard
deviation.
III. Conclusion
The pT spectrum created in this research is a starting point for further research. The final goal is to
attain a high pT spectrum for the Kos and compare this with the cold nuclear matter prediction. If there is a
significant decrease in the experimental pT spectrum at high pT, then this spectrum is quite plausibly a
signature for quark-gluon plasma.
IV. Acknowledgements
I would like to thank the NSF and Iowa State University for giving me the opportunity to do this
research. I would also like to thank Dr. Craig Ogilvie for mentoring me in my research and Dr. Alexander
Lebedev for his answers to my numerous queries. Also, thanks to Dr. Rosati for choosing me for this REU
project.
References
[1] G.D. Coughlan and J.E. Dodd, The Ideas of Particle Physics Cambridge Univ. Press, Cambridge, 1991.
[2] http://www.bnl.gov/RHIC/QGP.htm
[3] http://www.phenix.bnl.gov/WWW/run/drawing/Phenix_pionid_2002.gif
[4] http://www.phenix.bnl.gov