taylan yetkin cukurova university, physics department thesis defense

3/31/2006 Taylan Yetkin 1

SEARCH FOR SUSY IN MISSING TRANSVERSE ENERGY PLUS MULTIJET TOPOLOGIES AT √s = 14

TeV AND GEANT4 SIMULATION OF THE CMS HADRONIC FORWARD CALORIMETER IN THE 2004

TEST BEAM

Taylan YetkinCukurova University,Physics Department

Thesis Defense


Outline

• Introduction• Definitions of Jet and Missing Transverse Energy• Search for Supersymmetry in Missing Transverse Energy and Multijets Topologies• Geant4 Simulation of Hadronic Forward Calorimeter in CMS• Remarks and Conclusions• Appendix


Introduction

The thesis is divided in two parts:

In the first part a study entitled Search for SUSY in Missing Transverse Energy plus Multijet Topologies at √s = 14 TeV is presented where discovery potential of SUSY is shown by using a set of five parameters in mSUGRA model as well as discussion of the methods in the analysis. The study improves and develops the analysis tools that has been used in past experiments and can be used when we have data from CMS.

In the second part a Geant4 Simulation study for Hadronic Forward Calorimeters in CMS is presented. The simulation results were used to confirm test beam results as well as updating shower library in OSCAR which is one of the CMS simulation software that based on Geant4.


Working in a Transverse Plane

PT is conserved not P.

The collisions does not occur in fixed z-coordinate value (there is boost in z-coordinate). Also, most of the time, in each collision only two partons will experience hard scatter. The others and some of the collision remnants will go through the beam pipes. As a result, measurement in z-coordinate is impossible and only transverse quantities can be used.

Unfolded EcalPlusHcalTowers


Phenomenology of Jets

• pp collisions produce quarks/gluons• quarks/gluons fragments to hadrons• Hadrons interacts with calorimeter• Jets clustering algorithms adds towers inside cone • Fraction of energy is out-of-cone due to magnetic field•Underlying events contribute to signal p pq


Missing Transverse Energy

The missing transverse energy vector is calculated by summing individual calorimeter towers having energy Ei , polar angle i, and azimuthal angle i, and negating this sum:

The sources of missing transverse energy are particles that interacts weakly with the detector, mismeasured muons, cracks in the detector, beam halo particles, dead detector channels, cosmic rays, and everything that goes wrong in the detector. In any BSM theory there is additional source of missing transverse energy which is a neutral, weakly interacting stable particle.


Search for SUSY in Missing Transverse Energy plus Multijet

Topologies at √s = 14 TeV


Purpose of the Analysis

If SUSY exist and the sparticle masses are in the range 100 GeV~ 1TeV, it will be discovered in LHC. Therefore

• The goal is not just to show that we will be able to discover SUSY at 10 fb-1, because S/B is huge at this luminosity.• Develop analysis strategies and necessary tools for data handling.• Also make contribution to PTDR Vol. II (and to Vol. III).


Signal Characteristic

In the mSUGRA model we study R-Parity conserved scenario. Hence, there are two LSPs in the final state of each SUSY decay and they will contribute to the missing transverse energy measurement. Also there are multijets because of the squark/gluino decays. Therefore Missing Transverse Energy plus Multijes (3 jets) are chosen for the signal characteristic.


Properties of mSUGRA LM1-I


Properties of mSUGRA LM1-II


Example Events in mSUGRA LM1Event Event 11

Event Event 22

Event Event 33

2 quark 2 quark jetsjets

3 quark jets, 1 tau 3 quark jets, 1 tau jetjet

2 quark jets, 2 tau jets2 quark jets, 2 tau jets


Event Reconstruction

Event Event 22

jet 1jet 1

jet 2jet 2jet 3jet 3


Data Samples for Analysis-ILM1:

Generated by using PYTHIA 6.225 with ISAJET 7.69 interface, simulated with OSCAR 3_6_5 digitized and DSTed with ORCA_8_7_1 and analyzed with ORCA 8_7_4. The sample is digitized with low luminosity (2x1033 cm-2 s-2) pile-up conditions (with 5 on average pile-up events from the MU05b MBforPU dataset).

ttbar:Generated by using PYTHIA 6.215, simulated with OSCAR 3_6_5 digitized and DSTed with ORCA_8_7_1 and analyzed with ORCA 8_7_4. The sample is digitized with low luminosity (2x1033 cm-2s-1) pile-up conditions (with 3.5 on average pile-up events from the MU05b MBforPU dataset).Single top:Generated by using PYTHIA 6.215, simulated with OSCAR 3_6_5 digitized and DSTed with ORCA_8_7_1 and analyzed with ORCA 8_7_4. The sample is digitized with low luminosity (2x1033 cm-2 s-1) pile-up conditions (with 5 on average pile-up events from the MU05b MBforPU dataset).Znunubar: Generated by using PYTHIA 6.215, simulated with OSCAR 3_6_5 digitized and DSTed with ORCA_8_7_1 and analyzed with ORCA 8_7_4. The sample is digitized with low luminosity (2x1033 cm-2s-1 ) pile-up conditions (with 5 on average pile-up events from the MU05b MBforPU dataset).Others:Generated by using PYTHIA 6.215, simulated with OSCAR 2_4_5 digitized and DSTedwith ORCA 8_7_1 and analyzed with ORCA 8_7_4. The sample is digitized with lowluminosity (2x1033 cm-2 s-1) pile-up conditions (with 3.5 on average pile-up events from the MU03b MBforPU dataset).


Data Samples for Analysis-II

Transverse momentum pt hat is defined in the rest frame of the hard interaction for hard 22 processes,


Jets and MET

Jets:• We have adopted the Scheme A from the JetMET PRS group where different tower thresholds defined for different calorimeter components.• Jet algorithm is simple iterative cone algorithm with cone size 0.5. SplittedEcalPlusHcalTowerInput is used (in “split tower” geometry the 100 -towers are divided in two and tower 28/29 are further divided in at = 2.825 to provide equal energy sharing in divisions.) is used.• EcalPlusHcalTowerCut is 0.5 GeV.• ConeSeedEtCut is 0.1.• JetEtCut is 3 GeV.

• There is 30 GeV PT offline requirement on jets.

• || < 3.0 is chosen for all jets.

Met:• The missing transverse energy is calculated from EcalPlusHcalTower without any correction applied.


Trigger


Trigger-I

Since we want to see missing transverse energy trigger efficiency it is proper to use a dataset of events that doesn’t have missing energy. Therefore, from the ttbar sample we form a pseudo dataset that we use as reference to measure the L1 jet+MET trigger efficiency The sample is designed based on the L1+HLT trigger path referred to as L1_2CJ_130 as follows:• require a primary vertex• require L1 bit 11 on (L1 two central jets, 130 GeV, L1_2CJ_130)• since no HLT dijet trigger exists we require offline 2 jets of uncorrected PT 130 GeV to confirm the L1 bit 11.

We call this sample as JET130.

JET130 (L1-bit 11+HLT) Pass L1 JetMet L1 bit 28

7350 4014(54.6%)

Table: Pseudo JET130 data sample and L1 jetMET bit 28 test.


Trigger-II

L1 Trigger Efficiency

In Jet130 dataset the events that pass the L1_CJ_88_MET_46 trigger (L1 bit 28 on) determine the L1 missing transverse energy trigger efficiency. The efficiency reach to 95% at about 100 GeV. Parameterized curve is used in the analysis.

-Before

-After


Trigger-IIIHLT Efficiency

In Jet130 dataset, after applying L1 Trigger, the events that pass the HLT_CJ_180_MET_123 trigger (one central jet with PT 180 GeV and missing transverse energy with 123 GeV) determine the HLT missing transverse energy trigger efficiency. Since there is not enough statistics, as can be seen from the top right figure, instead of using the efficiency curve we simply require 200 GeV missing transverse energy for each event after L1.

-Before

-After


Data Cleanup and Pre-selections


Primitive Backgrounds in a PTmiss Trigger

Data Cleanup-I

• Beam Halo Particles • Data Acquisition problems• Detector problems (dead channels, cracks etc.)• Cosmic Rays• Everything that goes wrong in the detector.


Jet and Event EMF

Data Cleanup-II

• A jet is expected to have on average Electromagnetic/ETOT ratio (EMF) between 0 and 1*.• Cosmic bremsstrahlung depositions of energy in either the hadronic or electromagnetic calorimeter when clustered as jets will have EMF close to 0 or to 1.• All-hadronic depositions of energy resulting from beam halo events will have EMF close to 0 and have been studied at CMS in CMS-AN-2005- 48.• Electrons and photons that are also clustered as jets are expected to have EMF closer to 1.

Given these properties, the electromagnetic fraction of a jet has been used as a “jet-quality” control variable and discriminator against backgrounds.

* Energy fraction is found from EcalPlusHcalTowers.


Leading Jet EMF

Data Cleanup-III

LM1tt

;t Wb W


Event EMF

Data Cleanup-IV

is defined to be the PT weighted jet EMF sum over the electromagnetic calorimeter acceptance, |d| < 3.0:

where:• NJet is the number of IC jets of cone 0.5 with PT > 30 GeV and | d|<3.0• PT

j is the uncorrected PT of the jth jet • EMFj is the EMF of the jth jet


Event EMF in Beam Halo (CMS-AN-2005-48)

Data Cleanup-V

hadrons muons


Event EMF in Signal and Background

Data Cleanup-VI

LM1tt

We use EEMF 0.1 as a clean-up requirement to retain the signal efficiency while eliminating backgrounds such as the beam halo background.


Jet and Event Charged Fraction

Data Cleanup-VII

• The charged to neutral tracks ratio of a hadronic jet is about 65%.

• The jet charged fraction is defined as the ratio of the PT of the tracks associated with a jet over the total calorimetric jet PT .

• Jets that are found in the tracker coverage region that have charged fraction close to 0 which are not associated with a photon, can be pathological and would indicate potential backgrounds. The overall Event Charged Fraction can be used to distinguish between real jets and such fake jets.

N.B For analyses with photons in the final state the charged fraction might not be a proper clean-up variable.


Event Charged Fraction

Data Cleanup-VIII

The event charged fraction is calculated by finding all the tracks pointing toeach jet within a cone of 0.75 of the - centroid of the jet. A jet enters intothe event charged fraction variable if its absolute pseudorapidity is less than 1.7.


Event Charged Fraction in Signal and Background

Data Cleanup-IX

tt LM1

We use ECHF 0.175 as a clean-up requirement to retain the signal efficiency while eliminating backgrounds such as the beam halo background.


Data Cleanup-X

tt

EEMF and ECHF for Good Hadronic Jet(Details are in CMS-IN 2006-010)


Indirect Lepton Veto (ILV) As a Pre-Selection Tool


An “indirect lepton veto” method is studied as a strategy for eliminating W/Z+jets and ttbar backgrounds while retaining the efficiency to low mass mSUGRA-type signals where leptons from the decays of charginos and neutralinos are present.

ILV combines tracker (Leading Track Isolation) and calorimeter (EMF of two most energetic jets) information and it is used as an indirect way to veto leptons (and/or fake jets from leptons) in the events.

ILV-I


The two highest PT jets in the event are required not to be purely electromagnetic. The event is vetoed if:

EMF (leading jet) > 0.9 or EMF (second jet) > 0.9

This requirement will mainly eliminate events with high PT electrons inthe final state.

ILV-IIJet EMF

W(e) + 2 jets

First Jet Second Jet


Tracking isolation is used at CMS as a powerful criterion in selection (PTDR-Vol1). We developed a tracking isolation strategy in order to reject electrons, muons and taus from W and Z decays while retaining the SUSY signal efficiency.

The highest PT track is found among the tracks that are associated to primary vertex in each event where the tracks have the requirements:

• PT > 1.2 GeV/c • Nhits 5 • transverse impact parameter |d0| 600 µm • |zPV − ztrk| < 1 mm • |trk| < 2.4

ILV-IIILeading Track Isolation-I


If the leading track has PT > 15. GeV/c, a cone is cast around this track with a cone size dR = 0.35 where (dR)2 = (d)2 + (d)2. Then the PT of the other tracks inside the cone are summed up to construct an isolation parameter (Pisol) as follows:

ILV-VLeading Track Isolation-II

If Pisol 10% we tag the leading track as isolated track and reject the event. The fraction above we refer to as “leading track isolation parameter”. The requirement of rejecting events with anisolated leading track is noted as Isotrk=0. Both the cone size and the value of the fraction is determined such that the maximum rejection of the background is achieved with the minimal loss of signal efficiency.

Leading Track


ILV works well for rejecting backgrounds from W/Z and also from ttbar when the final state has high energy electrons and muons.

ILV-VISummary and Results

Table 1: Rejection efficiency of Indirect Lepton Veto in LM1.

Table 2: Rejection efficiency of Indirect Lepton Veto in W/Z Samples


SM Candle Normalization with W/Z + Jets


In collider experiments W/Z bosons will be produced associated to hadronic jets. Here we study the methods for SM Candle Normalizations as a preparation. Z(ℓℓ) + jets can be used in data for various things:

• W+jets sample can be estimated from the Z+jets data since Z+jets gives relatively clean signals.• In Z+ N jets sample, where N is the number of jets, the number of events each bin in N can be estimated since the

cross-section is proportional to sN in lowest order.

• In mSUGRA LM1 Z(invisible) + 3 jets will be a major background and neither kinematical nor topological cuts will remove it. But from Z(mumu) + 3 jets (or Z(ee) + 3 jets ) it can be estimated.

SM Candle Norm. -I


SM Candle Norm. -II


QCD Background and Cuts


The cross-section for the production of QCD dijet events are very high and therefore rate of the such events at LHC will be very high. The QCD jet production causes large missing energy because of the small

contents as well as jet mismeasurements and detector resolution. Three variables are used to suppress QCD background:•Angle between second highest PT jet and missing transverse energy

• Correlation between first, second jet and missing transverse energy

• Minimum of the angles between all jets and missing transverse energy

QCD Background and Cuts-I


QCD Background and Cuts-II

QCD_470_600 LM1


QCD Background and Cuts-III

QCD_470_600 LM1

R1 and R2 are chosen as 0.5


QCD Background and Cuts-IV

QCD_470_600 LM1


Analysis Results


Analysis Results-I

The number of events that pass all the pre-selection and analysis cuts for the 10 fb-1.

QC

D


Analysis Results-IV

There are two variables used in the literature for SUSY searches: HT and Meff. The former is frequently used in the experiments as an experimental variable independent from any model while latter is used as and index for the SUSY mass scale. They are defined as follows:

where PT,i are the PT of the jets. In general Meff is twice the SUSY mass MSUSY ≈ min(Mgluino , Msquark) in which Msquark is the mass of light squarks (e.g., sup,sdown).


Analysis Results-V

The signal is well visible above background.

HT and Meff :

HT Meff


Analysis Results-VI Signal/Background Ratio:

From the table in Analysis Results-I

Background

Signal


Systematic Uncertainties


We studied systematical uncertainties for missing transverse energy:

• Due to undermeasured jets: One jet or two jets or three jets cases.

• Due to Calorimeter miscalibration: 2% miscalibration in each tower as inter tower (randomly), or each tower scaled up 2%, or each tower scaled down 2%.

Systematic Uncertainties -I

Missing Transverse Energy

(Details are in CMS-IN 2006-015)

We studied systematical uncertainties for jets:

• Due to jet energy scale:

Jets


Systematic Uncertainties -IIUndermeasured Jets

1 Jet Scenario

2 Jets Scenario

3 Jets Scenario

1(2,3) Jet(s)/ Nominal

The weighted average of these three scenarios are taken, namely 7%, as an index of the positive systematic uncertainty due to the tails of the jet resolution in the tails of the PT

miss above 180 GeV.


Miscalibration (studied as 2% random, plus or minus for each tower) does not have significant effect on missing transverse energy.

Systematic Uncertainties -III2% Tower Miscalibration

tt LM1


Systematic Uncertainties -IVJet Energy Scale

C. Tully.The systematics for jet energy scale (JES) include the uncertainties on the absolute jet energy corrections, calorimeter stability, underlying event and relative jet energy corrections. We took the 2% value (although for the energies above 50 it is about 1.3 at 10 fb-1, the lowes value is effected from the tower miscalibration.) The jet four-vector is scaled with the uncertainty as follow


Conclusions

We have shown that SUSY can be discovered at 10 fb-1 with no difficulty by using jets and missing transverse energy and no leptons where mSUGRA LM1 point is taken as a point in m0 – m1/2 space.

• Since we already knew that SUSY can be discovered (the cross-section is very high) we concentrated more on method and developed and/or improved analysis tool such as:

o Event cleaning variables EEMF and ECHF

o Indirect Lepton Veto

o Estimating electroweak backgrounds (W/Z+jets) from Z+jets.

• Two measurement related systematical effects studied: Systematic on MET and Jets.


Geant4 Simulation of the CMS Hadronic Forward (HF) Calorimeter

in the 2004 Test Beam


HF Detectors

Active material is quartz fiber (~600μm diameter). Two set of fibers are embedded to the passive material which is steel: Long (165 cm) and Short (143 cm) fibers.

Figures from Geant4 Simulation


Physics of HF Detector

HF detector collects photons as other HCAL detectors with one difference: The source of the photons is not scintillating, it is Cherenkov processes.

ct/n

ct

Charged particles (mostly electrons) enters to fiber media and creates Cherenkov photons. The photons are captured if they hit the fiber-cladding surface with less than 190 angle.


Light Collection and Signal


Geant4 HF Simulation-I

In HEP experiments simulations are very crucial before building the detectors:Design Optimization, Performance Tests, Raw data input for the event reconstruction programs…

Also, when the detector and data are present simulations help to understand data, calibration, systematic effects from detector, the influence of the background…

Geant4 is the most used simulation toolkit for the passage of particles through matter in HEP. Current CMS Detector Software OSCAR is based on Geant4 and it is constantly improved according to test beam data and simulation results.

It should also kept in mind that the better we understand data the better we improve simulation and a well understood simulation helps to understand data better.We have studied the HF simulation in the light of above discussions.


Geant4 HF Simulation-II

HF simulation is done in multiple steps:

Beam Sim. Geometry Sim. Physics Sim. Analysis

Spatially distributed (randomly to generate square, circle, spherical, etc.) or point-like beam spot. In HF beam spot is square shape.

Build geometry as close as possible to the real geometry with same materials. In HF simulation passive material is iron and active material is quartz.

Electromagnetic and Hadronic Physics Simulation with the interface of Physics Lists (matter-particle interactions and showering). Cherenkov process is added externally for the energy loss of charged particles inside quartz fibers.

Number of photo-electrons are stored at the end of simulation. Towers are read out separately. ROOT is the package for analysis framework.

..

.. .. ~~ ~~~

n1

n2

Cerenkov Process

Shower construction

HistogramsGun Position

pName,P ,E


Results-I

Response of HF detector (L+S)

Electron Pion

30 GeV

150 GeV


Results-II

Energy Resolution (L+S)

Electron

Pion


Results-VI

Response Linearity

Linearity is the measure of detector response and it is defined as the ratio of measured energy to incoming beam

Electron

Pion

Long Short

HF response is constant when electrons are measured with the long fibers only. However with the increased energy the short fibers start to register energy and it becomes non-linear. For pions the non-linearity is seen in both cases. The simulation results are agree with the test beam data.


Results-VIII

pi/e Ratio

Taking the short fiber into account makes HF pi/e ratio independent from energy.


Conclusions

• There is excellent agreement between GEANT4 and H2 test beam data for electromagnetic interactions. • For pions, the different GEANT4 physics lists reproduce the test beam data successfully. • The best agreement is achieved by the LHEP physics list. The LHEP physics list agrees within 1% with the 2004 H2 test beam data.


Final Remarks and Conclusions

• In this thesis two different problems were studied: SUSY Search at CMS and Geant4 Simulation of HF Calorimeter as results of three years of work done at Fermilab (w/ S. Kunori) and CERN (w/ M. Spiropulu and S. Kunori). • The HF part of the study was easier than SUSY part since there was enough official documents and constant Geant4 team support. In SUSY part, since it involved simulation from particle generator to reconstruction, there was always need to experts in the field as well as physicists with the collider experince (thanks to S. Kunori and M. Spiropulu for helping and directing me to the right persons). • The SUSY part will look for approval at 10th of April from CMS to become a part of Physics TDR Vol.II.2. There are two CMS-IN (2006-010, 2006-015) from the study and a CMS-AN is in preparation. • The HF simulation part took place in one of the recent HF CMS-IN (FIXME number) where the test beam dataset and the simulation were from different HF tower, and it will be submitted as NIM paper. We also submitted a separate HF note as CMS-IN from our study. Also, based on HF simulation, HF shower library is updated which was from Geant3. • In SUSY study, scanning the m0-m1/2 space and surveying 5 discovery reach is remained. We plan to continue to study by using FAMOS for this study


Final Remarks and Conclusions

• We mostly used samples from Phytia production and it is well known that one need to have samples from the generators that uses matrix element calculations. A recent ATLAS study ( TeV4LHC Conference, 2005, Fermilab ) has shown that the background increases 2-4 times when the samples from Alpgen is used. The study may need to be repeated to have accurate results although

we see from our results (see HT or Meff plots ) that the signal is well above the

background. • We don’t have enough simulated QCD events and it won’t be until we have data from LHC. None of the events generated pass our selection criteria. • The simulation program in CMS group is changing. There will be a need to repeat this study (hopefully with Alpgen samples) for validation.• The HF geometry in HF simulation was perfect. But it is not the reality. The uniformity of HF response studied in test beam studies wasn’t able to compared with the simulation for this reason. One can, however, mimic the cause of non-uniformities in HF due to the geometry in the simulation and study it.• There were some abnormal events in the test beam data which gave TeV energies from GeV range incident particles. These types of events were guessed that they likely direct hits of the particles to the readout boxes or fiber bundles behind HF wedge. The HF simulation program can be used for testing these hypothesizes.


Appendix (Backup Slides)


Standard Model (SM)


Standard Model of Physics -II

The color theory of QCD of the strong interaction SU(3)C with the Weinberg-Salam model of SU(2)L x U(1)Y electroweak unification is combined to obtain the standard model of electromagnetic, weak, and strong interactions as gauge theory with symmetry group:

SU(3)C x SU(2)L x U(1)Y

QCD: Describes the interaction among quarks and gluons.

Electroweak: Describes the symmetric theory of electromagnetism and weak interactions. The symmetry is broken by the Higgs field.

Higgs Mechanism is added ad hoc to explain the origin of the masses

Higgs Sector: Describes the mechanism which explains how W and Z receives their masses and also explains the interactions of quarks and leptons with Higgs field that give their masses and mixing angles.


Standard Model of Physics -III

QCD measurements of strong coupling “constant” S(Q), and their theoretical predictions. The coupling occurs among quarks and gluons. The strength of the coupling changes with the distance. The scale of Q is up to 100 GeV. The measurements QCD that will come from LHC will increase the scale.


Standard Model of Physics -IV

Electroweak measurements from LEP (Summer2005).Electroweak theory has four parameters: (Q2), electromagnetic coupling constant; W, mixing angle; MW and MHiggs.Describes remarkably all the properties of the gauge bosons and the interactions they involve.


Standard Model of Physics -V

Higgs Sector is responsible for the masses of the particles. If a symmetry breaking Lagrangian term is written as follows:

†( ) ( ) ( ),HL D D V

where2 † † 2

0

( ) ( ) ; 0

.2 2

V

i iD g W g B

: a fundamental, renormalizable, simplest complex field which composed from real, scalar fields (+ = 1 + i 2, 0 = 3 + i 4)μ: is the mass parameter: is the strength of the Higgs self-coupling.W and B: are the gauge fields of the SU(2) and U(1) respectively.g and g’: are the gauge couplings of the SU(2) and U(1) respectively.


Standard Model of Physics -VI

If μ2 > 0 then <0||0> = 0

If μ2 < 0 then † = -μ2/2 v2/2

When this is used in SM Lagrangian the masses are found as follows:


Standard Model of Physics -VII

Higgs Sector of SM in the LHC project will be studied by following the strategy: Discovery, measurements of the coupling of Higgs boson to other bosons and fermions, measurement of the Higgs self coupling (Higgs potential).


Beyond Standard Model (BSM)


Why we need BSM Theories?

SM predictions agree precisely with all the collected data from the collider experiments

BUT

That does not give us explanations for fundamental questions in HEP.



• The origin of mass (Is there a Higgs Boson?)• Why are there 3 generations of fermions?• Why do quark generations mix?• Why does CP violate?• Why is the universe mater dominant?• Hierarchy problem?• Unification of the gauge couplings?• The origin of Electroweak Symmetry Breaking• Incorporation of the Gravity• The number of free parameters• Dark Matter in the universe

Open Questions:




Open Questions:



SM predictions and measurements give three fermion generations:

Theory gives the ratio as 1.99xN . Experiments find the ratio as 5.94.

N =3.04




Open Questions:



SM does not have a deep principle for quark flavor mixing. Also the CKM matrix is not completely diagonal, the off-diagonal terms are related to small symmetry breaking effects. Some GUT theories give diagonal CKM matrix.

Weak forcequark mass eigenstates.

Strong forcequark mass eigenstates.

CKM Matrix




Open Questions:



In weak interactions helicity plays important role for particles and antiparticles behavior. In SM there is no explanation why does CP violate.

PL R

CL L

CPL R

only the observed

one

• The Parity (P) is not consered.• Charge-conjugation symmetry (C) is violated.




Open Questions:



More matter than antimatter. Why?

Number of baryons in the universe are >> 104 (???)times more than the antibaryons. How did this happen?Baryon number violation is one of the answers but SM prohibits it.




Open Questions:



In theoretical physics, when fundamental parameters (e.g. masses) of a Lagrangian are very different from the parameters measured by the experiment it is called that there is a “hierarchy problem”.

Consider the following simple Lagrangian of a complex scalar field and Weyl fermion

The fermion masses have the radiative corrections:

is ultraviolet cutoff value and corresponds to the energy scale where SM is still valid.



The boson masses have the radiative corrections:

The GUT theories incorporate gravity to explain interactions by using only one “meta” group at very high mass scale (MGUT~1015 GeV):

here MGUT >> MZ. Then boson masses become of the order of largest mass parameter in the theory. (Solution to this is fine-tuning not “natural”)

They receive large corrections if all the fermions and bosons are taken into account.




Open Questions:



In GUT theories of extended SM the coupling constants do not unify.

For SM the constants bi are found as (41/10, -19/6,-7) after considering number of families and Higgs bosons.



• The origin of mass (Is there a Higgs Boson?)• Why are there 3 generations of fermions?• Why do quark generations mix?• Why does CP violate?• Why is the universe mater dominant?• Hierarchy problem?• Unification of the gauge couplings?• The origin of Electroweak Symmetry Breaking• Gravity is not incorporated• The number of free parameters• Dark Matter in the universe

Open Questions:




Open Questions:



The SM contains 19 free parameters which have to be determined from the experiment.

• 3 parameters for gauge couplings gi.

• 2 parameters for Higgs boson mass and self-interaction of Higgs boson.• 9 parameters for quark and charged lepton masses. (possible increase due to neutrino masses)• 4 parameters for quark mixing angles and phase.• 1 parameter for QCD phase which characterizes the QCD vacuum state.




Open Questions:



When the energy scale goes higher and higher in the colliders SM meets with the cosmology, especially with the Bing-Bang.

From the astronomical observations such as rotational velocity of galaxies, it has been found that there is a lot of dark matter in the universe which is composed of neutral, non-baryonic, weakly interacting particles. Only candidate form SM is neutrino but they are too light.

Cosmic wave background radiation.

Wilkinson Microwave Anisotropy Probe (WMAP)


What kind of BSM Theories?

• Extension of the SM:o GUTso Supersymmetryo Superstringso Supergravity

• Exploring new ideas such as new forces.

But all these new theories should be more fundamental than SM where SM is just a low energy approximation of them.

There can be two approaches towards BSM Theories:


Supersymmetry as a BSM Theory-III

SUSY operator Q has the following properties:

TranslationOperator

SUSY relates external symmetries with inertial symmetries.

Generators of internal symmetries commute with Q, therefore particle and its sparticle has identical quantum numbers (e.g. charge, mass, color,…)

SUSY must be a broken symmetry since no sparticle with equal mass to its particle has been observed. Sparticles must be heavier than particles.


Supersymmetry as a BSM Theory-IV

There is no single SUSY Theory:

• Different SUSY models due to different symmetry breaking mechanisms

• Supergravity• Gauge Mediated SUSY• Anomaly Mediated SUSY• R-Parity Violating SUSY• …

Experimentally, Minimal Supersymmetric Standard Model (MSSM) and minimal Supergravity (mSUGRA) are the most studied SUSY models.


Supersymmetry as a BSM Theory-VI

Super Solutions (a few examples):

• Mass hierarchy:Since every fermion has a boson partner and vice versa there are extra terms for the radiative corrections. Boson masses will have contributions from the bosons itself and each extra term will cancel out since the contribution terms from fermions and bosons have opposite sign. • Coupling Constants:Because of the new particles in the theory coupling constants unify at a high mass scale.

• Dark Matter:SUSY theories, especially MSSM and mSUGRA have a natural candidate for dark matter: LSP (Lightest Supersymmetric Particle).


Supersymmetry as a BSM Theory-VII

MSSM

• MSSM is an extension of SM which has minimal particle content.• The number of particles in the model doubled (every SM particle has a sparticle partner).• R-Parity is conserved.• Two complex Higgs doublets are present in order to give mass to up-type and down-type quarks. This results in five physical states, usually referred to as H± , h (CP-even, neutral lighter scalar), H (CP-even, neutral heavier scalar) and A (CP-odd, neutral pseudoscalar). • All MSSM particles share the same quantum numbers under the group structure of SM, except from spin and mass.


Supersymmetry as a BSM Theory-VIIIParticle Content of MSSM


Supersymmetry as a BSM Theory-IX

MSSM: Charginos and Neutralinos

The gauginos and higgsinos mix to form four new neutral fermions “neutralinos”and two new charged fermionic state “charginos”.

Observables are the mass eigenstates of the matrices.


Supersymmetry as a BSM Theory-X

SUperGRAvity:

SUSY + General Relativity

Any attempt to combine Gravity with the other three forces requires SUSY (combination of local symmetries with the global ones).

Minimal SUGRA:A SUSY breaking mechanism should exist for the SUSY theories: SUGRA GUT or minimal SUGRA (mSUGRA) is one of the mechanism which breaks the SUSY.

Because of the symmetry breaking mechanism mSUGRA at low energies look like MSSM.

In mSUGRA the breaking of supersymmetry naturally triggers the breaking of electroweak symmetry and leads to predictions of masses of sparticles lying in the 100 GeV-1 TeV energy range.


Supersymmetry as a BSM Theory-XI

mSUGRA common masses:

In mSUGRA, the gaugino masses M1, M2, M3 (corresponding to U(1), SU(2),and SU(3), respectively) are unified to a common gaugino mass m1/2 at some high-energy scale MX :

Also all scalar particles (sfermions and Higgs bosons) in mSUGRA have a common mass m0.

The mSUGRA model is completely specified by five parameters:


Supersymmetry as a BSM Theory-XII

mSUGRA and MSSM mass relations:

taylan yetkin cukurova university, physics department thesis defense

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