SUSY-Sumrules and MT2 Combinatoricsinsti.physics.sunysb.edu/~curtin/presentations/... · (1) (2)...

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SUSY-Sumrules and MT2 Combinatorics David Curtin bla arXiv:1004.5350, arXiv:1XXX.XXXX In Collaboration with Maxim Perelstein, Monika Blanke bla Cornell Institute for High Energy Phenomenology High Energy Seminar University of Florida Tuesday, October 12 2010

Transcript of SUSY-Sumrules and MT2 Combinatoricsinsti.physics.sunysb.edu/~curtin/presentations/... · (1) (2)...

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SUSY-Sumrules and MT2 Combinatorics

David Curtinbla

arXiv:1004.5350, arXiv:1XXX.XXXXIn Collaboration with Maxim Perelstein, Monika Blanke

bla

Cornell Institute for High Energy Phenomenology

High Energy SeminarUniversity of Florida

Tuesday, October 12 2010

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Outline

1. Motivation(i) The SUSY-Yukawa Sum Rule→ The Υ Observable(ii) How can we use it at the LHC?→ Υ′

2. MT 2 Review

3. Collider Physics Investigation(i) Objective: measure Υ′

(ii) Measuring all the masses in 2 g̃ → 2b̃1 + 2b → 4b + 2χ̃01

(iii) Measuring t̃1 mass

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Introducing the

SUSY-Yukawa Sum Rule

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Introduction

Hierarchy problem: In the SM, Higgs mass receives quadraticallydivergent corrections, most importantly from the top quarkIn SUSY, top contribution cancelled by stop

hh

t

(a) (b)ythh

t̃L,R

yt y2t

This relies on both particle content and coupling relations. Wewant to test the coupling relations.

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How to probe the Quartic Higgs Coupling?

M2t̃i t̃j

=

[M2

L + m̂2t + guLm̂2

Z c2β mt (At + µ cotβ)mt (At + µ cotβ) M2

T + m̂2t + guRm̂2

Z c2β

]

=

[m2

t1c2t + m2

t2s2t ctst (m2

t1 −m2t2)

ctst (m2t1 −m2

t2) m2t1s2

t + m2t2c2

t

]

Extract this contribution to diagonal sfermion mass terms!

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SUSY-Yukawa Sum Rule

Consider stop/sbottom LL mass terms at tree level:

M2t̃L t̃L

= M2L + m̂2

t + guLm̂2Z cos 2β = m2

t1c2t + m2

t2s2t (1)

M2b̃Lb̃L

= M2L + m̂2

b + gbLm̂2Z cos 2β = m2

b1c2b + m2

b2s2b (2)

Soft masses Higgs Quartic Coupling D-term contributions measurable

(1)− (2) eliminates the soft mass:

m̂2t − m̂2

b = m2t1c2

t + m2t2s2

t −m2b1c2

b −m2b2s2

b − m̂2Z cos2 θw cos 2β

We call this the SUSY-Yukawa Sum Rule: It has its origins in thesame coupling relations that cancel higgs mass corrections.

Testing this sum rule at a collider wouldconstitute a highly nontrivial check on SUSY.

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How to test the sum rule?

SUSY-Yukawa Sum Rule:

m̂2t − m̂2

b = m2t1c2

t + m2t2s2

t −m2b1c2

b −m2b2s2

b − m̂2Z cos2 θw cos 2β

Define an observable Υ for which the sum rule gives a definiteprediction:

Υ ≡ 1v2

(m2

t1c2t + m2

t2s2t −m2

b1c2b −m2

b2s2b

)Tree-Level Prediction for Υ from SUSY-Yukawa Sum Rule

ΥtreeSUSY =

1v2

(m̂2

t − m̂2b + m2

Z cos2 θW cos 2β)

=

{0.39 for tanβ = 10.28 for tanβ →∞ (converges quickly for tanβ >∼ 5)

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Caveat: Radiative Corrections!

Radiative Corrections wash out SUSY tree-level prediction for Υ

ΥmeasSUSY =

1v2

physical stop, sbottom masses & mixings︷ ︸︸ ︷(m2

t1c2t + m2

t2s2t −m2

b1c2b −m2

b2s2b

)= Υtree

SUSY︸ ︷︷ ︸≈0.3

+ΥloopSUSY(mti , θt ,mg̃ , tanβ, . . .) = ?

Properties of Υloop:Kicks in at energies below Msoft .is a function of many SUSY-parameters, so could be theoreticallyconstrained by measurements of those parameters.is very complicated1, but one can try to numerically estimatepossible range with parameter scans.

1Pierce, Bagger, Matchev, Zhang 1996Cornell University David Curtin SUSY-Sumrules and MT2 Combinatorics 6 / 42

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Numerically Estimate Radiative Corrections

Tool: use SuSpect to do MSSM Parameter Scan

Examine a ‘Worst-case’ scenario: no BSM experimentalconstraints other than MSUSY < 2 TeV and Neutralino LSP:

ΥtreeSUSY ≈ 0.3 −→ |ΥSUSY| <∼ 1

(For comparison, the ‘generic’ perturbative theory prediction is |Υ| <∼ 16π2.)

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Upshot

Introduce the SUSY-Yukawa Sum Rule,

m̂2t − m̂2

b = m2t1c2

t + m2t2s2

t −m2b1c2

b −m2b2s2

b−m̂2Z cos2 θw cos 2β

which relies on the same coupling relations that cancelcontributions from stop & top loops to the higgs coupling.

Introduce new observable which can be measured at a collider:

Υ ≡ 1v2

(m2

t1c2t + m2

t2s2t −m2

b1c2b −m2

b2s2b

)SUSY-Yukawa Sum Rule⇒ |Υ| <∼ 1

Measuring Υ constitutes a powerful nontrivial check that SUSYis the solution to the hierarchy problem.

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How can we use the

SUSY-Yukawa Sum Rule

at the LHC?

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SUSY-Yukawa Sum Rule at the LHC

To measure every ingredient of Υ (especially θb) we probablyneed a lepton collider.

What good is the sum rule at the LHC?⇒ Use SUSY-predictionfor Υ to constrain ‘unmeasurable’ parameters!

Which parts can we measure? Often t̃2, b̃2 are too heavy for theLHC.

Υ︸︷︷︸∼ known

=1v2

(m2

t1 −m2b1

)︸ ︷︷ ︸Υ′ (maybe measurable)

+s2

tv2

(m2

t2 −m2t1

)−

s2b

v2

(m2

b2 −m2b1

)︸ ︷︷ ︸

unknown

We can try to measure Υ′ at the LHC.

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What does Υ′ tell us?

Υ = Υ′ +s2

tv2

(m2

t2 −m2t1

)−

s2b

v2

(m2

b2 −m2b1

)

Υ′ � 0⇒ RH t̃1 Υ′ ∼ 0⇒ LH t̃1, b̃1 Υ′ � 0⇒ RH b̃1

Even a rough measurement of Υ′ gives strong constraints onthe stop and/or sbottom mixing angles!

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This gives us motivation tomeasure mt̃1

, mb̃1.

Let’s talk Collider Physics!

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MT 2 Review

Main MT2 references used here:

Barr, Lester, Stephens ’03 [hep-ph/0304226] (old-skool MT2 review)

Cho, Choi, Kim, Park ’07 [0711.4526] (analytical expressions for MT2

event-by-event without ISR, MT2-edges)

Burns, Kong, Matchev, Park ’08 [0810.5576] (definition of MT2-subsystemvariables, analytical expressions for endpoints & kinks w. & w.o. ISR)

Konar, Kong, Matchev, Park ’09 [0910.3679] (Definition of MT2⊥ to project outISR-dependence)

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Warm-up: W-mass measurement

Want to measure mW fromW → `ν.

We can reconstruct pνT andhence calculate mT (`, ν),assuming mν = 0.

Can measure mW from edge inmT -distribution! mmax

T = mW0

100

200

300

400

500

600

700

50 55 60 65 70 75 80 85 90 95 100mT (GeV)

num

ber

of e

vent

s

χ2/dof = 79.5/60KS Prob = 25%

Could we use a similar method for SUSY-like decays?

Two generalizations. LSP is- massive- always produced in pairs

Image source: D0 website

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Classical MT 2 Variable

MT2(~pTt1, ~p

Tt2, m̃N) =

min~qT

1 +~qT2 =~/p

T

{max

[mT

(~pT

t1, ~qTt , m̃N

),mT

(~pT

t1, ~qTt , m̃N

)]}

p

p

t

t

N

N

X

X

chain 1

chain 2

If pTN1, pT

N2 were known, thiswould give us a lower bound on mX

However, we only know total ~/pT

⇒ minimize wrt all possible splittings,get ‘worst’ but not ‘incorrect’ lowerbound on mX .We don’t even know the invisiblemass mN ! Insert a testmass m̃N .

For the correct testmass, MmaxT 2 = mX ⇒ Effectively get mX(mN).

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MmaxT 2 gives us mX as a function of mN

60 80 100 120 140 160 180 200Χ

340

360

380

400

mX

MT2maxH ΧL for mN = 98, mX = 341 GeV without ISR

MmaxT 2 (m̃N) = µ+

√µ2 + m̃2

N , where µ =m2

X−m2N

2mX

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Simple Example: Stop Pair Production without ISR

t̃1

t̃1

t

tχ̃0

1

χ̃01

Find edge for zero testmass:

MmaxT2 (0) =

m2t̃−m2

χ

mt̃

⇒ Obtain stop mass as a function of LSP mass!

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Longer Chains: MT 2-Subsystem Variables

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Longer Chains: MT 2-Subsystem Variables

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Complete Mass Determination

Dependence of endpoints ontestmass & ISR more in-teresting → each containsunique information.

2+ steps⇒ complete mass determination possible!

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Upshot:

We can use the classical MT 2 variable for 1-step decays to findone of the masses as a function of the other.

t̃1

t̃1

t

tχ̃0

1

χ̃01

For 2-step or longer chains, the MT2-subsystem variables couldallow complete mass determination.

b b

b b χ̃01

χ̃01

b̃1b̃1

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Remarks

1 We have not discussed what happens in realistic measurementswith ISR. This is well understoood. (Maybe say more later.)

2 There are two types of combinatorics problems when using MT 2:

(a) Distinguishing ISR from hard process final state (depends on theprocess).

(b) For subsystem variables: correctly placing each particle at itscorrect place in the long decay chain.

We will later discuss some strategies for addressing (b).

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Collider Physics Investigation

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Measuring Υ′ = (m2t1 −m2

b1)/v2 at the LHC

Want to demonstrate that the SUSY-Yukawa Sum Rule can beused to measure stop & sbottom mixing angles at the LHC.

Choose a particular MSSM Benchmark Point with light t̃1, b̃1 andsmall mixing:

Parameters:tanβ M1 M2 M3 µ MA MQ3L MtR At10 100 450 450 400 600 310.6 778.1 392.6

Spectrum: (GeV)

mt1 mt2 st mb1 mb2 sb mg̃ mχ̃01

371 800 -0.095 341 1000 -0.011 525 98

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Required Mass Measurements

We will measure Υ′ = 1v2 (m2

t1 −m2b1)

Parton-level Analysis with gaussian momentum smearing and noISR. (More realistic analysis in progress, some preliminarycomments later.)

Gluino pair production =⇒ mb1 (Bonus: mg̃ and mχ01)

Stop pair production =⇒ mt1

b b

b b χ̃01

χ̃01

b̃1b̃1 t̃1

t̃1

t

tχ̃0

1

χ̃01

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Measuring all the masses in

b b

b b χ̃01

χ̃01

b̃1b̃1

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Monte Carlo

Simulate g̃g̃ → 2b̃1 + 2b → 4b + 2χ̃01 with

MadGraph/MadEvent and BRIDGE at parton-level.

σg̃g̃ ≈ 11.6 pb @√

s = 14 TeV. Use L = 10 fb−1.

Signal: 4b + MET. We impose the following Cuts:- 4 b-tags- pb−jet

T > 40 GeV, pmaxT > 100 GeV

- MET > 200 GeV

σSignal = 480 fb after cuts⇒ 4800 signal events.

Backgrounds:- no SUSY background due to choice of BP- SM backgrounds2 suppressed by b-tag requirement

σBG . 30 fb after cuts: Ignore!

2MGME & ALPGEN

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Outline of Measurements

We want to measure 3 masses: mb1,mg̃ ,mχ̃01.

→ Must measure the edges of at least 3 independent kinematicvariables.

→ We will use Kinematic Edge Mmaxbb and MT2-Subsystem Variables!

Combinatorial Background! Final state is 4b + MET

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Measuring the Kinematic Edge

Mmaxbb =

√(m2

g̃−m2b1)(m2

b1−m2χ̃0

1)

m2b1

With known decay chainassignments get (Mb1b2 ,Mb3b4)for each event, plotMbb-distribution⇒ edge at 382 GeV.Main problem:Combinatorial Background!Can reduce CB with ∆R cutsand by dropping largest Mbb’sper event.

Mbbmaxmeas = 395± 15 GeV

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MT 2-subsystem Edges

Example: M210T 2 (0)

Combinatorial Background is more dangerous!

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Different combinations for calculating M210T 2 (0)

To calculateM210

T 2 , need todivide 4b into anupstream- and adownstream-pair:6 possibilities

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M210T 2 (0) without Combinatorial BG Reduction

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Need to reduce Combinatorial Background!

This is an example of the MT2 Combinatorics Problem (assignment offinal states in the decay chain).

We will need two methods for reducing Combinatorial Background:1 ‘Min’-Method2 ‘Kinematic-Edge’-Method

Why two methods? Necessary consistency check!

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Method 1: ‘Min’-Method

For each event, have 6 possibilities for M210T 2 (0).

→ 2 are particularly bad: if b’s from the same chain are assignedup-stream, the corresponding MT 2-distribution extends far beyondthe correct edge.

Simple way to eliminate those maximally bad combinations:Drop the largest 2 MT 2’s per event.

(Can think of this as anextension of the min/max-imaziation for calculating

MnpcT2 (M̃c) =

minp(1)

cT ,p(2)cT

{max

[M(1)

T ,M(2)T

]}to ‘min’/min/max)

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Method 2: ‘Kinematic-Edge’-Method

We’ve already measured the Mbb-edge.

Recall: For a given event with 4 b’s there are three possible decaychain assignments: (M12,M34), (M13,M24), (M14,M23)

For ∼ 30% of events, situation like

⇒ Can deduce correct decaychain assignments!

With this information we canreduce the number of possibleMT 2’s for that event.

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Procedure for extracting MT2-Edges

For each MT 2-subsystem variable:

1 Construct MT 2 distributions using both the Min-Method and theKinematic-Edge-Method.

2 For each distribution, do unbinned ML fits using a linear kink trialPDF over many possible domains.

3 Only accept an edge measurement ifBoth distributions have the same edge.

For each distribution, the edge-fit is stable under change offit-domain.

This double-check method is vital for rejecting artifacts & fakeedges due to low statistics!

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MT 2 Edge Measurements

Using this procedure, two MT 2-edges are recoverable.

edge th. measurementMbb 382 395± 15 GeVM210

T 2 (0) 321 314± 13 GeVM220

T 2 (0) 507 492± 14 GeV

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Obtaining Masses from Edge Measurements

M210T2 (0), M220

T2 (0), Mbb Edge Measurements:

Numerical Mass Extraction:

Assume edge measurementerrors are Gaussian.

Assign each point in(mg̃ ,mχ̃0

1,mb̃1

)-space a weightaccording to ‘distance’ fromedge measurements.

To get measured PDF of eachmass, project to one axis:

300 350 400m

b�

1

5

10

15

PDF

Extract confidence levelintervals.

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Mass Measurements

mass th. 68 % c.l.mb1 341 (316, 356)mg̃ 525 (508, 552)mχ̃0

198 (45, 115)

(Imposed mχ̃01> 45 GeV bound from LEP measurement of invisible Z decay width.)

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Measuring mt1 from

t̃1

t̃1

t

tχ̃0

1

χ̃01

and determining Υ′

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Stop Pair Production and mt1 measurement

Analyze the process t̃1 t̃∗1 → t t̄ + 2χ̃01.

σt̃1 t̃∗1≈ 2 pb @

√s = 14 TeV.

Impose standard cuts & use hadronic tops3. t̃1

t̃1

t

tχ̃0

1

χ̃01

Use L = 100 fb−1. After cuts: 1481 signal and 105 BG events.

Easy to extract MmaxT 2 edge =⇒ Gives mt1(mχ̃0

1)

Combine with (I)⇒ th. 68 % c.l.mt1 371 (356, 414)

3Meade, Reece 2006

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Υ′ Measurement

When determining Υ′, correlations between mass measurements arevital! This is why Υ′ must be defined as a separate observable.

th. meas.

Υ′ 0.350 0.525+0.20−0.15

Υ 0.423 —

Unless there is a strong accidental cance-lation, such a small Υ′ measurement im-plies that both stop and sbottom mixingangles are small, <∼ 0.1.

Compare to actual values:st = −0.095sb = −0.011

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Aside:A More Realistic Investigation

(Preliminary!)

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Beyond Parton-Level

Let’s go beyond parton-level and do a (more) realisticinvestigation.

Method for reducing Combinatorial Background carry overdirectly.

To deal with ISR takes a bit more work, but it can be done.

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ISR dependence of MmaxT 2

The edges of the classical MT 2 andthe MT2-subsystem variable distributionsdepend on both the testmass and theamount of total pISR

T .

p

p

t

t

N

N

X

X

chain 1

chain 2ISR

ISR

How can the endpoint of a distribution depend on ISR, which is definedevent-by-event? →Only plot the MT2 distribution for events with a certainpISR

T and find edge, this gives MmaxT2 (m̃N , pISR

T )

Useful properties to keep in mind (both classical & subsystem):

MmaxT2 (m̃N ,0) < Mmax

T 2 (m̃N ,pISRT )

edge shift = MmaxT 2 (m̃N ,pISR

T )−MmaxT2 (m̃N ,0) < pISR

T /2

When m̃N = mN , MmaxT2 (m̃N) = mX indep. of ISR.

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One Measurement Method: Lump it all together

This method does not take advantage of any of the analyticalexpressions we have for Mmax

T 2 and is extremely tedious, but shouldwork with ISR.

1. Pick a test mass m̃N

2. Calculate MT2(m̃N) for each event.

3. Plot MT 2 distribution of all events (regardless of ISR) & extractedge. We have now obtained Mmax

T2 (m̃N)

→ Repeat 1. - 3. for many different test masses. (Ouch!)

Plot MmaxT 2 vs m̃N : still gives mX (mN) since Mmax

T 2 (m̃N = mN) = mX

The edge will be more washed out for test masses far away fromthe actual mN due to ISR.

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A Simpler Method: ISR bins

Wouldn’t it be nice to just do one MmaxT 2 measurement at zero test

mass (like for the stop example), and hence extract µ =m2

X−m2N

2mX?

Simplest Idea: Could only keep events with pISRT < pISR

T max.

Pretend that there is no ISR for that sample and extractMmax

T2 (m̃N = 0,pISRT = 0)→ µ. Easy!

Reduces statistics! (Depends on choice of pISRT ).

Introduces Systematic Error!e.g. choose pISR

T max = 40 GeV→ edge shift < 20 GeV→ systematic error ≈ 10 GeV

Works OK!

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New Idea: Project out ISR Dependence

Using ISR bins reduces statistics in each bin.

It would be great to project out pISRT -dependence event-by-event!

Then we could extract the edges with full statistics.

Solution: Define new variable MT 2⊥.For each event, MT 2⊥ is evaluated exactly like MT2, exceptpT −→ pT⊥ (component ⊥ to pISR

T ).Endpoints same as MT 2 with pISR

T = 0.

This works very well, but makes the edges shallower:

−→

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Summary of realistic MT2 measurement methods

Three main approaches to doing realistic measurements with ISR:

1 Lump it all together (find edge for each test mass individually,very tedious, we don’t like it)

2 ISR bins (reduced statistics)

3 MT2⊥ (shallower edge, especially for M220T2 )

We do do both 2 + 3 and combine measurements.

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Conclusions

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Summary & Conclusions

Confirmation of the SUSY-Yukawa Sum Rule

m̂2t − m̂2

b = m2t1c2

t + m2t2s2

t −m2b1c2

b −m2b2s2

b − m̂2Z cos2 θw cos 2β

(probably at a lepton collider) would be strong support forTeV-scale SUSY as the solution for hierarchy problem.

At the LHC, the sum rule provides powerful constraints on stopand sbottom mixing angles (hard to come by otherwise) usingonly a mass measurement .

We developed new techniques for reducing MT2-combinatorialbackground, allowing application to 4b + MET final states.

→ Were able to measure or strongly constrainmt1,mb1,mg̃ ,mχ̃0

1, θt , θb from analyzing just two processes.

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