Dilepton Program with Time-of-Flight Detector at the STAR Experiment

Abstract

Pairs of lepton and antilepton (dilepton) in a continuous mass range are one of the most experimentally challenging and golden probes of the quark-gluon plasma (QGP) produced in heavy ion collisions because they do not strongly interact with the hot and dense medium, and reflect the properties of the medium at the time the dilepton is generated. The measurements of dileptons require lepton identification with high purity and high efficiency at large detector acceptance. STAR is one of two large experiments at the relativistic heavy ion collider with a primary goal of searching for the QGP and studying its properties. The STAR experiment launched a comprehensive dielectron ($e^{+}{e}^{-}$) program enabled by the time-of-flight (TOF) detector that had been fully installed in 2010. In this article, we review the decade-long $R\&D$, the construction and performance of the STAR TOF detector, and dielectron measurements, including thermal dielectron production and dielectron production from the Breit–Wheeler process. Future perspectives are also discussed.

1. Introduction

Quark–gluon plasma (QGP) consists of fundamental building blocks of matter at the most extreme temperature and density conditions. QGP existed briefly during the first few microseconds after the Big Bang and can be recreated in ultrarelativistic heavy-ion collisions in which quarks and gluons are liberated from confinement within nucleons. The thermodynamic and hydrodynamic properties of the QGP, such as temperature and viscosity, have been under intense investigation by means of theoretical lattice quantum chromodynamic (QCD) computations [1,2], and in experiments utilizing the world’s most powerful supercomputers and particle accelerators [3,4]. Thermal lepton pairs ($e^{+}{e}^{-}$ and ${\mu }^{+}{\mu }^{-}$) from QGP radiation [5,6,7] are penetrating probes of the true temperature of the emitting source and are considered the holy grail of the study of QGP since they do not suffer from either final state interactions or the blue-shift effects from collective motion [8,9,10,11].

Despite the focus on nuclear physics, heavy-ion collisions have been understood as an opportunistic tool for studying quantum electrodynamics (QED) in unique regimes for nearly a century [12,13], and have attracted significant interest in the last 40 years [14,15,16], with generations of powerful accelerators. Some of the earliest measurements of electromagnetic processes in heavy-ion collisions were studied by the BEVALAC at LBNL [17], the AGS at BNL [18], and by the SPS at CERN [19]. In 2000, the relativistic heavy ion collider (RHIC) began operation and ushered in a new era of high-energy nuclear physics with ultrarelativistic Au beams, providing collisions with a center-of-mass energy per nucleon pair from $\sqrt{s_{\mathrm{NN}}}$ = 200 GeV at top energy to 3.0 GeV in fixed-target mode. The payoff from this next-generation facility was almost immediate, with all four RHIC experiments reporting the observation of a new state of nuclear matter in 2004: the QGP [20,21,22,23]. In an influential workshop in 1990 titled “Can RHIC be used to test QED?” [24], the top priority was said to be “to understand the validity of the best available descriptions of $e^{+}{e}^{-}$ pair production in peripheral heavy-ion collisions, especially for the domain where this process is known to be nonperturbative (multiple pair production)”. It positively concluded that “A study of electromagnetic phenomena in extremely peripheral collisions of relativistic heavy ions can become a rich and exciting field that will complement studies of central collisions.” However, none of the three (Landau–Lifschtz, Bethe–Heitler and Breit–Wheeler) processes was explicitly mentioned. Right from the start of RHIC operation, the two “large” experiments at RHIC (STAR and PHENIX) studied the electromagnetic production of $e^{+}{e}^{-}$ from the electromagnetic fields of colliding ultrarelativistic Au nuclei [25,26]. Multiple experiments performed measurements of the total cross-section of electromagnetically produced $l^{+}{l}^{-}$ from ultraperipheral heavy-ion collisions [26,27,28] or from exclusive p + p [29] collisions. Significant progress through multiple discoveries was achieved in the physics of photon interactions. Experimental measurements and theoretical descriptions have been progressing from the initial discoveries toward quantitative and precise comparisons. Polarized photons were used and proposed as a tool to test and define the photon Wigner function [30,31,32,33,34,35,36], to probe the properties of the QGP [37,38,39,40,41,42,43], to measure nuclear charge and mass radii [37,44,45,46], to study gluon structure inside nuclei [47,48,49], and to investigate new quantum effects [45,48,50,51,52,53]. The subject has evolved significantly in the last decade, with new measurements and a new understanding of thermal radiation and strong QED fields.

With the installation of a time-of-flight detector (TOF) surrounding the STAR time projection chamber (TPC) starting in 2009–2010, the combination demonstrated effective electron particle identification with the necessary purity and large acceptance in a very cost-effective configuration. We dedicate this review article to the relevant STAR TOF detector at the RHIC facility, with special attention given to its unique capabilities and limitations with respect to measuring thermal dielectron radiation from QGP and the novel QED phenomena, especially the Breit–Wheeler process and vacuum birefringence.

2. Time-of-Flight Detector

The multigap resistive plate chamber (MRPC) was first developed by the ALICE TOF group in the 1990s [54] to efficiently identify copiously produced charged particles in relativistic heavy ion collisions. As a new type of gaseous detector with precision timing performance, the MRPC is suitable for applications requiring a large area, high granularity, and low cost.

The MRPC in China was first developed by the high-energy physics group led by Prof. Hongfang Chen at the University of Science and Technology of China (USTC) in 2000, when the STAR experiment at RHIC sought to build an MRPC-based TOF to improve the identification capability of charged particles. USTC was responsible for the $R\&D$ of MRPC to meet the requirements of STAR TOF.

The first MRPC prototype was very simple, with only one readout pad and a sensitive area of about $3\times 3{\mathrm{cm}}^2$ and five 0.22 mm thick gas gaps (see the left panel of Figure 1), aiming to verify the feasibility of this technique. In late 2000, the performance of this prototype was studied in the T10 test beam facility at CERN. The prototype functioned well, with a time resolution of 70 ps and detection efficiency of >95% (right panel of Figure 1) [55,56]. Soon after this success, a batch of MRPC modules with different structures were developed and tested [57]. Figure 2 shows the structure of an MRPC prototype with a sensitive area of $20\times 6.3{\mathrm{cm}}^2$ and six gas gaps. The sensitive area was divided into 12 regions by 12 readout pads with a size of $3.1\times 3.0{\mathrm{cm}}^2$. The time resolution of this prototype reached 60 ps, and its detection efficiency exceeded $97\%$ in the beam test with good uniformity [57]. An MRPC prototype with the same sensitive area, but with two stacks of five gas gaps, was also constructed and tested. Its time resolution reached 50 ps, and its detection efficiency exceeded 99%. Considering the limited available space for STAR TOF installation, the 6-gap MRPC structure was chosen for the STAR TOF. The readout pads were recombined into a size of $3.1\times 6.1{\mathrm{cm}}^2$ to reduce the total number of readout channels [58].

In 2002, a TOF tray prototype (TOFr) with 28 MRPC modules was built by USTC and Rice university. A team led by Prof. Hongfang Chen tested the performance of the TOFr under various operating conditions at the AGS facility for 10 weeks prior to installation in the STAR experiment for the 2002–2003 physics run. The optimal parameters of high voltage, gas mixture, and threshold voltage for the operation of the prototype at STAR were determined from the beam test results [59]. TOFr was installed in STAR after the test at the AGS replacing one central trigger barrel module, and was part of the p+p and d+Au physics runs. In the STAR environment, the detection efficiency of the TOFr tray, averaged over all the channels, was around 95%, and the time resolution was 85 ps. The performance of the TOFr tray met the STAR physics goals and could significantly extend STAR particle identification capabilities [60]. With 2$\sigma$ separation, protons/(pions + kaons) and kaons/pions were identified up to 3 and 1.6 GeV/c, respectively. Although the acceptance of the prototype was only 1/120 of the TOF system, several important physics results were achieved from the acquired data thanks to the extended particle identification capability [61,62]. With the success of the TOFr physics run, the STAR collaboration decided that all TOF MRPC modules were to be produced in China.

Thanks to the experiences of producing and operating the TOFr, and the extensive study of the MRPC technology [63,64,65,66], the production-process and quality-control requirements for MRPC module mass production for the STAR TOF were established. In 2006, funded by the National Natural Science Foundation of China, the Chinese Academy of Sciences, and the Ministry of Science and Technology, the Chinese STAR group launched the construction of the STAR TOF. By 2009, over 4000 MRPC modules were produced by Tsinghua University and USTC. Due to the strict quality management, the final yield was $>95\%$, with excellent uniformity in performance [67,68]. The whole STAR barrel TOF consisted of 120 trays (each tray was analogous to the TOFr), 3840 MRPC modules, and 23,040 channels in total. It covered approximately the pseudo-rapidity interval (−1, 1) and full azimuthal range. Operating with a $94.7\%{\mathrm{C}}_2{\mathrm{H}}_2{\mathrm{F}}_4+5.3\%$ iso-Butane gas mixture, the MRPCs of the STAR barrel TOF showed a better intrinsic time resolution than 70 ps (the overall time resolution of STAR TOF also depended on the time jitter of the “start” time detector, which varied with different heavy ion collision systems). This time resolution and the corresponding particle identification capability were consistent with those achieved by TOFr and remained stable for more than 10 years of STAR operation.

After the success of the STAR TOF project, the USTC group continued to develop the MRPC technique and applied it to large facilities, such as a muon telescope detector and end-cap TOF for the STAR experiment, an end-cap TOF upgrade for the Beijing Spectrometer (BESIII), the TOF for the compressed baryonic matter (CBM) experiment, and the TOF for the CSR external-target experiment (CEE) [69].

3. Thermal Dileptons

Photons and dileptons ($e^{+}{e}^{-}$ or ${\mu }^{+}{\mu }^{-}$) are emitted at various stages during the space-time evolution of the nuclear medium created in ultrarelativistic heavy-ion collisions. As penetrating electromagnetic probe dileptons do not suffer from strong interactions, they keep undistorted information of the sources from which the dileptons are coming. These sources are expected to contribute differently in lepton-pair invariant mass ($M_{ll}$), which are usually categorized into three regions:

(1) In the low-mass region (LMR), below $\varphi$ mass ($M_{ll}<$ 1.1 GeV/c${}^2$), the main contributions are from light meson (${\pi }^0$, $\eta$, ${\rho }^0$, $\omega$, $\varphi$) decays or Dalitz decays. In particular, one can investigate hadronic in-medium properties via ${\rho }^0$ spectral modifications, which is sensitive to the mechanisms of chiral symmetry restoration in QCD matter [70]. Modified dilepton yields in LMR are expected to be related with the medium’s lifetime and the transition from hadronic into partonic degrees of freedom [71].

(2) In the intermediate-mass region (IMR), namely, between $\varphi$ and $J/\psi$ mass ($M_{ll}\simeq$ 1.2–3 GeV/c${}^2$), the invariant-mass spectrum is continuum-like in both heavy flavor decays and nuclear matter emissions. This provides the chance to measure the direct radiation signals of QGP, which are expected to be a clean thermometer of the nuclear medium [10] by extracting the inverse slope of the mass spectra, which is unaffected by the blue shift of the expanding system.

(3) In the high-mass region (HMR), $M_{ll}\ge$ 3 GeV/c${}^2$, the main sources are heavy flavor/quarkonium decays and the Drell–Yan process.

Thermal dileptons from QGP radiation are of particular interest since they are sensitive to the properties of the produced medium. By investigating QGP radiation in different invariant-mass regions, one can probe different stages during the time evolution of the QGP phase.

The measurements of the above dileptons require large detector acceptance, large event statistics, and clean lepton identification. STAR collected a large sample of Au + Au collision events with the TOF detector. The TOF detector greatly extended the capability of the STAR experiment for particle identification. Combining the timing measurement from the TOF detector, and the momentum and ionization energy loss ($dE/dx$) measurements from the tracking detector, namely, the time projection chamber (TPC), one can cleanly identify low-momentum electrons with high efficiency and purity. Figure 3a shows the n${\sigma }_e$ (the n times of the standard deviation of measured $dE/dx$ to the Bichsel prediction) as a function of particle momentum. The electron band largely overlapped with charged hadrons when using data from the TPC alone. With a TOF velocity close to the speed of light in vacuum, most of the hadrons were rejected. The remaining hadrons were a clean electron band and fast hadrons, as shown in Figure 3b.

The wide, uniform pseudorapidity and azimuthal acceptance of the STAR TPC and TOF detector allow for the precision reconstruction of dielectron pairs with the good systematic control of uncorrelated and correlated backgrounds. After the removal of these background contributions, dielectron invariant-mass spectra were measured with STAR at various collision energy levels. Decays from light mesons after a freeze-out (usually called a cocktail) can be removed by simulating the cocktail contributions. The remaining dielectron spectra are of particular interest and expected to contain radiation information from various stages of heavy-ion collisions before freeze-out.

Figure 4 shows $e^{+}{e}^{-}$ invariant-mass spectra after cocktail subtraction in Au + Au collisions at $\sqrt{s_{{}_{\mathrm{NN}}}}$ = 27, 39, 62.4, and 200 GeV [73,74]. The figure shows model calculations for total thermal radiation (solid lines), including both in-medium hadronic (dashed lines) and QGP (dotted lines) contributions. The model calculations provide a consistent description of the measured dielectron spectra across broad-energy and invariant-mass regions. In the LMR, the dominant hadronic radiation is mainly generated through $\rho$ meson in-medium broadening through interactions with the hadronic medium, particularly baryons. The same model also provided a consistent description of the invariant-mass spectrum of the dimuon pairs measured in the NA60 experiment at SPS [75]. The $\rho$ meson in-medium broadening was suggested to be evidence of the partial restoration of the chiral symmetry in the hot QCD medium [76]. The QGP radiation contribution was expected to take over at the IMR, where the precision of the current measurements is limited. The search and investigation of the QGP thermal radiation are future directions in the dilepton programs at both RHIC and LHC.

Figure 5 shows the collision energy dependence of the integrated dielectron yield, normalized to the charge pion $dN/dy$ in the low-mass region of $0.3<M_{ll}<0.7$ GeV/c${}^2$ measured from HADES [78], NA60 [75], and STAR [73,74]. Theoretical model calculations on dielectron yields (dashed blue line) and the fireball lifetime (solid red line) are also shown in the figure. The model provides a good description of the energy dependence, which exhibited a modest increase from the SPS to the top RHIC energy. This increase also shows the good tracking of the fireball lifetime across a broad collision energy range. The measurements from STAR shown here are from the Beam Energy Scan (BES) Phase I. The recorded BES-II data and analyses further extend the measurements from 19.6 GeV down to 7.7 GeV, offering new insights of the hot medium properties in the high-baryon-density region. Future experiments, such as NA60+, CBM and MPD, could further extend the measurements to low energy [79,80,81].

4. Dileptons from the Breit–Wheeler Process

When matter and antimatter [82] interact in a process called annihilation, they both disappear, and their mass is instantly converted into energy [83,84]. In 1934, Breit and Wheeler started the theoretical study of the simplest reverse process of the collision of two light quanta ($\gamma \gamma \to e^{+}{e}^{-}$) to create mass from energy [85]. The Breit–Wheeler study indicated that it is impossible to achieve this process via $\gamma$-ray collisions in existing Earth base experiments, which still holds true. Alternatively, they proposed observing the process via relativistic heavy-ion collisions in which the highly Lorentz-contracted electromagnetic field induced by fast-moving ions can be treated as a powerful source of photons for collisions. The treatment of quantizing the Lorentz-boosted Coulomb field was first proposed by Fermi [86], and further developed by Williams and Weizsacker [13], which is called the Williams–Weizsacker method or equivalent photon approximation (EPA).

Over the past few decades, dielectron production from the collision of light quanta was observed at various hadron and electron–positron collider experiments [19,25,26,27,29,87,88,89,90,91,92]. However, the existing experimental results lack precision and differential measurements to demonstrate themselves as the Breit–Wheeler process. The pioneering study of the Breit–Wheeler process at RHIC was conducted by STAR with Au + Au collision data from $\sqrt{s_{\mathrm{NN}}}$ = 200 GeV taken in 2001 [25]. The data were collected with the trigger of ultraperipheral collisions (UPCs) in order to reject hadronic interactions. The specific energy loss ($dE/dx$) from the TPC only allows for the identification of electrons from pion backgrounds in a very limited kinematic range ($65<p_T<130$ MeV/c). In total, 52 candidate events were selected out of 800,000 triggered events in which the limited statistics prevents further claims from being made. For the data taken in 2010 with the fully installed TOF, the contamination background from hadron pairs could be largely reduced by using the double difference in the time of flight between the two measured tracks, and the expectation for dielectrons calculated using the measured momentum and path length from the TPC. Together with $dE/dx$ information from the TPC, the optimized section criteria could ensure a 99% purity of dielectron candidates.

Measurements of the production rate of exclusive dielectron pairs from the data taken in 2010 [93] are shown in Figure 6. The measurements were performed in the fiducial phase space reported in the figure. Figure 6a shows the invariant-mass spectrum of exclusive dielectron pairs, which was smooth and featureless. The potential background contribution from exclusive vector meson photoproduction with the decay branch of dielectrons was estimated with STARLight [94] model and is shown as solid purple lines in the figure; the results were negligible in comparison with the experimental data. Figure 6b displays the differential $|cos{\theta }^{\prime }|$ distribution in which ${\theta }^{\prime }$ is defined as the polar angle of the electron (positron) with respect to the beam in the electron–positron center-of-mass frame. The falloff of the distribution resulted from the detector acceptance. In comparison with isotropic emission (dashed line in the figure), the measured exclusive process exhibited enhancement toward a small polar angle. The differential cross-section, as a function of the pair transverse momentum ($P_{\perp }$), is shown in Figure 6c. The data characterize a clear peak in the production rate at very low transverse momentum. All these features were the consequence of the energy spectrum and quantum numbers of the two photons involved in the Breit–Wheeler process. Therefore, the Breit–Wheeler process was unambiguously identified for relativistic heavy-ion collisions in this measurement.

Conventionally, the Breit–Wheeler process is only studied in UPCs to reject hadronic backgrounds. Furthermore, photon-induced processes are not generally considered to add up coherently for collisions with nuclear overlap. This begins with $J/\psi$ measurements at a very low transverse momentum in Pb + Pb collisions from ALICE [28], in which significant excesses were observed in peripheral collisions. The abnormal excesses of $J/\psi$ were confirmed via the STAR measurements [95], and well-described by the phenomenological model with a coherent photon-nucleus production mechanism [50,96,97,98,99]. Assuming that coherent photon nuclear production is responsible for the observed $J/\psi$ excesses, the Breit–Wheeler process should also exist and contribute to dielectron production for collisions with nuclear overlap.

Utilizing the datasets collected in 2010, 2011, and 2012, STAR performed dielectron measurements at a low transverse momentum for hadronic heavy-ion collisions (non-UPCs) [38]. The electron identification criteria were the same as those described in Section 3. Figure 7 shows the transverse momentum distributions of dielectron pairs in different mass regions for 60–80% Au + Au and U + U collisions. As expected, a significant excess was observed and concentrated below $p_T\sim$ 0.15 GeV/c with respect to the hadronic cocktail. The magnitude of the excess could be well-described with the model incorporated with the Breit–Wheeler process in hadronic heavy-ion collisions [100]. To further investigate the features of the Breit–Wheeler process in hadronic heavy-ion collisions, STAR measured the $p_T^2$ distributions of excess yields within acceptance in different mass regions for peripheral collisions, as shown in Figure 8. The aforementioned model calculations are also plotted in the figure. The theoretical results fell below the data points at large $p_T^2$ values, and overshot the data at low $p_T^2$. Such a discrepancy can be well-quantified by the corresponding $\sqrt{\langle p_T^2\rangle }$ of $p_T^2$ distributions, as shown in Figure 8d. The disagreement between the data and the model calculations suggests the possible origins of the $p_T$ broadening from the hot medium created in the nuclear overlap region. By introducing a magnetic field trapped in an electrically conducting QGP, the $p_T$ broadening can be reasonably described. ATLAS collaboration also found a significant $p_T$ broadening effect via the dimuon channel in comparison to those in UPCs [39], and quantified the effect via the acoplanarity of dimuon pairs. Alternatively, the broadening was explained by the electromagnetic scattering of leptons in the hot and dense medium [40]. All these descriptions of the broadening effect assumed that there was no impact-parameter dependence of the $p_T$ distribution in the production process. Recent theoretical calculations [30,31] that recovered the impact parameter dependence demonstrated that the broadening was mainly from the initial light quantum collisions. This was further experimentally confirmed via CMS measurements [34] through exclusive dimuon production from photon–photon collisions in UPCs. Small tension still existed between data and theoretical calculations, which left room for possible effects from the hot medium.

Due to the extreme Lorentz contraction in relativistic heavy-ion collisions, the induced electromagnetic field was almost fully perpendicular to the direction of motion of the heavy nuclei, suggesting that the induced photons were fully linearly polarized in the transverse plane. Li et al. [101] proposed that the collisions of linearly polarized photons can lead to second- and fourth-order modulations in the azimuth (in the plane perpendicular to the beam direction). As shown in Figure 9, STAR performed the first measurement of the decay angular distribution ($\Delta \varphi$) for the Breit–Wheeler process in relativistic heavy-ion collisions. Significant $cos(4\Delta \varphi )$ modulation was found, which could be described well via the numerical lowest-order QED calculation [102]. The observed angular modulation was closely related to the vacuum birefringence in which the vacuum was polarized by the extremely strong electromagnetic field in the absence of a medium [103]. This also inspired the discovery of $cos(2\Delta \varphi )$ modulation for vector meson photoproduction [45,48,51] in heavy-ion collisions.

5. Future Perspectives

The dilepton measurements at SPS with NA60 in the dimuon channel were performed with high statistics and with high data quality almost two decades ago. RHIC could provide important insights in the dielectron channel at the top energy and in the Beam Energy Scan Phase I (BES-I). The high-statistics data from BES-II and future data at the top energy level showed potential for providing the temperature measurements around the phase boundary and at the QGP phase. Future ALICE upgrades and experiments at high baryon density also promise an exciting dilepton program with LHC energies [79,80,81,105].

The future data-taking plan at RHIC and the LHC would provide an opportunity to perform the high-precision multidifferential analysis of these two photon-related physics [106,107]. The incoming RHIC run would allow for STAR to significantly improve the precision of the transverse momentum spectra and the angular modulation strength for the Breit–Wheeler process. The improved precision of transverse momentum spectra provides an additional powerful constraint to the proposed final-state broadening effects. The added precision in the angular modulation measurements is expected to experimentally demonstrate the impact parameter dependence of angular modulation strength, which is predicated by lowest-order QED calculations. Furthermore, precise angular modulation measurements could also serve as a sensitive probe of the hot medium, since the final state interactions would destroy the angular modulation resulting from the linear polarization of the initial photons. The much larger statistics provided by the future data-taking plan makes more differential measurements, such as angular modulation strength versus pair transverse momentum for dielectrons from the Breit–Wheeler process possible. The data-taking campaigns planned at the LHC would also allow for ALICE to measure the Breit–Wheeler process with much more precise measurements in a similar region of phase space as that measured at RHIC, but in collisions with a much larger Lorentz boost factor. Such measurements provide additional information on the photon kinematic distributions over a broad range of photon energy. Similarly, analyses of the $\gamma \gamma \to {\mu }^{+}{\mu }^{-}$ process in events with a hadronic overlap by CMS and ATLAS [107,108] from the future data-taking plan would shed new light on the presence (or lack) of medium-induced modifications. In much of the progress achieved in the last decade, TOF played an indispensable role. We anticipate that future progresses on this subject would continue to rely on the time-of-flight detector with its revolutionary technology advances.