Direct Hadronic Reconstruction of D ± Mesons at STAR

Transcription

1 Direct Hadronic Reconstruction of D ± Mesons at STAR Nathan Joseph Department of Physics and Astronomy, Wayne State University, Detroit, MI September 2, Introduction: Quark-Gluon Plasma The theory of Quantum Chromodynamics (QCD) is currently accepted as the most likely theory of the strong interaction, the quarks and gluons affected by it, and the hadronic matter of which they are constituents. QCD makes two very important predictions about the behavior of quarks and gluons (partons): 1. They are normally confined to the internal structure of a hadron and cannot be removed from it, as the force separating them does not weaken with distance thus energy required to do so would be infinite, a property aptly named Confinement. 2. In very high energy collisions between hadrons, quarks and gluons interact very weakly, a property known as Asymptotic Freedom. From these QCD also leads to the prediction that in relativistic heavy ion collisions of sufficient energy a new phase of matter is created, one in which quarks and gluons are de-confined and locally thermalized causing the formation of a phase of matter known as Quark-Gluon Plasma (QGP). It is currently believed this new phase forms at temperatures approaching K or 175 MeV. The only time that this phase of matter could exist in nature is moments after the big bang when the temperature of the universe was much higher than it is today, making QGP an excellent probe for conditions of the early universe. However, at certain particle accelerator such as Brookhaven s Relativistic Heavy Ion Collider (RHIC) it is believed that we are able to recreate and observe this matter. The primary constituency of QGP is the light flavored quarks (u,d,s), while heavier quarks (c,b,t) are produced much more infrequently; for the charm quark, about once for every 2000 q q pairs, the bottom and top are produced even more infrequently. By understanding the production mechanism for the heavier quarks we can gain knowledge about the plasma that would otherwise be unavailable to us by study of the light flavors alone. This REU project focused on the charm quark and certain mesons it forms as a manner of examining the heavier flavors. 2 The Charm Flavor The charm flavor is the lightest of the heavy flavors as well as being the most common in QGP. It is theorized that charm quarks are generated during the initial stages of the plasma via gluon fusion from parton-parton hard scattering: gg c c. From this, the most abundant channels indicate that the c would bind with a d and the c to a d to form either of the charged D mesons. If this is indeed the production mechanism, it suggests that the charm makes a good probe for the early conditions of the plasma such as its temperature as well as the behavior of heavy quarks as the medium evolves. Two important quantities regarding the behavior of the heavy quarks are the elliptic flow of the heavy flavors, v 2, and the nuclear modification factor R AA of the charm. Specifically we are interested in measuring these quantities by reconstructing the D ± mesons, two of the lightest mesons containing a charm quark. 1

2 Particle Quark Content Mass Average Lifetime Decay Length (cτ) D + c d ± 0.20 MeV (1040 ± 7) s 312 µm D d c Table 1: D ± Attributes [1] 2.1 Momentum-Space Azimuthal Anisotropy and Elliptic Flow The elliptic flow parametrizes what is known as the Momentum-Space Azimuthal Anisotropy, a well studied phenomenon in heavy ion collisions that arises due to differences in the amount of medium traversed by particles traveling parallel to the reaction plane and those traveling perpendicular to the plane. If the particles interact with the medium their momentum distributions will differ, causing an observed azimuthal anisotropy in the momentum space. This anisotropy only occurs in non-central collisions where the overlap area of particles is asymmetric. Mathematically we can analyze this particle distribution in momentum space as a Fourier series, [ ] E d3 N dp 3 = 1 d 2 N 1+2 v n cos[n(φ Ψ RP ] (1) 2π p T dp T dy where p T, y, and φ are the transverse momentum, rapidity, and the azimuthal angle, respectively, Ψ RP is the reaction plane azimuthal angle, and v n is the anisotropy parameter of the nth harmonic, n=1 v n =< cos[n(φ Ψ RP ] > (2) For the second harmonic coefficient v 2 the anisotropy parameter is known as the elliptic flow. 2.2 The Nuclear Modification Factor The nuclear modification factor R AA is a related quantity that examines the energy loss of the partons in the medium. It is defined as the ratio of the p T spectra from Au + Au events to those from p + p events, scaled by the number of binary nucleon-nucleon events, R AA (p T )= d2 N AA /dp T d η T AA d 2 σ NN /dp T dη Where T AA is known as the nuclear overlap integral when averaged over each of the centrality bins. When graphed against p T if R AA begins to decrease at high momenta it is indicative of energetic partons losing their energy as they traverse the medium. Measuring this quantity would allow us to measure the difference of the charm and light quark energy loss. 3 Reconstruction Techniques Using data from RHIC we will attempt to recreate the charged D meson by utilizing the Silicon Inner Tracker and Time Projection Chamber components of the STAR Detector. There are multiple methods in which the D mesons could be reconstructed from their decays. Focusing on the semi-leptonic channels and hadronic channels there are two main modes. (3) 3.1 Decay Modes The mode we focus on is the hadronic decay D ± Kππ. This channel holds an advantage because when using the semi-leptonic channel the invariant mass is never reconstructed because we only measure the displaced electron and not the other particle. This leads to an ambiguity of decay with the B 0 meson which 2

3 Channel Decay Products Branching Ratio Decay Length (cτ) Semi-Leptonic D ± e ± + X 17.2% 312 µm Hadronic D ± Kππ 9.2% Table 2: D ± Decay Channels [1] Figure 1: Semi-Leptonic and Hadronic Decays for D 0 holds a very similar decay (B 0 e + + X), which would need to be disentangled from the decay in order to subtract the background it would contribute. Not only that but it would also require the model to connect the kinematics of the electron to the D meson even when there is no contamination from a B meson. This makes for a very inefficient reconstruction compared to the method we perform along the hadronic channel. By identifying the hadronic decay products of the D ± we are able to perform what is known as direct hadron reconstruction by utilizing combinatorial methods. As mentioned above, the charged D decays into three charged daughter particles. This decay occurs before the detectors so visualization of the vertex at which it occurs, known as the secondary vertex, is not possible. Rather, sets of decay particles are grouped and their decay trajectories projected toward the primary vertex of the collision. If the trajectories cross at some point before the vertex they can be considered candidates for the decay. The momentum of these candidate daughter particles are then grouped in order to calculate the momentum of the original charged D which in turn is then used to calculate the invariant mass of the charged D. M invariant = (E 1 + E 2 + E 3 ) 2 p 2 mother (4) p 2 mother = (p x1 + p x2 + p x3 ) 2 +(p y1 + p y2 + p y3 ) 2 +(p z1 + p z2 + p z3 ) 2 (5) Where E 1,E 2,E 3 represent the energies of the daughter particles and p x1,p x2,... represent the respective momentum components of each daughter. If we were correct in choosing the right daughter tracks from the decay of a charged D we would then indeed see the calculation produce the correct mass of a charged D, allowing for some margin of error in the momentum determination from the detector resolution in STAR. 3.2 Detectors The two main detectors we utilize, as mentioned above, are the Silicon Inner Tracker (SIT) and the Time Projection Chamber (TPC). The SIT is further divided into two components, the Silicon Strip Detector (SSD) and the Silicon Vertex Tracker (SVT). The SSD is located between the TPC and the SVT and consists of one barrel supporting up to 20 ladders each supporting 16 silicon drift detector (SDD) modules. The SVT is the innermost component of the detector and consists of 3 barrels of 8, 12, and 16 ladders respectively. These ladders can accommodate up to 4, 6, and 7 SDD modules on their respective barrels for 3

4 a total of 216 modules. The SVT barrels are radially positioned at 5.97cm, 10.16cm and 14.91cm, while the SSD barrel is positioned at 23cm. Figure 2: Cross Section of STAR showing size of detector and TPC and SVT For our reconstruction to be efficient it must have an impact parameter resolution in a range similar to that of the decay length of the D mesons, 312 µm. With such a short lifetime most of the D ± vertices will be found within a millimeter of the primary vertex. The TPC has an event vertex resolution of 2 mm at best, making it highly inefficient to use alone. By utilizing the SVT and SSD in our analysis, however, we can obtain an event vertex resolution of 90 µm, making them crucial to our work. Figure 3 shows the improvements to the impact parameter resolution at various momentum levels by adding in the SVT and SSD detectors to our reconstruction. Figure 3: Impact Parameter Resolution as SVT and SSD hits are added 3.3 Tracking Code In our method of reconstructing the charged D mesons we utilize an effective tracking method through a code applied to data sets. The code sorts through the possible daughter particles from each event and then matches unlike sign particles within each event and check to see if they originate from a common decay vertex. It must also check that the particles we have matched are the in fact the kaon and pion particles we are interested in. This can be done by using Particle ID (PID) to mark the trajectories. We are able to do this over a certain momentum range by examining the energy loss of the particles, de dx, through the TPC. 4

5 Figure 4: Distribution of de dx vs. p T This is done according to the Bethe-Block formula, de dx = 4π ( ) m e c 2 nz2 e 2 2 [ ( β 2 2me c 2 β 2 ) ] ln 4πɛ 0 I (1 β 2 β 2 ) where z is the particle charge, n is the electron density of the gas in the TPC, I is the mean excitation potential of the gas, and β is the ratio v c.the energy loss is then plotted against the momentum of the candidate particle and the resulting distribution allows us to differentiate between different possible particles, as shown in Figure 4. However, this does not solve the problem alone and we must also perform other techniques to remove background from the data. We do this by adding in what are known as cuts, which are cutoffs at selected points on variables of the data, to our tracking code. 3.4 Geometric Cuts For maximum efficiency of the analysis we must obviously remove as much background as possible in order to attain a clean signal. To do this we perform cuts on the geometric variables of the decay. Because the daughter particles are charged their trajectories are bent into a helical shape by the solenoidal magnetic field of the detector. As we project the paths back towards the primary vertex the distance between paths is known as the distance of closest approach (dca), as shown in Figure 5. By cutting these various dcas in the system we can eliminate much of the background as the majority does not share similar geometric decay patterns with the charged D. Other cuts to the data can be applied as well, not necessarily restricted to the geometric variables of the decay but to kinematic variables like the momentum distributions and hits in the detectors. After applying a series of cuts to the data we are able to obtain an invariant mass distribution, ideally, from which a clean signal can be extracted. We do this by fitting a polynomial function to the distribution according to bands on the side of the D ± peak in order to first represent the background. The background is subtracted in the mass range of the signal according to the polynomial fit which is followed by fitting a Gaussian function over the selected peak mass range to represent the signal. If all goes well one would expect to see a fit as shown in Figure 6. 4 The Analysis 4.1 Determining Cut Sets and Their Application We began our analysis of the charged D by first comparing a background selection of 800,000 events against a sample of 200,000 simulated pure D + events generated in a realistic event generator known as PYTHIA (6) 5

6 (a) D + Decay Paths (b) Example of dca and cuts for D 0 Figure 5: Projected Images of D meson Decays (a) Polynomial Fit (b) Gaussian Fit Figure 6: Example Fits from 13M Au+Au Events that contains realistic descriptions of all the known physical processes to be expected based on QCD calculations and experimental data. This, combined with repeated random sampling through Monte Carlo methods allows PYTHIA to generate events [2]. We examined various combinations of the aforementioned geometric variables and looked for areas in which we could cut out as much background as possible while retaining a much higher amount of pure signal. Initially, we were able to determine that we could cut along four main variables that are shown in Table 3. A comparison of the simulated events and the background is shown in Figure 7. These cuts led to retentions of only 0.096% of the background and 6.286% of the pure signal, a 65 times difference. Cut Variable D + Pure Sample Background Sample No Cuts Decay Length > V0DcaPV < DDCaKaonPV < DDcaPionPV < Table 3: Statistics retained after cuts based on Fig. 7 were applied 6

7 (a) Decay Length (b) V0dcaPV (c) DDcaKaonPV (d) DDcaPionPV Figure 7: Geometric Variables Cuts: Blue indicates Pure D + sample, Red Indicates Simulated Background These cuts then were applied to two Au-Au, s NN = 200 GeV D + data samples from STAR, each of approximately 3.5 million events. It was found that the cut sets did not work as effectively as planned: we found that with all cuts enacted we had removed too much from the data and were not able to yield anything even with just the first Decay Length cut placed. This led us to re-consider our original cut set and experiment with changing the points at which we had cut previously. 4.2 Updated Cut Set By experimenting with our original cut sets we were able to determine a set of new points from which we could cut that actually increased our original signal yields, allowing both samples to now exhibit a cleaner signal. Variable Original Cut Set Updated Cut Set Decay Length > 0.06 < 0.08 V0dcaPV < 0.04 < 0.04 DDcaKaonPV < 0.04 < 0.04 DDcaPionPV < 0.04 Not Cut Table 4: Original and Updated Cut Sets This new cut set was then implemented on five D + data sets totaling about approximately 22.5 million events when combined. We also implemented the cuts on five D data sets for almost 23.9 million events after being combined. For the D + data we found this cut set to be extremely successful as we were able to yield a fairly strong signal, however when applied to the D samples we were not able to find much of 7

8 anything resembling a signal as shown in Figure 8. Interestingly, all conceivable production mechanisms tell us that the probability for producing the negative charge state should be equal to that of the positive state, D i.e. + D = 1. The effects causing our observed discrepancy are under investigation and are beyond the scope of this project. (a) 13M Au+Au Events, Signal: 15700, runid is below (Normally 22.5M Events) (b) 23.9M Au+Au Events, No Signal Figure 8: Invariant Mass Distributions, minus Background, fit to Gaussian - Combined Samples 4.3 Attempts to create a p T spectrum The lack of signal yield from the D samples led us to focus primarily on the D + sample for the remaining time. After we had established a fairly efficient set of cuts on the data sets as a whole we proceeded to attempt to create a spectrum of p T bins showing the concentrations of signal. Optimally this data would be further used to graph what should be an exponential function given by 1 dn p T dp T versus p T, where N is the number of particles and p T is their transverse momentum. It can easily be seen that this function bears a strong resemblance to the portion of (2) that starts the right hand side of the equation. From this fit to the decreasing exponential function we would proceed to calculate a full charm cross-section. An example of what such a fit might look like is given in Figure 9, in this case the fit is from a D 0 + D 0 reconstruction from 200 GeV Cu + Cu collisions [3]. Data for this example fit resulted in a measurement of dn D 0 dy = ± Figure 9: Example of spectra fit to exponential function from 200 GeV Cu-Cu collisions [3] 8

9 Of this measured yield, %87 lies in the reconstructed momentum range from 0.1 GeV/c to 1.9 GeV/c. This yield measurement was then extrapolated to a find a full charm cross-section. Doing this required an extrapolation to full rapidity, the ratio of D 0 to c c, a normalization to the number of binary collisions, and a scaling to the inelastic cross-section of nucleons, according to the formula, σ NN c c = dn D 0 dy σinelastic pp Nbin CuCu Where f is the normalization to full rapidity, R is the ratio of D 0 to c c pairs, Nbin CuCu is the average number of binary collisions in a Cu + Cu collision, and σpp inelastic is the proton-proton inelastic cross-section. Once these factors are applied a total charm-cross-section in NN collisions can be calculated, in this case it is found to be 1.15 ± 0.20(stat.)+0.34(sys.) 0.35(sys.) mb [3]. In our case we would obviously need replace and alter some of these factors in order to fit our reconstruction method as we are working with the charged D mesons and Au + Au collisions. f R Variable Third Cut Set Decay Length < 0.08 V0dcaPV < 0.03 DDcaKaonPV Not Cut DDcaPionPV Not Cut RunID < Table 5: Cut Set used for p T Binning (7) To create the necessary bins for our reconstruction we generated a set of 25 smaller bins of 200 MeV each, from 0 to 5 GeV, on a new cut set (Table 5) and applied the cuts we had previously found to each in order to create multiple invariant mass distributions. Because the average transverse momentum of a produced D meson is about 1 GeV/c it is unlikely that we would find a signal in the early bins by themselves, so we added the distributions until we were able to yield a signal and then picked up where that range left off. Additionally, the bins needed to hold a significance of at least 3 sigma according the formula: σ = Signal Signal + Background (8) We already had values for the signal from the gaussian fits we performed as we created the momentum bins, but the background is removed when such fits are performed. To find the value we needed we performed an integral under the area of the original invariant mass distributions over the original signal range. This would allow us to find an estimate of the significance for any bins we created. At first we were not able to create a full spectrum with our existing cut set, but by tightening our V0dcaPV cuts to 300µm and removing our DDcaKaonPV cut we were able to create 4 different bins over the whole 0 to 5 GeV range as shown in Figure Conclusions and Outlook Due to time restrictions of the program and problems experienced along the way it was not possible to actually measure the two quantities mentioned earlier, v 2 and R AA, but the data collected could potentially be further used to do so. Whether or not accurate results would be produced is still a major issue however. Looking at the mass figures for the majority of our fits it is seen that we are reproducing something with slightly higher mass than should be expected for the charged D mesons. Our p T bins are especially of concern as we expected something substantially different from what we observed. Our low p T bins show a very wide 9

10 (a) GeV, Signal: 15700, σ = 4.8 (b) GeV, Signal: 18400, σ = 3.3 (c) GeV, Signal: 7200, σ = 3.1 (d) GeV, Signal: 15300, σ = 3.0 Figure 10: Four p T bins from 0 GeV to 5.0 GeV, Cut Set 3 gaussian with a mass shifted higher, normally we would expect to see a thinner fit than normal with the mass shifted lower, while we expect to see a wider fit with a mass shifted higher at the upper p T bins. We expect the wider gaussian distribution at higher momentum because the higher momentum particles will travel along a straighter trajectory having been bent less by the magnetic field, this causes the resolution of our analysis to go up which in turn causes our gaussian to widen as we cannot get as precise results. The same goes for the lower momentum bins having a thinner distribution, their curvature happens very early and is very helical, lowering the resolution and thinning the distribution. Momentum would also be the likely factor causing any mass shifts in the distributions, however, the deviation from the expected invariant mass due to high and low p T particles should still not be as large as the one we have recorded. The problem most likely lies somewhere in the subtraction of the background. Another area of concern is the reconstruction of the D meson. Ideally the same cuts should work for either of the charged D mesons as they both have the same properties other than the charge. However, our reconstructions have all indicated that something is wrong with our process. This is especially troubling because it, combined with the background subtraction problem, also suggests we are reconstructing the D + improperly. If both these problems are indeed true and cannot be removed simply, it suggests that the p T data, among other data, collected is not correct. Once these issues and others are resolved we should see much better fits when applied to the invariant mass distributions. This would directly lead to more successful p T spectra which in turn would allow us to begin measuring quantities essential the the state of the QGP. Measuring the temperature would give us some indication if our current theories are right in predicting the crossover temperature from ordinary nuclear matter to QGP and measuring the energy loss and collectivity of the charm and heavier mesons will surely give insight into their production mechanisms and the hydrodynamic behavior of the medium which 10

11 is currently believed to be behaving like an ideal fluid. Insight into all of these matters in turn gives us insight into aspects of QCD in general and allows us better insight into the world of nuclear physics. 6 Acknowledgements I would like to thank Rene Bellwied for his guidance and support, and Sarah LaPointe for her guidance, patience and allowing me to work with her. I would also like to thank the Wayne State University Department of Physics and Astronomy for providing the facilities in which this research was conducted. This REU project was made possible by the National Science Foundation through grant PHY References [1] C. Amsler et al (Particle Data Group), Physics Letters B667, 1 (2008) and 2009 partial update for the 2010 edition [2] Torbjörn Sjöstrand et al (PYTHIA Authors), torbjorn/pythia.html, [3] S. Baumgart, A. Knospe, A. Shabetai, STAR Collaboration, baumgart/paper Proposal/proposal.html,