CERN SUMMER STUDENT REPORT 2016

Search for dark matter with CMS

Anna Hallin

Supervisors: Nicola De Filippis, Michele De Gruttola

August 12, 2016

Abstract

During this summer student project I have followed the analysis procedures for a search for Dark Matter with the

CMS experiment. The project has included studying how the detector works, learning how to analyse physics objects

using the CMS software framework, studying the theory and analysis strategy for this particular search, and doing

some work with observables and event displays to contribute to the analysis.

1 INTRODUCTION

This summer project has introduced me to data analysis

with CMS in general, and to the mono-Higgs analysis in

particular. This analysis searches for dark matter candi-

dates produced through so-called Higgs portal models,

with a signature of four leptons and missing transverse

energy in the final state.

This report begins with a description of my activities

during the project. I give a brief theoretical introduc-

tion and motivation for the current analysis in section 3,

which is followed by an overview of the CMS detector and

a description of the analysis strategy in sections 4 and 5

respectively. In section 6 I present and discuss some of

the results of my work, followed by concluding remarks

in section 7.

2 PROJECT ACTIVITIES

Starting from zero knowledge of C++ and ROOT at the

beginning of the summer, a lot of time has been spent

learning these languages and how to use them in the

CMS software framework. I have also worked with CMS

Data Analysis School excercises, learning how to analyze

muons, electrons and missing transverse energy in the

full framework. This was followed by studying the Stan-

dard Model H→ZZ→4l analysis, which is used for the re-construction of the Higgs boson in the mono-Higgs anal-

ysis. In the end I did not work on the actual code for

the mono-Higgs analysis, but have instead been building

a macro that plots observables from background, signal

and data files produced through the analysis. In addition

to histograms, it also produces a yield table of total back-

ground and signal events, together with the number of

observed candidates. Finally, I also used the event dis-

play software to study some events in more detail.

3 THEORY AND MOTIVATION

Although the Standard Model works extremely well, it

can only account for 5% of the energy density in the Uni-

verse [1]. The remaining energy is divided between dark

matter (25%) and dark energy (70%). If the dark matter

is made of particles that couple to any of the Standard

Model particles, particle colliders such as the LHC can

be used to search for it.

In the Standard Model (SM), fermions and the W±

and Z bosons acquire mass through the electroweak

symmetry breaking caused by the vacuum expectation

value of the Higgs field. The Higgs potential is given by

V = µ2H †H+λ(H †H)2, where H is a complex scalar dou-blet. For µ2 < 0 this potential has a minimum not at zero,

1

but at H †H = µ22λ . Since H is a complex doublet, it hasfour degrees of freedom. Three of these are used to give

mass to the W± and Z bosons, while the fourth remainsas a real scalar field, h, whose associated particle is the

Higgs boson with mass mh =√−2µ2.

If dark matter (DM) is stable and couples only weakly

to Standard Model particles, it could not be directly de-

tected in a collider experiment. What we could detect

is instead an imbalance in the transverse momentum,

when the DM recoils against a visible SM particle and es-

capes undetected through the detector.

A promising probe for DM searches is the Higgs bo-

son [2]. In contrast to other particles, like γ, W±, Z andjets, the Higgs boson is unlikely to be emitted through

initial state radiation. Using the Higgs boson as a probe

therefore means probing the effective DM vertex directly.

Since the second term in the Higgs potential is of di-

mension two, it it possible for scalar DM to couple to

the Higgs via the effective interaction λ|H |2χ2, where λis now a coupling constant, without being suppressed

by a mass scale Λ. Going up in dimension, for fermion

DM the interaction will be suppressed by a factor of 1/Λ.

Other higher dimensional operators can also be consid-

ered. If mχ < mh/2, Λ is constrained by the currentmeasurement of BR(H→invisible). Figure 3.1 shows aschematic of this effective field theory approach. A medi-

ator particle, which can be a Standard Model electroweak

boson or a new intermediate particle, couples to quarks

or gluons. Through an effective interaction, the final

state consists of one Higgs boson and two DM particles.

h

DM

DM

q, g

q̄, g

Figure 3.1: Schematic of effective field theory for DM mono-

Higgs coupling.

An alternative to the effective field theories are sim-

plified models, which specify the underlying UV physics.

In these models, the DM is coupled to a mediator par-

ticle, which is in turn coupled to the SM particles. An

example of such a model is shown in figure 3.2, where

a new massive particle A0 mediates the Higgs-DM cou-

pling, and Z’ is a heavier version of the Z boson. A range

of other models exist, where the mediator can be a scalar,

a pseudoscalar or a vector [1].

q

q̄

Z ′h

DM

DMA0

Figure 3.2: Schematic of Z’2HDM (two Higgs doublet model)

for DM mono-Higgs coupling.

4 THE CMS EXPERIMENT

The Compact muon solenoid (CMS) is a general-purpose

detector at the LHC. Central to the detector is the 4 Tesla

superconducting solenoid, enabling very good measure-

ments of muon momentum. Figure 4.1 shows a trans-

verse slice of the detector [3], where the colliding proton

beams travel perpendicular to the plane of the paper in

the very left end of the image.

Figure 4.1: A transverse slice of the CMS detector. ©2016

CERN, for the benefit of the CMS Collaboration [3].

The detector consists of several layers, each with a

specific purpose [4]. The innermost layer is the tracker,

where charged particles are tracked. Closest to the beam-

line are the silicon pixels, providing high resolution track-

ing. As charged particles pass, electrons are ripped from

the silicon atoms, creating electron-hole pairs that can be

read out as electrical signals. The pixels are surrounded

by silicon strips, completing the tracker.

Next after the tracker comes the electromagnetic

calorimeter (ECAL) consisting of lead tungstenate crys-

tals that provide a compact showering of electrons and

photons. All electrons and photons are stopped here.

Following the ECAL is the hadron calorimeter (HCAL)

that measures the energy of the hadrons. The muons

continue all the way through the detector, whose outer-

most parts consists of the muon chambers tracking the

2

muons on their way out.

5 ANALYSIS STRATEGY

5.1 DATA ANALYSIS

This analysis searches for four leptons and missing trans-

verse energy (MET) in the final state, where the leptons

can be traced back to a pair of Z bosons produced by a

decaying Higgs boson.

Central to the data analysis is the event selection.

Great care must be taken to reconstruct physics objects

in a way that includes all real particles relevant to the

analysis, while avoiding those that may be distorted by

detector defects, noise, or that are simply misidentified.

Making these types of decisions requires optimisation, as

there is usually a trade-off between efficiency (the frac-

tion of objects that are reconstructed) and how good or

trustworthy the reconstructed objects are.

In addition to the event selection, cuts are applied to

remove background events while maintaining as much of

the signal as possible. This is crucial since the signal, hav-

ing a much lower cross section, would otherwise drown

in the background events. In order to determine which

cuts to apply, the different distributions need to be stud-

ied. Once an observable has been found, the cut needs to

be optimised. Background that can mimic the signal but

also have other observables or a different kinematic dis-

tribution in the final state is called reducible background.

Background that have the exact same final state as the

signal we are looking for is called irreducible background.

5.2 EVENT SELECTION

The main observables in this analysis are the 4 lepton

invariant mass (needed to reconstruct the Higgs boson)

and the MET. The MET is defined as the magnitude of the

quantity ~E mi ssT = −∑

i ~pT,i , where the sum is over all vis-

ible particles. Since it depends entirely on the measure-

ment of the visible particles, any uncertainty or error in

the reconstruction of other physics object will propagate

to the MET. The reconstruction of the Higgs boson fol-

lows the methods of the Run2 Standard Model H→ZZ→4lanalysis from the HZZ working group [5], outlined below.

Electrons are identified using a Gradient Boosted De-

cision Tree (BDT) classifier algorithm. Starting from a

loose requirement of peT > 7 GeV, |ηe | < 2.5 and the pri-mary vertex constraints d x y < 0.5, d z < 1, electronsare selected if they pass the MVA identification working

point set by the BDT. Electrons are required to have a

relative isolation of less than 0.35 in a cone of ∆R = 0.3.The relative isolation is defined as the sum of transverse

momentum of charged hadrons and transverse energy of

neutral hadrons and photons in a cone centered around

the electron candidate, divided by the transverse mo-

mentum of the electron. The cone size is given by ∆R =√∆η2 +∆φ2. Muons are required to have pµT > 5 GeV

and |ηµ| < 2.4, and the same primary vertex and isolationconstraints as the electrons. Electron energy is corrected

by accounting for final state radiation (FSR) photons that

can be associated with radiation from a selected electron.

Electrons that are within ∆R < 0.05 of a selected muonare discarded.

Using the selected leptons, Z candidates are built

from same-flavour opposite-sign leptons, requiring

12 < ml l < 120 GeV. These candidates are used to defineZZ pairs, where the Z candidate with reconstructed mass

closest to the nominal Z mass is called Z1 and the other

is called Z2. Additional requirements are now placed on

the leptons, including ∆R > 0.02 between any of the lep-tons to remove “ghosts”, at least one out of the four lep-

tons needs to pass pT > 20 GeV and one pT > 10 GeV,ml l > 4 GeV for all possible lepton pairs to suppress QCDbackground, mZ1 > 40 GeV and m4l > 70 GeV.

5.3 SIGNAL AND BACKGROUND

The chosen model for this analysis is the Z’2HDM, illus-

trated in figure 3.2, with mA0 = 300 GeV and mZ ′ rangingfrom 600 to 2500 GeV.

Irreducible background, giving 4l+MET in the final

state, comes from ZH production with decay chains (Z→νν,H → ZZ → 4l) or (Z → 2l,H → ZZ → 2l2ν). TheSM Higgs background consists of gluon-gluon fusion

(gg→H), vector boson fusion (VBF), and associated pro-duction with a vector boson (WH, ZH) or top quarks

(tt̄H). Other background samples used in the analysis in-

clude SM ZZ production, and leptons from tt̄ and Drell-

Yan processes.

6 OBSERVABLES AND EVENT DISPLAY

The figures in this section show reconstructed Monte-

Carlo generated background (BG) and signal, summed

over the three channels 4µ, 4e and 2e2µ. Since the re-

sults of the analysis are not yet public, the data (2.9 fb−1

of 2015 data atp

s = 13 TeV) is not shown in the plots. Thetotal yields of the background and signal are presented in

3

table A.1 in the appendix (again with the number of ob-

served events left out).

Figure 6.1 shows the invariant mass of the four lep-

tons. Three peaks can be seen in the MC, at the sug-

gestive values 90, 125 and around 200 GeV. These masses

correspond roughly to the mass of the Z boson, the Higgs

boson, and two Z bosons. The shapes of the background

and the signal distributions are very similar.

In figure 6.2 the missing transverse energy is shown.

In contrast to figure 6.1, we can see a difference in the

shapes of the signal and the background. This informa-

tion can be used in the event selection, to apply cuts re-

ducing the background but leaving the signal mostly in-

tact. In the figure we can see the signal MET peaking at

higher values for larger values of mZ ′ , corresponding to

the DM carrying away more of the energy as they escape

the detector.

A related observable is the transverse mass of the

four leptons and MET. This quantity is defined as

mT =√

2p4lT Emi ssT

(1−cos∆φ(4l ,E mi ssT )

), and is plotted

in figure 6.3. Here the shapes are even more separated,

indicating that the transverse mass is a good observable

to use in the event selection.

Another observable that can be used to discriminate

between signal and background is |∆φ|, the azimuthalangle between the MET and the 4 leptons, which is

shown in figure 6.4. In the signal, the 4 leptons (the re-

constructed Higgs boson) and the MET (the A0 that de-

cays into DM in the Z’2HDM) are expected to go back-

to-back, which implies |∆φ| =π. This can also be seen inthe figure, while the background distribution is more flat.

Finally, the invariant mass of the highest pT jets,

shown in figure 6.5, can be used to place cuts on Higgs

VBF production.

[GeV]4lm

210

310

Ev

en

ts /

10

Ge

V

7−10

6−10

5−10

4−10

3−10

2−10

1−10

1

10

210

-1 = 13TeV, L = 2.9fbs. µ+4e+2e2µ, 44lm

Drell-Yan

H→gg

ν2l2→tt

VBF

ν2l2→WW

WZ

ttH

SMZZ

WH

ZH

=1000Z’m

=1200Z’m

=1400Z’m

=1700Z’m

=2000Z’m

=2500Z’m

=600Z’m

=800Z’m

Figure 6.1: Invariant mass of the four leptons.

PF MET [GeV]

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Ev

en

ts /

10

Ge

V

7−10

6−10

5−10

4−10

3−10

2−10

1−10

1

10

210

-1 = 13TeV, L = 2.9fbs. µ+4e+2e2µPF MET, 4

Drell-Yan

H→gg

ν2l2→tt

VBF

ν2l2→WW

WZ

ttH

SMZZ

WH

ZH

=1000Z’m

=1200Z’m

=1400Z’m

=1700Z’m

=2000Z’m

=2500Z’m

=600Z’m

=800Z’m

Figure 6.2: Missing transverse energy in the event. The shapes

of the background and the signal are very different

to each other.

[GeV]Tm

0 500 1000 1500 2000 2500 3000 3500 4000

Ev

en

ts /

40

Ge

V

7−10

6−10

5−10

4−10

3−10

2−10

1−10

1

10

210

-1 = 13TeV, L = 2.9fbs. µ+4e+2e2µ, 4T

m

Drell-Yan

H→gg

ν2l2→tt

VBF

ν2l2→WW

WZ

ttH

SMZZ

WH

ZH

=1000Z’m

=1200Z’m

=1400Z’m

=1700Z’m

=2000Z’m

=2500Z’m

=600Z’m

=800Z’m

Figure 6.3: Transverse mass of the 4l and MET. Here, the back-

ground and signal shapes are even more differenti-

ated.

|φ∆|

0 0.5 1 1.5 2 2.5 3

Ev

en

ts (

bin

siz

e 0

.1)

7−10

6−10

5−10

4−10

3−10

2−10

1−10

1

10

210

-1 = 13TeV, L = 2.9fbs. µ+4e+2e2µ| MET/4l, 4φ∆|

Drell-Yan

H→gg

ν2l2→tt

VBF

ν2l2→WW

WZ

ttH

SMZZ

WH

ZH

=1000Z’m

=1200Z’m

=1400Z’m

=1700Z’m

=2000Z’m

=2500Z’m

=600Z’m

=800Z’m

Figure 6.4: |∆φ|, the azimuthal angle between the MET and the4 leptons. This plot also shows a good difference be-

tween signal and background shapes.

4

[GeV]jj

m

0 1000 2000 3000 4000 5000 6000

Ev

en

ts /

65

Ge

V

7−10

6−10

5−10

4−10

3−10

2−10

1−10

1

10

210

-1 = 13TeV, L = 2.9fbs. µ+4e+2e2µ, 4jj

m

Drell-Yan

H→gg

ν2l2→tt

VBF

ν2l2→WW

WZ

ttH

SMZZ

WH

ZH

=1000Z’m

=1200Z’m

=1400Z’m

=1700Z’m

=2000Z’m

=2500Z’m

=600Z’m

=800Z’m

Figure 6.5: Invariant mass of the highest pT jets.

While studying the data, some data points were found

that needed further investigation. Using the CMS event

display software Fireworks, the events could be exam-

ined to decide which physics objects would need to be

checked. Since neither the event display in question nor

the details about the analysis of these physics objects can

be published here, figure 6.6 is instead given to illustrate

what the event display can look like.

Figure 6.6: Event display of a Monte Carlo generated event,

showing a transverse slice through the detector.

This event is a Monte Carlo generated event, showing

four muons (red lines) and the hits in the muon cham-

bers (red rectangles), two jets (yellow), missing trans-

verse energy (purple arrow), tracks in the tracker (green)

and deposits in the ECAL (red stacks) and HCAL (blue

stacks). Not all physics objects are shown here as low-

energy objects have been removed for clarity.

7 CONCLUSIONS

The CMS detector is a very complex machine, and find-

ing the physics behind the electrical signals generated by

the detector is not an easy task. During this project I

have learned an immense amount of physics, program-

ming and data analysis techniques, and gained insight

into how physics research is carried out in the particle

physics community. Hopefully the work I have done has

also made a small contribution to the large amount of

work that goes into an analysis like this.

8 ACKNOWLEDGEMENTS

I wish to thank my supervisors for patiently bringing me

along this journey, providing me with both challenges

and encouragement, enabling me to gain an understand-

ing of both the analysis process and the work contained

in it. I am also immensely grateful for all the discussions

with other summer students and interns, be it about

specific project issues or physics in general, exchanging

ideas and experiences with people from all corners of the

world. Of course, none of this would have been possible

without CERN providing me with this opportunity, and

the Summer student team who has made it such a well-

organised and valuable experience.

REFERENCES

[1] G. Brooijmans et al. “Les Houches 2015: Physics at

TeV colliders - new physics working group report”.

In: 9th Les Houches Workshop on Physics at TeV Col-

liders (PhysTeV 2015) Les Houches, France, June 1-19,

2015. 2016. arXiv: 1605.02684 [hep-ph].

[2] L. Carpenter et al. “Mono-Higgs: A new collider

probe of dark matter”. In: Phys. Rev. D89.7 (2014),

p. 075017.

[3] D. Barney. “CMS Detector Slice”. CMS Collection.

Jan. 2016.

[4] S. Chatrchyan et al. “The CMS experiment at the

CERN LHC. The Compact Muon Solenoid experi-

ment”. In: J. Instrum. 3 (2008), S08004. 361 p.

[5] M. Ahmad et al. “Measurement of the properties

of the Higgs boson in the four-lepton final state atps = 13 TeV”. CMS draft note. Mar. 2016.

5

A APPENDIX

Table A.1: The number of estimated background and signal events, after the final selection, in the full measurement range

70 < m4l < 1000 GeV. Note that three backgrounds are brought to zero by the event selection: W+Jets (W→lν), QCD,and ST (single top quark).

Channel 4µ 4e 2e2µ 4l

Drell-Yan 1.03 ± 0.60 1.09 ± 0.45 5.69 ± 1.80 7.82 ± 1.95gg→H 2.33 ± 0.01 1.32 ± 0.01 3.11 ± 0.01 6.76 ± 0.02tt→2l2ν 0.10 ± 0.07 0.30 ± 0.12 0.69 ± 0.19 1.08 ± 0.24VBF 0.11 ± 0.00 0.06 ± 0.00 0.14 ± 0.00 0.31 ± 0.00W+Jets (W→lν) 0.00 ± 0.00 0.00 ± 0.00 0.00 ± 0.00 0.00 ± 0.00WW→2l2ν 0.00 ± 0.00 0.00 ± 0.00 0.02 ± 0.02 0.02 ± 0.02WZ 0.00 ± 0.00 0.00 ± 0.00 0.86 ± 0.35 0.86 ± 0.35ttH 0.02 ± 0.00 0.01 ± 0.00 0.03 ± 0.00 0.07 ± 0.00QCD 0.00 ± 0.00 0.00 ± 0.00 0.00 ± 0.00 0.00 ± 0.00SM ZZ 39.12 ± 0.08 23.86 ± 0.06 54.54 ± 0.09 117.52 ± 0.13ST 0.00 ± 0.00 0.00 ± 0.00 0.00 ± 0.00 0.00 ± 0.00WH 0.03 ± 0.00 0.02 ± 0.00 0.04 ± 0.00 0.09 ± 0.00ZH 0.21 ± 0.00 0.15 ± 0.00 0.33 ± 0.00 0.69 ± 0.00Total background 42.95 ± 0.61 26.82 ± 0.47 65.45 ± 1.84 135.22 ± 2.00mZ ′=600 GeV 1.88e-2 ± 3.95e-4 1.04e-2 ± 2.94e-4 2.69e-2 ± 4.72e-4 5.61e-2 ± 6.82e-4mZ ′=800 GeV 7.32e-3 ± 1.88e-4 4.64e-3 ± 1.50e-4 1.14e-2 ± 2.36e-4 2.34e-2 ± 3.37e-4mZ ′=1000 GeV 5.81e-3 ± 1.15e-4 3.48e-3 ± 8.87e-5 8.66e-3 ± 1.40e-4 1.80e-2 ± 2.02e-4mZ ′=1200 GeV 4.06e-3 ± 7.50e-5 2.70e-3 ± 6.13e-5 6.64e-3 ± 9.59e-5 1.34e-2 ± 1.36e-4mZ ′=1400 GeV 2.27e-3 ± 4.15e-5 1.53e-3 ± 3.38e-5 3.77e-3 ± 5.34e-5 7.56e-3 ± 7.56e-5mZ ′=1700 GeV 9.97e-4 ± 1.69e-5 6.86e-4 ± 1.40e-5 1.57e-3 ± 2.12e-5 3.26e-3 ± 3.05e-5mZ ′=2000 GeV 4.51e-4 ± 7.67e-6 2.99e-4 ± 6.24e-6 7.05e-4 ± 9.52e-6 1.45e-3 ± 1.37e-5mZ ′=2500 GeV 1.21e-4 ± 2.27e-6 8.17e-5 ± 1.87e-6 1.90e-4 ± 2.85e-6 3.93e-4 ± 4.09e-6

6