SUSY Searches and Parameter Determination at CMS in the ... · SUSY Searches and Parameter Determination at CMS in the Fully Hadronic Channel Project B2 – Supersymmetry at the LHC

SUSY Searches and Parameter Determinationat CMS in the Fully Hadronic Channel

Project B2 – Supersymmetry at the LHC

C. Autermann, S. Bobrovskyi, U. Gebbert, G. Kaussen,K. Kaschube, B. Mura, F. Nowak, N. Pietsch, C. Sander,

H. Schettler, P. Schleper, M. Schröder, T. Schum, J. Thomsen

SFB 676 Annual Workshop - Hamburger Sternwarte - 3rd and 4th March 09

SUSY Searches at CMS in theFully Hadronic Channel

Project B2 – Supersymmetry at the LHC

C. Autermann, B. Mura, C. Sander, H. Schettler,P. Schleper, T. Schum (Hamburg)

SFB Annual Workshop - Hamburger Sternwarte - 3rd to 6th March 09

Outline● Introduction

● SUSY Signatures at LHC● Discriminating variables

● Estimation of important backgrounds from data

● New event shape variables inspired from QCD matrix elements

● SUSY parameter determination● Inclusive weak gauge boson and top production rate

● Invariant trijet mass distributions from reconstructed squark decays

● Simultaneous kinematic fit of many events (SUSY masses are free parameters)

● Event-by-event kinematic fit (scanning over SUSY masses)

● Summary and outlook

3rd March 09 SUSY at the LHC 3

Introduction: Supersymmetry● Last possible symmetry: between

fermions and bosons

● Each SM particle gets a SUSY partner equal in all quantum numbers except for spin (½)

→ Opposite sign of loop corrections solves fine tuning problem

→ New particles change slope of running couplings gauge unification

→ Graviton (s = 2) ↔ g/W/Z/ (s = 1)

→ Provides perfect DM candidate

→ “Natural” EWSBreaking

● No candidates for supersymmetric partners discovered so far

→ SUSY has to be broken, but sparticles should have masses of ~1 TeV to keep advantages of SUSY

cancellation of loop corrections:

unification of gauge couplings:


Current Status

Hadronic searches:● Best limits from CDF and D∅● Within mSUGRA:

Leptonic searches:● Best limits on SUSY masses from

Tevatron and LEP experiments● “Golden channel at Tevatron”


mSUGRA

● m0 : unified mass breaking

term of scalar particles

● m1/2

: unified mass breaking term of gauginos

● tan : ratio of VEVs of the

two higgs dubletts

● A0 : unified trilinear coupling

● sign : sign of higgs

potential parameter

● Very popular breaking scenario by coupling to (yet unknown) supergravity sector

→ Only 5 new parameters

CMS benchmark points in m0-m

1/2-plane

from PTDR Vol II


Typical SUSY Signature

● R-parity conserved:

● SUSY particles are produced in pairs

● Cascade decay down to stable LSP

●

● large number of jets

● jet pairs compatible with weak gauge boson masses

● Fully hadronic decay mode has large branching ratio

Example diagram offull hadronic channel:

(1) Discover SUSY at the LHC

(2) Determine model parameters of underlying theory

Two goals:


Part IDiscovery of SUSY at LHC


Compact Myon Solenoid

● Multi purpose detector at LHC

● Size: 16 x 21 m2 - weight: 12.500 tons

● Inner magnetic field B ≈ 3.8 T

● Calorimeter mostly inside the magnet 7 ... 10 hadronic interaction length

● High granularity ECal with excellent energy resolution (electrons and photons)

● Typical jet resolution


SUSY Event Display

A good understanding of the reconstruction of physics objects from detector signals like jets, electrons, muons, and is crucial

Example event:● 6 central jets (well separated,

pT = 35 ... 480 GeV)

● One electron pT = 25 GeV

● Large = 250 GeV


SM Backgrounds● Even in optimistic SUSY scenarios

( ~10 pb) more than 7 orders of magnitude larger SM background

● Robust and stable preselection/trigger needed, e.g. :

● Njets

> 3

● > 200 GeV

● ( ,leading jets) < 0.3

● + ET, jet2

+ ET, jet3

+ ET, jet4

> 500 GeV

● ET, jet1

> 180 GeV and ET, jet2

> 110 GeV

● Lepton veto, cleaning cuts ...

Susy

cuts from PTDR Vol II


Inclusive Searches: All-Hadronic

● S/B ~ 300 can be achieved at LM1 with signal efficiency of ~ 10%

● For such optimistic scenario almost bg free SUSY sample; discovery might be more difficult for heavier SUSY scenarios

n–1: After all cutsexcept

dominant bg:QCD

J. Thomsen (Hamburg)


QCD Background from Data

● Signal region C defined by cuts on various variables

● Do all cuts except on two (uncorrelated) vars with sufficient separation power

● Use NC = N

D ∙ N

B / N

A to estimate bg

events in C

tails from MC: incomplete understanding of the detector and insufficient statistics

T. Schum (Hamburg)Challenges:

● Vars are not uncorrelated normalization factor N

B / N

A has to be extrapolated

● Signal contamination in A, B and D

● Estimate should be conservative including all systematic uncertainties


QCD Background from Data: Estimate

● Cross check possible by using different pairs of variables

● Signal contamination leads to overestimation (only present for high S/B no problem for discovery)

● Data driven background estimations for other channels ( Z , ...) also under development Torben Schum

min( , 3 leading jets)

vs. missing HT (vectorial

sum of jet pT)

true QCD

estimate QCD

true QCD + LM1


Special Helicity Amplitudes

● Special Helicity Approximation (SPHEL): special helicities are typical for all other possible configurations other contributions can be expressed by combinatorial factor

● Application: approximation for QCD matrix element on Born niveau

● Colour contributions of leading order are taken into account

● Calculation of helicity amplitudes with Weyl spinors

● Special helicity amplitudes can be expressed in compact way

Sergei Bobrovskyi

Antenna structure


Antenna Variables● Tevatron (Run I) energies SPHEL approximation

overestimates cross section by factor of 1.4 but shapes are described well

● Idea: Construction of new eventshape variables out of reconstructed jets and incoming partons (estimated from energy conservation)

● Hope: Event shape variable looks different for QCD (radiation of massless gluons) and SUSY events (decay of massive particles)

● Various definitions, e.g. with two incoming partons and n additional jets

QCD SUSY

n = 6Selection:

● 1st jet: and

● 2nd jet: and

● 3rd ... 6th jet: and

New discriminating variable


Part IIDetermination of Model Parameters


W/Z Boson Identification● Jet algorithm: iterative cone 0.5

● Jet cuts and

● Candidates: dijets with

● Large combinatorial background

Reconstruction efficiency:

● Low efficiency at small boson pT due to

small jet reconstruction efficiency

● Low efficiency at large boson pT due to

jet merging

Friederike Nowak


Supression of Combinatorial Bg

Discriminating variables:

● : angle (in the W rest frame) between a W jet and the flight direction

● pT of W candidate

● Angle between and W candidate

Reduction of combinatorial background by factor up to ~3

● If W candidate can be combined with third jet to m top

top candidate


Constrain Parameter Space

● Scan hypothesis and compare (2 test) with pseudo data (here: m0 = 800

GeV and m1/2

= 600 GeV)

● Boson candidate rate contains information in addition to absolute event rate larger parts of the parameter space can be excluded

Signal event rate only + information about W/Z and top candidates


Reconstruction of Mass Edges

Trijet candidates:

● W/Z candidate combined with one of two p

T hardest jets (large mass gap

between and )

● Up to 20 combinations per event

● Start with small S/B of ~1/100

Search for other discriminating variables:

● Hadronic decay of squarks: invariant trijet mass distribution

● No sharp peak but upper and lower mass edge (due to unmeasured LSPs)

● Degenerated squark mass spectra: define only 1. and 2. generation as signal

Ulla Gebbert


Reconstruction of Mass Edges cont.

● Select out of 17 kinematic variables up to 5 best separating and least correlated variables

● Use likelihood ratio method to separate signal from background

● Improve S/B from ~1/100 to ~1/10

● Background might be “signal like”

R between boson candidateand remaining jets

invariant dijet mass


Constrain Parameter Space

● Scan over hypothesis

● Compare with pseudo data (here: m0 =

600 GeV and m1/2

= 400 GeV) via binned maximum Likelihood

● Shape of trijet mass distribution provides enough information to constrain the parameter space

bad hypothesis good hypothesis


Kinematic Fits and Parameter Determination

● If some masses are (almost) degenerated (e.g. squark masses or 0 and ± in mSUGRA scenarios) it might be possible to select events with a rather similar cascade topology

● In these cascades the masses of the SUSY particles at a particular position in the decay chain can be assumed equal for each event

Global unknowns: SUSY masses

Local unknowns: momenta of two LSPs

Constraints 1: right combinations of the final state particles should have invariant masses of corresponding SUSY particle

Constraints 2: Momentum balance in transverse plane

If there are more constraints than local unknowns, the problem is overconstrained for a large number of events

● Analogy: Tracker alignment (global unknowns: alignment parameters, local unknowns: track parameters, constraints: vertex ...)


Example: Full Hadronic -decayUnknowns for N events:

● LSP momenta ( )

● 4 SUSY masses ( )

7 Constraints per event:

●

●

●

● balance ( )

Overconstrained: e.g. N = 100

constraints + 700local unkowns – 600global unknowns – 4

+ 96 constraints “left”proof of principle shown

for semi-leptonic eventsTorben Schum


Potential Problems● Suppression of SM and SUSY background

● 7 jets in final state (huge combinatorial bg)● all reconstructed

● No perfect mass degeneration

● Width of virtual particles

● +FSR

● +ISR

additional jets important formomentum balance

27th Janurary 09 Global Kinematic Fits 26

Global Fit: A Simple Example● No combinatorial background: only use right

combinations

● Avoid non-degenerated masses: use specific cascade only

● Perfect momentum balance: use MC information of ISR

● Use Toy-MC: Take parton kinematics from generator process and smear them in E

T, ,

according to expected resolutions (no correlated and systematic errors)

● Start values for global mass parameters from invariant multi jet masses

● Start values for unmeasured LSP momenta: Truth ? Zero ? Arbitrary ? W/Z ? ...

● Non-linearity: iterative solution with outlier rejection (e.g. Cauchy scaling)

27th Janurary 09 Global Kinematic Fits 27

Global Fit: A Simple Example● For each “Newton-step” the sum of

all constraints has to be reduced

● Neutralino mass: no free parameter

● First results for 41 events

Fit result True Mass

~710 GeV ~685 GeV

~673 GeV ~660 GeV

~218 GeV ~210 GeV

● Fitted masses agree on 5% level with true mass values

Used mSUGRA parameters: LM4

Benedikt Mura


Combinatorial Background● For 7 jets overall 1260 combinations

● Use information of decay (invariant mass, angles ...)

● Use leptonically decaying ● Smaller branching ratio

● No decay can be used (+3 unmeasured parameters from )

● But much reduced combinatorics

● Alternative approach:● Scan mass hypothesis H

● For each H fit all events (event-by-event) for all combinations

● Choose smallest i2 per event as right combination

● Smallest i

i2 for best mass hypothesis

● Scanning of high dim. mass space (needs large resources)

Simple parametrization, e.g.


Combinatorial Background cont.

● Distribution of squark mass with smallest 2

● Right combinations peak very close to true mass (LM4: ~650 GeV)

● Combinatorial background has broader distribution

● For true mass hypothesis correct combinations have slightly better 2

● Only combinations with best 2 shown

correct

falsecorrect

false

Hannes Schettler

Drastic reduction of combinatorial bg:1:1260 ~ 1:1


Scanning over Mass HypothesisSignal Background

Bes

t

2 c

ombi

nat

ion

Fra

ctio

n o

f co

nve

rged

com

binat

ions

“Realistic” scenario:

● 7(+1 for ISR) hardest jets

● Full combinatorial background

● Best 2 and fraction of converging combinations contains information on parameter space

● Background might be “signal like”

stop masslight squarks


Fitting Techniques● Constrained ( f

i = 0) fitting via Method of Lagrangian Multiplier

● Find stationary point where all derivatives vanish equivalent to minimum of 2 under fulfilled constraints f

● Invariant mass constraints are (highly) non linear linearization via Taylor expansion and iterative approach

● General problems:

● Alternative approach:

● Write constraints as additional 2 term “cost function”

● Interpretation of cost function as 2: all correlations have to be taken into account

with

● Minimize cost function: many possible algorithms (gradient, simplex, LBFGS, simulated annealing ... genetic algorithm)

● Fit can converge at local (and not global) minimum

● Non linear problems can suffer from “Maratos effect” (no decrease of constraints in step direction)


Genetic Algorithm

1) Starting from starting values create first generation of individua (starting population): use all possible jet combinations (1260 for 7 jets)

2) Select N best fitting individua (here 25)

3) Create M (here 1000) new individua by selecting randomly two parents and take randomly the genes from either one or the other parent

4) Mutate (variation within the measurement errors) each gene (except jet combination) with given probability (here 10 %)

5) Back to step 2) until convergence is reached (here: no change within 3 generations) or fixed iteration number is reached (here 300)

Charles Darwin(1809 – 1882)

On the origin of species (1859)

● Final state 4-momenta are properties (genes) of individuum; jet combination is one additional gene

● Fitness function (here 2) defines if individuum is fittest


Genetic Algorithm (cont.)

pT,1

1

1

pT,2

2

2

3754521

pT,1

1

1

pT,2

2

2

1235764

pT,1

1

1

pT,2

2

2

1235764parent 1

parent 2

child

mutate


Preliminary Results: Toy MC

iteration

2 o

f fi

ttes

t in

div

idua

one example event

Advantage of genetic algorithm:might overcome local minima

flat !


Summary and OutlookSummary:● If SUSY is around the corner discovery of supersymmetry at the LHC is possible

with first data (in case of heavy SUSY particles situation will be more difficult)

● Data driven methods for important background estimations are on the way

● Antenna variables are new event shape variables with additional discriminative power

● Inclusive production rates of weak gauge bosons or top quarks as well as invariant mass distributions can be used to constrain the SUSY parameter space

● Kinematic fits provide an additional tool to excess the sparticle masses

● New fitting techniques are under development

Outlook:● How to get best constraints on parameter space from the combination of various

information?

● For kinematic fits: simultaneous tests of more cascade hypotheses?


Backup


Open Questions of the SMShortcomings of the SM:

● Why are there 3 Generations ?

● Why is electric charge of electron and proton equal ?

● Why are ~17 orders of magnitude between EW and Planck scale ?

● How can the fine tuning problem be solved ?

● Should the gauge couplings unify at high energies ? In the SM they do not !

● Can the large numbers of free parameters 19 (+7(9) from s) in the SM be reduced ?

● What is the nature of dark matter and dark energy ?

● Why is the gravitational force so weak? How can the gravity be included in one formal description of all forces ?

● ...

There are many models which address one or more of these question !


Starting Values for Neutralinos● In typical Susy scenarios:

small relative momentum of W and 0

● Assume same direction of W and 0 and adjust 0 momentum to fulfill mass constraint

● No analytical solution use Newton method


Visualization of Best Combinations

first gluino jet

first squark jet

first W jet

first W jet

second W jet

second W jet

second squark jet

~ 20% complete right cascademost wrong combinations are exchange of the two branches

good 2 bad


Genetic Algorithm vs. KinFitter● No combinatorial background

● KinFitter: only 77 out of 269 events converge for right combination (constraints are not fulfilled as required)

● KinFitter: no correlation of invariant masses and jets

● KinFitter: Lagrangian multiplier for momentum balance

KF convergedKF allGA


Genetic Algorithm vs. KinFitter (cont.)

● Genetic Algorithm: RMS ( R) = 0.41

● KinFitter: RMS ( R) = 0.52

Documents

SUSY Searches and Parameter Determination at CMS in the ... · SUSY Searches and Parameter Determination at CMS in the Fully Hadronic Channel Project B2 – Supersymmetry at the LHC