Low-mass vector-meson production at forward rapidity
The PHENIX experiment at the Relativistic Heavy Ion Collider has measured low mass vector meson, , , and , production through the dimuon decay channel at forward rapidity () in collisions at GeV. The differential cross sections for these mesons are measured as a function of both and rapidity. We also report the integrated differential cross sections over GeV/ and : nb and nb. These results are compared with midrapidity measurements and calculations.
Low-mass vector meson (LVM) production in collisions is an important tool to study quantum chromodynamics (QCD), providing data to tune phenomenological soft QCD models and to compare to hard perturbative QCD calculations. Various experiments Abelev et al. (2009a); Adare et al. (2011a); Alexopoulos et al. (1995); Abelev et al. (2012a); Abelev et al. (2012b); Aaij et al. (2011) have studied LVM at different colliding energies and in different kinematic regions.
In addition, LVM production in collisions provides a reference for high-energy heavy-ion-collision measurements. LVM studies provide key information on the hot and dense state of the strongly interacting matter produced in such collisions. Among them, strangeness enhancement Koch et al. (1986), a phenomenon associated with soft particles in bulk matter, can be accessed through the measurements of -meson production Alt et al. (2008); Alessandro et al. (2003); Adamová et al. (2006); Arnaldi et al. (2011); Adare et al. (2011b); Abelev et al. (2009b) and the /() ratio. The measurement of the spectral function can be used to reveal in-medium modifications of the hadron properties close to the QCD phase boundary linked to chiral symmetry restoration van Hees and Rapp (2008); Adamová et al. (2008); Arnaldi et al. (2006). However, measuring the spectral function in the two-muon channel requires better mass resolution than is provided by the muon spectrometers of the PHENIX experiment at the Relativistic Heavy Ion Collider.
Having two muon spectrometers covering the rapidity range , PHENIX is able to study vector-meson production via the dimuon decay channel. Because there is no similar measurement in this kinematic regime at this energy, the forward rapidity measurements are a valuable addition to the database and are complementary to previously published midrapidity results Abelev et al. (2009a); Adare et al. (2011a). We report the differential cross section as a function of and rapidity of and mesons for GeV/ and . Results presented in this paper are based on the data sample collected in 2009 using the PHENIX muon spectrometers in collisions at = 200 GeV. The sampled luminosity of the data used in this analysis corresponds to 14.1 pb.
The PHENIX apparatus is described in detail in Adcox et al. (2003). This analysis uses the dimuon decay channel of the low mass vector mesons. The detectors relevant for reconstruction and triggering are the two muon spectrometers Aronson et al. (2003) and the two beam-beam counters (BBCs) in the forward and backward rapidities.
The muon spectrometers, located behind an absorber composed of 19 cm copper and 60 cm iron, include the muon tracker (MuTr), which is in a radial magnetic field with an integrated bending power of 0.8 Tesla-meter, followed by the muon identifier (MuID). The muon spectrometers cover the range over the full azimuth. The MuTr comprises three sets of cathode strip chambers while the MuID comprises five planes of Iarocci tubes interleaved with steel absorber plates. The composite momentum resolution, , of particles in the analyzed momentum range is about 5% independent of momentum and dominated by multiple scattering, and the LVM mass resolution is 85 MeV/. Muon candidates are identified by reconstructed tracks in the MuTr matched to MuID tracks that penetrate through to the last MuID plane. The minimum momentum of a muon to reach the last MuID plane is 2 GeV/.
Beam-beam counters (BBC), consisting of two arrays of 64 Čerenkov counters covering the pseudorapidity range , were used to measure the collision vertex along the beam axis () with 2-cm resolution in addition to providing a minimum-bias trigger.
Iii Data Analysis
The data set for this analysis was recorded in 2009 using a minimum-bias trigger that required at least one hit in each of the BBCs. Additionally, the MuID Level-1 dimuon trigger was used which required that at least two tracks penetrate through the MuID to its last layer.
A set of quality assurance cuts is applied to the data to select good muon candidates and improve the signal to background ratio. The BBC collision z vertex is required to be within 30 cm of the center of the interaction region along the beam direction. The MuTr tracks are matched to the MuID tracks at the first MuID layer in both position and angle. In addition, the track trajectory is required to have at least 8 of 10 possible hits in the MuID.
The invariant mass distribution is formed by combining muon candidate tracks of opposite charge. In addition to low mass vector mesons, the invariant mass spectra contains uncorrelated and correlated backgrounds. The uncorrelated backgrounds arise from random combinatoric associations of unrelated muons candidates while the correlated backgrounds arise from open charm decay (e.g., where both decay semileptonically to muons), open bottom decay, and Dalitz decays and the Drell-Yan process.
Traditionally, the combinatorial background is estimated and subtracted by two methods. The first method uses the mass spectra of the like-sign pairs that are reconstructed within the same event. The other forms unlike-sign and like-sign pairs from different events and is often referred to as the “mixed-event method.” In the like-sign method, the like-sign pairs are expected to originate from combinatorial processes; in addition there can be correlated pairs within a single event Adare et al. (2011c). In the case of the mixed event method, unlike-sign pairs are formed from tracks from different events which provides purely combinatorial pairs Adare et al. (2011c, 2013). The results of using these two methods are shown in Fig. 1.
It is clear from Fig. 1 that the two methods are not able to reproduce the background in the low mass region. Hence, we introduce a new data driven technique here.
The background below 1.4 GeV/ is dominated by
decays that occur before reaching the absorber
punch-through hadrons with high that are misidentified as muons and
muons that result from decay in the muon tracker volume.
A statistic is calculated from a simultaneous fit of the two muon tracks with a common event determined by the BBC. Tracks due to the backgrounds listed above produce a broader distribution than that of true muon tracks, and this difference can be used to discriminate statistically between foregrounds and backgrounds. We classify pairs with as foreground pairs and those with as background pairs. The value, , was selected such that we retain as much of the signal as possible, while still allowing enough statistics in our background sample.
Figure 2(a) shows the unlike-sign pairs distribution, which is narrower in the resonance region dominated by prompt dimuons (e.g, in the region, GeV/), and wider in the nonresonant regions. On the other hand, the distribution for the like-sign pairs is the same in both mass regions. In addition, the unlike-sign distribution matches very well that of the like-sign in the nonresonant region. After selecting the foreground and background from the data, the background is normalized to the foreground by two normalization methods: The first method uses the unlike-sign pairs, where the ratio of the foreground to background spectra is fitted by a polynomial in the nonresonant region and the background spectra are then multiplied by the fit function. The other uses the ratio of like-sign pairs corresponding to and to determine the functional form of the shape of the background. This function is then normalized to match the unlike-sign distribution in the nonresonant regions, GeV/ and GeV/. Background estimates using those two methods are shown in Fig. 3.
Both estimates of the background match the nonresonant region of the unlike-sign spectrum. However, because the second method includes a two-step normalization which introduces higher statistical fluctuations upon the background subtraction, the second method is only used for a cross check. The insert in Fig. 3(b) shows that the acceptance and reconstruction efficiency drops quickly at low mass which explains the higher yield compared to the low mass vector mesons.
To ensure the robustness of the yield extraction, an additional yield extraction procedure is employed. The background is fitted with a polynomial and the result of the fit is added to signal fits which are then fitted to the dimuon invariant mass spectrum while constraining the added function with the background spectra fit parameters. The background normalization is a free parameter.
The unlike-sign dimuon spectra, with , in the region of interest ( GeV/) have contributions from three mesons, , , and . The meson is partly resolved while and mesons are completely merged, hence the combined yield for and mesons was extracted. It was found that the reconstructed mass spectra of the simulated and are fitted well by Gaussian distributions, while in the case of , a Breit Wigner distribution matched the mass spectrum, which motivated using these distributions to fit the invariant mass spectra.
The background subtracted dimuon spectra in the low mass region, GeV/, are fitted with two Gaussian distributions and a Breit Wigner distribution. The means and widths ( for Breit Wigner distribution) of the reconstructed , and were extracted using the PHENIX simulation chain and used as a first approximation in fitting the data. The masses and widths are free parameters in the fit to account for small detector effects which result in % variations with respect to the PDG values. In addition to these distributions, the dimuon spectra without background subtraction are fitted with a polynomial. It is important to note that the parameters from data and simulation fits converged to the same values within uncertainties without any systematic shifts.
Figure 4 shows an example of the different yield extraction methods. Figure 4(a) shows the unlike-sign dimuon invariant mass spectrum (solid black circles) and the background spectrum (empty blue circles), while (b) shows the same background spectrum fitted with a fourth order polynomial. Figure 4(c) shows the unlike-sign dimuon invariant mass spectrum after subtracting the normalized background spectrum, shown in (b), fitted by two Gaussian distributions and a Breit Wigner distribution. s a cross check, a first order polynomial was added to the fit and the yields re-extracted and the resulting yields changed by less than 1%. Figure 4(d) shows the unlike-sign dimuon invariant mass spectrum without background subtraction fitted by two Gaussian distributions, a Breit Wigner distribution and a fourth order polynomial constrained from the fit results shown in Fig. 4(b). The yields extracted using the two methods illustrated in Fig. 4(c) and (d) gave consistent results, well within uncertainties.
The data are binned as a function of over the range GeV/ for the rapidities . In addition, the data integrated over the range GeV/ were studied as a function of rapidity. The raw yields in this measurement were extracted using background subtraction as well as background fit methods, and in the case of the background fit, several polynomials of different orders were attempted. As an example, the invariant mass spectra are fitted by the function that includes a fourth order polynomial, as defined below,
where and are a Breit-Wigner and a Gaussian functions, respectively, and is a fourth order polynomial. and are the yields of and , and and are their mean values. The fit functions of (Gaussian) and (Breit Wigner) are constrained to have the same mean value and the ratio of their yields, is set to 0.58. The factor 0.58 is the ratio of and cross sections, Adare et al. (2010), multiplied by the ratio of their branching ratios Beringer et al. (2012). The results of fitting the invariant mass spectra for different bins at are listed in Table 1.
|(GeV/)||1.0 - 2.0||2.0 - 2.5||2.5 - 3.0||3.0 - 4.5||4.5 - 7.0|
|(68 5)||(63 8)||(39 4)||(36 5)||(4.8 1.2)|
|(GeV/)||(77 1)||(77 1)||(77 1)||(76 1)||(80 2)|
|(GeV/)||(18 4)||(22 4)||(22 2)||(18 4)||(19 2)|
|(GeV/)||(8.8 1.3)||(85 8)||(8.8 1.2)||(8.1 1.3)||(7.2 1.6)|
|(39 8)||(53 6)||(32 4)||(28 3)||38 10|
|(GeV/)||(100 1)||(99 1)||(100 1)||(100 2)||(106 6)|
|(GeV/)||(7.5 1.4)||(8.8 1.3)||(8.8 1.1)||(8.8 1.0)||(7.2 1.1)|
|p0||(20 4)||(5.9 3.8)||(13 3)||(9.5 2.8)||8.6 1.3|
|p1||(-3.8 2.0)||(3.0 1.8)||(-2.5 1.3)||(-1.8 1.3)||-15 2.2|
|p2||(6.2 3.1)||(-4.9 2.5)||(3.4 1.8)||(2.2 1.8)||39 1.5|
|p3||(-3.6 2.0)||(2.6 1.4)||(-2.1 1.0)||(-1.3 1.0)||-35 1|
|p4||(6.7 4.3)||(-4.7 2.9)||(4.6 2.1)||(2.6 2.1)||9.2 0.4|
The extracted yields of and were consistent among all fits. Therefore, the yields and their uncertainties of the fit with the best are used in the differential cross section calculations. The variations between the yields of the fit with the best and those of the other fits are considered as systematic uncertainties on the yield extraction.
The acceptance and reconstruction efficiency () of the muon spectrometers, including the MuID trigger efficiency, is determined by individually running pythia 6.421 (Default) Sjostrand et al. (2001) generated , , and through a full geant simulation of the PHENIX detector. The simulated vertex distribution was tuned to match that of the 2009 data. The simulated events are reconstructed in the same manner as the data and the same cuts are applied as in the real data analysis.
The and rapidity distributions of the generated events match the measured ones very well. The insert in Fig. 3 shows the as a function of invariant mass, while Fig. 5 shows the as a function of and rapidity for , as an example; the for and look very similar. The dependent drops quickly at lower which is the reason for limiting this study to GeV/.
The differential cross section is evaluated according to the following relation:
where is the PHENIX BBC sampled cross section, mb at GeV, which is determined from the van der Meer scan technique Adare et al. (2009). is the branching ratio to dimuons (, , and ) Beringer et al. (2012). = , is the BBC efficiency for hard scattering events Adler et al. (2004). is the number of MB events, and is the number of the observed mesons. In the dependent study, the LVM yields were extracted for each arm separately and the weighted average of the two arms was used in the differential cross section calculations. is the acceptance and reconstruction efficiency.
The and yields are measured together and the dependent and rapidity dependent differential cross sections are reported as and , respectively, to minimize the contribution of uncertainties from branching ratios and total cross sections needed to calculate the absolute () differential cross section. The for is taken as the weighted average of the individual , where the averaging is done based on and branching ratios.
The systematic uncertainties associated with this measurement can be divided into three categories based upon the effect each source has on the measured results. All uncertainties are reported as standard deviations. Type-A : point-to-point uncorrelated uncertainties allow the data points to move independently with respect to one another and are added in quadrature with statistical uncertainties, and include a 3% signal extraction uncertainty. Type-B : point-to-point correlated uncertainties allow the data points to move coherently within the quoted range. These systematic uncertainties include a 4% uncertainty from MuID tube efficiency and 2% from MuTr overall efficiency. An 8% uncertainty on the yield is assigned to account for a 2% absolute momentum scale uncertainty, which was estimated by measuring the mass. A 9% (7%) uncertainty is assigned to the () rapidity due to the uncertainties in the determination method itself. The at the lowest bin is small, as shown in Fig. 5, and sensitive to variations in the slope of the input distribution which affects the differential cross section calculations at this bin. To understand this effect, the -dependent cross section is fitted by three commonly used fit functions (Hagedorn Hagedorn (1965), Kaplan Kaplan et al. (1978), and Tsallis Adare et al. (2011a)) over the range , GeV/, and the fitted functions are extrapolated to lowest bin, GeV/. The differences between the values extracted from these fits and the measured one at the lowest bin is within 8%, hence an 8% systematic uncertainty is assigned to lowest bin to account for these differences. For the integrated and rapidity dependent cross sections the 8% uncertainty is assigned to all data bins because the lowest bin is dominant. Type-B systematic uncertainties are added in quadrature and are shown as shaded bands on the associated data points. Finally, an overall normalization uncertainty of 10% was assigned for the BBC cross section and efficiency uncertainties which allows the data points to move together by a common multiplicative factor, and are labeled as type-C. These systematic uncertainties are listed in Table 2.
|B||9% / 7%|
|B||Absolute momentum scale||8%|
|Total||Quadratic sum of (B)||13% / 12%|
|C||BBC efficiency (Global)||10%|
The open charm contribution to the signal is a possible source of systematic uncertainty. Even though the background subtracted dimuon spectrum in Fig. 4(c) shows no evidence of a remaining background, a Monte Carlo simulation was carried out to verify that the open charm contribution to the signal is negligible after background subtraction. A single particle pythia simulation of open charm was generated and run through the PHENIX simulation chain. The charm differential cross section at forward rapidity, mb Adler et al. (2007), is used with an inclusive branching ratio, = 0.176 Beringer et al. (2012). The simulated events were then reconstructed using identical code to that used in the real data analysis, and after applying all cuts used in the analysis, the surviving rate of open charm was negligible in comparison to the low mass vector meson yields. Additionally, similar study of the and Dalitz decays showed that they were negligible in comparison to the low mass vector meson yields.
The differential cross sections for and as a function of are shown in Figs. 7 and 7, respectively, and listed in Table 3. The appropriate value where each point was plotted is chosen such that the fit function, a function selected to fit the distribution, is equal to its mean value Lafferty and Wyatt (1995) where the results are listed in the first column in Table 3. Figs. 7 and 7 also include some standard tunes of pythia (atlas-csc Buttar et al. (2004), default Sjostrand et al. (2001) and perugia-11 Skands (2010)) and phojet Engel (1996). The bottom panels in Figs. 7 and 7 show the ratio between the measurement and the model predictions.
|(GeV/)||(b / (GeV/))||(b / (GeV/))|
|1.38||(8.41 0.67 1.26)||(2.76 0.35 0.41)|
|2.17||(7.19 0.71 0.93)||(3.19 0.36 0.41)|
|2.65||(1.95 0.19 0.25)||(8.16 0.93 1.06)|
|3.58||(2.68 0.29 0.35)||(1.09 0.14 0.14)|
|5.40||(1.10 0.16 0.14)||(4.71 0.90 0.61)|
pythia atlas-csc and perugia-11 tunes, reproduce the differential cross section at both midrapidity and forward rapidity for and , respectively, while phojet under predicts the data in both cases. The pythia atlas-csc reproduces the differential cross sections at forward rapidities. The pythia atlas-csc and perugia-11 tunes and phojet fail to match the data below 1 GeV/. Generally, pythia and phojet seem to do better job reproducing than .
|-2.10||61.1 6.7 9.2||21.5 3.7 3.2|
|-1.84||67.9 5.6 10.2||23.3 2.8 3.5|
|-1.54||81.0 7.1 12.2||28.1 3.8 4.2|
|1.54||80.3 7.6 11.2||26.3 3.2 3.7|
|1.85||66.9 5.4 9.4||21.0 2.8 2.9|
|2.14||58.4 7.4 8.2||18.9 2.2 2.6|
|1.38||0.33 0.04 0.03|
|2.17||0.44 0.05 0.04|
|2.65||0.43 0.05 0.04|
|3.58||0.40 0.05 0.04|
|5.40||0.45 0.09 0.04|
Figure 10 and Table 4 show the differential cross section as a function of rapidity for in (a) and in (b), along with pythia tunes (atlas-csc, default, and perugia-11) and phojet. It can be seen in Fig. 10 that default and sc perugia-11 tunes reproduce the results, while the atlas-csc tune matches the forward rapidity results.
The acceptance at low is very small to negligible in the low mass region which prevents us from extracting the differential cross sections, , summed over all directly from the data. Instead, we report integrated over the measured range, nb and nb.
The ratio , corrected for acceptance and efficiency, was determined for GeV/ and , giving , as shown in Fig. 11 and listed in Table 5. Systematic uncertainties including MuID and MuTr efficiencies, absolute momentum scale and BBC efficiency cancel out when taking the yield ratio.
Figure 11 also shows pythia (atlas-csc, default, and sc perugia-11 tunes) and phojet. The atlas-csc tune reproduces the ratio while the other models underestimate it. The ALICE experiment also measured this ratio in collisions at 7 TeV in the dimuon rapidity region . The reported value is Abelev et al. (2012b) over the range which is consistent with our result.
V Summary and Conclusions
In summary, we studied the low mass vector meson, , , and , production in collisions at = 200 GeV for and GeV/, through the dimuon decay channel. We measured , and differential cross sections as a function of as well as a function of rapidity.
The differential cross sections, of and , were evaluated over the measured range, nb and nb. The ratio , at GeV/ and , was also determined, and is , which is consistent with ALICE measurement at larger rapidity and higher energy. This agreement with the ALICE result at , which is higher than pythia default at , suggests a higher contribution to production.
The data are compared to some commonly used pythia tunes and phojet. Overall, the pythia atlas-csc and default tunes describe forward rapidity data except for the rapidity distribution and describe midrapidity data above 1 GeV/. The pythia perugia-11 tune describes the differential cross section while it underestimates the differential cross section. Generally, all these event generators describe the shape of the LVM distribution indicating that leading-order perturbative QCD-based event generators can describe distribution.
We thank the staff of the Collider-Accelerator and Physics Departments at Brookhaven National Laboratory and the staff of the other PHENIX participating institutions for their vital contributions. We acknowledge support from the Office of Nuclear Physics in the Office of Science of the Department of Energy, the National Science Foundation, Abilene Christian University Research Council, Research Foundation of SUNY, and Dean of the College of Arts and Sciences, Vanderbilt University (U.S.A), Ministry of Education, Culture, Sports, Science, and Technology and the Japan Society for the Promotion of Science (Japan), Conselho Nacional de Desenvolvimento Científico e Tecnológico and Fundação de Amparo à Pesquisa do Estado de São Paulo (Brazil), Natural Science Foundation of China (P. R. China), Ministry of Science, Education, and Sports (Croatia), Ministry of Education, Youth and Sports (Czech Republic), Centre National de la Recherche Scientifique, Commissariat à l’Énergie Atomique, and Institut National de Physique Nucléaire et de Physique des Particules (France), Bundesministerium für Bildung und Forschung, Deutscher Akademischer Austausch Dienst, and Alexander von Humboldt Stiftung (Germany), OTKA NK 101 428 grant and the Ch. Simonyi Fund (Hungary), Department of Atomic Energy and Department of Science and Technology (India), Israel Science Foundation (Israel), National Research Foundation of Korea of the Ministry of Science, ICT, and Future Planning (Korea), Physics Department, Lahore University of Management Sciences (Pakistan), Ministry of Education and Science, Russian Academy of Sciences, Federal Agency of Atomic Energy (Russia), VR and Wallenberg Foundation (Sweden), the U.S. Civilian Research and Development Foundation for the Independent States of the Former Soviet Union, the Hungarian American Enterprise Scholarship Fund, and the US-Israel Binational Science Foundation.
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