unf undergrad physics

Dimuon Analyses at the LHC and the Age of ‘Big Data’

T. Nicholas Kypreos, Ph.D.CMS Collaborationnow Amazon Web Services

my favoriteundergraduate university!

1Friday, September 6, 2013

Outline

• outline

• what weʼre looking for

• why hadron colliders

• muons in particle physics

• dimuon analysis in practice

• what weʼve learned

• what Iʼve learned…


the Standard Model

SU(3)c × SU(2)L × U(1)Y

strong interaction mediated by gluons

weak interaction -- mediated by massless photons and massive gauge bosons

Higgs?

SU(2) x U(1) broken by the Higgs mechanism.Higgs candidate discovered in 2012!

36 CMS Collaboration / Physics Letters B 716 (2012) 30–61

Table 3The number of selected events, compared to the expected background yields and expected number of signalevents (mH = 125 GeV) for each final state in the H ! ZZ analysis. The estimates of the Z+ X backgroundare based on data. These results are given for the mass range from 110 to 160 GeV. The total backgroundand the observed numbers of events are also shown for the three bins (“signal region”) of Fig. 4 where anexcess is seen (121.5 <m4! < 130.5 GeV).

Channel 4e 4µ 2e2µ 4!

ZZ background 2.7 ± 0.3 5.7 ± 0.6 7.2 ± 0.8 15.6 ± 1.4Z+ X 1.2+1.1

"0.8 0.9+0.7"0.6 2.3+1.8

"1.4 4.4+2.2"1.7

All backgrounds (110 <m4! < 160 GeV) 4.0 ± 1.0 6.6 ± 0.9 9.7 ± 1.8 20 ± 3Observed (110 <m4! < 160 GeV) 6 6 9 21

Signal (mH = 125 GeV) 1.36 ± 0.22 2.74 ± 0.32 3.44 ± 0.44 7.54 ± 0.78

All backgrounds (signal region) 0.7 ± 0.2 1.3 ± 0.1 1.9 ± 0.3 3.8 ± 0.5Observed (signal region) 1 3 5 9

and the other pair is required to have a mass in the range12–120 GeV. The ZZ background is evaluated from MC simula-tion studies. Two different approaches are employed to estimatethe reducible and instrumental backgrounds from data. Both startby selecting events in a background control region, well separatedfrom the signal region, by relaxing the isolation and identificationcriteria for two same-flavour reconstructed leptons. In the first ap-proach, the additional pair of leptons is required to have the samecharge (to avoid signal contamination) while in the second, twoopposite-charge leptons failing the isolation and identification cri-teria are required. In addition, a control region with three passingleptons and one failing lepton is used to estimate contributionsfrom backgrounds with three prompt leptons and one misidenti-fied lepton. The event rates measured in the background controlregion are extrapolated to the signal region using the measuredprobability for a reconstructed lepton to pass the isolation andidentification requirements. This probability is measured in an in-dependent sample. Within uncertainties, comparable backgroundcounts in the signal region are estimated by both methods.

The number of selected ZZ ! 4! candidate events in the massrange 110 < m4! < 160 GeV, in each of the three final states, isgiven in Table 3, where m4! is the four-lepton invariant mass. Thenumber of predicted background events, in each of the three fi-nal states, and their uncertainties are also given, together withthe number of signal events expected from a SM Higgs boson ofmH = 125 GeV. The m4! distribution is shown in Fig. 4. There is aclear peak at the Z boson mass where the decay Z ! 4! is re-constructed. This feature of the data is well reproduced by thebackground estimation. The figure also shows an excess of eventsabove the expected background around 125 GeV. The total back-ground and the numbers of events observed in the three binswhere an excess is seen are also shown in Table 3. The combinedsignal reconstruction and selection e!ciency, with respect to themH = 125 GeV generated signal with m!! > 1 GeV as the only cut,is 18% for the 4e channel, 40% for the 4µ channel, and 27% for the2e2µ channel.

The kinematics of the H ! ZZ ! 4! process in its centre-of-mass frame, for a given invariant mass of the four-lepton system,is fully described by five angles and the invariant masses of thetwo lepton pairs [123–125]. These seven variables provide signif-icant discriminating power between signal and background. Themomentum of the ZZ system may further differentiate signal frombackground, but would introduce dependence on the productionmechanism, and on the modelling of the QCD effects, and is there-fore not considered here. A kinematic discriminant is constructedbased on the probability ratio of the signal and background hy-potheses, KD = Psig/(Psig + Pbkg), as described in Ref. [126]. Thelikelihood ratio is defined for each value of m4! . For the signal, thephase-space and Z propagator terms [127] are included in a fullyanalytic parameterization [124], while the background probability

Fig. 4. Distribution of the four-lepton invariant mass for the ZZ ! 4! analysis.The points represent the data, the filled histograms represent the background,and the open histogram shows the signal expectation for a Higgs boson of massmH = 125 GeV, added to the background expectation. The inset shows the m4! dis-tribution after selection of events with KD > 0.5, as described in the text.

is tabulated using a simulation of the qq ! ZZ/Z" process. Thestatistical analysis only includes events with m4! > 100 GeV.

Fig. 5 (upper) shows the distribution of KD versus m4! forevents selected in the 4! subchannels. The colour-coded regionsshow the expected background. Fig. 5 (lower) shows the same two-dimensional distribution of events, but this time superimposedon the expected event density from a SM Higgs boson (mH =125 GeV). A clustering of events is observed around 125 GeV witha large value of KD , where the background expectation is low andthe signal expectation is high, corresponding to the excess seenin the one-dimensional mass distribution. The m4! distribution ofevents satisfying KD > 0.5 is shown in the inset in Fig. 4.

There are three final states and two data sets (7 and 8 TeV),and thus the statistical treatment requires six simultaneous two-dimensional maximum-likelihood fits for each value of mH, in thevariables m4! and KD . Systematic uncertainties are evaluated fromdata for the trigger e!ciency and for the combined lepton re-construction, identification, and isolation e!ciencies, as describedin [128]. Systematic uncertainties in the energy/momentum cal-ibration and in the energy resolution are estimated from data.Additional systematic uncertainties arise from limited statisticalprecision in the reducible background control regions.

The expected 95% CL upper limit on the signal strength # /#SM,in the background-only hypothesis, for the combined 7 and 8 TeV


beyond the standard model...

• many questions left un-answered by the standard model

• electromagnetic and weak interactions unify at ~100 GeV

• what about the strong and gravitational interactions?

• relative strength between forces? baryogenesis?

• LHC is built to answer these kinds of questions as a “discovery machine”

• first machine to directly probe beyond the TeV scale

• CMS is a multi-purpose detector to detect all known particles (neutrinos are inferred)


the general idea for hadron smashing

• protons are stable (lifetime > 1034 years [1])

• give them a bunch of energy, smash ʻem, get new things

• partons (quarks) inside the proton start to interact inside the proton via gluons

• energetic protons donʼt look like 3 quarks…

• left with lots of quark-antiquark collisionswith a whole spread of quark energies

• more energy --> higher mass particlescan be created (E = M)

• hadron colliders are commonly referred to as“discovery machines”

[2]

[3]

where c=1 in natural units


The Large Hadron Collider

• LHC is a proton-proton collider designed to produce collisions with a center-of-mass energy of 14 TeV

• operated at COM 8 TeV in 2012 (and 7 TeV in 2011)

• ring is 17 milesin diameter builtfrom the LEPtunnel

• the last colliderwas the Tevatronthat operated at 1.96 TeV -- the LHC is a strongerprobe beyond the 1 TeV energy scale


obligatory travel photos

• itʼs really all underground -- the rest is the French-Swiss frontier

!!"#!$%&'()(*+!,#!-&./0) -&%1('*!122*+!34%(5!6788 !!!!!!!!!!!!!!!!!!"#


MORE OBLIGATORY TRAVEL PHOTOS?!?!

!!"#!$%&'()(*+!,#!-&./0) -&%1('*!122*+!34%(5!6788 !!!!!!!!!!!!!!!!!!"#

lots of Swiss vineyards...


luminosity LHC 2010-2011 LHC 2012

Nevents = σ (pp → X)Lprobability x trials

• higher luminosity -> more events➔ BIG DATA

• LHC can produce all SM particles across a range of energies

• production is not equiprobable -- governed by the cross section, σ

• small cross sections correspond to rarer processes in nature

• event production depends on integrated luminosity of the machine

0.1 / 40e-12 = 2.5e9 = 2.3PB


dimuons in the standard model

• lots of particles create have dimuons final states

• most are mesons

• main interest here is in the Z/γ -- called the Drell-Yan process

Figure 2-2. Feynman diagram showing the quark-antiquark annihilation into a neutralZ/γ∗ propagator that decays into a lepton pair.

2.2 Search Motivation

The electromagnetic and weak forces appear as separate forces at low energies

of particle interactions. EWK theory predicts a unification at a higher energy scale

(O(100 GeV) ) where the symmetry of the two forces is restored. With current

experimental knowledge, the strong and EWK forces are in different symmetry groups.

A natural extension of the SM is to treat the strong, weak and electromagnetic forces as

manifestations of the same fundamental interaction. The symmetry of the fundamental

interaction is restored at very high energies. Such overarching complex symmetries

are often referred to as grand unified theories (GUTs). Many of these theories predict

a narrow mass resonance from a new vector boson, which is generically referred to as

a Z�, that decays to dimuons. A new high-mass dimuon resonance has not yet been

observed, but LHC has the potential to either discover or stringently limit the phase

space of theoretical predictions. This section provides some of theoretical background

for the high-mass dimuon resonance search but is not exhaustive.

As mentioned above, the underlying premise behind GUT models is to describe the

SM as a low-energy manifestation of a higher symmetry. The first GUT model was made

using the SU(5) symmetry group, which is the smallest symmetry group to contain the

SM as represented in Equation 2–2 [18]. One of the associated predictions from SU(5)

GUTs is the finite lifetime of the proton, which has thus far been experimentally excluded

up to roughly the lifetime of the universe [18, 19].

22

this guy

quark-antiquark meetannihilate to force carrierdecays to two leptons

60 < M < 120 GeVσ7 TeV ≅ 970 pbσ8 TeV ≅ 1120 pb


new physics search

• goal is to find a “Grand Unified Theory”

• new force carriers can also decay to dimuons…

• creates a general framework to parameterize a search and deal with a discovery

Z �(β) = χ cos β + ψ sin β• one popular GUT gauge group is E6 (another is SO(10))

• couplings and mass are closely inter-related

SU(3)c × SU(2)L × U(1)Y × U �(1)

LZ� =g�

4 cos θWfγµ

�gV − gAγ

5�fZ �µwith couplings:

?


extra dimensions -- Randall-Sundrum graviton models• Randall-Sundrum model predicts

resonant graviton

• small extra spatial dimension

• curved bulk space with curvature k -- graviton propagates in the bulk

• gravitons are spin-2 (tensor)Zʼs are spin-1 (vector)

Figure 17: Drell-Yan production of a (a) 700 GeV KK graviton at the Tevatron with k/MP l =1, 0.7, 0.5, 0.3, 0.2, and 0.1, respectively, from top to bottom; (b) 1500 GeV KK gravitonand its subsequent tower states at the LHC. From top to bottom, the curves are for k/MP l =1, 0.5, 0.1, 0.05, and 0.01, respectively.

44

controlled by k/MPlR

xµ

x5 ! R!

Figure 1: A 5D hypercylindrical spacetime

Ex. Show that if AM is in a general gauge it can be brought to almostaxial gauge via the (periodic) gauge transformation

!(x, !) ! Peig! !0 d!!RA5(x,!!)e!igA(0)

5 (x)!. (2.6)

Note that the sum over n of the fields in any interaction term must bezero since this is just conservation of fifth dimensional momentum, where forconvenience we define the complex conjugate modes, A(n)"

µ , to be the modescorresponding to "n. In this way a spacetime symmetry and conservationlaw appears as an internal symmetry in the 4D KK decomposition, withinternal charges, n.

Since all of the n #= 0 modes have 4D masses, we can write a 4D e"ec-tive theory valid below 1/R involving just the light A(0) modes. Tree levelmatching yields

Se! $E# 1

R

2"R Tr

"d4x

#"

1

4F (0)

µ" F (0)µ" +1

2(DµA

(0)5 )2

$. (2.7)

The leading (renormalizable) non-linear interactions follow entirely from the4D gauge invariance which survives almost axial gauge fixing. We have a

5

G∗

g

g

�+

�−

b

g t

tW−

b

W+

q

q

ν

�

�

ν

1

extra Feynman diagram


the detector


The Compact Muon Solenoid (CMS) Detector• general purpose detector

• can directly detect known particles

• beryllium beam pipe• tracking detector

• silicon pixel+strip

• calorimeter• electron

• hadron• muon spectrometer

• drift tubes

• cathode strip chambers• resistive plate chambers

yz

x14000 tlocated ~100 m underground3.8 T solenoidal magnetic field


particle interactions

• electrons -- ionize in the tracker, end as a shower (lots of interactions) in the calorimeter

• photons -- no ionization, shower in the calorimeter

• muons -- ionize in the tracker, not stopped in the calorimeter

• hadrons -- charged hadrons ionize in the tracker, neutrals do not.often appear as jetsin high-energy collisions

• neutrinos -- not detecteddirectly, but are inferredby measuring the momentum imbalance


the hard part of muon reconstruction

• detector alignment

• algorithmic smoothing (Kalman filtering)

• knowing resolution

• high momentum tracks are harder to measure


so what about big data?

• collision rate of 40 MHz

• 100 Hz can be written to tape➞ rate reduction is necessary

• rate reduced in two phases

• Level-1 (hardware)

• collects the full event 100 kHz out

• High Level Trigger (HLT) (software)

• on-site computing farm performs fast partial reconstruction

• final output is 100 Hz


how that works…

• custom hardware preprocesses data

• interfaces with other systems (they have to agree on time)

• information is aggregated and a central brain decides if an collision event is “interesting”

• automated in a feedback loop…

• data are then categorized into analyses that flag on observed topologies to keep sizes almost manageable

Figure 3-16. Architecture of the CMS Level−1 trigger.

through the TCS, the L1A is distributed to all detector front-ends through the timing,

trigger, and control (TTC) system, which also distributes the clock and synchronous

signals to perform fast operations such as resetting the event counter. Upon receipt of

the L1A, each front end module reads out the high resolution detector data which has

been stored in pipelined memory, and is passed on for final reconstruction in selected

events. The logical flow between the GT, TCS and DAQ is shown in Figure 3-17 [38].

When the DAQ accesses the raw data, that data is sent to the HLT. The HLT is an

on-site computer farm that performs fast reconstruction algorithms that turn low-level

raw data into a list of usable high-level physics objects, such as muons, electrons, /ET ,

and jets. This fast reconstruction enables the HLT to apply a more stringent selection on

the available fast-reconstructed high-level physics objects. The HLT categorizes each

event by its constituent physics objects (the particles that are seen) and decides if that

event is potentially “interesting” for offline physics analysis. Offline physics analyses

collaborate to define “trigger paths” for the HLT that govern what the HLT determines to

be “interesting.” Rates of different HLT trigger paths are estimated and algorithm paths

46

Figure 3-17. Overview of the CMS trigger control system.

are designed to maximize and balance rates for different offline physics analyses. The

final rate at which the HLT selects events for the DAQ to send for offline analysis is about

100 Hz.

Events built by the DAQ are marked by the run in which they were taken, the

luminosity section of the beam fill, and the event number number of that fill. Physics

events that are written out by the DAQ are categorized by the CMS computing network

into primary datasets to optimize user access.

47


data selection


data-simulation comparisons• use the detector to check monitoring distributions and select good muons

N(Tracker hits)0 5 10 15 20 25 30 35 40

Even

ts

-210

-110

1

10

210

310

410

510 / ndof2

Tracker partχ

0 0.5 1 1.5 2 2.5 3Ev

ents

-210

-110

1

10

210

310

410

510

LayersN0 2 4 6 8 10 12 14 16 18 20

Events

-210

-110

1

10

210

310

410

510 Dataµµ →DY ττ →DY

WZZZWW

νµ →W tt

tW

Number Of Matches0 2 4 6 8 10

Even

ts

-210

-110

1

10

210

310

410

510

N(Pixel hits)0 2 4 6 8 10

Even

ts

-210

-110

1

10

210

310

410

510

N(Mu hits)0 2 4 6 8 10 12 14

Even

ts

-210

-110

1

10

210

310

410

510


efficiencies

• L1 efficiencies in 2011-2012 (measured in-data)

• less efficient in 2012 from low-level changes

• full dimuon efficiency in simulation

dimuon invariant mass (GeV)200 400 600 800 1000 1200 1400 1600 1800 2000

effic

ienc

y

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

/ ndf 2! 25.5 / 33Prob 0.823a 0.00306± 0.849 b 1.51e+07± -1.22e+08 c 28.9± 510

/ ndf 2! 25.5 / 33Prob 0.823a 0.00306± 0.849 b 1.51e+07± -1.22e+08 c 28.9± 510

wrt triggered events in acceptancewrt events in acceptancetotalfit to a + b/pow(m+c, 3) for m in (200,2000)


dimuon event

• dimuon event passing all selection criteria for final analysis


new physics search


philosophy• looking for a narrow “bump” on a steeply smooth falling (irreducible)

background (the Drell-Yan Continuum)

• normalize to the Z resonance to cancel out efficiencies and potentially unknown systematic uncertainties

JHEP05(2011)093

) [GeV]-µ+µm(200 400 600 800 1000

Ev

en

ts /

5 G

eV

-310

-210

-110

1

10

210

310

410DATA

-µ+µ!*"Z/

+ other prompt leptonstt

jets

-µ+µ ! (750 GeV) SSMZ'

-1 L dt = 40 pb# = 7 TeV sCMS

) [GeV]-µ+µm(200 400 600 800 1000

Ev

en

ts /

5 G

eV

-310

-210

-110

1

10

210

310

410

) [GeV]eem(200 400 600 800 1000

Ev

en

ts /

5 G

eV

-310

-210

-110

1

10

210

310

410DATA

-e

+e!*"Z/


jets (data)

-e

+e ! (750 GeV) SSMZ'

-1 L dt = 35 pb# = 7 TeV sCMS

) [GeV]eem(200 400 600 800 1000

Ev

en

ts /

5 G

eV

-310

-210

-110

1

10

210

310

410

Figure 2. Invariant mass spectrum of µ+µ! (left) and ee (right) events. The points with errorbars represent the data. The uncertainties on the data points (statistical only) represent 68%confidence intervals for the Poisson means. The filled histograms represent the expectations fromSM processes: Z/!", tt, other sources of prompt leptons (tW, diboson production, Z ! ""), andthe multi-jet backgrounds. The open histogram shows the signal expected for a Z#

SSM with a massof 750 GeV.

) [GeV]-µ+µm(50 100 150 200 250 300 350 400 450 500

)-µ

+µ

m(

! E

ve

nts

1

10

210

310

410DATA

-µ+µ"*#Z/


jets

-1 L dt = 40 pb$ = 7 TeV sCMS

) [GeV]-µ+µm(50 100 150 200 250 300 350 400 450 500

)-µ

+µ

m(

! E

ve

nts

1

10

210

310

410

) [GeV]eem(50 100 150 200 250 300 350 400 450 500

)e

e m

(!

Ev

en

ts

1

10

210

310

410DATA

-e

+e"*#Z/


jets (data)

-1 L dt = 35 pb$ = 7 TeV sCMS

) [GeV]eem(50 100 150 200 250 300 350 400 450 500

)e

e m

(!

Ev

en

ts

1

10

210

310

410

Figure 3. Cumulative distribution of invariant mass spectrum of µ+µ! (left) and ee (right) events.The points with error bars represent the data, and the filled histogram represents the expectationsfrom SM processes.

and correcting for a small (" 0.4%) background contamination (determined with MC

simulation). The uncertainty on µZ is about 1% (almost all statistical) and contributes

– 10 –

JHEP10(2011)007

) [GeV]llM(

]-1

) [G

eV

ll/d

M(

σ d

llσ1/

-710

-610

-510

-410

-310

-210

-110

1

15 30 60 120 200 600

channels)µ Data (e+

NNLO, FEWZ+MSTW08

CMS = 7 TeVs at -1

36 pb

ll →*/Z γ

Figure 4. DY invariant mass spectrum, normalized to the Z resonance region, r =(1/σ��)dσ/dM(��), as measured and as predicted by NNLO calculations, for the full phase space.The vertical error bar indicates the experimental (statistical and systematic) uncertainties summedin quadrature with the theory uncertainty resulting from the model-dependent kinematic distribu-tions inside each bin. The horizontal bars indicate bin sizes and the data points inside are placedaccording to ref. [31]. The width of the theory curve represents uncertainties from table 10.

Chinese Academy of Sciences, Ministry of Science and Technology, and National Natu-ral Science Foundation of China; the Colombian Funding Agency (COLCIENCIAS); theCroatian Ministry of Science, Education and Sport; the Research Promotion Foundation,Cyprus; the Estonian Academy of Sciences and NICPB; the Academy of Finland, FinnishMinistry of Education and Culture, and Helsinki Institute of Physics; the Institut Nationalde Physique Nucleaire et de Physique des Particules / CNRS, and Commissariat a l’EnergieAtomique et aux Energies Alternatives / CEA, France; the Bundesministerium fur Bildungund Forschung, Deutsche Forschungsgemeinschaft, and Helmholtz-Gemeinschaft DeutscherForschungszentren, Germany; the General Secretariat for Research and Technology, Greece;the National Scientific Research Foundation, and National Office for Research and Tech-nology, Hungary; the Department of Atomic Energy and the Department of Science andTechnology, India; the Institute for Studies in Theoretical Physics and Mathematics, Iran;the Science Foundation, Ireland; the Istituto Nazionale di Fisica Nucleare, Italy; the KoreanMinistry of Education, Science and Technology and the World Class University program ofNRF, Korea; the Lithuanian Academy of Sciences; the Mexican Funding Agencies (CIN-VESTAV, CONACYT, SEP, and UASLP-FAI); the Ministry of Science and Innovation,

– 20 –


• use simulation to model backgrounds

• fit the background to a template shape and look for a bump on something smooth

• fitting function is often arbitrary, but itʼs nice when thereʼs analytical meaning to it because itʼs easier to defend

• not the only background shapein this analysis

primary background -- the Drell-Yan continuum

f(m) = Nea·mmb


“prompt” backgrounds• prompt dimuon background -- contaminating our samples

• ttbar, diboson

ttbar WW


check these backgrounds with the “e-μ” method

• Drell-Yan continuum conserves lepton flavor (model constraint)

• these prompt backgrounds violate flavor so they create an orthogonal control sample

• comprised mostly of the t-tbar process

• if data and simulation agreefor the eµ spectrum, the prompt background is undercontrol

) (GeV)

±

µ±m(e200 400 600 800 1000

Even

ts /

20 G

eV

-110

1

10

210

310

DATA & other prompt leptonstt

pairsµfake e

-1 L dt = 3.7 fb! = 8 TeV sCMS preliminary

QCD


QCD “jet” background

• isolation requirement on muons efficiently removes jets faking muons

• use data-driven method to estimate the QCD background...

isolation on simulatedQCD dimuons

• simulation leaves nothing left to predict

simulation


same-sign dimuon background

• control plot comparison for the same-sign dimuon spectrum

• using the jets background estimated from data

• electron selection from the dielectron analysis


invariant mass spectrum

• compare data with simulation and the cumulative distribution

• compare simulated background shape with data

) [GeV]-µ+µm(80 100 200 300 1000 2000

Eve

nts

/ GeV

-410

-310

-210

-110

1

10

210

310

410

510

DATA-µ+µ!/Z"

+ other prompt leptonsttjets

-1 L dt = 4.1 fb# = 8 TeV, sCMS,

) [GeV]-µ+µm(80 100 200 300 1000 2000

)-µ+

µ m

(!

Eve

nts

-210

-110

1

10

210

310

410

510

610DATA

-µ+µ"/Z# + other prompt leptonstt

jets

-1 L dt = 4.1 fb$ = 8 TeVsCMS Preliminary,

8 6 Statistical analysis and results

) [GeV]-µ+µm(300 400 500 600 1000 2000 3000

(dat

a-fit

)/fit

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

/ ndof = 18.0/232!

-1 L dt = 3.9 fb" = 8 TeVsCMS Preliminary,

m(ee) [GeV]300 400 500 600 1000 2000 3000

(dat

a-fit

)/fit

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

/ ndof = 25.7/222!

-1 L dt = 3.6 fb" = 8 TeVsCMS Preliminary,

Figure 4: The relative difference between the data and the fitted parametrization of the simu-lated background, where the latter is normalized to the data, is shown in a variety of mass binsfor the muon (top) and electron (bottom) channels. The binning was chosen so that there is aminimum prediction of 10 events in each bin and a minimum bin size of 20 GeV was required.The horizontal error bars simply represent the bin width and should not be interpreted as anuncertainty.

The pdf fS(m|Γ, M, w) for the resonance signal is a Breit-Wigner of width Γ and mass M con-211

voluted with a Gaussian resolution function of width w. The width Γ is taken to be that of the212

Z�ψ. This width is sufficiently small that the detector resolution dominates.213

The Poisson mean of the signal yield is µS = Rσ · µZ · R�, where R� is the ratio of selection214

efficiency times detector acceptance for Z� decay to that of Z decay. The variable µB denotes215

the Poisson mean of the total background yield, and µZ is the Poisson mean of the number of216

Z → �� events.217

The Poisson mean µZ of the number of Z → �� events in the sample is estimated by counting218

the number of events in the Z peak mass region and correcting for a small (∼ 0.2%) background219

contamination (determined using MC simulation).220

A background pdf fB was chosen and its shape parameters fixed by fitting to the simulated221

Drell–Yan spectrum in the mass range 200 < m�� < 2500 GeV. The functional form used for the222

background is m−κe−αm, where the shape parameters κ and α were determined from a fit to a223

simulated background mass spectrum. The agreement between this fit and the observed data224

over a range of mass bins is shown in Fig. 4.225

The extended likelihood L is then226


muon channel limits• dimuon channel limits

• structure from 2011 data not seen in 2012

CMS Collaboration / Physics Letters B 714 (2012) 158–179 163

Fig. 5. Upper limits as a function of the resonance mass M on the production ratioR! of cross section times branching fraction into lepton pairs for Z!

SSM, Z!" , Z!

St ,and GKK production to the same quantity for Z bosons. The limits are shown from(top) the µ+µ" final state, (middle) the ee final state and (bottom) the combineddilepton result. Shaded green and yellow bands correspond to the 68% and 95%quantiles for the expected limits. The predicted cross section ratios are shown asbands, with widths indicating the theoretical uncertainties. The differences in thewidths reflect the different uncertainties in the K factors used. (For interpretationof the references to colours in this figure legend, the reader is referred to the webversion of this Letter.)

nominal resonance mass [9,38]. The NNLO prediction for the Z/# #

production cross section in the mass window of 60 to 120 GeV is0.97 ± 0.04 nb [37].

The uncertainties described above are propagated into a com-parison of the experimental limits with the predicted cross sectiontimes branching fraction ratios (R! ) to obtain 95% CL lower limitson Z! masses in various models. No uncertainties on cross sectionsfor the various theoretical models are included when determiningthe limits. As a result of the dimuon analysis, the Z!

SSM can be ex-cluded below 2150 GeV, the Z!

" below 1820 GeV, and the RS GKK

Fig. 6. The 95 % CL upper limits on the Z! cross sections for given masses are equiv-alent to excluded regions in the (cd, cu) plane which are bounded by the thin blacklines in the figure. They are compared with the predicted values of (cd, cu) in threeclasses of models. The colours on curves correspond to different mixing angles ofthe generators defined in each model. For any point on a model curve, the masslimit corresponding to that value of (cd, cu) is given by the intersecting experimen-tal contour.

below 1990 (1630) GeV for couplings of 0.10 (0.05). For the dielec-tron analysis, the production of Z!

SSM and Z!" bosons is excluded for

masses below 2120 and 1810 GeV, respectively. The correspondinglower limits on the mass for RS GKK with couplings of 0.10 (0.05)are 1960 (1640) GeV.

The combined limit, obtained by using the product of the like-lihoods for the individual channels, is shown in Fig. 5 (bottomplot). The signal cross section is constrained to be the same inthe two channels and lepton universality is assumed. The 95%CL lower limits on the mass of a Z! resonance are 2330 GeV forZ!SSM, 2000 GeV for Z!

" , and 890 (540) GeV for Z!St with $ = 0.06

(0.04). The RS Kaluza–Klein gravitons are excluded below 2140(1810) GeV, for couplings of 0.10 (0.05). The observed limits aremore restrictive than those previously obtained via similar directsearches by the Tevatron experiments [10–13,42,43] and indirectsearches by LEP-II experiments [16–19], as well as those obtainedby ATLAS [8] and CMS [9] using smaller data samples. The re-sults are also presented in the (cd, cu) plane in Fig. 6 [9,44]. Theparameters cd and cu contain all the information about the model-dependent couplings of the Z! to fermions in the annihilations ofcharge "1/3 and 2/3 quarks, respectively. The cross-section lim-its at any particular mass are contours in the (cd, cu) plane. Themodel classes are described in [9,38].

The largest deviation from SM expectations at high masses isaround 1 TeV, in both spectra. The statistical significance of the ob-servations is expressed in terms of Z-values, which are the effectivenumbers of Gaussian standard deviations in a one-sided test. Forthe dimuon sample, the maximum excess occurs at 1005 GeV, withlocal Z = 1.2, while for the dielectron sample, the maximum excessoccurs at 960 GeV, with local Z = 1.7. In the combination of thetwo channels, the maximum excess is found at 965 GeV, with lo-cal Z = 2.1. The probability of an enhancement at least as large asthe one found occurring anywhere between 600 and 2500 GeV inthe observed sample size corresponds to Z = "0.7 for the dimuonsample and Z = 0.3 for the dielectron sample. For the combineddata sample, the corresponding probability in a joint peak searchis equivalent to Z = 0.4.

JHEP05(2011)093

400 600 800 1000 1200 14000

0.2

0.4

0.6

M [GeV]

-3 1

0!

"R

68% expected

95% expected

=0.1Pl

M k/KK

G

=0.05Pl

M k/KK

G

SSMZ'

#Z'

95% C.L. limit

-1dt = 40.0pbL $CMS,

a)

-µ+µ

400 600 800 1000 1200 14000

0.2

0.4

0.6

M [GeV]

-3 1

0!

"R

68% expected

95% expected

=0.1Pl

M k/KK

G

=0.05Pl

M k/KK

G

SSMZ'

#Z'

95% C.L. limit


b)

ee

400 600 800 1000 1200 14000

0.2

0.4

0.6

M [GeV]

-3 1

0!

"R

68% expected

95% expected

=0.1Pl

M k/KK

G

=0.05Pl

M k/KK

G

SSMZ'

#Z'

95% C.L. limit


c)

+ee-µ+µ

Figure 4. Upper limits as a function of resonance mass M , on the production ratio R! of crosssection times branching fraction into lepton pairs for Z!

SSM and GKK production and Z!" boson

production. The limits are shown from (top) the µ+µ" final state, (middle) the ee final state and(bottom) the combined dilepton result. Shaded yellow and red bands correspond to the 68% and95% quantiles for the expected limits. The predicted cross section ratios are shown as bands, withwidths indicating the theoretical uncertainties.

– 14 –

7 TeV, 40 pb-1

7 TeV, 5.3 fb-1

8 TeV, 4.1 fb -1

Z’SSM 1140 2150 2270

Z’ψ 887 1810 1940


combine with electrons• combined dimuon and dielectron

channels for 2011 and 2012 data

badger

m(ee) [GeV]80 100 200 300 1000 2000

Eve

nts

/ GeV

-410

-310

-210

-110

1

10

210

310

410

510

DATA-e+e!/Z"

+ other prompt leptonsttjets (data)

-1 L dt = 3.6 fb# = 8 TeV, sCMS,

7 TeV, 40 pb-1

8 TeV, 4.1 fb -1

8 TeV, 4.1 fb -1

Z’SSM 2330 2440 2590

Z’ψ 2000 2110 2260

GKK: k/Mpl = 0.1 2140 2260 2390

GKK: k/Mpl = 0.05 1810 1900 2030


how this translates into business

• engineering problems are often hard

• business problems are often ill-posed

• the tools:

• building models, distributed computing, computer simulations, statistics

• use every bit of math and computer science you know

• know how to suffer with an unclear problem statement


references

• [1] proton lifetime http://www-sk.icrr.u-tokyo.ac.jp/whatsnew/new-20091125-e.html

• [2] basic proton http://largehadron.files.wordpress.com/2010/05/quark_structure_proton_svg.png

• [3] energetic proton http://www.ep.ph.bham.ac.uk/exp/H1/images/Proton.jpg


http://www-sk.icrr.u-tokyo.ac.jp/whatsnew/new-20091125-e.html

http://www-sk.icrr.u-tokyo.ac.jp/whatsnew/new-20091125-e.html

http://largehadron.files.wordpress.com/2010/05/quark_structure_proton_svg.png

http://largehadron.files.wordpress.com/2010/05/quark_structure_proton_svg.png

http://www.ep.ph.bham.ac.uk/exp/H1/images/Proton.jpg

http://www.ep.ph.bham.ac.uk/exp/H1/images/Proton.jpg

supporting slides


measuring track parameters

• simplified 3-point version: s ≈ 1

8

qL2B

pT�δpTpT

�

ms

∝�L/X0

qBL

�δpTpT

�

meas

∝ σxpT

qBL2

on the curvature measurement

multiple scattering

• whatʼs actually measured is q/pT (transverse curvature)

• 5 parameters are measured in tracking: cot θ − θ is the polar angle

φ− azimuthal angle

q/pT − transverse curvature

d0 − distance of closest approach in x-y

z0 − distance of closest approach in z36Friday, September 6, 2013

cosmic muon background• cosmics are rejected by

a highly efficient (>99%) cut on the 3D angle

• final expected cosmic background <1 event

Events

-210

-110

1

10

210

310

410

3D angle-510 -410 -310 -210 -110 1 10

Events

-110

1

10

Dimuon mass, GeV60 210 210!2 310 310!2

Muon!

-3 -2 -1 0 1 2 3

Events

-110

1

10

Mass [GeV]N pass (before angle cut)

>120 4>200 2

events failing the angle cut

acts as a high-mass background

π-37Friday, September 6, 2013

high energy muons• muons usually leave a tracking signature via

minimum ionization

• high energy muons have more energy loss from radiation -- leads to muon showering (lots of hits)

• energetic electrons (E > 1 GeV) develop into full showers


cosmic muon reconstruction• cosmic ray muons studied in CMS to asses detector performance and to

evaluate cosmics as a background

• a single cosmic muon can be reconstructed as independent two muons with respect to the IP


cosmic ray muons in CMS• cosmic muons are secondary particles from

cosmic rays scattering off the atmosphere

• lose energy in the material above CMS -- some enter through the shafts


studies with cosmics• cosmic charge ratio was first precision physics measurement with

muons

(GeV/c) Z! cos"p 10 210 310

R

1.1

1.3

1.5

1.7CMS 2006-2008 CMS

MINOS Utah OPERA L3+C Schreiner et al CMS fit

CMS 2006-2008

R =Nµ+

Nµ− • led to first data-driven study of charge mis-identification comparing top and bottom legs


pics


cu-cd

• coupling limits produced in 2011in the cu-cd plane

• shown as thin black lines

• specific sets of charges given by some models are shown as color bands intersecting with thin lines

CMS Collaboration / Physics Letters B 714 (2012) 158–179 163

Fig. 5. Upper limits as a function of the resonance mass M on the production ratioR! of cross section times branching fraction into lepton pairs for Z!

SSM, Z!" , Z!

St ,and GKK production to the same quantity for Z bosons. The limits are shown from(top) the µ+µ" final state, (middle) the ee final state and (bottom) the combineddilepton result. Shaded green and yellow bands correspond to the 68% and 95%quantiles for the expected limits. The predicted cross section ratios are shown asbands, with widths indicating the theoretical uncertainties. The differences in thewidths reflect the different uncertainties in the K factors used. (For interpretationof the references to colours in this figure legend, the reader is referred to the webversion of this Letter.)

nominal resonance mass [9,38]. The NNLO prediction for the Z/# #

production cross section in the mass window of 60 to 120 GeV is0.97 ± 0.04 nb [37].

The uncertainties described above are propagated into a com-parison of the experimental limits with the predicted cross sectiontimes branching fraction ratios (R! ) to obtain 95% CL lower limitson Z! masses in various models. No uncertainties on cross sectionsfor the various theoretical models are included when determiningthe limits. As a result of the dimuon analysis, the Z!

SSM can be ex-cluded below 2150 GeV, the Z!

" below 1820 GeV, and the RS GKK

Fig. 6. The 95 % CL upper limits on the Z! cross sections for given masses are equiv-alent to excluded regions in the (cd, cu) plane which are bounded by the thin blacklines in the figure. They are compared with the predicted values of (cd, cu) in threeclasses of models. The colours on curves correspond to different mixing angles ofthe generators defined in each model. For any point on a model curve, the masslimit corresponding to that value of (cd, cu) is given by the intersecting experimen-tal contour.

below 1990 (1630) GeV for couplings of 0.10 (0.05). For the dielec-tron analysis, the production of Z!

SSM and Z!" bosons is excluded for

masses below 2120 and 1810 GeV, respectively. The correspondinglower limits on the mass for RS GKK with couplings of 0.10 (0.05)are 1960 (1640) GeV.

The combined limit, obtained by using the product of the like-lihoods for the individual channels, is shown in Fig. 5 (bottomplot). The signal cross section is constrained to be the same inthe two channels and lepton universality is assumed. The 95%CL lower limits on the mass of a Z! resonance are 2330 GeV forZ!SSM, 2000 GeV for Z!

" , and 890 (540) GeV for Z!St with $ = 0.06

(0.04). The RS Kaluza–Klein gravitons are excluded below 2140(1810) GeV, for couplings of 0.10 (0.05). The observed limits aremore restrictive than those previously obtained via similar directsearches by the Tevatron experiments [10–13,42,43] and indirectsearches by LEP-II experiments [16–19], as well as those obtainedby ATLAS [8] and CMS [9] using smaller data samples. The re-sults are also presented in the (cd, cu) plane in Fig. 6 [9,44]. Theparameters cd and cu contain all the information about the model-dependent couplings of the Z! to fermions in the annihilations ofcharge "1/3 and 2/3 quarks, respectively. The cross-section lim-its at any particular mass are contours in the (cd, cu) plane. Themodel classes are described in [9,38].

The largest deviation from SM expectations at high masses isaround 1 TeV, in both spectra. The statistical significance of the ob-servations is expressed in terms of Z-values, which are the effectivenumbers of Gaussian standard deviations in a one-sided test. Forthe dimuon sample, the maximum excess occurs at 1005 GeV, withlocal Z = 1.2, while for the dielectron sample, the maximum excessoccurs at 960 GeV, with local Z = 1.7. In the combination of thetwo channels, the maximum excess is found at 965 GeV, with lo-cal Z = 2.1. The probability of an enhancement at least as large asthe one found occurring anywhere between 600 and 2500 GeV inthe observed sample size corresponds to Z = "0.7 for the dimuonsample and Z = 0.3 for the dielectron sample. For the combineddata sample, the corresponding probability in a joint peak searchis equivalent to Z = 0.4.


limit model

• exclusion limits are performed with respect to the number of observed Z events for a cross section ratio

Rσ =σ(pp → Z � +X → ��+X)

σ(pp → Z0 +X → ��+X)

= µS�Z�

�Z0·NZ0

µS: expected number of signal eventsNZ: number of observed Z events (replaces dependence on luminosity)

• signal and background models are modeled with a likelihood function

• signal model: Gaussian convolved with Lorentz function

6.4 Limits

This section describes the statistical procedure for producing upper limits on the

ratio of a rare process of unknown mass that is normalized to the number of observed

Z0 events mass counted in a lower mass window, Rσ .

An extended unbinned likelihood function is used to model the signal and

background probability density functions (pdfs2 ). The background pdf, fB (m|a, b), is the

analytical shape of the DY continuum presented in Equation 6–2. The template pdf used

to model a theoretical signal is the convolution of a relativistic Breit-Wigner resonance

having a width of Γ and mass M with a Gaussian resolution function of width σg. The

ROOT [101] implementation of the Voigt [102, 103] function is used to approximate

the signal shape. The reference width of the Z� is taken from of the Z �ψ model where

Γψ = 0.6%Mψ. The Z �ψ width is chosen as a reference because it provides a sufficiently

narrow resonance such that detector resolution dominates. The background shape for

each added channel is normalized to the number of observed events in data above

200 GeV. The extended likelihood function, L, is

L (m|Rσ,M,Γ,σg, a, b,µB) =µNe−µ

N!

N�

i=1

�µS (Rσ)

µfS +

µBµfB

�, (6–7)

where “m” represents the observable in the measurement, which is the the invariant

mass of lepton pairs. “N” is the total number of observed events where M�� > 200 GeV.

“µB” is the Poisson mean of the total number of expected background events. “µ’ is the

Poisson mean of the distribution from which N is an observation such that µ = µB + µS .

2 Not to be confused with PDF for the Parton Density Function.

114


likelihood model

• signal and background models are modeled with a likelihood function

• signal model: Gaussian convolved with Lorentz function

• written in terms of the number of expected signal events and parameterized in terms of the cross section ratio via the Rσ transformation

6.4 Limits

This section describes the statistical procedure for producing upper limits on the

ratio of a rare process of unknown mass that is normalized to the number of observed

Z0 events mass counted in a lower mass window, Rσ .

An extended unbinned likelihood function is used to model the signal and

background probability density functions (pdfs2 ). The background pdf, fB (m|a, b), is the

analytical shape of the DY continuum presented in Equation 6–2. The template pdf used

to model a theoretical signal is the convolution of a relativistic Breit-Wigner resonance

having a width of Γ and mass M with a Gaussian resolution function of width σg. The

ROOT [101] implementation of the Voigt [102, 103] function is used to approximate

the signal shape. The reference width of the Z� is taken from of the Z �ψ model where

Γψ = 0.6%Mψ. The Z �ψ width is chosen as a reference because it provides a sufficiently

narrow resonance such that detector resolution dominates. The background shape for

each added channel is normalized to the number of observed events in data above

200 GeV. The extended likelihood function, L, is

L (m|Rσ,M,Γ,σg, a, b,µB) =µNe−µ

N!

N�

i=1

�µS (Rσ)

µfS +

µBµfB

�, (6–7)

where “m” represents the observable in the measurement, which is the the invariant

mass of lepton pairs. “N” is the total number of observed events where M�� > 200 GeV.

“µB” is the Poisson mean of the total number of expected background events. “µ’ is the

Poisson mean of the distribution from which N is an observation such that µ = µB + µS .

2 Not to be confused with PDF for the Parton Density Function.

114

background model: template fit to simulation

µ = µS + µB


limits + systematics

• create Bayesian credible intervals to construct the limit

• systematic uncertainties modeled as nuisance parameters in the Bayesian model with log-normal priors

• Zʼ/Z efficiency ratio: 3%

• background amplitude: 20%

• integral is performed with the Markov Chain Monte Carlo technique with the RooStats framework

In order to combine the√s = 7 TeV with

√s = 8 TeV data, a scale factor is applied

on the ratio of Rσ . This scale factor is given by

Rσ,b(m) = Rσ,a(m) ·σZ�b

�σZb

σZ�a�σZa, (6–8)

where σ is the cross section, a and b are the two COM energies in the model. The

NNLO Z0 cross sections used for 7 TeV and 8 TeV data were 970 pb and 1117 pb

respectively. PYTHIA was used to generate cross sections with Z �ψ model parameters.

The ratio of Rσ is shown in Figure 6-22, where there is a linear relationship on the

predicted Z� cross section as a function of the theoretical Z� mass between 7 TeV and

8 TeV collisions.

Upper limits are created for Rσ with Bayesian credible intervals [19]. Bayesian

credible intervals are defined from Bayes’ theorem:

f (θ, ν|x)p(x) = L(x |θ, ν)p(θ, ν), (6–9)

where “x” represents model data, “θ” represents the model parameters and “ν”

represents the nuisance parameters of the model. “L” is the likelihood function, and

“p(θ, ν)” is the prior pdf describing the model parameters. An integral is performed over

nuisance parameters to obtain:

p(θ|x)�(x) = L(x |θ)p(θ) (6–10)

The posterior pdf is then written down as

p(θ|x) = L(x |θ)p(θ)p(x)

=L(x |θ)p(θ)�L(x |θ)p(θ)dθ

. (6–11)

Given the posterior pdf of Rσ , the 95 confidence level (CL) upper limit is defined on R95σ

such that � R95σ

0

p(Rσ|x)dRσ = 0.95. (6–12)

115

34 9 Statistical interpretation

9 Statistical interpretation452

9.1 Treatment of systematic effects453

The uncertainty on the Drell-Yan background results from the uncertainty of evolution of data-454

MC efficiency scale factor with energy, NLO effects, and PDF uncertainties. The NLO uncer-455

tainty is taken to be 6% from the 2010 analysis. The PDF uncertainties vary from 4% at 400 GeV456

to 16% at 1.5 TeV and 20% at 2 TeV. However by the time the PDF uncertainty becomes large,457

the Drell–Yan background is already well below one event, so a 20% uncertainty has little effect458

on the limits. An average uncertainty of 10% is used in the limit calculations. The tt background459

has a 15% uncertainty due to the uncertainty in the tt cross-section. The summary of the var-460

ious uncertainties is given in Table 9. The 3% uncertainty on the ratio of total efficiencies is461

mainly from the uncertainty on the Z acceptance and the evolution of the efficiency estimates462

with dimuon mass, estimated from simulation, as discussed in Sec. 6. All uncertainties were463

summed together and the total rounded up to 20%.464

Observable Origin UncertaintyZ� acc.×eff. / Z acc.× eff. MC evolution of efficiency with energy 3%

Z/DY background NLO effects 6%Z/DY background PDF effects 5-20% (10% average)

Table 9: The systematic uncertainties on input parameters for the limits. The total backgrounderror, taking in account each backgrounds relative size, is 20% to account for any missed un-certainties.

9.2 Input to limit setting tool465

The input to the limit setting tool is summarised in Table 10. The number of Z events in the466

range of 60–120 GeV, the Z acceptance × efficiency and the uncertainty on the Z� -to-Z ratios467

are derived as described in Section 6. The background event count is the number of events468

found in data in the specified mass range, also reported in Table 4. The parameterization of469

Z� acceptance × efficiency as a function of the dimuon invariant mass is taken from the fit in470

Fig. 3 of Section 2. The invariant mass resolution parametrization is illustrated in Section 4,471

specifically Fig. 11. Finally, we described the extraction of the background lineshape in Section472

7, and the fit is illustrated in Fig. 22.473

Input ValueNZ in 60–120 GeV from prescaled trigger, bkg. subtracted 5021

Z acc.×eff. in 60–120 GeV, divided by prescale factor 0.286/250Z� acc.×eff. / Z acc.×eff. uncertainty 3%

Nbkg in m > 200 GeV 3358Nbkg uncertainty 20%

Z� acc.×eff. 0.735 − 1.21×108/(m + 536)3

mass resolution 0.006598 + 4.43×10−5 m − 7.1×10−10 m2

background shape exp (−0.002 m) · m−3.66

Table 10: The input parameters to the limit setting code. Masses m are in GeV.

9.3 Limits474

The limits are set using the same procedure as in 2011. The technique and results of the limit475

calculation are described in a dedicated note [24]. Here we show just a simple counting experi-476

“µb” is the expected background amplitude calculated with the counts observed in

data. “δµb” is the uncertainty on the background yield. “βb” is a normally distributed

nuisance parameter that is integrated over as part of the likelihood model, which uses a

log-normal prior.

The uncertainty on the efficiency ratio does not affect the limit on the number of Z�

events, but it does affect Rσ :

Rσ =µsη, (6–14)

where1

η=

�Z0

NZ0�Z�. (6–15)

The uncertainty on the efficiency ratio is modeled as a gaussian distributed nuisance

parameter on Rσ that is folded into the likelihood model:

µs = ηRσ (1 + δη)βη , (6–16)

where a log-normal prior distribution is assumed for the nuisance parameter.

The muon resolution increases with mass, and the momentum scale is constrained

to be 1% up to the 5 TeV scale. This has a negligible effect on the limit compared to the

6% and is not added into the muon model.

118

“µb” is the expected background amplitude calculated with the counts observed in

data. “δµb” is the uncertainty on the background yield. “βb” is a normally distributed

nuisance parameter that is integrated over as part of the likelihood model, which uses a

log-normal prior.

The uncertainty on the efficiency ratio does not affect the limit on the number of Z�

events, but it does affect Rσ :

Rσ =µsη, (6–14)

where1

η=

�Z0

NZ0�Z�. (6–15)

The uncertainty on the efficiency ratio is modeled as a gaussian distributed nuisance

parameter on Rσ that is folded into the likelihood model:

µs = ηRσ (1 + δη)βη , (6–16)

where a log-normal prior distribution is assumed for the nuisance parameter.

The muon resolution increases with mass, and the momentum scale is constrained

to be 1% up to the 5 TeV scale. This has a negligible effect on the limit compared to the

6% and is not added into the muon model.

118

µb = µb · (1 + δµb)βb


normalizing 7 and 8 TeV data

• production cross sections for Z0 and Z’ differ between 7 TeV and 8 TeV

• cannot directly couple 2011 and 2012 likelihoods with same σ-ratio parameter

• use ratio of ratios to transform 7 TeV data to compare with 8 TeV data in the likelihood

• dielectron channel uses the same likelihood model so combining channels is simple

!M500 1000 1500 2000

(8 T

eV)

"(7

TeV

)/R"

R

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

CMS Preliminary

NNLO σ(Z) [60-120 GeV]7 TeV: 970 pb, 8 TeV: 1117 pb

Rσ, 8 TeV = Rσ, 7 TeV ·�σZ�

�σZ

�8 TeV

�σZ�

�σZ

�7 TeV PYTHIA simulation


muon reconstruction


unf undergrad physics

Science

zz background

mass energy

x background e

luminosity lhc

mass range

observed signal region

backgrounds signal region

tev energy scale