**A Heavy Flavor Tracker**

**for STAR**

![](media/image1.jpeg){width="7.0in" height="7.933333333333334in"}

938316.doc

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**A Heavy Flavor Tracker for STAR**

Z. Xu

Brookhaven National Laboratory, Upton, New York 11973

Y. Chen, S. Kleinfelder, A. Koohi, S. Li

University of California, Irvine, California

H. Huang, A. Tai

University of California, Los Angeles, California 90095

V. Kushpil, M. Sumbera

Nuclear Physics Institute AS CR, 250 68 Rez/Prague, Czech Republic

C. Colledani, W. Dulinski, A. Himmi, C. Hu, A. Shabetai, M. Szelezniak,
I. Valin, M. Winter

Institut de Recherches Subatomique, Strasbourg, France

M. Miller, B. Surrow, G. Van Nieuwenhuizen

Massachusetts Institute of Technology, Cambridge, MA 02139

F. Bieser, R. Gareus, L. Greiner, F. Lesser, H.S. Matis, M. Oldenburg,
H.G. Ritter, L. Pierpoint, A. Rose, K. Schweda, E. Sichtermann, J.H.
Thomas, H. Wieman, N. Xu

Lawrence Berkeley National Laboratory, Berkeley, California 94720

I. Kotov

Ohio State University, Columbus, Ohio 43210

(The contributing authors to this proposal, listed above, gratefully
acknowledge the support of their funding agencies.)

Contents

List of Figures

List of Tables

#  {#section .unnumbered}

#   {#section-1 .unnumbered}

# Executive Summary

We propose to construct a Heavy Flavor Tracker (HFT) for the STAR
experiment at RHIC. The HFT will bring new physics capabilities to STAR
and it will significantly enhance the physics capabilities of the STAR
detector at central rapidities. The HFT will ensure that STAR will be
able to take heavy flavor data at all luminosities attainable throughout
the proposed RHIC II era.

## Scientific Motivation

The primary motivation for the HFT is to extend STAR's capability to
measure heavy flavor production down to very low transverse momenta by
the measurement of displaced vertices. These are key measurements for
the continuing heavy ion and spin physics programs at RHIC. Heavy quark
measurements will facilitate the heavy ion program as it moves from the
discovery phase to the systematic study of the dense medium created in
heavy ion collisions as well as the nucleon spin structure in polarized
p+p collisions. The primary physics topics to be addressed by the HFT
include open charm measurements, thermalization, heavy quark energy loss
and flow.

A precise measurement of the spectra of several D meson states will shed
light on several open questions in heavy ion collisions. From the
spectra and the production ratios of D states we will be able to
extrapolate to the total yield for charm quark production. Furthermore,
the open charm production rate is high enough at RHIC, that the
coalescence process becomes relevant for Charmonium production.
Knowledge of the total production cross section for charm quarks is also
essential as a baseline for J/ measurements. A meaningful answer to the
question of whether the J/ meson are suppressed or enhanced at RHIC will
need a precise knowledge of the charm production in heavy ion reactions.

The most exciting prospective measurement with the pixel detector is to
perform a measurement of the elliptic flow of D mesons down to very low
p~T~ values. It is a generally accepted fact that elliptic flow is
established in the partonic phase. If charm quarks, with a mass much
larger than the temperature of the system, acquire elliptic flow then it
has to come from many collisions with the abundant light quarks. Thus,
flow of charm quarks can be taken as a probe for frequent re-scatterings
of light quarks and thus is an indication of thermalization that may
reached in the early stages of heavy ion collisions at RHIC. Proof of
thermalization requires further measurement like thermal photons and low
mass dilepton spectra. We believe that proof of thermalization
constitutes the last step towards the establishment of the QGP at RHIC.
This measurement requires a very thin detector.

Re-scattering with light quarks is an important process because it will
affect the D meson transverse momentum spectrum. Re-scattering at the
hadronic level, mainly -D interactions, will also affect the D meson
transverse momentum spectrum. We will measure the effects of
re-scattering by comparing transverse mass spectra measured in d+Au and
Au+Au collisions.

The pixel detector will also allow us to measure the ratio of different
D meson states with high precision. This measurement can be used to test
if the different states are produced in the same ratio as in elementary
particle collisions or if the ratios are established according to
chemical equilibrium.

The heavy quark can also be used to probe the properties of the medium
created in heavy ion collisions. The production of gluons is
kinematically suppressed for heavy flavors (due to the dead cone effect)
and as a consequence heavy flavors should loose less energy in the dense
medium.

The pixel detector offers the possibility of measuring the low mass
e^+^e^-^ spectrum down to the vector meson region by removing the gamma
conversion background, while electrons and positrons are identified in
the TPC and TOF. Vector mesons reconstructed in the dilepton channel may
have decayed at any stage of the systems evolution, since leptons are
very unlikely to re-interact. Thus, studying low mass e^+^e^-^ spectrum
may yield crucial insights into the nature of the system before it
reaches the low-density hadronic freeze-out stage. Measuring the
low-mass vector mesons through their leptonic decay channel may also
yield information about the onset of chiral symmetry restoration.

With the current STAR detector configuration, heavy quark production has
been measured in p+p and d+Au collisions through the observation of
single electrons and the use of the event-mixing technique. These
methods are limited in their accuracy due to the systematic
uncertainties resulting from large background subtractions. Furthermore,
these methods require large amounts of data to overcome a poor signal to
background ratio. The HFT detector will bring extremely high precision
tracking capabilities to STAR with a point resolution of less than 10
µm, over a large pseudo-rapidity range, and complete azimuthal angle
coverage. The HFT will enable STAR to perform high precision
measurements of heavy-quark production over the broadest range of phase
space, colliding system sizes and energies.

## Detector Concept

The proposed HFT detector sits inside the STAR TPC and surrounds the
interaction vertex. It has two tracking layers composed of monolithic
CMOS pixel detectors with 30 m 30 m square pixels. These critical
innermost tracking layers lie at radii of 1.5 cm and 5 cm, respectively.
The two layers of detectors are active over 20 cm in Z and have \~ 100
Million pixels. The HFT will provide tracking information for decaying
particles that are displaced by only a few 10's of microns from the
primary vertex. The silicon chips for the detector will be thinned to 50
m and will be mounted on low mass carbon fiber structures to minimize
pointing errors generated by multiple coulomb scattering. In this
respect, the STAR HFT is unique at RHIC.

## Cost and Schedule

The total resources required to complete the Heavy Flavor Tracker is 8
to 10 million dollars, including the costs of the contributed labor
which will come from the base support of the participating institutions.
This number includes a 75% contingency on most items, including the
labor. The detector will be constructed and installed over a three year
period in time for the next full energy Au+Au run at RHIC.

# The Physics of the HFT

## Introduction

The goal of high-energy nuclear physics is to understand Quantum
Chromodynamics (QCD) at extreme temperatures and energy densities. Under
these extraordinary conditions, we believe that the fundamental entities
and symmetries of QCD will reveal themselves: quarks and gluons will be
the relevant degrees of freedom, color will be deconfined and chiral
symmetry will be restored. Calculations within the framework of
regularized lattice QCD predicts a fast cross-over from ordinary nuclear
matter into a deconfined and locally thermalized state of quarks and
gluons called the Quark-Gluon Plasma[^1] (QGP).

High-energy nuclear collisions can be characterized by three distinct
phases: the initial phase where hard interactions between the partons of
the incoming nuclei dominate, an intermediate phase where
re-interactions between the constituents in the matter result in
collectivity, and a final stage where hadronization, chemical, and
thermal freeze-out occur. The matter produced in high-energy nuclear
collisions can be investigated by studying the dynamics of the
collective expansion of the bulk of the produced particles and by
studying the interaction of the medium with penetrating probes such as
jets. The measurement of large elliptic flow[^2] and the observation of
strong modifications of high *p~T~* particle production[^3]^,^[^4] have
provided evidence for a high density and strongly interacting state of
matter at RHIC. The goal of our research is to elucidate the nature of
this matter, in particular whether it is dominated by hadronic or
partonic degrees of freedom.

Rare processes provide additional ways to probe the medium generated in
high-energy nuclear collisions. Bjorken[^5] proposed that hard scattered
partons (quarks and gluons) drawn from the incoming nuclei will interact
with the medium in a density-dependent way. Bjorken's initial energy
loss mechanism (elastic scattering) did not provide effects large enough
to be observed but medium-induced radiation (gluonic bremsstrahlung) can
generate significant energy loss effects[^6]^,^[^7]. For example, hard
partons are indirectly observable in elementary particle collisions (
*e^+^+ e*, *p* +*p* ) due to their fragmentation into collimated sprays
of energetic hadrons (jets) at large transverse angles with respect to
the beam. Jets can also be identified in high energy nuclear collisions
on a statistical basis; the modification of their properties may signal
novel energy loss mechanisms in a dense medium by the parton that
initiated the jet. Full jet reconstruction in heavy ion collisions is
exceedingly difficult but leading hadrons (i.e. high *p*~T~ hadrons,
which typically carry a large fraction of the jet energy) and their
correlations may provide the essential signals of partonic interactions
in the medium.

Collective flow measurements have played a prominent role in
understanding the physics of nuclear collisions because the magnitude
and pattern of the collective motion is closely related to the equation
of state (EOS) of the produced matter. If local equilibrium is achieved,
the EOS will be driven by the degrees of freedom relevant for the basic
constituents, which make up the matter. By studying flow it is possible
to determine key information about the nature of the matter and when it
is produced.

Heavy quark (*c,b*) production provides the most important observables.
Due to their large masses, *c* and *b* quarks are produced dominantly by
the interactions of the initial incoming partons whereas lighter quarks
are produced throughout the evolution of a heavy ion collision. Thus,
the total yields of *c* and *b* quark production provide a direct
connection to the initial state.

Due to their heavy mass and presumably small hadronic cross sections,
charmed quarks are a sensitive probe for the amount of interaction and
therefore the degree of thermalization among constituents before
hadronization. At high *p*~T~, heavy quarks may be less suppressed than
light quarks due to the \"dead cone\" effect, giving an additional way
to study partonic energy loss. If charmed quarks participate
sufficiently in re-scattering processes, they will develop flow (i.e.
transverse radial and elliptic flow) which can be observed in charmed
hadrons momentum distributions. Finally, charmed quarks might achieve
equilibrium in the surrounding medium leading to statistical
hadronization. In this case, the relative abundances of charmed hadrons
are significantly modified.

The study of the structure of the nucleon is an important frontier in
strong interaction physics. Despite considerable experimental and
theoretical progress over the past several decades, many open questions
remain. A striking example is the spin structure of the proton which has
been of key interest ever since the European Muon Collaboration
published their data on the spin structure function
*g~1~(x,Q^2^)*[^8]^,^[^9]. The EMC data and subsequent data indicate
that the quark helicity contribution to the proton spin is remarkably
small. The natural question regarding the fraction of the nucleon spin
carried by gluon helicities remains basically unanswered. Unlike
previous nucleon spin measurements, STAR will observe processes where
the polarized gluon distribution function *G(x,Q^2^)* contributes at
leading order via a hadronic, not electromagnetic, probe. Heavy quark
production is expected to provide direct access to gluons in the proton
with a large analyzing power for longitudinal spins.

## Initial Heavy Quark Production 

Quarks are elementary particles. Depending on the interacting energy
scales, there are two mechanisms are responsible to their mass
generation^11^: current quark masses (Higgs mass) are generated by the
electroweak symmetry breaking mechanism and, in QCD, the spontaneous
Chiral symmetry breaking leads to the constituent quark masses (QCD
mass). The QCD interactions affect only the light quarks (u, d, s) while
the heavy quark (c, b, t) masses are totally dictated by the Higgs
mechanism, see Figure 1. In high-energy collisions at RHIC energies,
heavy quarks are produced through gluon fusion and *qq*
annihilation[^10]. Heavy quark production is also sensitive to the
parton distribution function and the mass of the heavy quark. Therefore,
the production of heavy quarks in nuclear collisions should scale with
the number of binary nucleon-nucleon collisions. Unlike the light
quarks, heavy quark masses are not modified by the surrounding QCD
medium[^11] and the values of their masses are much higher than the
initial excitation of the system. There fore, heavy quarks constitute
ideal probes to study the properties of the hot-dense medium created in
high-energy nuclear collisions.

![](media/image2.png){width="5.006944444444445in"
height="3.0631944444444446in"}

Figure XXX: Masses of the six quark flavors. The current and constituent
masses are shown by blue- and yellow-boxes, respectively. The figure is
adapted from Ref. 11.

Understanding the charm hadron yield in hadron-hadron collisions
requires a knowledge of the projectile and target parton distribution
functions, the cross sections for gluon fusion ( *gg* *cc* ), the
cross-section for quark anti-quark annihilation ( *qq* *cc* ), and the
fragmentation functions for *c*(*b*) quarks into charm (bottom) hadrons.
These cross-sections are usually calculated in a perturbative QCD
framework up to next-to leading-order (NLO)[^12]. The parton
distributions within the proton are extracted by parameterizing the data
from electron-proton collisions. We note that the parton and gluon
distribution functions within the nucleus, relevant to the charm and
bottom quark production at RHIC energies, are poorly understood[^13] and
thus leave room for precise measurements of charm cross sections in p+p,
d+Au and Au+Au collisions.

Perturbative QCD predictions for the cross section (*cc*) and (*b*) in
p+p collisions at √s~NN~ = 200 GeV may be found in the literatureError:
Reference source not found.

+-----------------------------------------------------------------------+
| (*cc* ) = 289 - 445 µb                                                |
|                                                                       |
| 8 - 13 *cc* pairs per central Au+Au collision at √s~NN~ = 200 GeV     |
+-----------------------------------------------------------------------+
| (*b*) = 1.64 - 2.16 µb                                                |
|                                                                       |
| 0.04 - 0.06 *b* pairs per central Au+Au collision at √s~NN~ = 200 GeV |
+-----------------------------------------------------------------------+

The uncertainty in these cross-sections arises from a reasonable
variation of quark masses (*m~c~* = 1.2-1.4 GeV, *m~b~* = 4.5-5.0 GeV),
factorization and renormalization scales (~R~ and ~F~), and parton
distribution functions (MRST, CTEQ, GRV). In these estimated, the number
of pairs produced per central Au+Au collision was obtained by
multiplication with the nuclear overlap integral T~AA~ (29.3 mb^-1^),
corresponding to \~ 1150 binary nucleon-nucleon scatterings per Au+Au
collision. The cross section values are normalized per participating
nucleon-pair, thus in the calculation of yield for central Au+Au
collisions, a factor of N~binary~ = 350 must be taken into account.

Final state interactions may enhance charm production relative to the
binary scaling of initial parton collisions and may also lead to thermal
production of charm. An analogous mechanism dominates strangeness
production. The heavy quark mass (*m~c~* ≈ 1.2 to 1.8 GeV, *m~b~* ≈ 4.5
to 5.0 GeV), however, should greatly suppress this channel[^14], making
heavy quark production rates sensitive to the dynamics of the early
partonic stage of the collision. Figure 1 shows the calculated
contributions to the total charm production at *y* = 0 at √S~NN~ = 200
GeV, with an energy density of 3.2 GeV/fm^3^ at the moment of thermal
equilibration.

![](media/image3.jpeg){width="3.5277777777777777in"
height="3.9930555555555554in"}

Figure 1: Contributions to charm production at RHIC energies. The
distributions were calculated with an energy density of 3.2 GeV/fm^3^ at
the moment of thermal equilibration. The figure is from Ref. \[Error:
Reference source not found\].

In Au*+*Au collisions at RHIC, a large thermal enhancement with respect
to the expectations of pQCD is ruled out by the recent single electron
spectra measured by the PHENIX collaboration[^15]. On the other hand,
the STAR collaboration has reported an unexpectedly large cross-section
for open charm in dAu collisions by doing a direct reconstruction of the
open charm hadrons[^16] as well as through single electron spectra. The
data are shown in Figure 2. In general, single electron spectra only
provide an indirect measurement of the charmed (bottom) hadron yield
because additional, secondary, decays of charm and bottom decay products
account for a significant fraction of the electron yield at high
momentum (above 2-3 GeV/c for charm hadrons and above 5 GeV/c for the
bottom hadrons). Large systematic errors are associated with the
extraction of these charmed (bottom) quark yields because of the large
background subtraction required at low momentum and the assumptions that
need to be made on the charm (bottom) hadron composition and spectra.

In contrast, the HFT will directly measure the spectra of the various
charmed hadrons, including the D^+^, D, D^0^, D~s~^+^, and possibly
~c~^+^, thus overcoming these systematic problems.

![](media/image4.png){width="5.991666666666666in"
height="4.290277777777778in"}

Figure 2: Total cc production cross-sections per nucleon-nucleon
collision vs. collision energy. The dashed line depicts a PYTHIA
calculation[^17]. The solid and dot-dashed lines depict two NLO pQCD
calculations with MRST HO, m~c~ = 1.2 GeV/c^2^, µ~F~ = 2m~c~, µ~R~ =
m~c~ and 2m~c~, respectively[^18]. The figure is from Ref. \[[^19]\].

## Probing the Density of the Medium: Heavy Quark Energy Loss

Key words: *heavy-quark energy-loss, charm-quark correlations,
charm-quark jets, beauty production*

**2.3.1 High p~T~** **transverse momentum distributions**

The discovery of a factor of 4 to 5 suppression of high *p~T~* hadrons
(5 \< *p~T~* \< 10 GeV/c) produced in Au+Au collisions at RHIC and the
disappearance of the away-side jet has been interpreted as evidence for
jet quenchingError: Reference source not found^,^[^20]^,^[^21]^,^[^22].
This effect was predicted to occur due to radiative energy loss of high
energy partons that propagate through a dense and strongly interacting
medium[^23]. Heavy quarks are also predicted to lose energy as they
traverse the medium, however, their energy loss is predicted to be
significantly less because of a suppression of gluon radiation at angles
\< *M~Q~ /E*, where *M~Q~* is the heavy quark mass and *E* is the heavy
quark energy[^24]. This kinematic effect is known as the "dead cone"
effect. The suppression of small angle radiation has the advantage that
the heavy quark fragmentation function and the spectrum of light
particles produced in association with the heavy quarks can be
calculated perturbatively.

Figure 3 shows the result for the ratio of charm (H) to light (L) quark
suppression from QCD calculations assuming a size of about 5 fm for the
static medium traversed by the fast quark. Above a transverse momentum
p~T~ \> 7.5 GeV/c this ratio is predicted to be about 2.0 due to the
smaller energy loss of the heavy quark. In the case where heavy quarks
suffer the same amount of energy loss as light quarks, this ratio would
be one. This ratio is exponentially sensitive to the density of color
charges in the medium, therefore, the measurement of nuclear
modification factors of open charm mesons at large transverse momentum
is a promising tool for the study and further characterization of QCD
matter at RHIC.

![](media/image6.png){width="4.00625in" height="2.6805555555555554in"}

Figure 3: The ratio of suppression factors in hot matter for charm (H)
and light (L) quarks. The solid line represents results from
calculations with unrestricted gluon radiation, while the dashed line is
based on calculations with a cut on gluon energies \> 0.5 GeV. The size
of the static medium traversed by the fast quark is assumed to be 5 fm.
The figure is from Ref. \[Error: Reference source not found\].

Recent results \[Ref. HBuesching,JDunlop,XDong\] of the non-photonic
electron R~AA~ up to p~T~ \~ 10 GeV/c show that the suppression factor
is in the range of 0.2-0.3 which is almost exact the same as that of
observed for charged hadrons and pions \[Ref. RAA of STAR charged
hadron, phenix pion0 RAA\]. With the extreme limit of the initial gluon
density, dN~g~/dy = 3500 (Note: for light-quark hadron like pions, the
gluon density is 1000), a pQCD calculation \[Ref. gyulassy1\] with gluon
radiative energy-loss could barely reproduce the electron R~AA~
excluding the contributions from bueaty-hadrons, see blue-band in Fig.
4. When the beauty is included, the model overpredicted by a factor of
2-3, see yellow-band in Fig. 4. The results raise a serious challenge to
our understanding of both the heavy-quark production and the mechanism
for energy-loss in hot and dense medium. In order to resolve these
important issues, one has to measure the charm contributions with the
reconstructed D-mesons as the electron distributions are greatly
compromised by the decay kinematics.

![](media/image7.png){width="5.356944444444444in"
height="3.8152777777777778in"}

Figure 4: Non-photonic electron R~AA~ in central Au+Au collisions from
PHENIX (filled-symbols, top 10%) and STAR (open-symbols, top 5%)
experiments \[Refs. Phenix electron RAA qm05,STAR electron RAA
qm05,XDong\]. Theoretical predictions for charm-hadron and both charm-,
bueaty-hadron decayed electrons are shown as blue- and yellow-bands,
respectively. In these calculations, a number of 3500 for the initial
gluon density was used \[gyulassy1\] .

As mentioned earlier, at the intermediate p~T~ region 2 \< p~T~ \< 6
GeV/c, light-quark baryon productions were found to be enhanced compared
to that of the mesons in Au+Au collisions at RHIC. Furtheremore, the
enhancement is found to be proportional to the collision centrality.
These observations have been confired by the R~AA~ and v~2~
measurements. Rather than the indpendent vavuum fragmentation, a
hadronization mechanism involving a collective multi-partons coalescence
was employed to explain the observation. The success of the coalescence
approach implies deconfinement and possibly thermalization of the light
quarks prio to hadronization. Since ~c~ is the lightest charm-baryons
and its mass is not far from most of the D-mesons, it is very
interesting to measure the R~AA~ of ~c~ and compare with that of the
other charm-mesons. Heavy quark deconfinement and collectivity can be
tested from the comparisons. In addition, deu to different branching
ratios of the semi-leptonic decays, the measurement of the ~c~ spectra
will help us to understand the surprising suppresion observed in the
non-photonic electrons. In this case, even if charm quark production
scales with the number of binary collisions, an increase in the ratio
~c~ /D-meson similar to that seen for the /Kaon ratio will lead to about
a 20% suppression in non-photonic electrons in central Au+Au collisions
\[ref. sorensen\].

\[Phenic electron RAA qm05\]: H. Buesching, (Phenic Collaboration), QM05
proceedings.

\[STAR electron RAA qm05\]: J. Dunlop, (STAR Collaboration), QM05
proceedings.

\[XDong\] X. Dong, charm production overview, QM05 proceedings.

\[STAR RAA\] J. Adams, et al. (STAR Collaboration), Phys. Rev. Lett. 91
(2003) 072304.

\[Phenix pion0 RAA\] S.S. Adler et al. (Phenix Collaboration), Phys.
Rev. Lett. 91, 072301(2003).

\[gyulassy1\] M. Djordjevic, M. Gyulassy, R. Vogt, and S. Wicks,
nucl-th/0507019.

\[sorensen\] X. Dong, P. Sorensen, N. Xu, in preparation, Sept. 2005.

Measuring high transverse momentum charm and bottom quark production
requires a good trigger and data acquisition system because their
production cross section is very small. A significant fraction of B
(\~10%) and D (6-17%) meson decays include an electron/positron in the
final state. The STAR electromagnetic calorimeter allows us to trigger
on high transverse momentum electromagnetic showers, which include
electrons and positrons. Since the only source of high transverse
momentum electrons and positrons are D and B decays, the D and B
transverse momentum distribution can be inferred above a certain
momentum from the electron and positron spectra.

If an electromagnetic shower can be matched to a track reconstructed in
the TPC, it is tagged as an electron or positron. A significant
background that lies under the reconstructed electron signal comes from
charged pions going through a charge-exchange process, i.e. becoming
neutral pions, in the calorimeter. The neutral pions decay immediately
into two photons, which produces an electromagnetic shower identical to
an electron shower. The charge-exchange cross-section is poorly known,
which leads to large uncertainties in the estimates for such processes.
The only measurable difference between an electron/positron from D and B
decay and a high transverse momentum pion producing an electromagnetic
shower is their spatial origin. High p~T~ charged pions come from the
primary vertex while electrons and positrons come from the B and D decay
vertex which are displaced from the primary vertex by a few hundred m.
These different decay locations can be selected by the HFT.

The CDF collaboration has shown that B jet tagging can be achieved by
associating the electron or positron to one of the other charged hadrons
decay products[^25]. Figure 4 shows a feasibility study applying a
technique to remove background that is similar to what we would use with
the HFT. The channels they studied include
$B^{+} \rightarrow {\overline{D}}^{0} + e^{+} + \nu$ and
${\overline{D}}^{0} \rightarrow K^{+} + \pi^{-}$. The positron is
matched with either the kaon or pion from the D meson decay, if their
distance of closest approach is less than 150 microns. The B decay
vertex is then located at the mid-point between both points of closest
approach on each helix. The variable shown in Figure 4 is the distance
between the B and the primary vertices. The sign is given by the scalar
product of the electron momentum with the vector constructed from the
primary vertex to the reconstructed decay vertex. The background is
simulated by embedding high transverse momentum tracks into events that
match the momentum distribution measured in 200 GeV central AuAu
collisions below 3 GeV/c. The relative normalization between the
background and B decay distribution is arbitrary, as the charge-exchange
cross-section is not well known. By applying a signed-decay-length cut
of more than 250 m, the background is suppressed by a factor 200 while
keeping 60% of the signal. Thus, adding the decay vertex information
will help to significantly remove the background in the high transverse
momentum electron/positron spectra and substantially increase the
statistical significance of the measurement. We note that the charm and
bottom decay lengths differ substantially, thus improving the
statistical significance of the measurement.

![](media/image8.jpeg){width="4.196527777777778in"
height="3.0006944444444446in"}

Figure 4: Distance of the B^+^ decay position from the primary vertex.
Full circles are from high-momentum simulated B^+^ e^+^ + X decays, open
circles show the distribution of combinatorial background. The arrow
indicates a cut at 250 m optimizing the signal to background ratio.

**2.3.2 Charm angular correlations**

Results reported at the recent QM05 conference on the nuclear
modification factor R~AA~ indicate that the heavy-quark energy loss in
central Au+Au collisions is similar to that of the light-quarks (u, d,
s). Since there is no directly reconstructed heavy-quark hadron
distributions in experiments at RHIC, the electron R~AA~ was used for
the heavy-quark study for the electron transverse momentum range: 4 \<
p~T~ \< 10 GeV/c. This experimental observation contradicts our early
understanding of the pQCD interactions of energetic partons in hot and
dense medium where much less energy loss is expected for heavy-quarks
compared with the light ones \[Kharzeev1,Gyulassy1,Armesto1\]. When
analysis the data with only electron p~T~ distributions, the issue is
further complicated by the unknown mixture of charm and beauty
contributions in heavy-ion collisions at RHIC energies. Reconstructed
charmed-hadron distributions and angular correlations are absolutely
needed in order to detangle the important problem at RHIC.

The correlation is defined as the normalized pair distributions:

C() = N(p~1~,p~2~)/N~0~

where p~1~ and p~2~ are the momenta of the charm hadron, N~0~ is the
total number pairs.

-   ![](media/image9.png){width="5.259722222222222in"
    height="3.907638888888889in"}

-   

-   **[Figure XXX:]{.underline}** D-meson correlation functions from 200
    GeV p+p collisions. Default parameters in the Pythia model \[1\]
    were used in the calculations. A clear back-to-back correlation in
    the charmed meson production is observed. Solid-line and diamonds
    represent the results with angular smearing for = /4 and /2,
    respectively.

-   without energy loss, respectively.

-   Similar to jets production, heavy-quark production requires large
    momentum transfer therefore one expects a distinct back-to-back
    topology. Again because their heavy masses, the charm- (or bottom-)
    hadrons are also formed with the back-to-back structure in
    elementary collisions as shown in Figure XXX by the open-circles. In
    this calculation, the Pythia (v6.2) was used with the default sets
    of parameters. As one can see in the figure, there is a clear
    back-to-back correlation for the D-mesons. Here we propose to
    utilize the distingue correlation to study the charm-quark energy
    loss in high-energy nuclear collisions. In the following, we will
    discuss few observables:

-   

(i) When a charm-quark interacts with the medium, it will not only loss
    its energy, the original angular correlation pattern as shown in the
    figure will also be modified. In Fig. 1, the tests with angular
    smearing of \< \> = /4 and /2 shown as solid-line and diamonds are
    also plotted. In addition, the change of the angular correlation
    depends on the nature of the interaction. Most of the (semi)elastic
    scatterings are forwarded \[Tai1,Rapp1\], while the inelastic
    scatterings, such as the gluon radiative energy loss \[Gyulassy1\],
    would lead to a much wider smearing in the final correlation. In the
    inelastic scattering scenario \[Gyulassy1,Armenstro1\], the
    energy-loss occurs in deep plasma and the final correlation function
    reflects the hot/dense properties of the medium. On the other hand,
    the resonant scattering happens at near T~c~ \[Rapp1\]. Although
    both scenarios lead to sizable energy-loss \[Gyulassy1,Rapp1\], the
    angular correlations should allow us to distinguish these two
    different mechanisms in high-energy nuclear collisions. In order to
    perform the measurement, a large acceptance with the reconstructed
    charm-hadrons is essential. The proposed HFT, plus STAR TPC and TOF,
    will be necessary for this study.

(ii) Recently, the measurements on charm production by the Bell
     Collaboration \[Bell\] showed a surprising large cross section for
     J/ in sqrt(s)=10.6 GeV e+e collisions. Even more surprising, more
     than half of the observed J/'s were accompanied with ccbar pairs.
     This result contracts our current understanding for J/ production
     in the pQCD framework, such as those discussed in Refs. \[Pythia,
     Cho, Baek, Yuan\], and implies a different production mechanism for
     heavy-quarks in elementary collisions \[Kharzee2\]. As proposed in
     \[Kharzeev2\], the gluon fragmentation will become increasingly
     important for collisions at higher bombarding energies. In
     elementary collisions, the main difference between the new and
     conventional processes lies in the angular correlation of the
     produced charm-hadrons. With the proposed HFT and STAR EMC
     (Electro-Magnetic Calorimeter), we will study the correlation to
     further the pQCD in p+p collisions at RHIC energies. In addition,
     in high-energy nuclear collisions, gluon density is high
     \[Gyulassy2, Kharzeev4\] which might enhance the effect observed in
     elementary collisions. Such correlation study will certainly shed
     light on the production mechanisms for charm and charmonium at
     RHIC.

(iii) As discussed above that heavy-quarks production leads to the
      correlation between particle and its anti-particles. It also
      reflected in their decayed products, such as the electron pairs.
      In this case, it causes the background at the intermediate mass
      region 1 \< m~ee~ \< 3 GeV/c^2^ \[Rapp2\]. Here m~ee~ is the
      invariant mass of the electron pair. Analyzing the correlated
      electron pairs with the proposed HFT, the charm background will be
      greatly reduced. More discussion on this will be presented in
      Section 2.5.

(iv) (***This part is more on the speculation part!)*** Recently, there
     have been several proposals to measure the sound velocity of the
     hot/dense medium created in high-energy nuclear collisions
     \[Stocker,Solana,Muller\]. In order to recognize the direction of
     the initial direction, a hard-soft correlation method is used
     \[FWang_qm05\]. Compared with the light quark jet the direction of
     a heavy quark jet is less affected in the medium. Therefore a
     charm-jet should provide a correlation with much better sensitivity
     in the shape of the QCD medium (Mach cone) \[Majumder\]. In such
     analysis, a large acceptance with the tagged charm-jet is
     essential.

-   [References:]{.underline}

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-   \[Armesto1\] [Nestor
    Armesto](http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+Armesto,+Nestor),
    [Andrea
    Dainese](http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+Dainese,+Andrea),
    [Carlos A.
    Salgado](http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+Salgado,+Carlos+A.),
    [Urs Achim
    Wiedemann](http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+Wiedemann,+Urs+Achim),
    Phys. Rev. D71, 054027(2005); hep-ph/0501225

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-   \[Baek\] S. Baek, P. Ko, J. Lee, and H.S. Song, J. Korean Phys. Soc.
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-   \[Bell\] K. Abe, et al. (Bell Collaboration), Phys. Rev. Lett. 89,
    142001(2002).

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-   \[Cho\] P.L.Cho and A.K. Leibovich, Phys. Rev. D54, 6690(1996).

-   

-   \[Gyulassy1\] [Magdalena
    Djordjevic](http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+Djordjevic,+Magdalena),
    [Miklos
    Gyulassy](http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+Gyulassy,+Miklos),
    and [Simon
    Wicks](http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+Wicks,+Simon),
    Phys. Rev. Lett. [94]{.underline}, 112301(2005);  hep-ph/0410372.

-   

-   \[Gyulassy2\] [Magdalena
    Djordjevic](http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+Djordjevic,+Magdalena),
    [Miklos
    Gyulassy](http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+Gyulassy,+Miklos),
    [Ramona
    Vogt](http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+Vogt,+Ramona),
    [Simon
    Wicks](http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+Wicks,+Simon),
    nucl-th/0507019.

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-   \[Kharzeev1\] Y.L. Dokshitzer and D.E. Kharzeev, Phys. Lett. B519,
    199(2001).

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-   \[Kharzeev2\] B.L. Ioffe and D.E. Kharzeev, Phys. Rev. D69,
    014016(2004).

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-   \[Kharzeev3\] "Quarkconium polarization ..." B.L. Ioffe and D.E.
    Kharzeev, Phys. Rev. C68, 061902(2003).

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-   \[Kharzeev4\] D.E. Kharzeev and K. Tuchin, Nucl. Phys. A753,
    316(2005).

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-   \[Pythia\]

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-   \[Rapp2\] R. Rapp, Phys. Rev. C63, 054907(2001).

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-   \[Rapp1\] [Hendrik van
    Hees](http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+van+Hees,+Hendrik),
    [Vincenzo
    Greco](http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+Greco,+Vincenzo),
    and [Ralf
    Rapp](http://www.slac.stanford.edu/spires/find/wwwhepau/wwwscan?rawcmd=fin+Rapp,+Ralf),
    nucl-th/0508055.

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-   \[Tai1\]

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-   \[Yuan\] F. Yuan, D.F. Aiao, and K.T. Chao, Phys. Rev. D56,
    321(1997).

    \[Stocker\] H. Stocker, Nucl. Phys. **A750**, 121(2005); *idib*,
    nucl-th/0506013.

    \[Solana\] J.Casalderrey-Solana, E.V. Shuryak, D. Teaney,
    hep-ph/0411315.

\[Muller\] B. Muller, J. Ruppert, nucl-th/0507043.

\[Fwang_qm05\] F. Wang, (STAR Collaboration), QM05 proceedings, 2005.

-   \[Majumder\] A. Majumder, lbl, private communications, 2005.

Probing Medium Thermalization: Charm Quark Re-interactions

Key words: *partonic EoS, partonic collectivity, local thermalization,
hadro-chemistry, charm elliptic flow, vector meson, in-medium masses*

The successful measurement of partonic collectivity of light flavor
hadrons is an important step towards the discovery of a QGP. However,
this is not sufficient. It is also important to address the issue of
thermalization together with collectivity. A measurement of transverse
radial and elliptic flow of identified hadrons consisting of light quark
flavors (*q = u, d, s*) has been performed at RHIC. The main conclusions
from these studies are: the system created in ultra-relativistic Au+Au
collisions at RHIC exhibits strong collective expansion. Compared to
measurements at lower SPS energies, the degree of collectivity is
stronger. Also multi-strange hadrons ( and ) appear to freeze-out at a
higher temperatures and lower collective velocities than lighter
hadrons. This has been interpreted as an indication that sizeable
partonic collectivity develops at RHIC. Details of these studies can be
found in the literatureError: Reference source not
found^,^[^26]^,^[^27]^,^[^28]^,^[^29].

At RHIC energies, theoretical calculations indicate that thermalization
may be reached at temperatures T~eq~ 0.3-0.5 GeV[^30] and that the
duration of the equilibrium period is on the order of 5-10
fm/c[^31]^,^[^32]. Thermal production of *cc* pairs is therefore
suppressed (m~cc~ = 2.2 -- 2.3 GeV/*c*^2^). However, charmed hadrons may
still be produced in a thermalized fashion if the *c* and *c* quarks
become embedded in a thermalized bath of light quarks. The relative
probability of creating different charmed hadrons will be driven by the
properties of the medium providing the additional quarks necessary to
form the hadrons. The relative yield of various charmed hadrons is thus
sensitive to the collective properties (temperature and chemical
potentials) of the light quark medium.

The strength of the charm hadron flow is potentially an indicator of
thermalization occurring at the partonic level. If charm quarks flow
together with the light flavor quarks, then there must be copious
interactions among light and charmed quarks. Therefore, thermalization
is likely reached through partonic re-scattering. In order to test the
question of thermalization experimentally, we propose to measure the
charmed hadron transverse radial and elliptic flow (v~2~) with the STAR
HFT detector. The combination of the open charm spectra and v~2~ will
allow us to determine the collective properties of the charmed quarks
and therefore the probable degree of thermalization of the light quarks.

### Transverse Momentum Distributions

The development of collectivity at the partonic level (among quarks and
gluons) in high-energy nuclear collisions and the degree of
thermalization are closely related to the underlying equation of state
of partonic matter. Theoretical arguments show that different aspects of
the measured final hadronic momentum distributions are determined at
different stages of the collision history. Hence hadronic observables,
and their corresponding parameterizations which characterize the
freeze-out distributions, constrain the dynamical evolution and so they
yield indirect information about different stages of the collision.
After hadronization, inelastic collisions which change the particle
species cease and particle abundances are fixed: this is commonly
referred to as chemical freeze-out. Later when elastic interactions
cease, the particle momentum spectra become fixed; this is referred to
as kinetic freeze-out. For most particle species, transverse radial flow
is accumulated throughout the whole collision history while transverse
elliptic flow is believed to saturate earlier.

Thermal motion and collective flow can only be distinguished in the
soft-hadron spectra by a thermal model analysis. Measured transverse
mass spectra can be fit with a hydrodynamically motivated approach using
a kinetic freeze-out temperature *T*~fo~ and a mean collective flow
velocity \<~r~\>. This type of analysis does not take into account the
abundances of particles and thus only tests the *kinetic* thermal
equilibrium and is not sensitive to chemical equilibrium.

The spectra of low mass particles, like pions, are dominated by a
temperature parameter, while the spectra of heavier mass particles are
dominated by a flow velocity. Transverse radial flow modifies the
particle spectrum by depopulating the yield at low momentum. The result
is a characteristic shoulder in the low-momentum region, strongly
depending on particle mass. Hence, the measurement of particles to the
lowest possible momentum is essential for spectral analysis in the charm
sector. Also, good momentum coverage is necessary to reliably extract
integrated yields. This minimizes systematic uncertainties in
extrapolating yields especially at low momentum where theoretically the
particle spectrum is not well known.

First measurements of D-meson spectra at RHIC energies have been
obtained in d+Au collisionsError: Reference source not found.  Both the
p~T~ integrated yield dN/dy and the value of \<p~T~\> of the measured
D-meson spectrum are larger than the pQCD model predictions \[16\]. When
direct measurements of heavy flavor hadrons are experimentally
unfeasable, non-photonic electrons from heavy flavor decays have be used
to study charm production. There are, however, serious limitations in
such substutions. As shown in Ref. \[37\], the decayed electron
distributions are insensitive in the intrinic shape D-meson transverse
momentum distribution. Due to the decay kinematics and the light mass of
the electrons (posotrons), the dynamical information in the mrimary
spectrum is lost. See Fig. \[xxx\], taken from Ref. \[37\], although a
clear difference between the zero mean free path hydrodynamic flow
prediction (solid) and the infinite mean free path pQCD Pythia
(dashed-line) calculations for D-mesons, the resulting electron spectra
become indistingqishable \[37\]. In order to extract the information of
heavy flavor production in heavy ion collisions, therefore, one must
measure the charm- and beauty-hadrons directly. The same conclusion is
reached when analysis the R~AA~ of heavy flavors.

![](media/image10.png){width="5.2652777777777775in"
height="4.245833333333334in"}

Figure 5: Solid- and dashed-curves represent the charm- (red) and
beauty-hadron (blue) spectra from blast-wave model and Pythia model
calculations, respectively. The corresponding heavy flavor decayed
electron spectra are shown as black curves. Symbols are fom the measured
single electron distribution in 10% central Au+Au collisions at 130 GeV
\[K. Adcox etal., Phys. Rev. Lett. 88, 192303(2002).\].

The nuclear modification factor, R~AA,~ for D-mesons is shown in Figure
6. As onu can see, there are drastic difference in  the two D-meson
R~AA~, their corresponding decayed electron R~AA~ curves  are almost the
same for p~T~ \< 5GeV/*c*. Additionally, an electron measurement
comprises large systematic uncertainties at lower momentum due to the
large experimental background from photonic electron productionError:
Reference source not found^,Error:\ Reference\ source\ not\ found^. For
a precise measurement of charmed quark flow, a direct reconstruction of
D  π + K is required. Similar conclusions have been drawn by Bastsouli
at[^33] At even higher p~T~, electrons from B-meson decays will become
more abundant making the electrn  measurement for charm physics even
less realistic.  This clearly calls for a  direct measurement of heavy
flavor hadrons, i.e. D- and B-mesons.

![](media/image11.jpeg){width="4.720833333333333in"
height="2.9972222222222222in"}

Figure 6: Nuclear modification factor R~AA~ of D-mesons, assuming the
measured spectrum from d+Au collisions scales as the light charged
hadrons in central Au+Au collisions (black dashed line, II) and from a
hydro-dynamically inspired parameterization assuming a collective flow
velocity of \<~r~\> = 0.4*c* for D-mesons (black solid line, II); the
corresponding electron decay-spectra are shown by the grey dashed (I)
and solid (II) line.

### Elliptic Flow

In nuclear collisions, the build-up of pressure and pressure gradients
leads to collectivity. In non-central collisions, the initial overlap
zone between the colliding nuclei is spatially deformed. If the matter
produced in the reaction zone re-scatters sufficiently, then this
spatial anisotropy is transferred into a momentum space anisotropy.
Re-scattering is a sufficient condition for the development of these
anisotropies; thermalization is not required. The largest momentum
anisotropies are obtained in the hydrodynamic limit[^34], where zero
mean free path length and therefore infinitely fast re-scattering is
assumed; this leads to instantaneous local thermal equilibrium.

The momentum space anisotropies lead to a dependence of the
transverse-momentum distribution on the emission angle relative to the
reaction plane. The anisotropy can be quantified by the coefficients of
a Fourier decomposition of the distribution in azimuth.

The largest contribution comes from the second Fourier coefficient
*v*~2~(*p*~T~, *y*), the *elliptic flow coefficient*. In the evolution
of elliptic flow, the strong and early spatial deformation decreases
because the matter begins to expand more rapidly in the short
direction[^35]. As the spatial deformation disappears, the build-up of
flow due to pressure gradients ceases and the elliptic flow saturates.
Therefore, elliptic flow is thought to be a signal that develops in the
early stages of a collision. RHIC dataError: Reference source not
found^,^[^36]^,^[^37] show that in semi-central Au+Au collisions the
elliptic flow reaches the hydrodynamic limit for transverse momenta up
to 2 GeV/c, suggesting early thermalization and pressure buildupError:
Reference source not found. Thus, information about the equation of
state[^38] can be determined. If all hadron species experience the same
anisotropic flow, their *v*~2~ coefficients should obey simple
hydrodynamic relationsError: Reference source not found and exhibit a
characteristic mass dependence. As an example, Figure 7 (top) shows the
measured elliptic flow of strange hadrons up to the multiply-strange
cascade baryon. At low momentum, all particles exhibit a linear rise in
*v*~2~ and a clear mass ordering appears; from the lower mass kaon to
the heavier cascade. These measurements demonstrate that collectivity is
established at the partonic level. The bottom plot of Figure 7 shows the
measured elliptic flow versus transverse momentum; where both axes are
scaled with the number of constituent quarks. Quark coalescence models
predict a universal scaling of *v*~2~/n versus *p*~T~/n at intermediate
momentum where quark recombination is (supposedly) the dominant hadron
production mechanism. In these models, collectivity -- the elliptic flow
of constituent quarks -- is intrinsically built in and supports the idea
of partonic collectivity.

![](media/image12.png){width="2.85in" height="4.022222222222222in"}

Figure 7: Elliptic flow of strange hadrons at RHIC as measured by the
STAR detector. The top panel demonstrates typical hydro-dynamical mass
ordering up to a momentum p~T~ \< 2GeV/c and saturation at larger
momentum. The bottom panel shows the scaling of elliptic flow with the
number n (baryons, n=3; mesons, n= 2) of constituent quarks in the
saturation region.

At RHIC energies, charmed quarks are abundantly produced. Due to their
high mass and small interaction cross section, the strength of elliptic
flow of heavy flavor hadrons may be a good indicator of thermalization
occurring at the partonic level. If heavy flavor hadrons flow together
with the light flavor hadrons, this indicates frequent interactions
between the light and heavy quarks. Hence, thermalization of light
quarks is likely to have been reached through partonic re-scattering.

Figure 8 shows the first indication of charm particle elliptic flow at
RHIC measured in the inclusive electron channel. The predictions assume
elliptic flow for the light quarks as determined by fits to experimental
data. Presently, the data support the idea that the heavy charmed quarks
flow. However, uncertainties are rather large, especially at low
transverse momentum where hydrodynamic behavior should occur. A precise
measurement of directly reconstructed open charm hadrons to low momentum
is essential to confirm and further quantify elliptic flow of the
charmed quarks.

![](media/image13.jpeg){width="6.002777777777778in"
height="3.748611111111111in"}

Figure 8: A hint of charmed elliptic flow at RHIC. Blue and Red symbols
are data of non-photonic electron v~2~ from PHENIX[^39] and STAR[^40].
Only statistical errors are shown for both results. The
dashed-dotted-line represents the input D-meson v~2~ distributions,
assuming the scaling of constituent quarks for meson v~2~. The
corresponding decayed electron v~2~ are shown as the hatched band[^41].
The dashed-line represents the results from Greco[^42] et al. In this
coalescence calculation, similar v~2~ distributions for c- and u-quarks
are assumed. The figure is adopted from Ref. \[Error: Reference source
not found\].

### Charm Hadro-Chemistry

Measured hadronic yields and their ratios, from AGS to RHIC energies,
have been successfully described with statistical models[^43]^,^[^44].
The relevant parameters are the chemical freeze-out temperature T~ch~,
and the chemical potentials ~i~ for conserved quantum numbers, i.e. net
strangeness, charge, and baryon number conservation[^45]. The extracted
chemical freeze-out temperature T~ch~ turns out to be higher than the
kinetic freeze-out temperature T~fo~ extracted from momentum
spectra[^46].

It has been claimed, at the SPS and RHIC[^47] that for most particles
the chemical freeze-out temperature coincides with the critical
temperature T~c~ predicted from lattice QCD. Wide resonances might be an
exception[^48]. Obviously, this critical temperature T~c~ serves as an
upper limit for hadronic systems. Larger temperatures from partonic
systems might be observed when measuring thermal spectra of penetrating
electro-magnetic probes such as dileptons and photons.

Charmed quarks are dominantly produced in initial parton-parton
scatteringsError: Reference source not found and the thermal production
of charmed quarks is suppressed due to their large mass. In case of
sufficient re-scattering, initially produced charmed quarks might
thermally (but not chemically) equilibrate with the surrounding medium.
This means their momentum distribution can be described by a temperature
parameter consistent with the spectra of light quarks; while the total
abundance of charmed quarks is conserved.

These arguments lead to the idea of statistical hadronization of charmed
quarks[^49]^,^[^50]. Statistical coalescence scenarios predict large
changes in open (regarding relative abundances, e.g. the D^0^ /
D~s~*^+^* ratio) and hidden charm production with strong centrality
dependence[^51]. Statistical coalescence implies that charmed quarks
travel over significant distances, e.g. in a QGP. Therefore, we believe
that a consistent description of precision data by these models would be
an indication of deconfinementError: Reference source not found.

Measuring the total charm and bottom yields requires measuring the
yields of several different hadrons. Indeed, charmed quarks may fragment
into a variety of hadrons as shown in the first column of Table 1. These
fragmentation ratios have recently been compiled[^52]^,^[^53] using
*e-p* and *e^+^-e^-^* collision data. These ratios are found to be
independent of the collision energies and the collision system (e-p or
e^+^-e^-^). They are likely to be the same in p-p collisions at
mid-rapidity where the HFT will detect charmed particles, even though
the ratios calculated using PYTHIA[^54], shown in the second column of
Table 1, differ significantly from the measured ratios. To avoid any
uncertainties in the charge yield measurement, these ratios will have to
be measured in *p+p* collisions at RHIC energies.

+-----------------+------------------+----------------+---------------+
|                 | *e*-*p* and      | Pythia         | Statistical   |
|                 | *e*^+^-*e*       |                | coalescence   |
|                 |                  |                |               |
|                 | average          |                |               |
+-----------------+------------------+----------------+---------------+
| (c *D* ^+^ )    | 0.232            | 0.162          | 0.21          |
+-----------------+------------------+----------------+---------------+
| (c *D* ^0^ )    | 0.549            | 0.639          | 0.483         |
+-----------------+------------------+----------------+---------------+
| (c *D~s~^+\ ^*) | 0.101            | 0.125          | 0.182         |
+-----------------+------------------+----------------+---------------+
| (c ~c~^+^ )     | 0.076            | 0.066          | 0.080         |
+-----------------+------------------+----------------+---------------+
| (c J/ )         |                  | 0.006          | 0.057         |
+-----------------+------------------+----------------+---------------+

Table 1: Charm quark fragmentation functions. The left column is from
Ref. \[Error: Reference source not found, Error: Reference source not
found\]. The right column is from Ref.\[Error: Reference source not
found\]. The D^+^ and D^0^ yields include feed-down from D^\*+^ and
D^\*0^ decays.

The effect of statistical coalescence is shown in the last column of
Table 1. This calculation assumes that charmed quarks statistically
coalesce with lighter quarks, i.e. according to the temperature and
chemical potential of the light-quark system. The temperature and
chemical potential are set so that the light hadron yields measured at
RHIC are reproduced. The number of charmed quarks present in the system
is set by pQCD calculations; this is reflected by a charm-chemical
potential in the statistical coalescence model. Statistical coalescence
increases the yield of the D~s~*^+^* meson by 80% and the J/ yield by a
factor of 10 compared to PYTHIA while the yield of D^0^ and D^+^
decrease slightly. Thus, the ratios D~s~^+^/ D^0^, D~s~^+^/D^+^ and
J/ / D^0^ are the most sensitive probes of thermal charm hadron
production.

Measuring the D~s~^+^/D^0^ and D~s~^+^/D^+^ ratios with the precision
required to separate direct and thermal production sets stringent
requirements on the HFT detector performance. When comparing D~s~*^+^*
and D*^+^* yields, most of the systematic errors cancel out because both
are reconstructed in very similar decay channels: D*^+^* K π^+^ π^+^ and
D*~s~^+^* K π^+^ K^+^. If heavy quarks become embedded within partonic
matter, they provide a unique tool to study the properties of the
matter. Indeed, their yield can be accurately extrapolated from p-p
measurements. Any change in the charm and bottom hadron behavior between
proton-proton and heavy-ion collisions will provide information about
the matter that is traversed by these hadrons. Thermal kinetic
equilibration and subsequent statistical coalescence of the charmed
quarks would be strong evidence for partonic matter formation since the
pion-charm hadron cross-section is small[^55].

Furthermore, exotic phenomena such as the formation of charmed
penta-quarks[^56] or enhancement of the B~c~ meson yield[^57] may also
take place. A precise measurement of the total charm production (mostly
carried by open charm mesons) will also serve as a baseline for J/
enhancement/suppression measurements suggested as a possible signature
for QGP formation.

## Measuring Vector Mesons with Dileptons 

Besides the direct measurement of open charm hadrons, the HFT will serve
as a powerful device to discriminate background in the measurement of
electromagnetic probes.

Photons and leptons emitted from the early stages of heavy ion
collisions suffer few interactions with their surroundings since they
interact via the electromagnetic force instead of the strong one.
Therefore, electromagnetic probes are ideal tools to study the
properties of matter created by relativistic heavy ion collisions.

On the other hand, processes which produce photons and leptons are rare
and are overwhelmed by photons and leptons from electromagnetic decays
of hadrons and subsequent conversions to leptons. In addition, the final
state electrons and positrons are the integrated yield of radiation over
the whole evolution of the colliding system. Despite all the
experimental difficulties, the low and intermediate mass dileptons have
been measured at the CERN-SPS and an excess of radiation above the
hadron cocktail has been observed in the invariant mass region at 0.2 \<
M~ee~ \< 0.6 GeV/c^2^ in semi-central Pb+Au collisions[^58]^,^[^59].
Also, new and exciting results from the first three RHIC runs indicate
that jets have lost a large fraction of their energy in dense matter and
the hadronic phase is relatively short. We believe that these
observations at RHIC favor experimental measurements of photons and
dileptons due to thermal radiation and will result in a clearer
signature than from lower energy heavy ion collisions.

At STAR, electron identification is made possible by a combination of a
measurement of the energy lost by charged particles due to ionization of
the TPC gas (dE/dx) and a velocity measurement with the time-of-flight
system. The relativistic rise of the electron dE/dx separates the
electron dE/dx from those of hadrons except at the crossovers with pions
at momentum of \~ 0.2 GeV/c, kaons at \~ 0.6 GeV/c, protons at \~ 1.1
GeV/c and deuterons at \~ 1.5 GeV/c. A time-of-flight measurement, using
a requirement that \|1-\| \< 0.03, eliminates slow hadrons and cleans up
the crossovers. This results in clean electron identification, as shown
in Figure 9. The plot on the top left shows the conventional dE/dx
measurement in the TPC gas as a function of particle momentum. The lower
plot shows the same dE/dx measurement but now requiring at TOF of
\|1-\| \< 0.03. The upper electron band is clearly separated from the
lower pion band. Heavier particles (e.g. kaons and protons) are
completely removed by the TOF requirement. The right hand plot of Figure
9 shows a dE/dx projection in the transverse momentum range p~T~ =
1.0-1.5 GeV/c. Even at this rather large momentum, the distribution of
electrons are clearly separated from the distribution of charged hadrons
at lower energy losses.

![](media/image14.jpeg){width="2.7944444444444443in"
height="2.7180555555555554in"}
![](media/image15.jpeg){width="2.9298611111111112in"
height="2.7055555555555557in"}

Figure 9: Left top: TPC dE/dx vs p in d+Au collisions. Left bottom: TPC
dE/dx vs p after TOFr PID selection of \| 1- \| \< 0.03. Clean electron
identification is achieved. Right: dE/dx from TPC after TOFr PID
selection (left bottom panel) for 1.0 \< p \< 1.5 GeV/c.

These electrons are, to a large extent, from photons converting into
electron-positron pairs e^+ ^e^-^ in the detector material. The HFT
detector will reduce the background electrons and positrons from these
conversions. By requiring hits in the HFT, electrons from photon
conversion outside the HFT, i.e. the SVT, SSD, and TPC inner field cage,
are rejected. Figure 10 shows the resulting yield from pure Monte Carlo
simulations (no tracking involved) of conversion electrons when
requiring hits in the TPC only (open circles), hits in the TPC and SVT
(open triangles) and hits in the TPC+SVT+HFT (closed circles). The
requirement of hits in the HFT reduces the detected yield of conversion
electrons by a factor of 50. Another source of electron background stems
from the semi-leptonic decays of heavy quarks, charm and bottom. The
dominant source at intermediate mass[^60]^,^[^61] is from the
semi-leptonic decays of open charm. Due to the lifetime of \~ 100 m of
heavy-flavor hadrons, this background can be greatly reduced by
measuring the displaced decay vertex with high resolution as provided by
the HFT detector. Detailed simulations are in progress.

![](media/image16.jpeg){width="5.000694444444444in"
height="3.410416666666667in"}

Figure 10: Electron p~T~ spectra from conversions reconstructed by
requiring TPC tracking, a TPC hit and 2 SVT hits, or a TPC hit and 2 SVT
hits and 2 HFT hits. The rejection factor with an additional SVT hit (2
hits) is 3 and with an additional HFT hit is 50.

The large reduction in electron background will enable us to observe
electromagnetic decays of short-lived vector meson, e.g. , *e*^+^*e*,
and intermediate mass dileptons with a few hundred thousand central
Au+Au events in STAR. The rejection of π^0^ and  Dalitz decays can be
achieved by measuring both electrons in the pair which is possible due
to the large acceptance of the STAR TPC. Table 2 shows our estimate of
central Au+Au collisions needed in order to observe a signal with a
statistical significance of 3. Compared to measurements incorporating
only the TPC and TOF, the HFT will enhance the sensitivity of
electro-magnetic vector meson decay by a factor 20-40. We are in the
process of simulating the effects of the combinatorial background in
more detail.

  ------------------------------------------- --------------- ------------
  Detectors                                                   

  TPC+TOF                                     8M              2M

  TPC+TOF+SVT+HFT                             200K            100K
  ------------------------------------------- --------------- ------------

Table 2: Number of central Au *+* Au events required to observe a 3-
signal for and in their leptonic decay channels under different detector
configurations.

# 2.6 Physics of Spin {#physics-of-spin .unnumbered}

The European Muon CollaborationError: Reference source not found
discovered that spin of the quarks only contribute only a small fraction
of the total to the spin of the proton and this has motivated and
continues to motivate considerable experimental and theoretical activity
to further unravel the nucleon spin structure. At present, only the
total quark spin contribution is known with fair precision. The most
prominent unknown is the spin-dependent gluon density, G.

The main goal of the RHIC spin program[^62] is to precisely determine G
by measuring double spin asymmetries in longitudinally polarized
proton-proton collisions for a series of complementary reaction channels
and over a broad range of the gluon momentum fraction x~g~ and
transverse momenta p~T~. One of the promising reaction channels in STAR
is the production of prompt photons and jets with high transverse
momenta.

The production of charm and bottom quarks proceeds, in leading order in
the strong coupling constant ~s~, through gluon-gluon fusion and quark
anti-quark annihilation. The gluon-gluon fusion process is known to be
dominant in the spin averaged case for all experimentally relevant
kinematic regions. In the spin dependent case both processes have large
analyzing powers, as measured by the parton-parton spin asymmetry a~LL~,
which approaches -1 for asymptotically large transverse momenta. The
masses of the heavy quarks lead to large modifications of the
parton-parton spin asymmetry in the kinematic region accessible with
STAR[^63]. Next-to-leading order corrections are available and predict
relatively sizable changes in the observed asymmetry as compared to
leading order expectations[^64].

These properties make charm and bottom production a good test to advance
the current understanding of the nucleon spin (unless G were to be found
vanishingly small).

As is the case for the study of heavy quark energy loss described in
this proposal, the relative smallness of the production cross section at
large transverse momenta requires triggering with the STAR
electromagnetic calorimeters. In spin measurements, the trigger serves
to relate the event to the RHIC beam bunch crossing, which determines
the spin orientations of the colliding protons. Commonly used
parameterizations of the deep-inelastic scattering data[^65] lead us to
expect measurable and negative double longitudinal spin asymmetries at
the level of --5\*10^-3^ in heavy flavor production in STAR. These
asymmetries originate from gluon polarization at intermediate momentum
fractions x~g~ and are expected to grow in size with increasing p~T~ of
the decay electron or positron.

In order to make these measurements, fast external pointing with
high-rate capability is required to distinguish collisions from
different bunch crossings and, hence, different spin orientations.
Feasibility studies indicate that the HFT can be used to reconstruct
displaced vertices in the proton-proton environment, too.

# HFT Conceptual Design and Performance {#hft-conceptual-design-and-performance .unnumbered}

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#   {#section-44 .unnumbered}

Summary

Probing charm quark flow and thermal equilibration at RHIC may prove to
be the final step towards the discovery of a Quark Gluon Plasma.
Furthermore, measuring the energy lost by high transverse momentum heavy
(c,b) quarks while traversing the medium will help disentangle between
energy loss scenarios in cold nuclear matter and in partonic matter. The
HFT is designed to tackle both tasks by precisely measuring open charm
hadron yields, spectra and elliptic flow (v~2~) as well as tagging the
electrons produced by high transverse momentum beauty hadrons. The
design requirements are fulfilled by having two thin ( ≤ 0.36% radiation
length) layers of Active Pixel Sensors (APS) with a position resolution
better than 10 m. APS technology is the only option that fits these
requirements while compromising neither the efficiency nor the readout
speed. Indeed, an APS can be thinned down to 50 m and their low power
consumption allows using air-cooling. Matching the readout speed
required at RHIC will be achieved in two steps, first by building two
separate chips, one readout chip mounted on a purely analog sensor, and
then by designing one chip combining both analog and digital features.
The mechanical support has been carefully designed so that the detector
can be easily retracted. This feature allows the detector to be
externally aligned, repaired and upgraded. By combining cutting edge
sensor and readout technologies with a flexible and robust mechanical
design, the HFT will provide the high precision data on heavy flavor
hadrons that are crucial to understand the nature of the medium formed
in Au+Au collisions at RHIC.

# Appendix I -- MIMOSTAR Specifications

Attached.

# Appendix II -- MIMOSTAR Users Guide

Attached.

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