Optimization of the reconstruction of B 0 D + π and D + D 0 π + decays with the ALICE detector

Transcription

1 Optimization of the reconstruction of B 0 D + π and D + D 0 π + decays with the ALICE detector Daan Leermakers Supervisor: Dr. André Mischke Daily supervisor: Dr. Alessandro Grelli Institute of Subatomic Physics Faculty of Physics and Astronomy, Utrecht University 18th June 2014 Abstract Quantum Chromodynamics (QCD) predicts that if quarks and gluons are at very high temperatures and/or densities they become asymptotically free and form what is called a quark gluon plasma (QGP). The ALICE detector at the Large Hadron Collider (LHC) is used to study matter at conditions hot and dense enough to produce a QGP. To study the properties of the QGP, we look at mesons which traverse the QGP containing the heavy quarks charm and beauty. This is done by colliding two ionized lead atoms. The same mesons are produced and measured in proton-proton collisions. The difference in their properties, after normalization, tells us more about the properties of the QGP. In addition to a statistical error, conclusions drawn from data from ALICE have systematic errors. By varying the methods used in the yield extraction of D + mesons in lead-lead collisions at 30-50% centrality we found that the systematic uncertainties of the yield extraction are in general below 10%. In 2015 the LHC will be upgraded to collide lead ions at 5.1 instead of 2.76 TeV and to collide protons at 13 instead of 7 TeV. To prepare for the planned beauty measurements we performed Monte Carlo simulations of proton-proton collisions at 13 TeV. We are interested in the decay chain: b B 0 D + + π D 0 + π + π + K + 2π + + π. In these simulations we will focus on the decay B 0 D + + π. The event generator PYTHIA is used to perform the simulations. We mainly look at what cuts could be applied and estimate how many particles ALICE will be able to detect in Among other results we found that at low transverse momenta (p t) almost twice as many B 0 D + + π decays as B 0 D + + other decays occur. At high p t values there are up to 2.5 times as many B 0 D + + other decays as B 0 D + + π decays. In the B 0 D + + π decay 20-30% more pions than D + mesons are in the acceptance region of the ALICE detector. In general particles with higher velocities are more likely to be in acceptance of the ALICE detector.

2 Contents 1 Introduction Standard Model Quantum chromodynamics (QCD) Quark-gluon plasma (QGP) Heavy quarks Structure of the thesis Experimental setup ALICE Inner Tracking System (ITS) Time Projection Chamber (TPC) Time Of Flight (TOF) Root and AliRoot Event generator PYTHIA Fixed Order plus Next-to-Leading Logarithm Systematic uncertainties of D + measurements in lead-lead collisions at 30-50% centrality Centrality Invariant mass Selection cuts Yield extraction Systematic uncertainties Performance study of B 0 D + + π PYTHIA configuration Analysis Outlook 35

3 1 Introduction Every atom consists of a positively charged nucleus surrounded by a cloud of negatively charged electrons. These two components are held together by the electromagnetic force described by quantum electrodynamics (QED). The mediators of this force are photons. The nucleus itself is build up of protons and neutrons which in turn are build up of quarks. These quarks are held together by the strong force described by quantum chromodynamics (QCD). The mediators of this force are called gluons. While quarks and gluons are usually confined in particles like the proton and the neutron, at high temperatures and densities they become deconfined and form what we call the quark-gluon plasma (QGP). Measurements and Monte Carlo simulations in this thesis try to make a contribution to the better understanding of this plasma. Hereto we investigate the systematic uncertainty in yield extraction of D + mesons from lead-lead collisions at 30-50% centrality, as well as studying the properties of beauty decay in proton-proton collisions using Monte Carlo simulations. 1.1 Standard Model The standard model of elementary particles, schematically shown in figure 1, describes all particles and forces that build up the matter around us. The model describes two basic types of particles: quarks and leptons. Both types consist of six particles and six anti-particles which are split up in three generations. The lightest generations are stable, while the heavier generations quickly decay into the lighter ones. Figure 1: The standard model of elemantary particles.[1] The first generation of quarks consists of the up and down quark, since these are most stable they are the building stones of protons and neutrons. Together with the electron, they form all the stable matter around us. The second generation is formed by the charm and the strange quark. Although unstable, the lifetimes of particles that include quarks of the second generation are long compared to particles containing quarks of the third generation. The quarks of the third generation are called top and bottom, although bottom is often referred to as beauty. This is 2

4 consistently done in this text as well. Even though the quarks in the third generation are least stable, they have a larger mass than the other quarks, which is useful in some experiments. Like quarks, leptons exist in three generations. These generations are made up of the electron and the electron neutrino, the muon and the muon neutrino and the tau and the tau neutrino. Unlike quarks leptons exist by themselves. The neutrino s have neutral charge and very small masses, while the electron, muon and tau are much heavier and have non-zero charge. These fundamental particles interact via the four fundamental forces of nature. The weakest of these forces, gravity is not incorporated in the standard model. Fortunately its contribution at small scales is so small that it can be neglected. The other three forces all work by exchanging a particle called a gauge boson. For the electromagnetic interaction the corresponding gauge boson is the photon, the weak interaction uses the Z and the W bosons and the strong interaction happens via gluons. As the name suggests, the strong force is the strongest of the four fundamental forces and therefore dominates in subatomic physics. However both the strong and the weak force are very weak at long distances. Therefore in scales larger than the nucleus, the electromagnetic and the gravitational force dominate. Since we are interested in the properties of the quark-gluon plasma, which is small enough for the strong force to dominate, we will look at the theory which describes the strong interaction in more detail: quantum chromodynamics. 1.2 Quantum chromodynamics (QCD) Quantum chromodynamics (QCD) descibes the interaction between quarks and gluons in hadrons. According to QCD, every quark has a quantum number we call colour. There are three colours and three anti-colours: red, green, blue, anti-red, anti-green and anti-blue. In nature however only colourless particles, that is particles with three different (anti-)colours or particles with a colour and its anti-colour, are observed. Therefore, quarks always group together to form particles made up of a quark anti-quark pair (mesons) or three quarks (baryons). Particles containing four or more quarks are in theory also possible but they prove to be very hard to detect. Particles containing four quarks have been found [2] but are very rare. Particles made up of quarks are called hadrons. In addition to the quarks, gluons also carry colour. Where quarks only carry one colour, gluons can carry more colours. This results in the fact that gluons, as well as quarks, interact strongly. The interaction in QCD is similar to the interaction in quantum electrodynamics (QED). The potential between a quark and anti-quark can therefore be approximated by a coulomblike potential, but because only colourless particles exist, a confining part must be added. The potential between a quark and an anti-quark is then approximated by: V (r) = 4 α s + κr. (1) 3 r Here α s is the coupling strength and κ can be seen as a string tension. At small distances r the first term dominates the potential, and the potential is very similar to the coulomb potential. The second term is linear and becomes important at larger distances. At a certain length the binding energy becomes so large that the quarks disconnect and a new quark anti-quark pair is created. This results in the creation of a meson. For the coupling contant α s the following proportionality holds: α s 1/ ln Q2 Λ 2 QCD, (2) where Q 2 is the momentum transfer and Λ QCD is the QCD length scale. We see that α s becomes smaller as the distance between the particles becomes smaller, as well as when the 3

5 momentum transfer increases. Thus in high energy collisions the strong interaction could become so weak that the quarks and gluons are no longer confined within the hadrons they usually form. This phenomenon is called asymptotic freedom. 1.3 Quark-gluon plasma (QGP) According to QCD, at high temperatures and/or densities quarks and gluons become asymptotically free. A phase transition occurs to a phase called the Quark-gluon plasma. In this phase the quarks and gluons are no longer confined in hadrons, but can move around in larger volumes. In the first few microseconds after the big bang the universe is thought to have been in such a state. The understanding of QGP is therefore crucial to understanding the early evolution of the universe. In figure 2 we see a phase diagram illustrating the above. At low temperatures and densities we see the ordinary matter. At very high densities but low temperatures QGP is believed to exist within neutron stars. At very high temperatures we have similar conditions as in the early universe. The Relativistic Heavy Ion Collider (RHIC) in the US and the Large Hadron Collider in Switzerland have sufficient energy to form the QGP at high temperatures as indicated in the diagram. Figure 2: Phase diagram in QCD.[3] The line in the phase diagram shows where a first order phase transition takes place. Beyond the critical point, the yellow dot in the diagram, the phase transitions are no longer first order. To properly study the QGP it needs to exist long enough, therefore higher temperatures are preferable. Currently the LHC runs at a collision energy of 7 TeV for proton-proton collisions, but in 2015 it is planned to run at 13 or 14 TeV. In this text we will assume the collision energy to be 13 TeV. The lead-lead collision energy will be upgraded from 2.76 TeV to 5.1 TeV. This upgrade will help improve the research done on the QGP. In this thesis simulations will be done at 13 TeV to help prepare for future measurements. At the LHC, the QGP is produced by colliding two ionized lead atoms. Since these atoms have such high speeds, relativistic length contraction reshapes the ions into thin colliding disks. 4

6 When the two disks hit, two things happen. At the moment of impact the temperature becomes so high that the quarks and gluons become asymptotically free and form a quark-gluon plasma. This extremely hot plasma will start to expand very fast. It can be seen as an expanding fireball. In addition to the QGP, heavy quarks are produced. Heavy quarks are mainly produced in two ways: gg Q Q, two gluons collide and form a heavy quark anti-quark pair. q q Q Q, a quark and an anti-quark collide to form a heavier quark anti-quark pair. At the LHC about 98% of the heavy quarks produced are due to gluons colliding. The production time of these new quarks is proportional to 1/m q, with m q the mass of the quark. Therefore, heavier quarks will be produced before the QGP is produced. These heavy quarks travel through the newly formed QGP and lose energy in the process. The properties of the mesons these quarks hadronize into can be measured, this gives us information about the properties of the QGP. 1.4 Heavy quarks The quarks travelling through the QGP lose energy in two ways. The quarks collide with other quarks and gluons, and the quarks radiate gluons while travelling through a medium. This radiation effect is similar to the Bremsstrahlung of electrons and is illustrated in figure 3. The energy loss via radiations of gluons is lower for heavier quarks than for lighter quarks. This is due to the dead cone effect. If the radiation angle is small compared to the mass of the quark θ < m q /E q, there will be no gluon radiation[4]. Therefore heavier quarks are more likely to produce mesons that can be observed sufficiently far away from the collision point. Figure 3: Energy loss of quarks in the QGP.[5] If we look at the standard model in figure 1 again, we see that the charm, beauty (bottom) and top quark are much heavier than the other three. The top quark being the heaviest by far, it is however also the fastest decaying quark. It is most likely to decay before any top mesons can be formed. This leaves us with the beauty and the charm quark. These quarks are heavy enough to travel through the QGP without being annihilate, but live long enough to hadronize into mesons which we can (indirectly) measure. Charm and beauty quarks are therefore suitable candidates to investigate the QGP. If we are to determine the properties of the QGP by measuring the properties of the mesons influenced by the QGP, we need to know the properties of the same mesons when they did not 5

7 travel through the QGP. The same mesons are produced by colliding two protons. In protonproton collisions the beauty and charm quarks produced do not travel through a QGP and the mesons they produce can be used as a comparison for the mesons produced in lead-lead collisions. We can then calculate the nuclear modification factor defined as: R AA (p t ) = dn AA /dp t T AA dσ pp /dp t. (3) This is the ratio between the particle yield in nucleus-nucleus collision and the yield in protonproton collisions. The factor T AA is a normalization factor to compensate for the fact that a lead ion consists of 207 nucleons while a proton is only one. If there would be no QGP, this factor would be one. If there is a QGP the mesons that travel through the QGP will lose energy and momentum. This will result in a R AA smaller than one. 1.5 Structure of the thesis In this thesis we will focus on two subjects. First we will investigate the systematic uncertainty of yield extraction in D + measurements. These measurements are done for lead-lead collisions at 30-50% centrality. We do this by varying the fitting function, fitting regions and binning in the invariant mass distribution for different transverse momentum (p t ) regions. We compare the yield we then obtain with the yield for our standard fit to find systematic uncertainties in the yield extraction. Secondly, we simulate proton-proton collisions using the event generator PYTHIA. In these simulations we fill focus on the decay of the beauty quark along the following path: b B 0 D + + π D 0 + π + π + K + 2π + + π. That is the beauty particle decaying into B mesons (mesons containing a beauty quark). Then a B meson decaying into (an excited state of) a D meson (mesons containing a charm quark) and producing two pions in the process. And finally the D meson decaying into a kaon and a pion. The kaon and the pions are the particles we measure with the ALICE detector. Every time we write down a particle e.g. the D + meson we are talking about the particle as well as its anti-particle, so about D + as well as D. So with the decay D + D 0 + π +, we also mean the decay D + D 0 + π. The probability that a particle decays a certain way is called the branching ratio. The B 0 D + + π has a branching ratio of (2.76 ± 0.13) 10 3 %, the D + D 0 + π + has a branching ratio of 67.7 ± 0.5% and the D 0 K + π + decay has a ratio of 3.89 ± 0.05% [6]. In these simulations we know the properties of all the particles created. With this information we know what kind of properties to expect and we can look for ways to distinguish the particles in our decay process from particles with different origins. We will focus on the transverse momentum (p t ) and the pseudorapidity (η). Unless noted differently the simulations for proton-proton collisions are done at 13 TeV. This is the energy the LHC will likely run at in 2015, so these simulations will be relevant for measurements done after

8 2 Experimental setup 2.1 ALICE ALICE is an abbreviation for A Large Ion Collider Experiment. It is located in the Large Hadron Collider (LHC) as one of the seven detectors in the ring. It is designed specifically to study heavy ions colliding with a center of mass energy of 2.76 TeV. This is expected to be enough energy for the QGP to form. One of the aims of ALICE is to study properties of this QGP. The detector weighs about 10,000 tonnes, it is 26 meters long 16 meters wide and 16 meters high. The entire detector is located 56 meters under ground in France where it receives beams for the LHC. Figure 4: The ALICE detector In figure 4 we see a sketch of the ALICE detector. The ALICE detector consists of two parts. The central part is mainly devoted to the measurement of hadronic signals and is therefore crucial to our purpose. The second part is the forward muon spectrometer which is devoted to studying quarkonia (a meson build of a quark and its own anti-quark) and is not relevant for our research. The central part covers an angle of η < 0.9. Here η is the pseudorapidity.the pseudorapidity is a measure of the angle with respect to the direction of the particle beam. Zero being perpendicular and infinite being parallel to the beam direction. A pseudorapidity of 0.9 correspond to about 45. The full azimuthal angle is covert. The entire central part in embedded in a large magnet which produces a weak solenoidal field. The Inner Tracking System (ITS)[8], the Time Projection Chamber (TPC)[9] and the Time Of Flight detector (TOF)[10] are of particular importance for the measuring of heavy quark spectra and will be discussed in more detail Inner Tracking System (ITS) The Inner Tracking System (ITS) is the detector closest to the collision point. Because of the short lifetime of the particles we want to measure, this is a very important detector for our purposes. The ITS has three function: Measuring the primary and secondary vertices (decay points) for the reconstruction of charm and hyperon (baryons containing strange, but no heavier quarks) decays. Identifying and tracking of low momentum particles. 7

9 Improving the momentum and angle measurements of the TPC. Figure 5: The Inner Tracking System.[11] The ITS consists of six cylindrical silicon detectors, see figure 5. These six detector come in three types. The two layers closest to the collision are silicon pixel detectors (SPD). They are located at radii of 4 and 6 cm. The SPD s have very high spatial resolutions. This allows us to reconstruct the vertices with high precision and is needed for determining the impact parameter of the tracks. The next two layers are silicon drift detectors (SDD), they are located at 14 respectively 24 cm. Here the track density is lower. The SDD gives information concerning the two dimensional positions of the particles. The two outer layers are double-sided silicon microstrip detectors (SSD), they are located at 39 and 44 cm from the collision. The SSD detectors are essential for the connection of tracks from the ITS to the TPC. The detectors overlap a bit to avoid ambiguity Time Projection Chamber (TPC) The Time Projection Chamber (TPC) is the main tracking device of ALICE. It surrounds the ITS and is filled with a Ne/CO 2 gas mixture. Particles that travel through the TPC ionize the gas. Electrons and ions are attracted by an electrode which produces an electric field in the beam direction. The strength of the electric field is about 400 V/cm. The gas has been optimized to allow for accurate momentum resolution and high multiplicity. The mixture is about 90% Ne, and 10% CO 2. The TPC has an inner radius of 84.1cm, an outer radius of cm and a length of 500 cm. In figure 6 we see an image of the chamber. The main functions of the TPC are track finding, track separation, charged particle momentum measurement and particle identification. Charged particles are identified by the amount of energy they lose per distance travelled (de/dx) for a given momentum. In figure 7 we see an example of the particle identification capabilities. In this example it is done for proton-lead collisions. 8

10 Figure 6: The Time Projection Chamber. [12] Figure 7: Particle identification in proton-lead collisions. [13] Time Of Flight (TOF) ALICE has two detectors dedicated exclusively to particle identification. The Time Of Flight detector (TOF) and the High Momentum Particle Identification Detector (HMPID). The TOF has a large acceptance and is optimized for average momentum bellow 2.5 GeV/c while the HMPID is optimized for higher momenta. The kaons and pions we measure in the lead-lead collision experiments in general have average momenta bellow 2.5 GeV/c. Therefore, the TOF is of importance for the identification of these particles. A sketch of the TOF is show in figure 8. The TOF is a cylinder covering between 45 and 135 degrees and as the ITS and the TPC it covers the full azimuth range. It is divided in 18 sectors in the φ direction. Each of these sectors are divided into five in the beam direction. The sections contain a total of 1638 detector elements (MRPC strips). Since every strip contains 96 pickup pads a there are a total of 157,248 readout channels. The total area covered is 160 cm2. The more pads the detector has, the more accurate it can measure. A time resolution of 120 ps will provide three sigma separation up to 1.9 GeV/c for pion/kaon and up to 3.2 GeV/c seperation 9

11 Figure 8: A sketch of the Time Of Flight detector.[14] for proton/kaon. This includes all other sources of timing errors. The time measured with the TOF is used in combination with the tracks from the ITS and the TPC for particle identification, similar to figure Root and AliRoot ROOT [15] is a framework for data processing. The Root project was started by René Brun and Fons Rademakers in January It is now used by thousands of physicist every day. ROOT can be used to analyse data obtained at CERN or to do simulations and analyse the results. It works by defining the data as a set of objects, we can then get direct access to the separate attributes of the selected objects, without concern for the rest of the data. We have mainly used it for histograming and fitting but a variety of other options are available. With the exception of a few large existing libraries, ROOT is based on the Object Oriented programming paradigm, and in written in the programming language C ++. ROOT was originally designed for particle physics and is therefore very useful for our purposes. Nowadays, Root is also used in other fields, e.g. astronomy. AliRoot is the ALICE Off-line framework. It is based of ROOT and is specifically designed for analysis, simulations and reconstructions related to the ALICE detector. To run AliRoot I have used the so-called quark cluster. The quark cluster is a small computer cluster available for students and staff at the institute of subatomic physics at the Utrecht University. This cluster has also been used to run simulations using PYTHIA. 2.3 Event generator PYTHIA PYTHIA [16] is a computer program that simulates high energy particle collisions. PYTHIA is a Monte Carlo simulator. In Monte Carlo simulations we run a simulation a large number of times to obtain a proper probability distribution. It gets its name from this connection with probability distributions in casinos like the Monte Carlo Casino. PYTHIA generates sets of outgoing particles in collisions of elementary particles like p, p, e, e +, µ and others. PYTHIA contains a library with the laws of QCD in hard processes and contains models for the interaction between partons, beam remnants, string fragmentation and particle decays. You might say it combines our most successful theories we have and the data acquired in research to do the 10

12 simulations. It therefore serves as an excellent simulator to study the behaviour of subatomic particles in, e.g. proton-proton collisions without the limitations detectors have. This gives us insight in what fraction of particles that appear are in fact detected. By comparing e.g. the transverse momentum (p t ) of particles from different origins, we can know what p t region to look at if we want to observe a particular particle. And maybe as important, what p t region not to look at. We can then apply cuts for various properties to optimize the chance we measure the particle of interest. In addition, we can prepare for the ALICE upgrade by doing simulations for proton-proton collisions at 13 TeV. This will be one of the focusses of this thesis. For the simulation done in this thesis two versions of PYTHIA have been used. For short simulations with a small number of events PYTHIA is used. This is done on a commercial notebook. Simulations where a lot of data is created PYTHIA on the quark cluster is used. Previous versions of PYTHIA were written in Fortran. PYTHIA 8 is completely rewritten in C++. PYTHIA 6 and PYTHIA 8 are both maintained for not all components are merged into PYTHIA 8. For our research this will not be an issue and PYTHIA 8 will suffice. The configuration of PYTHIA will be discussed in chapter Fixed Order plus Next-to-Leading Logarithm Fixed Order plus Next-to-Leading Logarithm or FONLL for short is a code that calculates differential cross sections of heavy quarks produced in p-p or p- p collisions. It uses Perturbative QCD (pqcd) combining next-to-leading order (NLO) calculations and next-to-leading logarithmic resummations. The leading order is the term in an equation with the highest order of magnitude. This combination makes better prediction for high values of p t than NLO by itself. In perticluar the uncertainty is smaller, while the uncertainty for NLO calculation is 30-40% at high p t, for FONLL this is only 10-15%. 11

13 3 Systematic uncertainties of D + measurements in leadlead collisions at 30-50% centrality For this data analysis we used data from lead-lead collisions at 30-50% centrality with center of mass energy of s NN = 2.76 TeV. The dataset is called LHC11h 2. The number of events is 9.1 million. These collisions were delivered by the LHC and were detected by ALICE. However, since the number of measurements is finite and every measurement has its own uncertainty we will always have a statistical uncertainty in our measurements. From the collected data we would like to learn more than just the quantities ALICE measures directly. In our case we would like to study the properties of D + mesons (e.g. the yield) from the kaon and pions we measure. The method we use to extract the yield brings with it an uncertainty of its own which we call the systematic uncertainty. In this chapter we determine the systematic uncertainties in the yield extraction of D + measurements in lead-lead collisions at 30-50% centrality. 3.1 Centrality When two lead ions collide in the LHC they do not hit each other head on every time. In fact they almost never do. It is however crucial for our understanding of the results to know how much overlap the colliding ions have. Because of this the quantity centrality is introduced. Centrality is a measurement for the overlapping region of the colliding nuclei, see figure 9. Figure 9: Two lead ions colliding with a centrality of about 50%.[18] A centrality of 0 means the ions collide head on. If the ions hit each other with a minimal overlapping region the centrality is 100%. We will look at data from two lead ions colliding with centralities between 30 and 50%. 3.2 Invariant mass To investigate the systematic uncertainty in yield extraction we must first find a way to determine the yield. The D + meson cannot be measured directly in the ALICE detector. Therefore, we will look at the decay D + D 0 + π + K + 2π +. The kaon and the pions that appear can be measured. Specifically we use data from the invariant mass method. The invariant mass characterizes the total energy and momentum of a particle or system and is given by the equation: M = E 2 + p 2, (4) 12

14 where E is the energy of the system and p is its momentum. The energy is defined as E = m2 + p 2. Where m is the rest mass. The invariant mass is a useful quantity since it is conserved in particle decays. Because we cannot measure the invariant mass of the D + directly we must reconstruct it from the decay. First we realize that the invariant mass of the D 0 is equal to the invariant mass of the kaon and the invariant mass of the second pion combined: M(D 0 ) = M(Kπ) = (E K + E π2 ) 2 + (p K + p π2 ) 2. (5) In the same way we can then reconstruct the invariant mass of the D + by taking the invariant mass of the D 0 and the invariant mass of the pion combined: M(D ) = M(D 0 π) = M(Kππ) = (E K + E π1 + E π2 ) 2 + (p K + p π1 + p π2 ) 2. (6) In this way we can determine the invariant mass of the D + meson by measuring the invariant mass of the kaon and the pions. In ALICE we measure the invariant mass difference between D + and D 0. This is done because this decreases the error in our measurements. This is because the resolution for M(D + ) M(D 0 ) is much better than the resolution for M(D + ). This can be understood by writing out the invariant mass, we see that M(D + ) M(D 0 ) = M(Kππ) M(Kπ) M(π). The error we get because of the detector resolution for measuring M(D 0 ) drops out, and our peak is much clearer. This decrease in error is an argument for looking at this specific decay as well. 3.3 Selection cuts To determined the invariant mass as discussed in the previous section, we need to know what particles we measure. This is done with the Particle Identification (PID) as discussed in section and as shown in figure 7. For the TPC as well as for the TOF we take all particles measured within 3σ of the expected value. Since now we measure all the kaons and pions produced we need to apply a number of cuts to remove the mesons that come from different decays (background). Up to 16 topological cuts are applied. The two most effective cuts will be discussed below. The most important cut we apply is based on the topology of the tracks. Figure 10: Decay topology of the D 0 K + π + decay.[19] The point in space where the D + meson decays into the D 0 is called the primary vertex. However since this decay happens through the strong interaction, this happens very fast. Therefore, the D + particle has a very short decay length. Its decay length is in fact so short that we cannot 13

15 distinguish the point in space where the D + is created from where the D 0 is created. Hence we assume the D 0 meson is created at the primary vertex as well. From the momentum of the kaon and the second pion we can reconstruct the flight line of the D 0 meson. The secondary vertex is the point where the D 0 decays into the kaon and the second pion. We can then apply are most useful cut which takes the best values of the cosine of the angle between the flight line of the D 0 and the line between the primary and secondary vertex, in figure 10 we call this angle θ p. So our most effective cut takes away the most far-of values of cos θ p. For the second most effective cut we look at figure 10 again. It is a cut applied on the product of the impact parameters (d K and d π ). If two random particles are created the product of the impact parameters will be symmetric. However since the kaon is much heavier than the pion, the pion gets bent by the magnetic field much more than the kaon. In our decay the product of the impact parameters will be far from symmetric. This can also be used to apply a very effective cut. More cuts are applied, but these two are the most important ones. 3.4 Yield extraction Even though we applied the cuts from the previous section, we will still measure a lot of kaon and pions that come from a different decay. To fit the invariant mass histograms we obtain we thus need a combination of two functions. One to fit the background and one to fit the peak we get at the invariant mass of the D +. The function we use for the background in first instance is: f background = a x m π e b(x mπ). (7) Here a and b are to be determined, x is the invariant mass and m π is the mass of the pion. This function is fitted to the data with the exception of the points 3σ from the peak. Then we initialize a and b to be the fitted values before we fit the entire fitting range with the background function plus a Gaussian term. f total = a x m π e b(x mπ) + c (x g)2 e 2d 2. (8) 2πd 2 here c, d and g are the new fitting parameters. The yield will be determined by integrating the Gaussian peak and the background 3σ from the peak and then subtracting the two to obtain the area under the peak but above the background. Normalization depending on the bin width then gives us our yield. Since we expect different yields at different transverse momentum (p t ) regions, we look at 7 different p t regions. They are 2-3, 3-4, 4-5, 5-6, 6-8, 8-12 and GeV/c. We have managed to plot the functions as described in these regions and the resulting plots are in figure 11. In addition to integrating the peak, we subtract the value of the background function at the data points from the value of the data points that lie in the peak and add them up in the 3σ range. We fit the background function for the region with (counting method 1) and without the data points in the peak (counting method 2). The results of the counting methods in addition to the yields from the integration method, the sigma and the significance are shown in figure Systematic uncertainties The method described in the previous section is not without its limitations. The fitting function we use is not a law of nature but just an approximations and the D + and fitting region are chosen to be decent values. Thus, if we make certain changes in our method of determining the yield, this will give us slightly different results while using the same data. So simply because we 14

16 Figure 11: Invariant mass distribution of Kππ - Kπ for different p t regions. 15

17 Figure 12: Fitting parameters from the fit in figure 11 use this method, there will always be a systematic uncertainty. We determined this uncertainty by varying the fitting function, the fitting region and the bin width. For our standard fit, for which the results are shown in figures 11 and 12, we used the following settings. Fitting interval GeV/c 2, binwidth GeV/c 2 and the background fit function from equation 7. We then varied the interval to GeV/c 2 and to GeV/c 2, we changed the bin width to GeV/c 2 and we changed the background fitting function to: f background2 = a(x m π ) b. (9) We then divided the yield obtained from the standard fit by the yield from fits with different parameters, changing one parameter at a time, to see how much they differed. The result is plotted in figure 13. We see that in the first p t region one of the variations results in a 13% deviation from the standard method. This data point might seem odd compared to the others, but we do not see a reason for it to be incorrect. In all other p t regions the systematic uncertainty is below 5% if the yield is higher and below 10% if the yield is higher than the yield obtained in the standard fit. In addition, we compared the bin counting method with the integration method. This is done by subtracting the yield we aquire using the bin counting method from the yield we find with the integration method and then dividing by the yield from the integration method. The deviation from zero then tells us the systematic error. We did this for 3, 4 and 5σ and for both counting methods. The results are plotted in figure 14. We see that for 3σ, which is the proper interval, the deviation is again within the 10%. If we change the interval to 4 and 5σ the deviation increases, but is mostly within 20% and even in the two exceptions only about 30%. From these results we can estimate the systematic uncertainty for each p t region. These numbers are listed in table 1. 16

18 Figure 13: Signal of the fits with mutated fitting parameters divided by the signal of the standard fit. Figure 14: Bin counting method compared with the integration method for different sigma s and fitting count methods. 17

19 Table 1: Systematic uncertainty per p t region. p t region (GeV/c) Systematic error % 3-4 9% 4-5 8% 5-6 7% 6-8 6% % % 18

20 4 Performance study of B 0 D + + π To reconstruct the properties of B 0 D + + π mesons using the method described in section 3 we need more data than in the D + D 0 + π + case since it is one more decay away from the mesons we measure. Simulations provide a way to do research concerning this decay with as much data as we need. When the ALICE detector will measure data from 13 TeV in proton-proton collisions in 2015, some properties of the particles we measure will change and hence different cuts need to be applied. Simulations give us the possibility to study the behaviour of the particles in a 13 TeV collision before the detector is ready so that we now what to expect. 4.1 PYTHIA configuration To do simulations we use the event generator PYTHIA (section 2.3). PYTHIA has a lot of configuration option which allows users to optimize the events for the phenomenon they want to study. The configuration we have used is given bellow. Beams:eCM = ParticleData:mbRun= 4.75 Here we set the center of mass energy of the colliding beams to 13 TeV. For some figures other center of mass energies are used but unless noted otherwise it will be 13 TeV. We set the mass of the beauty quark to be 4.75 GeV/c 2. We have used two different settings, beauty forced and minimum bias. Unless noted otherwise beauty forced is used in the figures in this chapter. For beauty forced: HardQCD:gg2bbbar= on HardQCD:qqbar2bbbar= on BeamRemnants:primordialKT= on BeamRemnants:primordialKTsoft= 0. BeamRemnants:primordialKThard = 2.03 BeamRemnants:halfScaleForKT = 0. BeamRemnants:halfMassForKT=0. With these settings we force PYTHIA to create a beauty anti-beauty pair every collision. This is useful because we need a lot of B 0 mesons to be created to learn about the properties of the decay. If we want to look, not only at the B 0 D + + π but also at the D + D 0 π + and the D 0 K + π + we need as much statistics as we can get. Forcing the creation of a beauty anti-beauty pair at every collision results in about 100 times as many beauty quarks, and thus B 0 mesons. This means that if it would take 100 days of simulations to get enough data with minimum bias, it takes only 1 day with beauty forced. For minimum bias: SoftQCD:all= on PartonLevel:MI= on MultipleInteractions:pTmin= 1.9 MultipleInteractions:pT0Ref=

21 MultipleInteractions:ecmRef= MultipleInteractions:expPow= 0.16 MultipleInteractions:bProfile=2 MultipleInteractions:coreFraction= 0.16 MultipleInteractions:coreRadius= 0.5 SigmaProcess:factorMultFac= 1 When we do not force a beauty anti-beauty pair at every interaction we use the minimum bias configuration. This configuration is set to simulate the collision as similar to reality as possible. Hereto multiple parton interactions are turned on as well. As discussed minimum bias will not provide us with enough data to investigate the properties of our decays of interest. It will however prove useful for comparison with our beauty forced model and will be used for normalization of the beauty forced as well. 4.2 Analysis Since we force a beauty anti-beauty pair to be created at every collision, in 10 8 collisions we expect at least beauty or anti-beauty quarks to be generated. We can then as well count how many times our decays of interest occur. The results are plotted in figure 15. We see that the number decays that occur are in correspondence with the branching ratio s mentioned in section 1.5. This is a first indication that our simulation works well. Before we start discussing results, it is useful to check if the simulation works properly and if we can draw conclusions about actual collisions from the beauty forced simulations. Figure 15: Possible decays of the beauty quarks. With minimum bias, the transverse momentum (p t ) of the B 0 is as in figure 16. Because of the shape of the distribution we can identify particles by looking what their lowest, mean 20

22 and highest momenta are. This gives us the possibility to identify a particle by measuring it s transverse momentum. The B 0 particles measured in figure 16 all have a beauty quark as a mother particle, meaning that we have looked at every beauty quark that hadronized into a B 0. Therefore, we can see that is we measure a B 0 particle with a p t larger than 25 GeV/c it is very unlikely that its mother particle is a beauty quark. In similar fashion we will try to find ways to distinguish particles in the decay we are interested in from particles that are created in different interactions. There are many ways to do this, you could look at the momentum, the direction, the lifetime, the decay length of the particles etc. In this thesis we will focus on the transverse momentum (p t ) and the pseudorapidity (η) to tune these cuts. Figure 16: Transverse momentum distribution of B 0 mesons in the minimum bias dataset. To check if the minimum bias configuration provides us with particles with similar properties as the beauty forced configuration we compare the p t and η distributions of the B 0 meson in both simulations. The p t distributions of the B 0 particles with minimum bias and beauty forced are plotted on top of each other in figure 17. The same is shown for η in figure 18. We see that the shape of the η distribution for the minimum bias case is very similar to the shape of the beauty forced distribution. The p t distributions are fairly similar, but do differ significantly. In particular we notice that the beauty forced distribution is a bit softer. However for the comparisons we ll make, the similarities will be sufficient. Therefore, from here on we will look at the properties of the decay with beauty forced and assume that the properties of the produced particles will be similar. It would be nice to check our results with results using a different method. For this purpose we compare with FONLL (section 2.4) calculations. We compare the p t distribution of the beauty quark with minimum bias at 14 TeV divided by the p t distribution at 7 TeV for the two methods. For FONLL the following settings were used: 21

23 Figure 17: p t distribution of B 0 mesons with minimum bias and beauty forced. Figure 18: η distribution of B 0 mesons with minimum bias and beauty forced. FONLL version and perturbative order: FONLL v1.3.2 fonll [ds/dpt 2 dy(pb/gev 2 )] quark = bottom 22

24 final state = Dstar from a single B. NP params (cm,lm,hm) = 24.2, 26.7, 22.2 BR(q meson) = 1 BR(B Dstar) = ebeam1 = 3500, ebeam2 = 3500 (this is for 7TeV for 14 TeV these values are doubled.) PDF set = CTEQ6.6 ptmin = 0 ptmax = 50 etamin = -0.9 etamax = 0.9 cross section is ds/dpt (pb/gev) The result is illustrated in figure 19. Figure 19: p t distribution comparison of the beauty quark using FONLL and PYTHIA. It is worth noting that the uncertainty in the FONLL distribution, as we mentioned in section 2.4, is in reality much bigger than it is portrayed here so that the data points produced by PYTHIA are well within the error bands of the FONLL ones. But even without these larger errors we see that the PYTHIA values correspond nicely to the central FONLL values. This gives us one more reason to be confident the results we obtain are correct. We perform one last check in order to be confident with our simulation. The angle φ is the angle a particle travels in the plane perpendicular to the collision. There is no preferred value of φ and therefore we expect all values of φ between π and π to be measure and simulated the same amount. In figure 20 the simulated values of φ of the beauty quark is shown. The data points are on a horizontal line as expected. Since all our results so far agree with existing theories we are very confident our simulations are accurate. 23

25 Figure 20: φ distribution of the beauty quarks. To distinguish the D + produced together with a pion from the D + produced alone or with any number of different particles, we compare the p t distribution of the D + from B 0 D + + π and the p t distribution of the D + from B 0 D + + other. In this case other can be any particle or set of particles. This comparison is shown in figure 21. Figure 21: p t distribution of D + comparison B 0 D + + others with B 0 D + + π. 24

26 First of all we see that the two distributions are significantly different. We notice that the ratio of the p t s varies a lot for different p t values. It is therefore a good idea to look at properties of the particles for different p t regions as we did in chapter 3. For small p t values the D + + π appear less than the D + + other. For p t values < 1 GeV/c the ratio is about one half. This means about two times as many B 0 mesons decay in D + + other as in D + + π. For larger p t values the D + + π are up to 2.5 times as likely to appear. From this we can conclude that for p t regions larger than about 6 GeV/c, we can apply much sharper cuts than in lower p t regions. We now turn our attention the the p t distribution of the D + from B 0 D + + π in different p t regions of B 0. Because our detector is only able to measure particles with 0.9 < η < 0.9 we have plotted the particles within acceptance, that is η < 0.9, in red as well as all the D + particles in blue. This is shown in figure 22. Figure 22: Transverse momentum distribution of D + from B 0 D + + π for different p t regions of B 0. For all η (Blue) and with 0.9 < η < 0.9 (Red). The p t distributions with and without the η cut applied are very similar. We therefore do not have to, in many cases, apply this cut to compare at p t distributions. This gives us more data and thus better statistics. The D + particles that appear in the different p t regions of B 0 clearly have different maximum values for their p t. We can therefore cut away all particles with a p t higher than this maximum value. Interestingly, this does not necessarily correspond very direct and simple to the maximum p t of the bin. In the 3-6 GeV/c 2 p t -bin for example we see the maximum p t value of the D + to be about seven, while in the GeV/c 2 p t -bin its about 25. In general we see that at higher p t regions of B 0 the maximum p t value of D + is smaller compared to the maximum value of the bin, but of course higher in absolute values. In figure 23 we have plotted the η value of the D + from the B 0 D + + π decay in different η regions of B 0. Here, we have only looked at the decay of B 0 particles that were already in acceptance. 25

27 Figure 23: Pseudorapidity distribution of D + from B 0 D + + π for different η regions of B 0. As you can see the η distribution is quite broad. This has negative implications for the number of B 0 s in acceptance. If the η value of the B 0 is in the η region -0.9, -0.6 for example, we see that little less than half of the D + s have an η < 0.9. This means that in this region we lose almost half of our data points if we only look at η values for B 0 that are already in acceptance. The reason for this big spread is that we take into account mesons of all p t values. Decaying mesons with lower p t values have a larger spread when it comes to the flight direction. Therefore, if we would have made these plots for higher p t values we would expect the peaks to be much sharper. For all the regions we see that mean value of η is closer to zero than the average of the region. For example in the first bin the mean value is about This is fortunate for that means a larger part of the mesons will stay in acceptance. The same figures we made for the D + particle, we can make for the pion from the B 0 D + + π decay. The p t distributions are shown in figure 24. Since the mass of the pion is much lower than the mass of the D + we expect the average p t to be much lower. And if we compare figure 22 with figure 24 we see that this is clearly the case, especially at the higher p t regions. We also expect the maximum p t value to be lower and this is also clear. This means that we can apply sharper cuts in the p t distribution of the pions. The η distributions of these pions are depicted in figure 25. Even more so than for the D + we see that the angle of the pions are closer to η = 0 than the angle of the B 0 particles. This results in a smaller part of the pions to be out of acceptance. Since there seems to be a difference in the η of the pion and the D + created we would like to compare the shapes of the η distributions. This is done in figure 26. We can see that outside the detectors acceptance the η shapes are fairly similar, but in the 0.9 < η < 0.9 region, there are significantly more pions than D + particles. The ratio plot 26