The Higgs boson. Jennifer Arnesson. SA104X Degree Project in Engineering Physics, First level. Supervisor: Jonas Strandberg

Transcription

1 The Higgs boson Jennifer Arnesson SA104X Degree Project in Engineering Physics, First level Supervisor: Jonas Strandberg Department of Physics School of Engineering Sciences Royal Institute of Technology (KTH) Stockholm, Sweden, 2012 TRITA-FYS-2012;43

2 Abstract In this essay the standard model of particle physics and the Higgs boson are discussed. It also contains information about CERN, the particle accelerator LHC and the ATLAS detector, all used in the search for the Higgs boson. Results on the Higgs boson searches from ATLAS are presented using three different data volumes at different times during These results will also be simplified by plots showing the excluded masses from the Higgs boson searches. The results are also used for searching for a dependency between different results and datasets and to use that to extrapolate to what we can expect to see this year. It is found that the dependency is linear with the size of the dataset and fits very well to the data points. By this linear fit a prediction of the needed luminosity for the exclusion of the Higgs mass GeV has been made.

3 Contents 1 Introduction Background Scope Objective Theory The standard model Quarks and leptons The forces Gauge bosons and the weak interaction The Higgs boson The Higgs boson Finding the Higgs boson Cross section Branching ratio CERN Background LHC ATLAS How to find particles Latest results Methods Methods Results and Discussion Results and Discussion Summary and Conclusion Summary and Conclusion Bibliography... 22

4 1 Introduction 1.1 Background In the 1960s, physicists realized that two of the fundamental forces, the electromagnetic and the weak interaction, are the same force at high energies. This is part of the foundation of the standard model, but to make it work mathematically all particles which mediate forces have to be massless. From experiments it is well known that they are not. To solve this dilemma the Higgs mechanism was introduced. The Higgs mechanism describes how all particles get their mass and the theory also solves the mathematical problems of the standard model. It also predicts a new particle, called the Higgs boson. The problem is that the Higgs boson never has been found, which means that the theory has not been verified experimentally. As the Large Hadron Collider, LHC, at the European Organization for Nuclear Research, CERN, was taken in operation 2009 the final search for the Higgs boson began. The mass of the Higgs boson is unknown, but is estimated to be GeV. In order to prove the existence of the Higgs bosons all these masses has to be studied. Some of the masses were excluded using earlier accelerators, both at CERN and in the US. These early accelerators were too small to create energies needed for the creation of Higgs bosons at higher masses. LHC is more powerful and during last year there have been major improvements regarding the search for the Higgs boson. Last year, 2011, three results with increasing datasets were presented from LHC and the ATLAS detector. Many possible Higgs masses were able to be excluded. One possible Higgs mass in particular has shown to be interesting, the mass of GeV. It is likely that this is the mass of the Higgs boson, but further investigations are needed. It is very possible that we during this year will find out if the Higgs boson exists or not [1]. 1.2 Scope This project will include the results from last year from the ATLAS detector at CERN, published in August, September and December 2011 [2][3][4]. 1.3 Objective The purpose of this project is to clearly present which Higgs masses has been excluded from the search for the Higgs particle. Also a dependency between the results and the different datasets used in the search will be looked for. Hopefully this will make an estimation of which dataset is needed to exclude specific Higgs masses possible. 1

5 2 Theory 2.1The standard model In the standard model of particle physics, particles are divided into three different groups; leptons and quarks which are fermions with spin- and gauge bosons which are spin- particles that mediate the forces in nature. Excluding gravity, the standard model explains how these three groups of particles interact and what attributes they have Quarks and leptons Quarks and leptons are the elementary particles that build up matter. This means that they are the smallest building blocks that have been discovered so far. There exist six different types of quarks, called different flavors, which are divided into three generations depending on how they occur in pairs, see table 1. The generations have similar properties but increasing mass. In contrast to the quarks in the first generation, which are stable, quarks in the second and third generation are heavier and are therefore unstable and decay. First Second Third up charmed bottom down strange top Table 1: The three generations with belonging quarks All generations consist of one quark with charge and one with the charge. All quarks have antiquarks with the same attributes except the charge, which for antiquarks have the same absolute value but opposite sign. In addition to the mentioned properties in table 2 quarks have one further attribute, color, either red, green or blue. The color is the charge of the strong force, which only affects colored particles. Quarks cannot be found alone, as the strong force behaves in a way which makes it impossible to have free colored particles. The quarks can however be found forming composite particles which are colorless. Name Symbol Charge Generation Mass Down First Up First Strange Second Charmed Second Bottom Third Top Third Table 2: The six different quarks and their attributes, the charge in units of e and the approximate masses in GeV/c². 2

6 Figure 1: A neutron consist of two down quarks and one up quark [5] Figure 2: A proton consist of two up quarks and one down quark [6] As shown in figure 1 and figure 2 both protons and neutrons consist of quarks from the first generation. The only differences between the two are that the proton consists of two up quarks and one down quark while the neutron consists of two down quarks and one up quark. This means that the total electric charge for the proton is e and for the neutron e. Particles which are made up by three quarks, like the neutron and the proton, are called baryons. The three quarks that form a baryon have different colors which result in that the baryon becomes colorless or white. Mesons are particles that consist of one quark and one antiquark. Antiquarks have the colors antigreen, antiblue or antired. A meson is like a baryon colorless or white, as it consist of one quark and one antiquark with opposite colors. However mesons are unstable [7]. The other group of fermions in the standard model is leptons. There are six different leptons that are known today, the best known is the electron. Like the quarks they occur in pairs of two and the pairs are again called generations, see table 3. As for quarks, the properties are similar for all generations but the masses increase with every generation. In a pair, one lepton is charged and the other one is neutral. First Second Third electron neutrino mu-neutrino tau-neutrino electron muon tauon Table 3: The three generations at its leptons Leptons have antiparticles called antileptons, the difference between them is the sign of the charge. As shown in table 4 the electron, muon and tauon are charged while the other three leptons are neutral. The neutral leptons (, and ) have very small masses, approximately zero [7][8]. 3

7 Name Symbol Charge Generation Mass Electron neutrino First Electron First Mu-neutrino Second Muon Second Tau-neutrino Third Tauon Third Table 4: The six different leptons, their symbol and charges in units of e Figure 3: An illustration of the standard model and the three generations, these are approximate masses [9] Figure 3 illustrates the standard model. It includes the six quarks and the six leptons where the three first columns in the figure represent the three generations. The fourth column includes the four gauge bosons,, and. The bosons are mediating different forces, discussed further in section below. 4

8 2.1.2 The forces There are three fundamental forces in nature that we know of; gravity, the electroweak and the strong interactions. Often four fundamental forces are mentioned, where the electroweak is separated into two; the electromagnetic and the weak interaction. However the electromagnetic force and the weak interaction have been shown to be the same force at high energies. Gravity is not included in the standard model and will therefore not be discussed further. Gauge bosons are spin- particles which act as carriers of the different forces. The photons mediate the electromagnetic force and the bosons, and are carriers of the weak interaction. As the notation of the bosons reveal, the -boson is neutral while the -boson can be either positively or negatively charged. The gluon is the force carrier for the strong interaction and like the photon the gluon is massless. The strong force binds the quarks, by color, into larger particles like protons and neutrons. The gluon itself has color which means it can interact with itself in contrast to the photon and the electromagnetic force as the photon not is electrically charged. The reason for the more complex properties of the strong force is that the gluon has color [7][10] Gauge bosons and the weak interaction The weak interaction can turn quarks and leptons into other types of quarks and leptons. In general the interactions have these restrictions; 1. When leptons interact, the total number of leptons must be conserved within each generation. 2. During quark interaction, the total number of quarks from any generation must be the same before and after (quarks minus antiquarks). 3. The interaction must be physically possible regarding mass and energy. A lighter particle cannot turn into a heavier, unless energy is supplied. Only and can transform quarks or leptons, never the boson. The total charge has to be preserved through the interaction [7]. 5

9 Figure 4: Feynman diagram of a quark interaction where a proton decays into a neutron. The number of quarks is the same before and after the interaction. In figure 4 can we see a proton transform to a neutron and a boson via the weak force. The boson then decays into a positron and an electron neutrino. Important to notice is that the charge is the same before and after the transformation. Also the number of quarks and leptons are preserved through the transformation, one quark in the beginning and end and zero leptons at the beginning and zero at the end because the positron and an electron neutrino cancel each other out. Figure 5: Feynman diagram of lepton interaction where the generation is conserved as the tauon partly decays into a tau-neutrino 6

10 When a lepton transform it always decays to a neutrino in the same generation and a boson. The boson can decay to lighter leptons or to quarks from the first generation, this is illustrated in figure The Higgs boson The Higgs boson Naively, for the standard model to be accurate the bosons, and have to be massless. The photon is in fact masless but the and bosons are heavy particles with the masses: and To give the bosons their masses and not to spoil predictability of the theory the Higgs mechanism is introduced. The Higgs mechanism itself introduces a field called the Higgs field. This field has two complex components and thus four degrees of freedom. By mixing with the Higgs field, the bosons and get their masses. They each absorb one of the degrees of freedom from the Higgs field. This leaves one degree of freedom for the field which manifests itself as the spin- Higgs boson. Finding the Higgs boson by experiments would prove that the Higgs mechanism is true and the correct theory of how the bosons get their mass. The fermions are also required to be massless in the naive version of the standard model, but they can also be shown to acquire mass through the interaction with the Higgs field via the Higgs boson. The stronger interaction between the particles and the Higgs boson, the more mass the particles get. The mass is proportional to the interaction strength. When including the Higgs boson in calculations, the solutions to equations gives reasonable results and does not result in unphysicalities such as probabilities larger than one. This is a good indicator that the Higgs boson in fact does exist, though today we do not have any experimental proof of its existence [7][10] Finding the Higgs boson To experimentally prove the existence of the Higgs boson, we first have to know what to look for. The attributes and the behavior of the Higgs boson are well known from the standard model; only the Higgs bosons mass is unknown and is a free parameter of the theory. This means every possible mass has to be tested against the data and excluded if no evidence exists. First the Higgs boson has to be created, this is discussed further in section The Higgs boson is an unstable particle and decays rapidly, making it impossible to see or measure directly. Instead the decay products from it have to be detected, for further discussion of the Higgs boson decay see section

11 The number of Higgs bosons that are created,, is given by the equation is the probability to create the particle. is the luminosity, which is the size of the dataset i.e. a measurement of the number of collisions that take place. Where m². The number of Higgs boson that are detectable,, is given by the equation: is the efficiency of the detector and the analysis selectors for identifying a Higgs event. is the branching ratio of the particular decay of the Higgs boson that is studied Cross section By colliding two protons, a number of reactions can take place that result in the creation of Higgs bosons (if the theory of the Higgs boson is correct). In figure 6 the possible production mechanisms are shown. Here stands for gluon, for quark (the,, or quark), for the bottom quark, for the top quark, for the boson, for the boson and is the Higgs particle. At high energies, the proton includes all of these particles, most of them as virtual particles. The probability of which reaction will take place change depending on the mass of the Higgs boson, the x-axis in figure 6. is actually a cross section for the collision between protons, but here it can be interpreted as the probability for a certain reaction to take place. For example, if the Higgs boson is light the reaction where two quarks transforms into one boson and one Higgs boson is more likely to occur than it would be if the Higgs boson was heavy. However the reaction where two gluons becomes one Higgs boson is the most probable for all Higgs masses [11]. 8

12 Figure 6: The different reactions for creating a Higgs boson that can take place by colliding two protons, the probability differs depending on the mass of the Higgs boson [12] Branching ratio A Higgs boson is not a stable particle, it decays rapidly. Therefore the actual Higgs boson cannot be detected, instead its decay products are searched for. In figure 7 the possible decays of a Higgs boson are illustrated. The branching ratio, the y-axis, is the probability that a certain decay will occur. What decay is most probable differs depending on the mass of the Higgs boson. For a light Higgs boson the most likely decay is a bottom quark and an anti-bottom quark, while a massive Higgs boson is most likely to decay into two bosons [13]. 9

13 Figure 7: The probabilities of different decay modes of the Higgs boson at different masses [14] In the search for the Higgs boson different hypothetical masses are tested in order to find it. As mentioned, the behavior of the Higgs boson such as how it decays for certain masses is well known. For every mass tested the mass can either be exclude or tested further. For example: When trying to find the Higgs boson different hypothetical masses are tested. If for example the hypothetical mass of GeV is tested, its most probable decay is illustrated in figure 7. In this case the most probable decay products for the Higgs boson will be two bosons. When colliding proton beams at LHC Higgs bosons are created. It is then possible to study the number of bosons pairs that are found. Thereafter, that number of events is compared to 1. The number of bosons pairs expected if the Higgs boson does not exists at this mass, this is what is called the number of background events. 2. The number of bosons pairs that would be created if the Higgs boson does exist at this mass, events from both background and signal. If the experimental data is very similar to point 1 above, then it is likely that the Higgs boson does not have the investigated mass. To be able to exclude the mass of GeV it has to have a confidence level 10

14 (C.L.) of 95%, which means that it is 5% chance or less that the Higgs boson exist at that mass. If the confidence level is smaller than 95% the mass cannot be excluded. By excluding masses with confidence level of 95% the search after the Higgs boson can be narrowed to a smaller range of possible masses. If the decays instead are similar or close to point 2 in the example above, the mass has to be investigated further [13]. 3 CERN 3.1 Background CERN is the largest physics laboratory in the world, that focuses on particle physics. It was founded in 1954 and is located in Switzerland and spans over the border to France. At CERN, particle accelerators and detectors are used to study particles and attempts to create those wanted to study more closely, like the Higgs boson [15] LHC LHC is a circular particle accelerator with a circumference of meter and located meters underground. Two beams containing either protons or lead ions are traveling through the accelerator in opposite directions. At full power the particles can travel at speed of light. The maximum energy for a traveling proton is TeV which gives an energy of TeV if two protons collide. For all current data the energies of each beam is TeV and this gives a total energy of TeV when to particles collide. LHC is the largest accelerator in the world and its main components are the magnets. Some of the magnets are used to bend the beams so they travel in a circular orbit through the accelerator. Others are used to squeeze the beams together and make them collide at four specific locations. These locations are where the four different detectors ATLAS, CMS, ALICE and LHCb are placed [16][17][18] ATLAS One of the detectors at CERN is ATLAS. It is a general-purpose detector which means it will be used to investigate a broad spectrum of particle physics, including attempts to find the Higgs boson. It is meters long, meters high, meters wide and weighs tonnes. It is the largest detector ever built. The ATLAS detector mainly consists of four components; the inner detector, the calorimeter, the muon spectrum and the magnet system. The energies carried by both charged and neutral particles are measured by the calorimeter, the yellow part in figure 8. Muons cannot be stopped and are the only detectable particles that pass through all calorimeter absorbers, nevertheless they can be detected by the muon spectrum that surrounds the calorimeter. The magnets in the magnet system are used to bend the charged particles so measurements of the momentum can be done. 11

15 Figure 8: The ATLAS detector [19] The inner detector is the grey part in the middle of figure 8 and is shown in greater detail in figure 9. It has three sections, the pixel detector, the semiconductor tracker (SCT) and the transition radiation tracker (TRT). The pixel detector takes measurement as close to the interactions points as possible. It makes it possible to detect short lived particles, like B-Hadrons. Momentum, impact parameter and vertex position are further measured by the SCT system. In the barrel SCT, coordinates are given from eight layers of silicon microstrip detectors. TRT can detect whether a particles passing through it by ionization of the gas inside the straw tubes [20][21]. Figure 9: The inner detector in ATLAS [22] 12

16 3.1.3 How to find particles To be able to track particles and to determine what type of particles they are, particles are forced to pass through four layers of materials which slows them down and finally stops them (except muons). In the first layer, called the tracking chambers, all charged particles leave a trace. In the electromagnetic calorimeter, the second layer, the photons and the electrons/positrons are stopped. It is possible to separate these particles from each other as the electron leaves a trace in the first layer in contrast to the photon. In the third layer, the hadron colorimeter, all hadrons (particles that consist of quarks) are stopped. Here, particles can also be separated by looking at the previous layers. The neutron leaves its first trace in the hadron calorimeter while the charged hadron leaves traces in all previous layers. The only visible particles reaching the muon chamber are the muons. Figure 10: A simple figure showing the different layers that are used to track the particles [23] 3.2 Latest results When searching for the Higgs boson, the best way to search for the particle is not always to search for its most probable decay products. This because those decay products can be very hard to separate from the background. Instead less probable decay products are searched for as it is easier to detect and differentiate from the background. One example of such a reaction is when the Higgs boson decays into two photons. The other main detection modes are: In figure 11 to figure 13 the results from three different dates during 2011 from ATLAS are shown. The figures show the expected and observed limits on the Higgs cross section. The difference between the measurements from the different months is the size of the dataset used i.e. luminosity. In the results 13

17 from August a luminosity of is used, in September and in December. These plots are hard to interpret and will therefore be simplified in this essay. The limit,the y-axis, is the limit on the production rate divided by the predicted production rate from the standard model, as a function of the Higgs boson mass. When, the mass can be excluded. This means that the observed is less than or the same as the expected from the standard model,, which means that the mass can be excluded as there is no unexpected events. If the ratio instead is larger than one, more data is needed to be able to conclude whether the Higgs boson exist at this mass or not. This could also be an indicator of the Higgs boson, which means these masses cannot be excluded. In figure 13, data from December 2011, a significant peak is shown around GeV see the right hand plot in figure 13, where the ratio. It is possible this is the mass of the Higgs boson, for now at least it is the most interesting point to study further [2][3][4]. Figure 11: Results from August 2011, in the graph to the right the most interesting Higgs masses [2] 14

18 Figure 12: Results from September 2011, in the graph to the right the most interesting Higgs masses [3] Figure 13: Results from September 2011, in the graph to the right the most interesting Higgs masses [4] 4 Methods 4.1 Methods The numerical computing program matlab will be used to illustrate which Higgs bosons masses have been excluded from the search. The program will also be used when searching for a dependency between the results at different luminosities. The data is given by CERN [2][3][4]. For some specific masses the expected limit on from the three ATLAS results, see section 3.2, will be used. For these three results the luminosity has changed from to and finally to 15

19 . This gives three limits at different luminosities. By plotting these limits as a function of the luminosity hopefully a simple dependence will be found. This will be done by using the function polyfit in matlab, which uses the least square method. By finding the dependency it would be probable to anticipate at which luminosity it would be possible to exclude specific masses. The masses this will be done for are,,,, and GeV. As the latest results from ATLAS indicates that the Higgs mass could be around GeV, the masses, and GeV are chosen. GeV is interesting as this mass is the hardest to exclude from the search, theoretically. If a luminosity needed for excluding this mass could be estimated, it would be possible to predict how soon not only this mass, but all masses could be excluded. The significance of a result is proportional to where is the number of signal events and is the number of background events. By doubling the amount of data, the signal and the background doubles and we get that This would indicate that when plotting the dependence between the luminosity and the limit we would expect to get a square root relationship. However this assumption can only be made when both and are large. If the background is very small we instead get that Which of these relationships that is most accurate is hard to predict. The plots regarding the excluded Higgs masses need to be simple and easy to understand, a thick line will illustrate the excluded masses and the still possible masses will be shown with a small discreet line. Three different plots will show each of the three latest results from ATLAS. This will illustrate the enormous progress done just during Results and Discussion 5.1 Results and Discussion In figure 14 to figure 16, each of the graphs represents a specific Higgs mass, three data points are plotted. These points represent the theoretical limits at the three different dataset sizes. A line was fitted to these data points. In contrast to what could be expected a linear dependence was found. This can have several explanations. The search channels with the relationship can be of more significance than those with. In addition, the analysis of the data and the technical aspects of the measurements have been improved during the year which leads to a steeper relation. Conclusions can be drawn regarding at what luminosity the mass GeV will be able to be excluded from the search. That is when the fitted line takes the value one, this will occur at a luminosity of 16

20 approximately, derived from figure 14. After this summer LHC is expected to have a luminosity at. As the mass GeV is theoretically the hardest Higgs mass to exclude, this result does not only say the exclusion of this mass is near, but all. This is if the Higgs boson does not exist. Figure 14: Limit on the expected at three different times with increasing large datasets, for the Higgs masses GeV to the left and GeV to the right Figure 15: Limit on the expected at three different times with increasing large datasets, for the Higgs masses GeV to the left and GeV to the right. 17

21 Figure16: Limit on the expected at three different times with increasing large datasets, for the Higgs masses GeV In figure 17 not only the fitted line and the theoretical limits are found, but also the three observed limits. For this mass the fitted line is very accurate. The expected limit for the dataset size already has a value under one, this means that the mass should already have been excluded. However the mass is not excluded yet, as the observed limits differs a lot from the expected. This means that more reactions than expected are occurring at this mass, it indicates that this could be the Higgs boson s mass. 18

22 Figure 17: Limit on both the expected and observed at three different times with increasing large datasets, for the Higgs mass GeV In figure 18the results from August 2011 are shown in my own representation. The wide lines represent the excluded masses, both the expected and the observed results are used. Figure 19 and figure 20 are constructed in the same way. The figures show the progress done during a few months and as shown in figure 20 there are not many possible masses left. The masses that are not excluded yet, in the gap in figure 20, are GeV and the masses between GeV. Also masses over GeV are not yet excluded, but Higgs masses this heavy are not likely. Therefore the most interesting masses for the moment are around GeV. This is because the abnormalities found around this mass, both shown in section 3.2 and figure 17. Given the expected increase of the dataset in 2012, there are two possible scenarios of what can happened: All masses will be excluded, thereby discarding the theory of the Higgs mechanism. The Higgs boson will be found around the mass GeV. If the Higgs boson does not exist, all masses can probably be excluded by this summer. Actually proving the existence of the Higgs boson is a lot harder than excluding masses. It will probably be known if the Higgs boson does exist by the end of this year. 19

23 Figure 18: Excluded Higgs masses in August 2011 Figure 19: Excluded Higgs masses in September

24 Figure 20: Excluded Higgs masses in December Summary and Conclusion 6.1 Summary and Conclusion In this project the standard model and the Higgs boson have been studied. The latest results from ATLAS are presented and the data is used to find dependency between the luminosities used in the search for the Higgs boson and the expected limits on. It is found that the dependency is linear and fits very well to the data points. By this linear fit a prediction of the needed luminosity for the exclusion of the Higgs mass GeV has been made. Plots have been made in order to clarify what Higgs masses still are possible and what masses have been excluded. These plots show the progress of the exclusion of masses done last year. It also shows the few remaining possible masses. During this year it will be known if the theory of the Higgs mechanism is correct. If the theory is correct a new particle will be found and an old theory will be verified. However if the theory is incorrect a new theory has to be presented. In any case this will be an interesting year. 21

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