Initial sensitivity studies of a dark matter-inspired SUSY model at the LHC

University of Amsterdam

NIKHEF

Bachelorthesis in physics, July 10th

2015

Initial sensitivity studies of a dark

matter-inspired SUSY model at the

LHC

1

A B S T R A C T

A γ-ray excess is found to be coming from the galactic center, possi-bly caused by annihilating dark matter particles. Dark matter parti-cles are included in the supersymmetric (SUSY) extension of the Stan-dard Model (SM) of which a basic explanation is included in the text. Calculations on the excess have infused SUSY with new information by significantly limiting the size of its parameter space. This research illuminates the effects of three combinations of parameters on our chance of observing these SUSY models at the Large Hadron Collider (LHC). This is done using only computer simulations of SUSY and Standard Model proton-proton collisions at an energy of √s=13 TeV. In these simulations, all squark and gluino masses are assumed too heavy to be produced. The discriminating collision variables looked at are Missing Transverse Energy, Transverse Mass and lepton flavour. It is found that for one combination of parameters, detection should be possible, while for the other two detection is less sure when using the cuts discussed. Finally a less detailed analysis of possible final states of models with lighter squarks as well as models with lighter gluinos is done. It is found that lighter squarks have the potential of improving the signal, while lighter gluinos do probably not.

Uit het centrum van onze Melkweg komen meer fotonen (licht) dan je zou verwachten op basis van de compositie. Dit zou kunnen komen door donkere materie deeltjes die annihileren en daarbij foto-nen uitzenden. Een theorie genaamd Supersymmetrie (SUSY) verk-laart het bestaan van donkere materie en kan in sommige modellen deze annihilatie beschrijven. Deze theorie zegt dat er voor alle tot nu toe bekende deeltjes in het Standaard Model (SM) een ’superpartner’ bestaat: een deeltje met grotendeels dezelfde eigenschappen maar met een andere massa. De parameters (voornamelijk massa’s en zgn. mixing angles) van SUSY zijn echter allemaal onbekend. Onderzoek-ers hebben bepaalde combinaties van parametOnderzoek-ers bedacht die voor een foton overschot met dezelfde eigenschappen zouden kunnen zor-gen. Dit onderzoek neemt een aantal van die combinaties en kijkt door middel van computer simulaties of het mogelijk zou zijn sporen van SUSY te vinden in de deeltjesversneller in Genève, mocht SUSY echt onderdeel van onze werkelijkheid zijn. De uitkomst is dat som-mige combinaties een grote kans op detectie hebben, terwijl andere moeilijker te detecteren zullen zijn.

C O N T E N T S 1 a b s t r a c t 2

2 i n t r o d u c t i o n 4

3 t h e o r y 5

3.1 The Minimal Supersymmetric Standard Model 5 3.2 Structure of the MSSM 5

3.3 Supersymmetry breaking and the LSP 6

3.4 The Phenomenological MSSM 6

4 m e t h o d 8

4.1 The LHC and the ATLAS detector 8 4.2 Collision variables 8

4.2.1 Missing Transverse Energy 8 4.2.2 Transverse Mass 10 4.3 Simulation 10 4.4 First Analysis 11 4.4.1 Masses 11 4.4.2 Crossections 11 4.4.3 Branching ratios 13 4.4.4 Generated ROOT-files 14 4.5 Background 14 4.6 Cuts 16 5 l i g h t e r s q ua r k s a n d g l u i n o s 19 5.1 Lighter squarks 19 5.2 Lighter gluinos 21 6 c o n c l u s i o n 22 6.1 Conclusion 22 6.2 Discussion 22

2

I N T R O D U C T I O N

With the discovery of the long awaited Higgs-boson, the Standard Model (SM) of particle physics has been completed. While the succes of the SM should not be underestimated, it still lacks some crucial qualities to convince us its completion is not the end of our search after a full, all-describing theory of particle physics. These qualities include an explanation of dark matter, gravity, massive neutrinos and the lack of naturalness, as explained later on.

In the search of physics beyond the SM, the theory of supersymme-try (SUSY) [1] has emerged. It gives a new understanding of particle physics that is able to explain some of the mentioned phenonema that the SM leaves untouched, namely dark matter and naturalness, while also promising a unification of all gauge couplings at higher energies, creating a pathway to the Grand Unified Theory. The theory of SUSY is not a new one, with the general ideas being mostly developed in the 1970’s already. However, it does not predict the values of any param-eters included (mostly masses and mixing angles), making the search for signs of SUSY difficult, as no one knows where to look. A pos-sibly valuable hint to resolve this issue is coming from a surprising corner: Astrophysicists have measured a γ ray excess coming from the center of our own galaxy [2]. Although not surely, this excess is proposed to find its origin in the annihilation of dark matter particles. As dark matter particles are an intrinsic part of many SUSY models, it follows logically to look closer into the consequences these findings have for SUSY. Using calculations on the excess, researchers have set boundaries on some of the parameters of a particular model called the phenomenological Minimal SuperSymmetric Standard Model [3]. In this analysis, I will take a closer look at the range of possible pa-rameter combinations and the chance of finding signs of these SUSY forms in future measurements in detectors of the Large Hadron Col-lider (LHC) during its second run at a √s=13 TeV center of mass energy.

3

T H E O R Y

3.1 t h e m i n i m a l s u p e r s y m m e t r i c s ta n d a r d m o d e l

Experimental data has shown that the Standard Model (SM) of par-ticle physics is not sufficient to explain all the phenonema visible in modern day physics [1]. A way of extending the SM to obtain a better model is by using the idea of Super Symmetry (SUSY). While there is more than one variation of this extension, this text will only dis-cuss the most popular one: The Minimal Supersymmetric Standard Model (MSSM). There are three main reasons to consider the MSSM as a possible extension:

1. Naturalness; the belief that fundamental parameters in physics should be of the same order of magnitude.

2. Dark matter; The lightest supersymmetric particle (more in sec-tion 3.3 is invisible to our detecsec-tion methods. This makes it a great candidate for dark matter.

3. The Grand Unified Theory (GUT); The search for one theory as a source for all gauge couplings.

3.2 s t r u c t u r e o f t h e m s s m

Just as there is an anti-partner for every particle in the SM, there is a super partner (SP) for every particle (and anti-particle) in the MSSM. SPs are denoted with a tilde (˜). However, particles that are fermionic (half-integer spin) in the SM, will have bosonic (integer spin) SPs, and vice versa. In general, when converting between SM particle and its SP, a particle becomes a sparticle, fermions become sfermions, and bosons become bosinos. More specific terminology follows in table 1:

SM particle type particle super partner

fermion quark q squark qe

lepton q slepton el

boson W-boson W wino We

B-Boson B bino Be

gluon g gluino eg

Higgs-boson H Higgsino He

Table 1: Fundamental particles of the MSSM

In the SM, Higgs symmetry-breaking mixes the W and B bosons into W±, Z and γ. Similarly in the MSSM, the wino, bino and

higgsinos mix to form two charginos (χe

±

1,χe

±

2) and four neutralinos

(χe 0 1,χe 0 2,χe 0 3,χe 0

4). Together, the neutralinos and charginos are called

gauginos.

3.3 s u p e r s y m m e t r y b r e a k i n g a n d t h e l s p

If the MSSM is a truly existing symmetry it must be a broken one, because we have not yet measured any SPs while SM particles are visible everywhere.

A concept called R-parity is included in the theory. R-parity is a conserved quantity that all particles carry. SM particles have an R-parity value of 1 and SPs a value of -1. The total R-R-parity is the prod-uct of all particles’ R-parity values in a reaction. So it is (−1)nSUSY

with nSUSY the amount of SUSY particles before or after the reaction.

This means that sparticles can only be produced from particles in pairs to conserve the total R-parity. In the same way, when only one sparticle decays on its own, another (lighter) sparticle must always stay in the decay chain. However, SM particles can still be produced during the decay. By measuring these particles it is possible to de-duce the existence of the SUSY particles they decayed from. As the symmetry is broken, we expect sparticles to decay into the Lightest Supersymmetric Particle (LSP) (which is not detectable directly as it barely interacts with anything) almost immediately. This makes the LSP a likely candidate for Dark Matter. The LSP is usually identified withχe

0 1.

3.4 t h e p h e n o m e n o l o g i c a l m s s m

As in the SM, there are three types of free parameters in the MSSM: masses, gauge coupling constants and mass eigenstate mixing angles. In total, the MSSM provides more than a hundred parameters in ad-diton to the existing SM parameters. At this time, none of these parameters have known values. It is possible to eliminate a large part of these additional parameters until there are only 19 left using 3 phe-nomonological constraints. The constraints are assumptions about the MSSM, supported by some experimental data [1]. This means assuming:

• no new sources of CP-violation

• no Flavour Changing Neutral Currents

• first and second generation sfermion universality

This version of the MSSM is called the phenomenological MSSM (pMSSM) and it is the version used for this research project. The 19 parametes of the pMSSM are as given in table 2, along with the input values I used for this project.

In this text, I assume all sfermions (squark and slepton) to be too heavy to be produced in the Large Hadron Collider (LHC). The same goes for the gluino. Because the used software needs an input value it is set at 4000 GeV, but this value is arbritrary as long as it is high enough to keep these sparticles from being produced. The remain-ing significant parameters are three bosino masses (M1, M2, µ) and

symbol description used input value

tan β ratio of the vacuum expectation values variable

of the two Higgs doublets

M1 mass of bino -110 GeV

M2 mass of wino variable

M3 mass of gluino 4000GeV

MA mass of Higgs-Boson 1000GeV

µ mass of higgsino 115GeV

m_eq, mueR, mde_R first and second generation squark masses

4000GeV m_el, m_eeR first and second generation slepton masses 4000GeV

m

e

Q, metR, meb_R third generation squark masses

4000GeV m

e

L, meτR third generation slepton masses

4000GeV At, Ab, Aτ third generation trilinear couplings 0

Table 2: 19 parameters of the pMSSM

tan β. Furthermore, because any sparticle is expected to finally leave its mark in the form of the LSP (as that is what it will decay to even-tually), the experimental focus lies on showing the existence of the LSP. Using computer simulations to try to fit the gamma ray excess from the Galactic Center to possible pMSSM parameter solutions, re-searchers have set boundaries on these parameters [3]. In these mod-els, the gamma rays are proposed to find their origin in LSPs that annihilate to form W+W− pairs. Part of these W bosons decay into π0 particles (via up and down quarks), of which most finally decay into two gamma rays [4]. Two kinds of information are then extracted from the gamma rays: their rate and their energy spectrum. Combin-ing these with measurements of dark matter density, it is possible to determine values for M1, M2, µ and tan β in the pMSSM. In this

re-search I will only look at different values for M2 and tan β, keeping

4

M E T H O D

To see if SUSY is detectable, it is necessary to simulate collisions in a model where sparticles are present and a model where they are not. These simulations are then analyzed to see if the model with sparticles stands out in any way that is detectable by the LHC. The most important collision variable that should display this difference is called the Missing Transverse Energy.

4.1 t h e l h c a n d t h e at l a s d e t e c t o r

The LHC is the worlds largest particle accelerator, consisting of a 27 km ring with two tubes in it for beams of high energetic protons to travel trough it in opposite directions. The particles are accurately guided around the ring by the magnetic field created by ultra low temperature superconducting magnets positioned around the tubes. At detector sites, the particle beams are steered to collide with ea-chother and with various kinds of measurements, it is tried to re-construct the collision process. The largest detector in the LHC is called ATLAS. The detector consists of a collection of layers around the LHC tube, with each layer having its own detection purpose. Fig-ure 1 shows a schematic drawing of the components and figFig-ure 2 shows a more detailed drawing of the ATLAS detector. Going from inner to outer layer, the first layer is a tracking chamber. It tracks the path of all charged particles. Because a magnetic field is present, charged particles (muons, electrons and charged hadrons) will have a circular deflection, with larger radii for higher momenta. The second is an electromagnetic calorimeter, able to detect and stop photons and electrons. Then comes the hadron calorimeter, detecting and stopping hadrons. Then the only measurable particles left are the muons. They have a whole detection layer for themselves (on top of the tracking chamber) and are therefore easy and sure to spot if they are created. On top of this, energy measurements on muons are more certain than on electrons. For these reasons, when searching for lep-tons without any preference for a particular flavour, it is common to look for muons only and disregard electrons (tau leptons decay into electrons or muons almost immediately).

4.2 c o l l i s i o n va r i a b l e s

4.2.1 Missing Transverse Energy

How does one detect an undetectable particle? In the LHC tube, the total component of the momentum lying in the plane perpendicular

Figure 1: Schematic drawing of a slice of the transverse plane in the ATLAS detector(from: http://atlas.ch/blog/?p=1071)

Figure 2: Detailed drawing of the ATLAS detector and its compo-nents

to the tube and to the direction of propagation (the transverse mo-mentum) should be zero at all times. After a collision, this will not be any different. In LHC-detector measurements, this momentum translates into something called Transverse Energy. If the Transverse Energy is non-zero after a collision, some particles must have escaped detection. The energy that is needed to make the total energy equate to zero is called Missing Transverse Energy or ET_miss. So to calculate the ET

miss, you have to sum the Transverse Energy vectors of all

par-ticles. The E_missT vector is this summed vector, but with an opposite sign. It should be noted that E_missT does not necessarily come from sparticles, as neutrinos are invisible to LHC detectors as well.

4.2.2 Transverse Mass

Another interesting variable to look at is the Transverse Mass MT. It is

the invariant mass, but only calculated for the transverse coordinates (x and y). When considering two particles A and B with transverse energy ET and transverse momentum pT, it is defined as:

M2_T = (E_TA+E_TB)2− (~p_TA+ ~pB_T)2

As we are looking at highly energetic particles, we can neglect both their masses (so ET = pT) and the equation can be rewritten as:

M_T2 =2(E_TAE_TB− ~pA_T · ~pB_T)

Particles A and B in this case are a lepton and an unknown parti-cle with an E_missT . SUSY events are prone to have a higher MT than

background events. This helps in differentiating them. 4.3 s i m u l at i o n

The process of simulating proton-proton collisions is as follows: Us-ing SUSY-HIT [5], I have generated SLHA [6] textfiles for three pa-rameter sets. These textfiles contain the papa-rameter spectra. M1 and

µare kept fixed at respectively 115 GeV and -110 GeV, while I have given M2 and tan β different values in each file. For each

particu-lar parameter set, I have given its SLHA file as input in a Pythia 8 script to calculate cross-sections of all possible SUSY particles result-ing from proton-proton collisions at a center of mass energy of 13 TeV. Pythia is a program to theoretically evaluate parton collisions us-ing libraries of hard (high energy) processes and models for parton showers [7]. Partons showers are cascades of radiation resulting from quarks and gluons after a collision. At the same center of mass energy, I have then done a simulation of 100.000 proton-proton collisions us-ing HERWIG++, again usus-ing the parameters from the SLHA file as input. HERWIG++ is a Monte Carlo package for simulating Hadron Emission Reactions With Interfering Gluons [8]. Its output is a ROOT file that can be analysed using the ROOT software package that uses C++. So the final results of importance are, for each parameter set: an SLHA file cointainging the parameters, a Pythia file cointaining the crossections and a ROOT-file containing the more specific collision data.

4.4 f i r s t a na ly s i s

4.4.1 Masses

The magnitude of the ET

missand thus of the SUSY signal, depends on

the mass differences between higher and lower mass sparticles as they follow their path on the decay chain towards the LSP. For this reason, any SUSY signal will be difficult to measure if the sparticle masses are all in the same range, with the LSP being only slightly lighter than the rest. On the other hand, if there are any sparticles that are much heavier than their daughters, their daughters will take a large amount of energy with them that is not seen in the LHC. As the background generally decreases with increasing energy, high E_missT events are the kind of events to look for in the search for SUSY.

Therefore, the first property of a parameter set to investigate is the distribution of its masses. The masses of interest are collected in table 3. As they are parameters and not actual physical masses, they are allowed have negative values. This is because they follow from a bino-wino-higgsino mixing matrix. Their actual physical masses however, would be positive. The same data is visualized in a more intuitive way in figure 3. In this figure, arrows between particles indicate decay possibilities, with thicker lines meaning higher branching ratios.

(M2[GeV], tan β) (300, 10) (600, 10) (600, 45) e χ0₁ −91.3 −90.5 −88.2 e χ0₂ 108.4 118.3 119.2 e χ±₁ 109.2 117.0 119.1 e χ±₂ 345.7 647.0 647.0 e χ0₃ −148.8 −147.2 −150.2 e χ0₄ 345.3 646.8 646.7

Table 3: Neutralino and chargino masses from the SLHA files in GeV As visible in figure 3, theχe

0 4andχe

±

2 have much higher masses than

the rest of the gauginos in each parameter set. Therefore the missing energy resulting from their decay into a lower-mass sparticle will be relatively high. Furthermore, the other gaugino masses are all very similar. This means that if one of them would decay into another, the SM particles from the decay would have very low energy and be hard to detect.

4.4.2 Crossections

In table 4, I have collected important cross-sections of the proton-proton collisions from the Pythia textfile. For each of the parameter sets, the largest cross-sections belong to the decays of a quark anti-quark pair to neutralinos and charginos. In the (300,10) scenario, the

e

χ0₄ andχe

±

2 crossections are still relatively large, but for the scenarios

(a) M2=300, tan β=10 0 200 400 600 800 1000 1200 Mass / Ge V h0 A0 H0 _H± ˜ χ˜0₁ χ0₂ ˜ χ0₃ ˜ χ±₁ ˜ χ0₄ χ˜±₂ (b) M2=600, tan β=10 0 200 400 600 800 1000 1200 Mass / Ge V h0 A0 H0 _H± ˜ χ˜0₁ χ˜0₂ χ0₃ ˜ χ±₁ ˜ χ0₄ χ˜±₂ (c) M2=600, tan β=45 0 200 400 600 800 1000 1200 Mass / Ge V h0 A0 H0 H± ˜ χ˜0₁ χ˜0₂ χ0₃ ˜ χ±₁ ˜ χ0₄ χ˜±₂

(M2[GeV], tan β) (300, 10) (600, 10) (600, 45) total SUSY 37.012 27.493 26.425 qq0 →χ_e+₁χe 0 2 7.724 5.242 5.003 qq0 →χ_e+₁χe − 1 6.976 4.904 4.600 qq0 →χ_e+₁χe 0 1 3.602 3.469 3.382 qq0 →χ_e−₁χe 0 2 4.869 3.273 3.119 qq0 →χ_e0₁χe 0 2 3.313 3.045 3.053 qq0 →χ_e0₄X 1.644 0.117 0.117 qq0 →χ_e±₂X 3.22 0.231 0.231

Table 4: Cross-sections in picobarn of various important SUSY decay modes in proton collisions, calculated with Pythia 8. The last entries represent the the total cross-section of decays where at least oneχe

0 4or χe

±

2 is produced, X being any by-product

The LHC is expected to deliver at least 10/fb of data in the first year of run two. This number is called the integrated luminosity L. Multiplying it with the total SUSY cross-section from table 4 you get the yearly amount of SUSY events. This means around 370.000 total events when M2=300 GeV and around 270.000 events when M2=600

GeV.

4.4.3 Branching ratios

To look for decays, it is necessary to know the end products of these decays. Each of these particles that is not the LSP (χe

0

1) will directly

or indirectly decay into it. The branching ratios of various significant decay modes are shown in table 5. From this table, SUSY-decays will in many cases involve the creation of W- and Z-bosons.

(M2[GeV], tan β) (300, 10) (600, 10) (600, 45) e χ±₁ → W±χe 0 1 100 100 100 e χ0₂ → Zχe 0 1 100 100 100 e χ0₄ → W±χe ∓ 1 59 52 52 → Zχe 0 2 15 18 16 → Zχe 0 3 10 12 15 e χ±₂ → Zχe ± 1 26 26 26 → W±χe 0 1 13 9 10 → W±χe 0 2 28 25 25 → W±χe 0 3 14 16 16

Table 5: Branching ratios of various neutralino and chargino decays in percentages, taken from the SLHA files

It is seen from table 5, that around half of theχe

0

4s that are produced

will decay into a high energy W boson and a high energy χe

±

1. The

W boson can then decay into an (anti)lepton and its neutrino or into an up-type quark and a down-type quark. Most of the rest of theχe

0 4s

produce a high energy Z-boson in their decay chain. This Z-boson can decay into a lepton anti-lepton pair or a quark anti-quark pair. A similar thing can be said about the decay ofχe

±

endproducts will have relatively high energies. To be able to reject a large part of the background, I consider only decays that involve lepton production. In practice, only muons are used to accomplish this, because they have advantages in terms of measurement (as ex-plained in section 4.1). The branching ratios of W →µνµand Z→µµ

are 10.5% and 3.4% respectively [9]. The threshold energy to detect a muon is around 20 GeV. This number will appear in the final cuts in section 4.6.

4.4.4 Generated ROOT-files

To get an idea of the ET_miss spectrum, I have first plotted a histogram of the ET

miss without any editing or scaling. This is pictured in figure

4a. As visible, all three sets peak at low energies. Because they are so low, these peaks are not interesting to us as the background will be high there. To check the viability of the previously proposed ideas about E_missT coming from χe

±

2 and χe

0

4, I have filtered the spectrum to

count only events with at least one of those two particles in it and plotted it in figure 4b. The spectum where M2=300 GeV clearly peaks

higher now, around 100 GeV. Although the sample is a bit too small to see a real peak in the spectra where M2=600, the peak appears to

be somewhere between 150 GeV and 350 GeV. Therefore, this is the energy range we are most interested in.

4.5 b a c k g r o u n d

The difficulty lies in differentiating between background (E_missT from neutrinos) and SUSY signal. To compare the two, I have studied 15 background processes using ROOT-files that should recreate all the relevant background coming from the SM. As we knew beforehand our signal would contain collisions with a high ET_missand leptons, the files are also based on these two characteristics. For practical reasons, the files were taken from another study. In this study they used a lower E_missT cut at 160 GeV, so that is also the minimum ET_miss I was able to look at.

The files can be grouped in three categories: the decay of the W-boson into leptons, the decay of the Z-W-boson into leptons and all decays of the tt pair. Because of the high mass of the top quark, tt decay products ususally have high energies. When neutrinos are included in the products (for example as pictured in figure 5), this will result in a high E_missT and thus this part of the background is expected to be largest.

To quantify the signal and background it is important to scale each signal and backround up with its cross-section (as the simulation soft-ware is set to only produce collisions of a certain kind) and also down with the size of the sample used (as a larger sample should not result in a higher event count). Multiplying this number with the integrated luminosity, one gets the yearly amount of events. So the desired scal-ing factor is:

α= σ· L N

(a) full spectrum

(b) only events containingχe

± 2 orχe

0 4

Figure 4: ET_miss spectra of three parameter sets without any scaling; y-values have only relative meaning

b

`

ν`

Figure 5: Possible decay of a top quark into a bottom quark, an an-tilepton and its neutrino

Figure 6: Histogram of the Transverse Mass of the muon and ET_missin signal and background. Applied cuts: ET

miss > 160 GeV and

exactly one muon with pT > 20 GeV

4.6 c u t s

In figure 6, I have plotted the transverse mass. To find the best cut-ting values, I have used a so called ROC curve. This is a graphical representation of the fraction of accepted signal versus the fraction of lost background. A ROC curve of the transverse mass cut can be seen in figure 7. Cutting at 80 GeV would mean a background rejection of around 90 % and a signal acceptance of around 45%. Al-though there are many ways to define the optimal cut value in a ROC curve depending on what variables you find important, these kind of curves can offer some insight. Another quantity I have looked at is the significance, defined as √ signal

background. When changing cut values of

variables, this quantity should be maximized. In this particular case I have chosen to cut at 90 GeV.

Another variable I have looked at is the momentum of the muon, as shown in figure 8. Here there seems to be no difference in signal and background signature. I have therefore not made a cut on the muon momentum, apart from the threshold cut at 20 GeV.

The cuts that I finally chose using the mentioned tools are: • ET

miss > 160 GeV. A ROC Curve of the EmissT bends to the

down-left corner. This means it would probably be better to cut at a lower value, but as my background starts at 160 GeV, this is the minimum possible cut.

• Exactly one muon with pT > 20 GeV (threshold to detect a

muon). I noticed an increase in significance when allowing only events with exactly one muon and no more, so I made it a cut. • MT >90 GeV of the muon and the E_missT .

A cutflow showing the effects different cuts have on the amount of signal and background events, is shown in table 6. This gives an idea

Figure 7: ROC Curve of the susy (300,10) signal and background in figure 6.

Figure 8: Histogram of the momentum pT of the muon in collisions

Cuts (300, 10) (600, 10) (600, 45) background TTbar Z W none 369839 274995 264098 3646487 30368 3560560 55558 1muon, p_T> 20 GeV 6140 7324 8974 81433 1442 73161 6828 ET miss> 160 GeV 544 245 309 3012 329 118 2563 MT> 90 GeV 300 118 164 256 131 0 124

Table 6: Cutflow for collisions at an energy of 13 TeV and an inte-grated luminosity of 10 fb−1, with columns for total back-ground and for separate components of the backback-ground. of the efficiency each cut has. When plotting the E_missT , the result of these cuts can be seen in figure 9

Figure 9: Missing Transverse Energy with all cuts applied. Looking at figure 9, the case where M2 = 300 GeV and tan β =

10 would clearly leave a visible signal in LHC experiments, as the signal is higher than the background. The other two cases would be less easy to spot, but might still be visible. Considering a systematic uncertainty of 10% (26 events) and a statistical uncertainty of √246 (16 events), the background can be expected to differ with±42events. In this way, a signal between 118 and 164 could be just enough to say something significant, but it is far from ideal.

5

L I G H T E R S Q U A R K S A N D G L U I N O S

5.1 l i g h t e r s q ua r k s

So far I have assumed all sfermions and the gluino to be too heavy for production at the LHC. However, although squarks are sure to be of significantly higher mass than their SM versions, they need not necessarily be unproducable. It is interesting to look what would happen if the squarks were lighter. I have not done any detailed sim-ulations for this, only an analysis of masses and crossections. There-fore I can not give a prediction of the size of the background and the sensitivity. A more in-depth explanation of SM quarks is needed first: In the SM, a difference is made between left- and right-handed particles to create a working theory of the electroweak force, as this force couples to handed particles only. The theory says the left-handed quarks form doublets, while the right-left-handed are singlets. This means there are in fact 2 mass parameters for the right-handed squarks, resulting in a total of 3 quark mass parameters per quark generation and thus 9 in total. In the SM however, the two right-handed quark masses are equal, reducing the amount of parameters back to 6. Because the right-handed masses cannot be assumed equal in the unknown parameter space of SUSY, it has 9 quark mass param-eters: M1 qL, M 2 qL, M 3 qL, MuR, MdR, McR, MsR, MtR, MbR

For the previous case where M2=300 and tan β=10, I have changed

the values for all first and second generation squark mass parameters to values that make production possible. The values I have looked at are 500 GeV, 750 GeV, 1000 GeV and 1500 GeV. The resulting val-ues for the physical masses of all first and second generation squark masses (left- and right-handed) lie very close to eachother and are approximately 910 GeV, 1080 GeV, 1280 GeV and 1720 GeV respec-tively. The cross sections of various decay modes are shown in table 7. As is to be expected, the total SUSY crossection increases with de-creasing squark masses. The crossections for left- and right-handed scharm and sstrange production in proton-proton collisions are ap-proximately 10 times lower than the ones for sup and sdown in each category, therefore I have not listed them.

(Mq [GeV])

500 750 1000 1500

total SUSY 47.5 42.4 40.1 38.8

total squark prod. 9.8 4.5 2.0 0.5 qg→χe + 2de_L 2.1 1.0 0.5 0.1 qg→χ_e−₂ueL 1.2 0.5 0.2 0.05 qq0 →u_eLde_L 0.7 0.4 0.2 0.04 qg→χ_e0₄ueL 0.4 0.2 0.1 0.02 qq0 →u_eRde_R 0.4 0.2 0.1 0.02

Table 7: Largest crossections involving squark production from proton-proton collisions for 4 models with different squark masses, in picobarn. Mq means all first and second

genera-tion squark mass parameters: M1_qL, M2_qL, MuR, MdR, McR, MsR

Just as the gauginos, squarks will immediately decay down the chain until the LSP is reached. The branching ratios of the sup and sdown squarks decays are shown in table 8. So when any of the left-handed first generation squarks is produced, there is a chance of 80-90% it will result in a heavy gaugino

e χ±₂ or χe

0

4 and a quark. The

right-handed ones will usually decay into a light neutralino and a squark.

So events like the number 1,2 and 4 in table 7 are likely to produce two heavy gauginos, one in the first collision of the quark and gluon and one coming from the decay of the sup or sdown. This will result in a high ET_miss(higher than events without squarks), accompanied by one jet resulting from the quark and 2, 3 of 4 leptons from a WW, WZ, or ZZ decay respectively. In case there are 3, 2 of them must be a lepton antilepton pair. In case there are 4, they must be two same-flavour lepton antilepton pairs. An example decay is shown in figure 10.

Figure 10: One of many quark gluon decay modes resulting in 1 jet, a lepton antilepton pair plus a single lepton and large ET_miss Another interesting case is the 3rd one in table 7 and similar ones. The production of a left-handed sup sdown pair (and other left-handed double squark productions) will in the majority of cases result in a large E_missT accompanied by exactly two jets and 2, 3 or 4 leptons with the same characteristics as the previous case. The last case in table 7 (and other right-handed double squark productions) will likely result

(Mq [GeV]) 500 750 1000 1500 e dL →χe − 2u 63 64 64 64 →χ_e0₄d 30 30 30 30 e uL →χe + 2d 55 55 55 56 →χ_e0₄u 29 29 29 29 e uR →χe 0 1u 60 59 59 59 →χe 0 3u 38 38 39 39 e dR →χe 0 1d 60 59 59 59 →χ_e0₃d 38 38 39 39

Table 8: Branching ratios of major decay modes of the left- and right-handed sup and sdown squarks in %.

in two high energetic jets but only a small amount of missing energy.

5.2 l i g h t e r g l u i n o s

A similar thing can be done with the gluinos. Keeping all squark masses fixed back at 4000 GeV again, I have lowered the gluino mass M3 to 5 different values and stated their crossections in table 9. As

they are displayed in femtobarns, these crossections are significantly lower than most of the crossection discussed earlier. The numbers stated in this table imply a very low expected event count, with around 185 yearly events involving gluino production in the best case, less than 1% of the expected events involving heavy gauginos χe

+

2 or

e

χ0₄ in that same model. This means that background events must of an exceptionally low number for signal to still stand out, which is possible only if the gluino decays have some special characteristic final state that is impossible or highly unlikely to reach from SM back-ground events. 49.6% of gluinos decay into two quarks and a heavy gaugino, resulting in a high ET_miss and 2 jets and possibly leptons as discussed before. However, this kind of events is also prevalent in the SM. The rest of the gluinos decay in the same way, but with a light gaugino and very little E_missT . For this reason the few gluino events that would be produced would probably be impossible to distinguish from their background.

(M3 [GeV])

1500 1750 2000 2250 2500

total SUSY 38425 38416 38407 38399 38395

total gluino prod. 18.5 10.8 2.8 0.7 0.2

gg→g_ege 12.5 6.7 1.5 0.3 0.07

qq→g_ege 4.2 2.3 0.5 0.2 0.07

qg→geueL 0.8 1.1 0.4 0.1 0.04

Table 9: Largest crossections involving gluino production from proton-proton collisions for 5 models with different gluino masses, in femtobarn.

6

C O N C L U S I O N

6.1 c o n c l u s i o n

If SUSY is a true theory of nature and its parameters are in the range of the ones I have investigated, it is not completely unlikely that the future will bring its exciting discovery. Especially models with a low wino mass (M2) will have a good chance of detection in the

LHC. Although I have not looked at the relevant background, mod-els with lighter squarks will probably increase sensitivity for SUSY signal, while lighter gluinos will have no significant effects on sensi-tivity. When nothing is found it reduces the space for SUSY to hide in the form of the pMSSM, making both the search for SUSY models with a broader parameter space, but also the search for completely alternative theories, more attractive.

6.2 d i s c u s s i o n

There are a number of ways to improve on this research:

• It is possible that there are more variables that might help in differentiating between signal an background even more. More time to look for them would possibly yield a better signal. • The simulations used are so called ’truth’ simulations. This

means they assume perfect detection abilities, while in reality this is obviously not the case. The simulations would be im-proved if they included a simulation of the LHC detector. • Larger and more specific SUSY samples. When making cuts,

only very little events were left sometimes, decreasing the sta-tistical certainty. With a larger sample size, and one that was pre-cut at a MET above 160 GeV, histograms would be smoother and less prone to statistical error.

• I have not looked at relevant backgrounds for models with lighter squarks. This is information is necessary to know for sure if they could make a contribution to the signal.

B I B L I O G R A P H Y

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[6] P.Z. Skands et al., JHEP 0407 (2004) 036, hep-ph/0311123.

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[9] Particle Data Group, K. Olive et al., Chin. Phys. C 38 (2014) 090001.