Utrecht University

Faculty of Physics and Astronomy

Optimization of D0→K

- π

+ extraction in p-p collisions with

ALICE

W.J.C. Koppert

Oktober 16th, 2008

Report number: UU(SAP) 08-05

Supervisors: Prof. dr. Kamermans and dr. M. van Leeuwen

Institute of Subatomic Physics

Buys Ballot laboratory

PO BOX 80 000, 3508 TA Utrecht, The Netherlands

1

Contents

1 Introduction 2

2 Quantum Chromo Dynamics 32.1 Parton Distribution Function . . . . . . . . . . . . . . . . . . . . 32.2 Fragmentation Function . . . . . . . . . . . . . . . . . . . . . . . 6

3 Quark Gluon Plasma 7

4 Experimental Setup 134.1 Inner Tracking System . . . . . . . . . . . . . . . . . . . . . . . . 134.2 Time Projection Chamber . . . . . . . . . . . . . . . . . . . . . . 15

5 Analysis Framework 155.1 Background Sample . . . . . . . . . . . . . . . . . . . . . . . . . 165.2 Signal Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195.3 Secondary Vertex Resolutions . . . . . . . . . . . . . . . . . . . . 20

6 Analysis 216.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226.2 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236.3 Initial Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246.4 Error analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246.5 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

6.5.1 Distance of Closest Approach . . . . . . . . . . . . . . . . 266.5.2 Pointing Angle . . . . . . . . . . . . . . . . . . . . . . . . 276.5.3 Decay Angle in D0-frame . . . . . . . . . . . . . . . . . . 286.5.4 Product impact parameters of decay products . . . . . . . 296.5.5 Transverse Momentum of Decay Products . . . . . . . . . 316.5.6 Impact parameters of decay Products . . . . . . . . . . . 33

7 Discussion/Conclusion 35

8 Acknowledgements 38

1

1 Introduction

The most common lepton is the electron. Its electromagnetic interaction isdescribed by the quantum field theory of electromagnetism (QED). In ordinarymatter the electron is bound in an atom, by adding energy the electron canbe easily isolated. In contrast quarks that are the building blocks of nucleons(protons and neutrons) cannot be isolated. Where the electromagnetic forcebecomes weaker at larger distances the strong interaction (QCD) among quarksbecomes stronger. Electrons in QED have a charge (U(1)), in addition quarksin QCD can have three color charges red, blue and green, their interactions aredescribed by the SU(3) gauge theory.

Up and Down quarks are the most common and lightest quarks [Mcurrent ∼1 MeV] they form protons and neutrons. These building blocks of atoms existout of three valence quarks and a sea of virtual quark anti-quark pairs (whichdo not contribute to the quantum numbers) held together by gluons, the gaugebosons of the strong force similar to photons in QED. Gluons carry two colorcharges, therefore two quarks with a different color are able to interact andgluons are able to interact with each other.

In a simplified model quarks are free if the strong interaction force is small,since the strong interaction is distance dependent, quarks can only move freein the region of the size of a hadron. However if is possible to create a systemwith a larger energy density than the binding energy density of hadrons (∼1 GeV/fm3), they might move free in a region larger than the hadron sizegiving rise to a new state of matter, the quark gluon plasma (QGP). At lowtemperatures and baryon densities quarks and gluons are confined into hadrons,at high temperatures hadrons are not able to hold quarks and gluons togetherand they are pulled out of each other. The deconfinement of quarks and gluonsexisted a few microseconds after the big-bang and it might still be present atthe dense cores of neutron stars.

In this thesis one of the probes of the QGP is studied: open charm produc-tion. Charm quarks are produced early during the collisions. They lose energywhile travelling through the medium by interaction with the QGP. The energyloss is reflected in the Pt spectrum of the charmed hadrons (D0s) that can bemeasured in the ALICE detector [1].

2

2 Quantum Chromo Dynamics

The study of a QGP [2] is of crucial importance for verifying the theory of stronginteractions that describes the interactions of quarks and gluons in hadrons.This theory called Quantum Chromo Dynamics, decribes one of the four funda-mental forces in nature. QCD is a non-abelian quantum field theory and playsan important role in the Standard Model that describes the three fundamentalforces of electromagnetism, weak interaction and strong interaction. In QCD noisolated quarks can be created. If quarks are pulled away from each other thepotential rises until the binding energy is large enough to spontaneously createa new quark anti-quark pair (string fragmentation). In this strong interactionprocess, instead of isolating the quark, new quark anti-quark pairs (mesons) arecreated. Quark pairs (mesons) or triplets (baryons) are stable if there is no netcolor charge, only color neutral particles can be observed in nature. The stronginteraction process can be described by using the Feynman rules of QCD whichare similar to the QED Feynman rules with the coupling constant α (present ateach vertex in the Feynman graph) replaced by the running coupling constantαs for QCD:

αs =4π

(11− 23nf ) ln( Q2

Λ2QCD

). (1)

In addition a color factor must be added to the QED Lagrangian and gluon-gluon interactions must be allowed. αs is proportional to the strength of thestrong interaction, Q2 is the momentum transfer, nf the number of flavoursand λQCD is the typical QCD length scale. αs will be small at large Q or atsmall length scales. In that case the matrix element M (probability amplitude)of the interaction can be described with perturbation theory in QCD. Thismatrix element is needed to do a theoretical prediction of an observable. TheD0 spectrum can be theoretically calculated by using the following expression:

ED0dσpp

D0

d3p∝

∑abcd

∫dzcdxadxb

∫fa(xa, Q2

a)fb(xb, Q2b)D

D0

c (zc, Q2c)

s

πz2c

dσ

dt(ab → cd)δ(s + t + u),

(2)

where Ehdσpp

h

d3p is the D0 spectrum, fa(xa, Q2a) and fb(xb, Q

2b) are the structure

functions of the two colliding protons, Dhc (zc, Q

2c) is the fragmentation function,

dσdt

(ab → cd) is the QCD cross section (trasnsition probability), the term δ(s +t + u) is due to energy conservation and z is defined as the energy fraction ofthe hadron and the quark. In order to fully describe the whole collision process,the Parton Distribution Function and Fragmentation function must be chosenin full agreement with the experimental data.

2.1 Parton Distribution Function

The Parton distribution function gives the distribution of partons in the collidingparticles before collision; it is the number of partons of a specific flavour perunit of rapidity η. Experimentally it is extracted from the data of the partonstructure functions F2(x,Q2) by analyzing the dependence of the resolution Q2

3

with [3]:F2(x) = x Σfz2

f (qf (x) + qf (x)). (3)

The sum over all flavours f , where x is the Bjorken x, zf is the charge of thequark flavour and qf is the parton density of quark flavour f . By measuringthe structure functions the distribution of the sum of quarks and sea quarks ismeasured. At higher momenta sea quarks dominate the measurements. The Qdependence comes from the splitting of gluons in quark anti-quark pairs. Thestructure function can be determined by probing the proton with electrons indeep inelastic e-p collision as is done in HERA [4]. Both the gluon and thequark distribution can be seen below as function of Bjorken x, the fractionof the partonic longitudinal momentum compared to the momentum of theproton. Figure 1 is produced using CTEQ4 PDFs [6] for extrapolating existing

Figure 1: Parton distribution functions for a proton at Q2 = 5GeV 2 [5]

experimental results to smaller x. The x regions covered by LHC and RHIC atcentral rapidities are indicated with the shaded areas. It can be concluded thatat higher energies at RHIC and even more at LHC the hadronization process isdominated by the fragmentation of gluons (∼ 80% at LHC) [5].

The Bjorken x scales with the transferred momentum squared over the in-variant energy squared: xBJ ∼ Q2

s , at high energy (14 TeV at LHC) x � 1. xwill be roughly ∼ 100 times smaller at the LHC than at HERA, therefore thestructure functions are extrapolated to LHC energies. The parton evolution isdescribed adequately by the BFKL [7]) and the DGLAP [8] equations for evolu-tion in the x and Q direction respectively. The BFKL equations are the resultof a resummation of large logarithmic terms in Q2 for deep inelastic scattering

4

with small Bjorken x. The DGLAP equations are the result of resummation oflarge logaritmic terms in Q2 for deep inelastic scattering with large Q. Both

Figure 2: Zeus data for the gluon structure functions for Q2 = 5 GeV 2, 20 GeV 2

and 200 GeV 2 [9]

equations predict an asymptotical growth in gluon density as can also be seenin figure 2. An asymptotical growth will result in a cross section σ →∞. Thisis a physically unacceptable result also known as the small-x problem. It can beconcluded that at small x and high Q2 both DGLAP and BFKL are invalid. Thesolution might be found in ”saturation”. At high densities the proton will be-come so crowded that the interactions between the partons cannot be neglectedanymore (saturation), this implies a decrease of the scattering cross-section. Fora given x, saturation occurs at the critical value [10].

Q2sat = αsNc

1πR2

dN

dy(4)

Where dNdy is the gluon distribution per rapidity unit between the quark and the

hadron, and αsNc is the color charge squared times αs of a gluon. The rapidgrowth of the gluon density in figure 2 implies that there must be a case wherethe saturation scale is larger than the the typical QCD scale:

Q2sat � Λ2

QCD (5)

By inserting this in the formula 1, it results in αs(Q2) < 1. This suggests thatin this case weak coupling techniques can be used.

However, since the effects of the interactions are amplified by the large gluondensity, the use of pertubation theory is not appropriate. The recently developedmodel called the Color Glass Condensate [11] provides a way to describe smallx gluons as the classical color fields radiated by partons at higher rapidity, byresummation of the high density effects. This model is in good agreement withrecent experimental (RHIC) results [16].

5

2.2 Fragmentation Function

The fragmentation part of equation 2 contains information about the hadroniza-tion process that is an interplay between hard and soft processes. The fragmen-tation function is a universal function for collisions at the same energy that isindependent of the colliding particle species. However at LHC p-p collisionsare done with 14 TeV and Pb-Pb collisions are done with 5.5 TeV, this has tobe taken into account. The fragmentation function cannot directly determinedfrom QCD, in stead there are models based on experiments and general QCDproperties. A summary of models that give reasonable results are summarizedbelow.

• Independent Fragmentation (ISAJET [15]): Jets are fragmentated fromthe initial quark according to a fragmentation function, these kind of mod-els are used to study the importance of string effects. They do not takecolour connection into account and therefore they are less succesful.

• String Fragmentation (JETSET [13] , PYTHIA [12]): Starts with a string→ hadron + (remaining) string. At each branching the probability rulesare given for the production of flavours and for the sharing of energy andmomentum distributions. The string breaking is done with the idea ofquantum mechanical tunneling that leads to a flavour independent gaus-sian Pt spectrum.

• Cluster Fragmentation (HERWIG [14]) is based on phase space fragmen-tation, the setup is simpler and is less time-consuming then string frag-mentation because there are fewer parameters, it gives reasonable results.However it might not be suitable for usage at LHC energies. HERWIG isonly reliable at high Pt, since the matrix elements have soft Pt singulari-ties.

The model used to generate background in this thesis is PYTHIA. It is the mostcommon model that gives the best results.

6

3 Quark Gluon Plasma

In heavy ion collisions both the initial baryon chemical potential (µB) and thetemperature rise at large

√s . The quark gluon plasma (QGP) phase transition

is suspected to exist at small baryon chemical potential and high temperatureor high baryon density and small temperature. At particle accelerators suchthe LHC at CERN, Geneva, temperatures are believed to cross the curve atsmall baryon density, therefore the LHC seems to be an ideal tool to studythe properties of a system where quarks and gluons are deconfined. A phasediagram of nuclear matter can be seen in figure 3, it describes the propertiesof quarks and gluons as a function of temperature and the baryon chemicalpotential. The scientific motivation to study the Quark Gluon Plasma (QGP)

Figure 3: QCD Phase Diagram

can be summarized into two main subjects that are predicted by QCD:

• Deconfinement; Where the hadron wave functions in the medium overlapand the partons are effectively free to move in volumes larger than thesize of a hadron.

• Chiral Symmetry Restoration; In quantum field theory, chiral symmetryis a symmetry of the Lagrangian under which the left-handed and right-handed parts of Dirac fields transform independently. In the ground stateof nuclear matter however the symmetry is broken. If chiral symmetry isrestored the symmetry of the QCD lagrangian between the quarks withpositive and negative chirality in the medium is restored.

The latter is of specific interest since the breaking of chiral symmetry is respon-sible for most of the visible mass in the universe.

In figure 3 can be seen that only the experiments done at RHIC, SPS and theexperiments that will be done at LHC have enough energy to reach a QGP phasetransition, however at RHIC and SPS the QGP did not exist long enough tomeasure its properties. As a reference ordinary nuclei can be found at µb = 0.93

7

GeV at low temperature. The dense cores of neutron stars can be found atµb ∼ 1.4 GeV. In an heavy ion collision at LHC lead ions collide with 5.5 TeVper nucleon. Due to the high speed the two ions are Lorentz contracted. Charmquarks are produced during the early stage, shortly after the collision ∼ 0 fm/c.After production the medium expands. Six different stages can be discriminated(figure 4):

0 fm/c Initial Stage: hard particles; jets, direct photons, heavy quarks

0.2− 2 fm/c Pre-equilibrium Stage: semi-hard particles; gluons, light quarks

2− 10 fm/c QGP Stage: Quarks and Gluons are in equilibrium

10− 20 fm/c Hot Hadron Gas Stage: Quarks and Gluons recombinating inhadrons

t →∞ fm/c Freeze-Out Stage: No inelastic interactions, no changes in com-position

Figure 4: Stages during the Heavy Ion Collision shown in a light cone

Charm quarks are excellent probes of the medium produced in heavy ioncollisions. The initial cc production is not affected by final state effects. Becausethe minimum value of the momentum transfer cmin = 2 mc in an interactionprocess implies very short space-time scales of 1

2mc∼ 1

2.4 GeV ∼ 0.1 fm. Theexpected formation of a QGP at the LHC is ∼ 1 fm. Heavy quarks are producedin early stages ∼ 0 fm/c when the color fields are strong due to hard scattering.The expected spectra of charm quarks should be the same in Pb-Pb and p-p collisions at the same energies when P charm

t > 5 GeV, at lower Pt nuclearshadowing is responsible for significant differences, see figure 5. In this caseheavy quark pairs are produced by low-x gluons.

Heavy quarks produced during the initial state are produced in three dif-ferent processes: Pair Creation (leading order) where gluons fuse and quarksannihilate and flavour excitation where an incoming heavy quark interacts withan incoming gluon. It turns out that the next to leading order diagrams cannotbe neglected. The next to leading order Feynman graphs can be seen in figure6. They are quite similar to the leading order but in the case of pair creationthere is gluon radiated off the quark, in the case of flavour excitation a three

8

Figure 5: Transverse momentum distribution and rapidity of charm quarks forpp and Pb-Pb at 5.5 TeV, the inset shows the ratio of the distributions, herethe nuclear shadowing can be seen more clearly. The information is extractedfrom PYTHIA [5]

gluon interaction vertex is added. In addition there is an extra process calledgluon splitting where a quark antiquark pair is created from g → QQ in thefinal state. All five processes have a significant contribution to the total charmproduction.

Figure 6: NLO Feymann Graphs of Pair Creation (Left), Flavour Excitation(Center), Gluon Splitting (Right)

Heavy quarks might also be produced thermally at later times ∼ 2−10 fm/c.The temperatures in the QGP that are expected in the LHC are of order 0.7GeV. The mass of a charm quark ∼ 1.3 GeV is of the same order of magnitude.Following the Boltzmann distribution there is a significant contribution of ther-mal quarks to the total spectrum of ∼ 1− 10%. Thoughts differ at this subject[17] and conclusions are carefully discussed since the thermal production yieldmight also give information about the temperature of the medium shortly afterthe collision. The general conclusion is that the order of magnitude of the initialcharm production at LHC energies is significantly larger than thermal charmproduction. If thermal production takes place during the Quark Gluon Plasmastage, thermal quark pairs have lower masses than initial produced pairs, there-fore they will be found in low Pt regions.

Shortly after the collision Charm quarks while travelling through the mediumlose energy. The energy loss of charm quarks is due to two processes:

• Collisonal energy loss: High-momentum partons undergo elastic scattering

9

with gluons in the QGP.

• QCD bremsstrahlung: When partons are moving through a colored medium,iInteractionwith the induced color field cause gluons to be radiated off, similar tobremsstrahlung in QED [18]

For QCD bremsstrahlung the average energy loss ∝ αsCRqL2 where αs is therunning coupling constant, CR is the QCD coupling factor (Casimir factor),q is the transport coefficient of the medium defined as the average transversemomentum squared transferred to the projectile per unit path length and L isthe the path length in the medium. In cold matter q ∼ 0.05 GeV/fm at the LHCthe transport coefficient is expected to be ∼ 1−10 GeV/fm. The contribution ofcollisonal energy loss dE/dx ' α2

√ε ∼ 0.1 GeV/fm [19] to the the total energy

loss is rather low, therefore QCD bremsstrahlung is the dominant contributingprocess. The average path length of partons in the medium is expected to be∼ 5 fm as is extracted from the Glauber model [21]. The probability distributionas function of the path length L is given in figure 7(b).

(a) Average energy loss for gluon, lightquarks and charm quarks at q = 4 GeV/fm[24]

(b) Probability distribution as function ofthe path length for partons produced in Pb-Pb with impact parameter < 5 fm

Figure 7:

The average energy loss for charm quarks, light quarks and gluons at LHC iscompared in figure 7(a). The difference in energy loss for light (massless) quarksand gluons can be understood with the Casimir factor that is equal to 4/3 forquarks-gluon coupling and to 3 for gluon-gluon coupling. In [25] is argued thatheavy quarks will lose less energy because of their large mass. This results in anenhancement of charmed mesons at moderate (5−10 GeV) transverse momenta.The ”dead cone effect” [25] for heavy quarks is responsible for this differencebetween light quarks and charm quarks. Heavy quarks with moderate momentatravel with a velocity smaller than the speed of light. As a consequent gluonradiation in a vacuum is suppressed at angles smaller than the ratio of the charmmass to its energy due to destructive quantum interferences.

Charm energy loss is strongly dependent of the transport coefficient of themedium and the path length that is in turn dependent of the lifetime of themedium. By comparing the spectrum of charm quarks in a QGP in Pb-Pbcollisions with the spectrum of charm quarks in a superposition of p-p collisions,the energy loss is measured and information about the lifetime and about the

10

transport coefficient of the medium are obtained. However when the mediumhas a long lifetime charm quarks lose most of their energy and they will comeinto an equilibrium. In figure 8 the relaxation time of charm quarks in a QGPis shown as function of the temperature with and without non-perturbativeresonance scattering ie. Charm-light quark interactions.

The equilibration time is a factor 3 lower than in pQCD. From figure 8 can beseen that charm quarks in a medium with T ∼ 0.3 GeV have a relaxation time of∼ 4 fm/c. However, since the medium is expanding and the density is decreasingthe relaxation time will be > 4 fm/c. By definition in thermodynamics an idealequilibrated medium has lost its historical information. In a heavy ion collisionsthe size and lifetime of the QGP is small and it will not be ideally equilibratedin its lifetime, however the historical information of charm quarks might beblurred, therefore it is more difficult to extract information about transportcoefficients and lifetimes. If a QGP is in full equilibrium the charm spectrafrom Pb-Pb collisions would show significant differences compared with p-p andan upperlimit of the relaxation time can be extracted. In this case the charmspectrum from central Pb-Pb collisions will have the shape of a Boltzmanndistribution with in addition an expansion of the medium.

Figure 8: Relaxation time of charm quarks with and without resonant interac-tions as function of the temperature [26]

During the hadronization process most of the charm quarks are recombiningwith light quarks (open charm), creating D mesons. It turns out charm hadronproduction goes dominantly via D (spin singlet) and D∗ (spin triplet) mesonswith a ratio of N(D0) : N(D+) : N(D∗0) : N(D∗+) = 1 : 1 : 3 : 3 [5]. Inprinciple all D mesons species can be used for open charm analysis. A D0

has a corresponding average decay length cτ = 123.7 ± 0.8 µm and the decaylength of the D+ is cτ = 315.3 ± 3.9 µm. Since the first detector is located at4 cm distance in the transverse plane from the interaction point, only the decayproducts can be measured. Most particle detectors can only measure chargedparticles, therefore decay channels containing only charged particles are themost interesting. In addition the amount of decay products must preferable be

11

two, in that case the probability of a total and useful reconstruction is large.This thesis is focused on the decay: D0 → K−π+ this decay channel has a

branching ratio of 3.8%±0.09. The expected yield of this channel in the detectorrange is 0.52 D0 → K−π+ per event in Pb-Pb and 7.5 10−5 for a p-p collision,the expected amount of events per year at LHC is 107 for Pb-Pb and 109 for p-p.The impact parameters of the decay products, in particular the product of theimpact parameters, is strongly dependent on the decay length (section 6.5.4), thebest property that discriminates the D0 from other particles. For discriminatingD0s from background in this analysis, impact parameter measurements with aresolution of 50 µm for the decay products of the D0 and precise momentummeasurements for a good invariant mass resolution are required.

12

4 Experimental Setup

The detector located at the LHC, CERN, used for measuring QGP propertiesis ALICE (A Large Ion Colliding Experiment). ALICE is a general purposedetector and its main strength will be the measuring of a broad Pt spectrumfrom 100 MeV up to 100 GeV with in addition the identification of particles.One of the main goals of ALICE is the measurement of the spectra of short livedparticles, such as hyperons, D and B mesons. Alice is designed to perform thisgoal at multiplicities of at most 8000 particles per unit of rapidity per event,a collision is measured 100 times per second. The Inner Tracker System (ITS)[23] and the Time Projection Chamber (TPC) [22] are of particular importanceto measure heavy quark spectra. In figure 9 the layout of the ALICE detectoris shown, the ITS is located in the center of the detector, it is the first detectorparticles are passing after the collision. The TPC is surrounding the ITS, it isthe second detector from the inside.

Figure 9: Layout the ALICE Detector

4.1 Inner Tracking System

The Inner Tracking System is the most important detector part for D0 ex-traction. Since D0s are short lived particles, the tracking must be done veryaccurately. The Inner Tracking System is able to track particles accurately, ina dense tracking environment. It gives 3D information about the tracks withsmall uncertainties (see figure 11) in a magnetic field of ∼ 0.5 T. In order todisturb tracks as little as possible the material budget in the contruction is keptminimal. The ITS is designed for the following purposes:

13

• Localize primary and secondary vertices (decay points) with a resolutionof better than 100 µm for reconstruction of charm and hyperon decays.

• Tracking and identification of particles with momenta less than 250 MeV.

• Improve the resolution of high momentum particles that are also detectedin the TPC.

Figure 10: Layout of the Inner Tracking System detector

The ITS (figure 10) [23] consists out of six cylindrical silicon detectors cover-ing a rapidity range of −0.9 < η < 0.9. The first two most inner cylinders consistof silicon pixel detectors that are essential for the determination of the primaryvertex and the impact parameters of the tracks in a dense track environment.The pixel size is 50 by 425 µm2, it defines the two track separation.

At the two middle cylinders the track density is lower, so that a SiliconDrift Detector is suitable for this position. The SDD gives two-dimensionalinformation about the position. The cell size is approximately 294 × 202 µm2,the SDD has a spatial resolution of ∼ 40 µm in the transverse plane over thewhole detector surface. The two most outer cylindrical detectors are SiliconStrip Layers. They are of crucial importance for the connection of the ITS tothe Time Projection Chamber and for Particle Identification. The SSD Sensorsare double sided silicon strip detectors that have small orientation difference,so that they overlap and thereby avoid ambiguities. Techical details about size,resolution and range in pseudorapidity of the Inner Tracking system are shownin figure 11.

Figure 11: Essential details of the Inner Tracking System [27]

14

4.2 Time Projection Chamber

The Time Projection Chamber [28] is the main tracking detector of ALICE.It has a large acceptance of −0.9 < η < 0.9. Its main functions are trackfinding, charged particle momentum measurement, particle identification andtrack separation. The TPC is divided in two pieces by a high voltages electrode(V = 100 kV) that provides an uniform electric field in the beam direction.The TPC (figure 12) has a cylindrical shape with volume that ranges fromr = 85 − 250 cm and a length of l = 500 cm filled with an Neon/CO2 gasmixture.

Particles passing through ionize the gas and electrons and ions are driftedunder influence of the electric field (E = 400 V/cm ) towards the electrode. Thedrift time of electrons is 88 µs. The two end plates exist of 18 trapezoidal sectorswhich are mounted with multi-wire proportional chambers with a cathod padreadout. The electrons (and ions) drift to electrodes and the track is projectedon the xy plane. The z component is known by measuring the drift time.The TPC also measures energy loss. Charged particles are identified by thereenergy loss dE/dx that is specific for different particle species and momenta.The TPC is optimized for an extremely high multiplicity ∼ 8000 tracks perunit of rapidity, it has a full radial coverage. The TPC is an ideal device formeasuring soft physics observables. The position resolution is estimated to bebetween 1100 and 800 µm, technical details can be found in table 13.

Figure 12: Layout of the Time Projection Chamber detector [27]

5 Analysis Framework

The software package used for the analysis is Root v5-21-01 and Aliroot v4-13-Release. Root is an object oriented program and library. It was originallydesigned for particle physics data analysis and contains several features specificto this field. Nowadays it is also used in other applications such as astronomyand data mining. Aliroot is the ALICE Off-line framework that is developed for

15

Figure 13: Essential details of the Time Projection Chamber [27]

Alice related simulation, reconstruction and analysis. It uses Root as a founda-tion and Geant 3.21 as the detector simulation code on which the framework andall applications are built. Geant describes the passage of elementary particlesthrough matter. The principal applications of GEANT in high energy physicsare the tracking of particles through an experimental setup for simulation of de-tector response and the graphical representation of the setup and of the particletrajectories. The collision Monte Carlo simulation is done with PYTHIA, it de-scribes collisions at high energies between elementary particles such as e+, e−,p and p in various combinations. It contains theory and models for a numberof physics aspects, including hard and soft interactions, parton distributions,initial- and final-state parton showers, multiple interactions, fragmentation anddecay.

5.1 Background Sample

The background data sample used in this analysis contains 990.000 p-p min-imum bias events with an ideal geometry ie. the detector behaves perfectlyand is located as designed. The magnetic field is 0.5 T . The background datasample is generated with Root v5-15-08, Aliroot v4-05-Rev-05 and Geant v1-8. It is produced as part of the Physics Data Challenge 2007 (it is the onlyavailable data at the time of analysis). The background data sample is takenfrom the LCG (LHC Computing GRID), a network based framework for worldwide distribution of jobs and data over CPUs and storage elements. The runrange is 6000 - 6011 as can be found on the ALICE GRID monitoring system:MonaLisa [29]. In this analysis the background is rescaled to 109 events, theexpected amount of events during the first year of operation. The PDC07 back-ground has the natural ratios of particles and therefore it also contains the decayD0 → K−π+, all π+ and K− that are reconstructed and coming from the sameD0 are rejected from the analysis. The primary vertex resolution is shown infigure 14(a). The x- and y-component of the primary vertex can be measured

16

with a resolution of ' 30 µm the z-component is measured with a resolution' 70 µm (figure 14(b)).

(a) Primary Vertex x-component resolu-tion Background

(b) Primary Vertex z-component resolutionBackground

Figure 14:

In approximately 7% of the events in the background sample the primaryvertex can not be reconstructed. In this case the primary vertex is set in theorigin by default. From figure 15 can be seen that this hardly affect the shapes ofthe product of the impactparameters distribution, the most efficient property tocut on as will be shown later on. In this thesis the contribution form this effectis expected to be negligible, however the size of this effect increases when usingmore data, that is why in the experiment while using larger data samples the twocases ”primary vertex reconstructed” and ”primary vertex not reconstructed”must be treated separately.

Figure 15: product of impact parameters in the cases ”primary vertex found”and ”primary vertex not found”, the distributions are properly weighted andscaled to one”

The transverse momentum resolution for primary particles gives an indica-tion about the reconstruction efficiency. In general it is expected an efficiency

17

of 0.9 can be reached. However for the sample used in this analysis it is foundthat the efficiency strongly depends of the amount of ITS hits that are requiredin this data sample. If only those tracks are selected that have the maximumamount of ITS hits, D0s can be identified more clearly. The efficiency is shownin figure 16 with requirements of 6, ≥ 5 and ≥ 4 ITS hits, from ≥ 4 to ≥ 1ITS hits the efficiency stays more or less constant. This inefficiency is not ex-pected, the efficiency should be approximately independent of the amount ofhits required and the values should be constant around 0.9. The source of thisproblem is found in the detector simulation. During the simulation an unnatu-ral amount of detector parts were swithed off, as can be seen from figure 17(a),due to bad detector treatment or tracking problems. As a comparison the ηφrange is shown for newer PDC08 data in 17(b), it can be seen that still largeregions are not operational, however this is according to reality. This results inan inefficiency of roughly 35%.

Figure 16: Efficiency vs PD0

t , number of ESD tracks divided by number of MCtracks, with different hits required in the ITS, TPC > 1, refits in both ITS andTPC.

(a) Distribution of the detector range in theeta-phi direction from PDC07

(b) Distribution of the detector rangein the eta-phi direction from newerFirst Physics data (production PDC08/LHC08c11, 10 TeV p-p)

Figure 17:

18

Comparison to PDC06 :At the start of this study PDC06 background was used, it was noticed our resultswere significantly different from published results, that is why the analysis wasswitched to PDC07. Still the question rises about the validity of PDC06 data.The product of the impact parameter, the most important distribution to cut onin this study is shown in figure 18(a), it gives a good indication of how well thetwo data samples match with each other. The product of the impact parametersis the product of the distance of closest approach to the primary vertex of thetwo decay products, which is strongly correlated with the distance between theprimary and the secondary vertex. The large differences in the distributions aredue to the large primary vertex resolutions in PDC06 compared with PDC07data. The primary vertex resolution in PDC06 data in figure 18(b) is ' 50 µm.This resolution is most likely responsible for the difference from the product ofthe impact parameters resolutions from PDC07 and PDC06.

(a) distributions of the product of the im-pact parameters of PDC06 compared withPDC07

(b) primary vertex resolution of x ofPDC06 and PDC07

Figure 18:

5.2 Signal Sample

The signal sample contains D0s that all decay to D0 → K−π+ with a marginaround the detector acceptance. The D0s have a flat Pt distribution that isweighted according the following expression [20]:

dN

dPt∝ Pt(1 +

dPt

P 0t

)−n (6)

where P 0t = 2.04 and n = 2.65, after weighting Σiwi = 24795 D0s are left. This

method results in better statistics at larger PD0

t . The primary vertex is definedby approximately 20 πs per event. Afterwards the vertex position is smearedwith a gaussian to 30 µm in order to have the same primary vertex resolutionas the p-p background events. The magnetic field is set to 0.5 T . The signal isrescaled to 109 events. The signal sample is simulated with Aliroot v4-04-Rev-14and Geant 3.

For this analysis it is crucial to use tracks that are reconstructed with smallerrors, therefore those tracks are selected which fullfill the following require-ments:

19

• The maximum (6) hits in the ITS

• At least one hit in the TPC

• A refit of hits in the ITS

• A refit of hits in the TPC

5.3 Secondary Vertex Resolutions

The vertex finding in the experiment is of crucial importance, since an excellentresolution is needed to measure the decay length of the D0 cτ ∼ 123µm. Thedecay length is a dominating property in discriminating signal from background.The decay length can be calculated by measuring the location of the primaryand the secondary vertex and calculating the distance in between. To measure areasonable decay length the error in determining the primary and the secondaryvertex must be low.

The primary vertex is perfectly defined in Pb-Pb collision because of highmultiplicity ∼ 10000 with a resolution of < 10 µm. In p-p the multiplicity islower by a factor ∼ 1000. In figure 14(a) is shown that the resolution in the p-pcase is < 30 µm. It can be concluded that the primary vertex resolution has asmall contribution to the error in the decay length.

(a) x-component of secondary vertex reso-lution with two decay products with hitsITS = 6, TPC > 1, and refits in both ITSand TPC

(b) resolution of the secondary vertex asfunction of the D0 reconstructed momen-tum, with hits ITS = 6, TPC > 1, andrefits in both ITS and TPC from the signalsample

Figure 19:

The secondary vertex measurement is based on two particles, independentof the type of collision the resolution is expected to be ∼ 120 µm integrated overPD0

t as can be seen in figure 19(a). From figure 19(b) can be seen that the sec-ondary vertex resolution is large at small PD0

t . Since D0s in small PD0

t regionshave a small decay length and the secondary vertex resolution is large, decaylength measurements are dominated by statistical uncertainties. Therefore inthis thesis only the region PD0

t > 1 GeV is considered.

20

6 Analysis

All negative and positive particles properly measured by the detector are com-bined in order to create a combinatorial background. By calculating an invariantmass spectrum using the kaon mass for negative particles and the Pion mass forpositive particles with the following formula:

Minv =√

(E+ + E−)2 − (P+ + P−)2 (7)

the spectrum of the combinatorial background can be calculated. In figure 20 thesum of combinatorial background and the signal can be seen as function of theinvariant mass. In the distribution a peak should appear around 1.865 GeV, theinvariant mass of the D0. However this peak is hardly visible due to statistical

Figure 20: Normalized invariant mass distribution before cuts: backgroundcontribution in black, signal contribution in red

fluctuations of the combinatorial background and can only be seen more clearlyby using a large amount of events. This peak is used for counting the amountof D0s per PD0

t region, that is used to extract the spectrum dN/dPD0

t , if aninvariant mass distribution is made for every PD0

t range. The significance ofthe signal is the ratio of the signal strength to its statistical uncertainty. It isgiven by

σ =S√

S + B, (8)

where σ is the significance, S is the number of D0s and B is the number of pairsfrom the combinatorial background. In this thesis the goal is to optimize D0

measurement by selecting on D0 properties and thereby deselecting background.The study of optimization of D0 extraction cuts has been done before in

the Physics Performance Report (PPR) [20], by using the iteration method (seesection 6.2). The resulting cut values from this study are taken and appliedon the PDC07 background and simulated signal samples as a comparison, seesection 6.5.4. Note that the results as taken from [20] are obtained after using

21

particle identification in the region PD0

t < 2 GeV using the measurement ofthe energy loss that is specific for the different particle species to reduce thecombinatorial background.

The method used in this thesis is based on multi-dimensional optimizationin one direction (see section 6.2). The integrated significances over the region1 < PD0

t < 10 GeV of the initial distributions with cuts as published in thePPR applied and the results after applying the multi-dimensional integrationalgorithm can be found below. After applying the multi-dimensional integration

Cuts: B/event S/event S/B Sign. Sign.Err.Initial 1.47× 10−1 1.89× 10−4 1.28× 10−3 16 0.06PPR 2.19× 10−4 2.31× 10−5 1.1× 10−1 47 0.8OPT 7.10× 10−6 1.65× 10−5 2.3 108 3.4

Table 1:

method, the significance compared to the initial significance is improved by afactor ∼ 7, the siginificance with PPR cust applied gives an improvement of afactor ∼ 4. The differences between the values reported here and the ones thatare published in the Physics Performance Report [20] are due to the larger masswindow σ = 12 MeV in the PPR and the fact that the 0 < PD0

t < 1 GeV regionis taken into account in the PPR.

6.1 Method

In order to optimize the significance, it is important to find properties of D0swhich differ from the combinatorial background. If such properties can be found,the regions that are more or less dominated by the signal (D0s) can be selectedby placing cuts in the distributions. As published in the PPR [20] there are sixparameters that are interesting for the selection of signal dominated regions:

• dK0 × dπ

0

• dca

• cos(θpointing)

• | cos(θ∗)|

• PKt and Pπ

t

• |dK0 | and |dπ

0 |

dK0 × dπ

0 is the product of the impact parameters in the tranverse plane asis illustrated in figure 21, the dca is the distance of closest approach of tworeconstructed tracks, cos(θpointing) is the angle between the D0 flight line andthe D0 reconstructed momentum, cos(θ∗) is the angle between the pion andthe D0 flightline in the D0 frame, PK

t and Pπt are the reconstructed transverse

momenta of the Kaon and Pion respectively.The most important property of the D0 is the decay length < L >∼ 123 µm

following an exponential distribution eLcτ . In order to distinguish D0s from the

combinatorial background by looking at the decay length an excellent primaryand secondary vertex resolution is required. The decay length distributions are

22

Figure 21: picture of D0 decay, the different parameters are used in section 6.5

strongly correlated with the product of the impact parameters, as is shown lateron, for large decay length it becomes larger and negative.

6.2 Algorithm

The analysis is based on the optimization of a six-dimensional correlated cutspace. That cannot be solved exactly due to a lack of processing time, memoryand statistics. The problem can be simplified by binning the data in large binsto reduce processing time. However this blurs the results and the optimummight be invisible or flatten down. There are two ways that can be used forgiving an approximation of the optimal cut values.

1. Iteration method: Optimization by treating on dimension at a time, untilthe optimum is believed to be reached. With this method the cut space isscanned for optima, however it may depend on the path taken, thereforesome local optimum can be interpreted as the global optimum.

2. Integration method: This way is based on integrating bin by bin in onedirection, starting from a corner of a multi-dimensional lattice where signalis dominating ending at the corner of the lattice where background isdominating. This method is garanteed to find a global optimum.

Both algorithms give considerable improvement and they can be used to crosscheck eachother. We now focus on the settings used in the integration methodused in this thesis. The input is a tree that contains the information of all cutparameters per particle. The output is a set of cuts that must be applied to getthe optimum significance. The resolutions of the found cut values are dependentof the amount of the bins that is directly related to the processing time sincetprocessing ∼ NNbins

dimensions. The program is written in an efficient way in order toavoid double calculations, for 25 bins in six dimensions it takes ∼ 10 minutes tofinish. The amount of 25 bins gives a good resolution if the ranges are chosensuch that they cover the most interesting part of the six-dimensional lattice.

The integration has to be done for the signal, background and error distri-butions in the four different PD0

t bins. Afterwards for each bin in the integrateddistribution the significance is calculated. Since the amount of background isof order one for some results, Baysian error analysis is used in the cases where0 < B < 5. The best optimum is selected when the error is smaller than 6%.

23

After finding the optimum the contributing cut set is checked on the data andfine tuned if necessary.

6.3 Initial Cuts

Most of the D0s are present in a region of three sigmas (with σ = 8 MeV ) aroundthe D0 mass MD0 = 1.865 GeV. Most of the background is present outside thisregion. The combinatorial background is reduced to the region of three sigmasaround the invariant D0 mass. The D0 reconstructed Pt-spectrum of the signaland the combinatorial background behave differently. This difference becomesmore clear at larger PD0

t . The combinatorial background has a steeper tail thanthe the signal. This results in a S/B ratio that grows at higher PD0

t regionsas can be seen in figure 22, since the exponent is momentum dependent. Sincethe distributions behave different at higher PD0

t regions the analysis has to bedone in different PD0

t regions. For higher transverse momenta the significancewill increase but the statistics will reduce fast, therefore the regions at higherPD0

t are chosen larger in order to keep the errors small enough. The analysisis done separately in the following regions: 1 < PD0

t < 2, 2 < PD0

t < 3,3 < PD0

t < 5 and 5 < PD0

t < 10 GeV. The region 0 < PD0

t < 1 GeV has alsobeen studied, but the significance is so low that it is not taken into account inthe final results. The signal can hardly be distinguished from background inthis region as is shown in section 6.5.4.

Figure 22: Transverse momentum spectrum of the signal (red) and the back-ground (black) at a logaritmic scale.

6.4 Error analysis

The statistical error in the significance can be calculated with:

4σ =

√(∂σ

∂SδS)2 + (

∂σ

∂BδB)2 (9)

24

Where σ is the significance, B is the amount of background entries, S is theamount of signal entries, δS is the error in S and δB is the error in B,this resultsin:

4σ =12

√4B2δS2 + 4BSδS2 + δB2δS2 + S2δS2

(B + S)3, (10)

where δB = WB

√B with WB the factor to normalize to 109 events, dS is

determined by bookkeeping and

δS =√

ΣNi W 2

S,i =√

ΣNi W 2

Norm ×W 2P D0

t ,i(11)

where WS,i is the weight of a signal entry, WNorm is the weight for normalizingto 109 events and W 2

P D0t ,i

is the weight per signal entry due to the natural D0

distribution.For large B the Gaussian approximation of Poisson statistics for the uncer-

tainty in X where X is an positive real integer is equal to√

X. However forB → 0 the significance σ →

√S in this case the approximation is not valid.

After applying the cut values found in this study the invariant mass distribu-tion shows only seven unweighted entries (7070 weighted) for the backgroundintegrated over the range 1 < PD0

t < 10 GeV as can be seen in figure 23, this isnot enough to use a Gaussian approximation of Poisson statistics.

Figure 23: Invariant mass distribution after found cuts normalized to 109 events:background in black, signal in red

To reduce the effects of the low statistics enlargement of the mass window ofthe background is used to artificially raise the statistics. The invariant mass cuthas an negligible correlation with the cut observables at small changes in themass window, therefore it does not affect the shape of the distributions. Thisgives the opportunity to artificially raise the combinatorial background statisticswith a factor 5 by enlarging the mass window by a factor 5. By weighting theentries with the factor the height of the significance is hardly changed. With

25

the enlarged invariant mass window the optimum cut per distribution can befound within ∆σ < 6%.

After applying this mass window enlargement 5 times more background en-tries are present. Unfortunately that means there are still PD0

t region where theerror analysis is not done in a proper way. Poisson statistics is based on certainrandom variables N that count a number of discrete occurrences that take placeduring some finite time-interval. If the expected number of occurances is λ, thenthe probability that there are k occurances is:

f(k;λ) =λke−λ

k!(12)

with k a non-negative integer and λ is a real number. If λ → 0 the Gaus-sian distribution for large λ changes into a distribution with an exponentialtail. Following the Bayesian approach to statistics the expectation value with acorresponding 68% uncertainty can be calculated in general by solving:∫ λ

0

f(k;λ)dλ = 0.68 (13)

This method is used for k ≤ 5, for the other cases the probability distributionis approximately symmetric and the Gaussian approximation holds as a goodmethod. resulting in the following solutions:

k λ0 1.141 2.352 3.503 4.644 5.755 6.85

Table 2: Values used to apply Baysian error analysis

By applying mass window enlargement and the Bayesian approach in thecases where B < 5 optima can be calculated with an error of < 6%. Both tricksare used because of a lack of available data, they can be used with small sideeffects. A larger data sample remains the most proper solution.

6.5 Optimization

Each cut parameter is correlated with the others, distributions change whileapplying cuts on other parameters. In this section each cut-parameter andmajor changes due to cutting on other parameters will be discussed. At the endof each subsection the results from the multi-dimensional integration algorithmwill be shown.

6.5.1 Distance of Closest Approach

In the experiment the signals that a particle leaves behind while passing thedetector are measured. The tracking algorithm reconstructs the tracks andextrapolates them back to the vertex (point of decay). The distance of closest

26

approach (dca) is a measure that selects out the badly reconstructed particlesand most of the particles that do not originate from the same vertex. The dcagives the closest distance of two reconstructed tracks at the vertex. At small dcathere is a large probability that the two tracks do come from the same decay,at large dca it is small. At smaller distances the reconstruction resolution playsan important role since it is smearing the process. Figure 24 shows that theoptimum dca cuts seems to be located from 300 µm at low PD0

t to 200 µm atlarge PD0

t . This can be understood with the fact that the secondary vertexresolution in figure 19(a) is better at high PD0

t . The significance increasesrapidly at small dca and drops slightly at values > 300 µm. By cutting on thedistance of closest approach only a few background entries are deselected, inspecific at larger PD0

t regions.

Figure 24: DCA distributions for signal in red, background in blue and signif-icance in black with found cuts applied in the regions 1 < PD0

t < 2 GeV (left)and 5 < PD0

t < 10 GeV (right), both signal and background distributions arescaled with 100/maximum

The dca is a relatively weak cut, by shifting the dca in the 200 − 300 µmregion 0.01% of the background particles are cut away resulting in < 1% im-provement in significance. At large PD0

t the other cuts have cut away mostof the background and the DCA hardly matters. The results of the multi-dimensional integration method are found using a resolution of 20 µm in theregion of 0 ≤ DCA < 500 µm, they are shown in table 3.

Cut name 1 < PD0

t < 2 2 < PD0

t < 3 3 < PD0

t < 5 5 < PD0

t < 10dca < 280 µm < 320 µm < 220 µm < 200 µm

Table 3: dca optimum cut values found by using the integration method.

6.5.2 Pointing Angle

The D0 flight line (figure 21) is defined by the vector through the primary vertexand the secondary vertex. The D0 momentum is reconstructed out of the Kaonand Pion momenta. In an ideal case the reconstructed D0 momentum matcheswith the D0 flight line in that case the cos(θpointing) = 1. Due to detectoreffects and reconstruction errors there is a small angle between the two vectorseven in the case where particles are coming from the same vertex. This is whythe signal is peaked at one. For pairs that are not coming from the same vertex

27

such as in the combinatorial background is uniformly distributed. In figure 25can be seen that the cosine pointing angle cut is most effective at small PD0

t .

Figure 25: cos(θpointing) distributions and significance with found cuts appliedin the cases 1 < PD0

t < 2 GeV (left) and 5 < PD0

t < 10 GeV (right), both thesignal (red) and the background (blue) distributions are scaled with 100/maxi-mum, the significance is shown in black

The pointing angle is the most efficient in combination with dK0 ×dπ

0 at largePD0

t only a few ∼ 103 background particles are cut away resulting in a fewpercent improvement in significance at large PD0

t . The binning of the data isdone in bins with a size of 0.04 in the region 0 ≤ cos(θpointing) ≤ 1, they can befound in table 4.

Cut name 1 < PD0

t < 2 2 < PD0

t < 3 3 < PD0

t < 5 5 < PD0

t < 10cos(θpointing) > 0.92 > 0.92 > 0.96 > 0.96

Table 4: CPA optimum cut values found by using the integration method.

6.5.3 Decay Angle in D0-frame

The | cos(θ∗)| (CTS) is defined as the cosinus of the angle between the D0

flight line and the momentum of the Pion in the D0-frame. The signal has anisotropic distribution because there is no preferable direction. The symmetricaldistribution of the signal allows it to take the absolute value. Below (figure 26| cos(θ∗)| distributions and significance are shown for 3 < PD0

t < 5 GeV and5 < PD0

t < 10 GeV.The decay angle in the D0 frame is a moderately strong parameter to cut on

for moderate PD0

t . For both small and large PD0

t only a few background pairsare rejected. For 5 < PD0

t < 10 GeV the location of the cut relies on a fewseparate background entries. The locations of the cuts have a resolution of 0.04and they are found by integrating from large to small | cos(θ∗)| in the region0 ≤ | cos(θ∗)| ≤ 1, they are shown in table 5

Cut name 1 < PD0

t < 2 2 < PD0

t < 3 3 < PD0

t < 5 5 < PD0

t < 10|cos(θ∗)| < 0.88 < 0.56 < 0.96 < 0.72

Table 5: | cos(θ∗)| optimum cut values found by using the integration method.

28

Figure 26: | cos(θ∗)| distributions and significance with found cuts applied in thecases 1 < PD0

t < 2 GeV (left) and 5 < PD0

t < 10 GeV (right), both the signal(red) and the background (blue) distributions are scaled with 100/maximum,the significance is shown in black

6.5.4 Product impact parameters of decay products

A D0 has a cτ of 122.9 µm, the decay length follows an exponential distribution,while the background follows a power law. The dK

0 × dπ0 is the product of

the impact parameters, that is defined as the product of the closest distancebetween the extrapolated tracks and the primary vertex. The tracks can begiven a sign by looking at the projection of the tracks on the bending planeand by determining at which side the primary vertex is located. This signcan be either positive or negative depending on the track projection on theprimary vertex. Since the background secondary vertices are in fact randomlysituated in space, a symmetrical distribution is expected. For reasonable largedistance between the secondary vertex with respect of the primary vertex (decaylength) it is suspected that one tracks passes the left side an the other the rightside. Therefore for the signal can be expected that the distribution will bea-symmetrical with a larger tail at the negative side.

The product of the impact parameters is by far the strongest cut parameterof all other cut parameters. It is largely dependent of the decay length. Ifthe decay length is small it can hardly be measured due to a large number ofbackground and a low resolution. The probability to have a small decay lengthis large in 0 < PD0

t < 1 GeV. In this case signal and background can hardly bediscriminated compared with higher PD0

t regions, as can be seen by comparingfigure 27 (left) to 27 (right). Therefore the 0 < PD0

t < 1 GeV is not taken intoaccount in this study.

After applying all cuts except for the product of the impact parametersfound with the optimization, it can be seen that the distributions become moreasymmetrical. Obviously all other cuts are tuned in such a way that cutting onthe product of the impact parameters is most efficient, for higher PD0

t regionsin specific. The distributions of signal and background and the significance in2 < PD0

t < 3 are shown below.The product of the impact parameters turns out to be a strong cut parameter

in applied in combination with the pointing angle. This can be seen in thescatterplot of dK

0 × dπ0 vs cos(θpointing) ± 1 below, where all other cuts are

applied except for those two. A negative tail for dK0 × dπ

0 at cos(θpointing) → 1is clearly visible for the signal sample while it is not present at the background

29

Figure 27: Initial distributions of dK0 × dπ

0 in the cases 0 < PD0

t < 1 GeV (left)and 2 < PD0

t < 3 GeV (right), both the signal (red) and the background (blue)distributions are scaled with 100/maximum

Figure 28: Distribution of background signal and significance dK0 × dπ

0 in 2 <

PD0

t < 3 GeV after applying all other cuts, both the signal (red) and thebackground (blue) distributions are scaled with 100/maximum, the significanceis shown in black

sample.By cutting on this tail the significance in this region will increase signifi-

cantly, however the statistics drops dramatically. For Pb-Pb collisions this evenmore visible. The round shape that can be seen in figure 29 is the effect ofa cut on PK,π

t here entries are missing at the positive side of dK0 × dπ

0 and acos(θpointing)± 1 these entries are due to asymmetrical decays with a large anda small Pt.

30

Figure 29: cos(θpointing) vs dK0 xdπ

0 in the 1 < PD0

t < 2 GeV region for signal(left) and background (right) with the found (integration) cuts applied, logar-itmic z scale

The locations of the optima from the integration method are shown in table6, they are found in the region −50000 ≤ dK

0 × dπ0 < 0 µm2 with a resolution of

2000 µm2.

Cut name 1 < PD0

t < 2 2 < PD0

t < 3 3 < PD0

t < 5 5 < PD0

t < 10dK0 × dπ

0 < −40000 µm2 < −14000 µm2 < −10000 µm2 < −6000 µm2

Table 6: product of impact parameters optimum cut values found by using theintegration method

Comparision with PPR :Since the product of the impact parameters is the strongest cut it is worthwhileto investigate if the distributions in different PD0

t bins agree with the results thatare published in the PPR. By applying the cut values proposed in the PPR onthe PDC07 data sample, the PPR results as can be seen in table 7 are confirmedin the region 2 < PD0

t < 10 GeV. However for 0 < PD0

t < 1 GeV, a significantdifference is found. PPR concluded the optimum is dK

0 × dπ0 = −20000 µm2,

however when all PPR cuts are applied except for the dK0 × dπ

0 the figure 30 isobtained. From this figure can be seen that the optimum of the significance islocated around dK

0 × dπ0 = −40000 µm2 a contradiction with the PPR study.

It can be seen the optimum dK0 × dπ

0 = −40000 µm2 found by applying PPRresults on PDC07 data is significantly different then the published location. Atpresent it is not known where this difference comes from. One distinct differencebetween out study and the PPR study is the use of particle identification in theregion 1 < PD0

t < 2 this might be a partial explanation.

6.5.5 Transverse Momentum of Decay Products

D0s are heavy particles and their transverse momentum spectrum is reflectedin the transverse momentum distribution of their decay products. The combi-natorial background is dominated by low energy particles. It is convenient toapply a lower cut on the Pt to reject all low energy particles. At high PD0

t theaverage Pt of the decay products is increasing, which implies the Pt cut will be

31

Figure 30: Distribution of dK0 xdπ

0 in 2 < PD0

t < 3 GeV after applying allother cuts with values as published in the PPR, both the signal (red) and thebackground (black) distributions are scaled with 100/maximum the significanceis shown in black

Cut name 1 < PD0

t < 2 2 < PD0

t < 3 3 < PD0

t < 5 5 < PD0

t < 10dca < 300 µm < 200 µm < 200 µm < 200 µm

cos(θpointing) > 0.6 > 0.8 > 0.8 > 0.8| cos(θ∗)| < 0.8 < 0.8 < 0.8 < 0.8dK0 × dπ

0 < −20000 µm2 < −20000 µm2 < −10000 µm2 < −5000 µm2

PK,πt > 600 MeV/c > 700 MeV/c > 700 MeV/c > 700 MeV/c

|dK,π0 | < 500 µm < 500 µm < 500 µm < 500 µm

Table 7: Optimum cut values found using the iteration method as published inPPR [20]

large at large PD0

t , however this way is dependent of the path used to obtainthe significance.

From small to large PD0

t the distribution of the particle with the lowesttransverse momentum of the pair is shifting for the signal, however the back-ground that background entries are dominated by pairs with a large and a lowmomentum. Since there are a lot of low momentum particles to combine oneexpects most of the background is present at small PK,π

t . For signal there isa large probability that the lowest momentum of the pair is still large, so thatmore entries are expected at moderate PK,π

t rather than for background.The results of the 5 < PD0

t < 10 GeV are rather high, 1100 MeV/c. Thisresult is based on a statistical fluctuation therefore the location of this cut isquestionable. The optimum values to cut on in the case of PK,π

t are shownper PD0

t in table 8, they are found in the region 0 ≤ PD0

t ≤ 1.25 GeV with aresolution of 0.05 GeV by integrating from large to small values.

32

Figure 31: PK,πt distributions and significance with found cuts applied in the

case 1 < PD0

t < 2 GeV (left) and 5 < PD0

t < 10 (Right), both the signal(red) and the background (blue) distributions are scaled with 100/maximum,the significance is shown in black

Cut name 1 < PD0

t < 2 2 < PD0

t < 3 3 < PD0

t < 5 5 < PD0

t < 10PK,π

t > 650 MeV/c > 800 MeV/c > 600 MeV/c > 1100 MeV/c

Table 8: Transverse momentum cut values found by using the integrationmethod

6.5.6 Impact parameters of decay Products

The impact parameter |dK,π0 | (figure 21) is defined as absolute value of the pro-

jection of smallest distance between the extrapolated track and the primaryvertex on the transverse plane. The impact parameter distribution of the back-ground is dominated by pairs where both particles have a small impactparame-ters. At larger |dK,π

0 | pairs with large and a small impact parameter are present.The absolute value is taken, because the product of the impact parameters dealswith the signs.

Figure 32: |dK,π0 | distributions and significance with found cuts applied in 5 <

PD0

t < 10 GeV, both the signal (red) and the background (blue) distributionsare scaled with 100/maximum, the significance is shown in black

The most contributing processes are the decay of hyperons and kaons. An

33

upper cut on this quantity would reject a small part of the background. There-fore the largest value of the pair of impact parameters is included in the distri-bution. The dK

0 × dπ0 cuts away pairs with small postive and negative impact

parameters. The effect of this is that all pairs with one low impact parametersare filtered out as can be seen in figure 32. The impact parameters distributionsof signal and background become more different at larger PD0

t regions, as afirst guess one would suspect that this is therefore a strong cut, however whenapplying other cuts the effect of this one is reduced. Shifting the cut around500− 600 µm hardly changes the resulting significance.

The resulting cut values can be found in table 9, the optima are found inthe region 0 ≤ |dK,π

0 | < 1000 µm with a resolution of 40 µm

Cut name 1 < PD0

t < 2 2 < PD0

t < 3 3 < PD0

t < 5 5 < PD0

t < 10|dK,π

0 | < 720 µm < 680 µm < 800 µm < 560 µm

Table 9: impact parameter of decay products optimum cut values found byusing the integration method

34

7 Discussion/Conclusion

The goal of this study was to optimize the significance for D0 extraction atALICE by placing cuts to reject background. This has been done before, theresults were published in [20] and the original study was done in 2003 [5]. Theresults are reasonable and the proposed topological and kinematical parametersto cut on still give good results as they are used in this thesis.

The optimization algorithm developed as part of the analysis is based onmulti-dimensional integration in one direction. In this thesis it is proven to bea strong method that gives significantly better results than other methods. Theinput of the algorithm is the data from a Monte-Carlo simulation (PDC07), theoutput is a set of optimum cuts per PD0

t region that might be used on anotherMonte-Carlo simulation or experimental data.

Cut name 1 < PD0

t < 2 2 < PD0

t < 3 3 < PD0

t < 5 5 < PD0

t < 10dca < 280 µm < 320 µm < 220 µm < 200 µm

cos(θpointing) > 0.92 > 0.92 > 0.96 > 0.96| cos(θ∗)| < 0.88 < 0.56 < 0.96 < 0.72dK0 × dπ

0 < −40000 µm2 < −14000 µm2 < −10000 µm2 < −6000 µm2

PK,πt > 650 MeV/c > 800 MeV/c > 600 MeV/c > 1100 MeV/c

|dK,π0 | < 720 µm < 680 µm < 800 µm < 560 µm

Table 10: Optimum cut values per parameter found using the six-dimensionalintegration method

The algorithm calculates the signal significance as function of all possiblecut set combinations on a six-dimensional lattice. The set of cuts that givesthe largest significance within a 6% statistical error range is the result of theanalysis. The study is done in four different PD0

t bins. In table 10, the optimumset of cuts is given per PD0

t bin. After applying these set of cuts a significanceof 108±3.4 is found which is an improvement of a factor ∼ 5−6 compared withinitial statistics.

The optimum cut results as published in the PPR can be seen in table 7.The application of both the PPR cut values and the values that are found afterusing the multi-dimensional together with the initial significance result in figure33.

Table 11 summarizes the distributions from figure 33 integrated over 1 <PD0

t < 10. The multi-dimensional optimization gives an improvement in allPD0

t bins compared with the initial numbers and the PPR results.

Cuts: B/event S/event S/B Sign. Sign.Err.Initial 1.47× 10−1 1.89× 10−4 1.28× 10−3 16 0.06PPR 2.19× 10−4 2.31× 10−5 1.1× 10−1 47 0.8OPT 7.10× 10−6 1.65× 10−5 2.3 108 3.4

Table 11: results after applying no cuts, PPR cuts and OPT cuts for 109 ppevents

To continue we focus on the uncertainties and statistical errors of the multi-dimensional integration analysis. There are four ceveats that turned up in the

35

Figure 33: Significance for the cases: no cuts, PPR cuts and OPT cuts asfunction of PD0

t

study that might affect the results.

• Large detector inefficiency during the data simulation: The backgroundsimulation sample that is used in this study has an unrealistic amount ofdetector parts turned off, while these detector parts are used in the signalsample. The result of this is a ∼ 35% decrease of the efficiency of thebackground. This reduces the background by a factor ∼ 2 resulting in a∼ 10% higher significance integrated over PD0

t . The signal sample alsohas some parts turned off, resulting in an error of ∼ 1%. The origin ofboth inefficiencies is unknown.

• Bad treatment of non-reconstructed primary vertices: For the backgroundused in this study the primary vertex is reconstructed in most of thecases. In approximately 7% of the events the primary vertex was notreconstructed and automatically set at the origin. Most of the pairs com-ing from such an event do not pass the cuts, due to the resulting largeimpactparameters of the tracks. It is shown that the distribution of theproduct of the impact parameters is hardly changed by this effect (see fig-ure 15), therefore it is expected that cut values in general are not affected.However the amount of background events used in this case is in fact 7%smaller resulting in a systematical error in the significance of rougly 2%.

• For 5 < PD0

t < 10 GeV the cut location of dK0 × dπ

0 is well known becauseof reasonable statistics. By cutting on this parameter most of the pairsare cut away resulting in poor statistics for determining the optima ofthe other cut parameters. Since the invariant mass window is by approx-imation uncorrelated with the cut parameters, the statistics is artificiallyenlarged by using a larger mass window. The effect of this approximationis expected to be small. After applying this method the statistics it isstill poor for high PD0

t bins. Therefore this study needs to be verified by

36

using s statistically independent simulaion which was not available for thisstudy.

• During the analysis a number of particles is measured for each possible cutcombination. For each combination the significance and its uncertainty iscalculated and compared with the all other cut combinations to find anoptimum. However all significances and its uncertainties are correlated,so that a proper comparison cannot be made. In this study it is expectedthat the effects of this structural problem are small, but still the resultsneed to be verified on a independent data sample.

Figure 34: Initial mass distribution (left) and the mass distribution after ap-plying the found cuts integrated over 2 < PD0

t < 10 GeV with the contributionof the background (black) and the signal constribution (red)

Although the systematical uncertainties play an important role in the anal-ysis, it is still believed that the results are reliable within uncertainty of 20%.As a conclusion the multi-dimensional integration algorithm gives a significanceof ∼ 90 − 110 with the systemical errors taken into account with respect tothe initial data. This method in combination with PID is expected to be evenmore efficient. Therefore it is worthwhile to repeat this analysis with PID inaddition. As a summary of the results the mass distributions integrated over2 < PD0

t < 10 GeV are shown in figure 34 for the cases no cuts and with thefound optimum cuts.

37

8 Acknowledgements

Allereerst wil ik mijn supervisors Rene Kamermans en Marco van Leeuwenbedanken voor het voeren van de vele verhelderende discussies die leidden tothet uiteindelijke resultaat in de vorm van deze scriptie. De personen die medehebben bijgedragen aan het resultaat zijn mede-master student Marta Verweijdie met haar betweterige gedrag, zonder dat ik erom vroeg, mij menigmaalbehoed heeft voor programmeerfoutjes. Jurriaan Biesheuvel die als prijs voorzijn afhaken nog veel meer flessen rose moet betalen dan ik hem ooit schuldiggeweest ben. Cristian Ivan, thanks for being my discussion partner, goodluckwith finishing your PHD thesis and do not forget to put this thesis in yourbibliography and my name in the acknowledgements and uhm.. good luck withyour PHD and exchange-student fishes, I hope they will survive next week.Marek Chojnacki for drinking beers and Polish wodka, good luck in the future!

Thomas Peitzmann voor het geven van de mogelijkheid om een summer-school te volgen bij CERN en het verstrekken van een Duitse referentie voormijn bronnenlijst. De technici Ton van den Brink, Arie de Haas en Kees Os-kamp voor het mee knutselen aan de ALICE detector en het weten van degezellige en goede restaurantjes rond CERN Site Prevessin. De rest van devakgroep voor het lunchen en de koffiepauzes.

Gerard Smit voor de vele kansloze gesprekken en voor de koffiekwartiertjesdie al snel uren werden. Rob van Rooij voor het feit dat ie het 6 jaar heeftuitgehouden als mijn huisgenoot en het lenen van zijn boeken zodat die van mijmooi bleven.

Femke Smits voor de steun als ik het niet meer zag zitten en voor het kokentijdens de avonden dat ik tot diep in de nacht aan het studeren was. Mijn oudersdie door middel van financiele en emotionele steun ervoor gezorgd hebben datik deze studie kon voltooien en mijn beide zussen met aanhang die geaccepteerdhebben dat ik nooit tijd had om te bellen hoe het met ze ging, terwijl ik hetmezelf wel afvroeg...

38

References

[1] ALICE Collaboration et al., technical proposal ALICE, CERN/LHCC(1995).

[2] D.Griffiths, Introduction to Elementary Particles, Wiley-VCH (2004).

[3] B. Povh, K.Rith, C.Scholtz, F.Zetsche, Teilchen und Kerne, Springer-Verlag (1997).

[4] N.Werner, arXiv:hep-ex/0305109 (2003).

[5] A.Dainese arXiv:nucl-ex/0311004v2 (2003).

[6] H.L. Lai, arXiv:hep-ph/9606399v2 (1996).

[7] L.N.Lipatov, ref Sov.J.Nucl.Phys 23 338 (1976).

[8] G.Altarelli and G. Parisi Nucl. Phys. B 126 (1977).

[9] L.McLerran, Lect.Notes Phys. 583, 291-334 (2002).

[10] E.lanchu, R.Venugopalan, arXiv:hep-ph/0303204v3 (2003).

[11] L.McLerran, arXiv:hep-ph/0104285v2, (2001).

[12] T. Sjosstrand et al. arXiv:hep-ph/0010017, (2000).

[13] H.U. Bengtsson, T. Sjostrand.,Comp. Phys. Comm. 46, 43 (1987).

[14] G. Marchesini et al.Comp. Phys. Comm. 67, 465 (1992).

[15] Pierce et al., Nucl. Phys. B491, 3 (1997).

[16] E.Levin, J. Phys.: Conf. Ser. 5 127-147 (2005).

[17] B. Zhang et al., arXiv:nucl-th/07091684v2, (2007).

[18] M. Gyulassy and M. Plumer, Phys.Lett. B243, 432 (1990).

[19] M.H. Thoma, Quark Gluon Plasma 2 (1995).

[20] ALICE Collaboration et al., Physics Performance Report Volume 2 (2006).

[21] R.J.Glauber and G.Matthiae, Nucl. Phys. B21, 135 (1970).

[22] P.Kuijer, Nucl. Instrum. Meth. A530, 28-32 (2004).

[23] ALICE Collaboration et al., Technical Design Report ITS, CERN/LHCC(1999).

[24] A.Dainese, Eur.Phys.J. C33, 495-503 (2004).

[25] Y.L.Dokshitzer and D.E.Kharzeev, Phys. Lett. B519, 199-206 (2001).

[26] H.van Hees and R. Rapp, Phys. Rev. C 71, 034907 (2005).

[27] E. Simili, PHD Thesis, (2008)

[28] ALICE Collaboration et al., Technical design report TPC, CERN/LHCC(2001).

[29] MonaLisa Alice Grid Monitoring System, http://pcalimonitor.cern.ch

39