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The latest and greatest tricks in studying missing energy events

Konstantin Matchev

With: M. Burns, P. Konar, K. Kong, F. Moortgat, L. Pape, M. ParkarXiv:0808.2472 [hep-ph], arXiv:0810.5576 [hep-ph], arXiv:0812.1042 [hep-ph], arXiv:0903.4371 [hep-ph], arXiv:0906.2417 [hep-ph], arXiv:090?.???? [hep-ph]

Fermilab, LPCAugust 10-14, 2009

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These slides cover: • “A general method for model-independent measurements of

particle spins, couplings and mixing angles in cascade decays with missing energy at hadron colliders”, JHEP (2008)– Burns, Kong, KM, Park

• “Using subsystem MT2 for complete mass determinations in decay chains with missing energy at hadron colliders”, JHEP (2009)– Burns, Kong, KM, Park

• “s1/2min – a global inclusive variable for determining the mass scale

of new physics in events with missing energy at hadron colliders”, JHEP (2009).– Konar, Kong, KM

• “Using kinematic boundary lines for particle mass measurements and disambiguation in SUSY-like events with missing energy”, JHEP (2009)– Burns, KM, Park

• “Precise reconstruction of sparticle masses without ambiguities”, JHEP (200?)– KM, Moortgat, Pape, Park

67 pp

46 pp

32 pp

47 pp

Total No of pages : 229 pp

37 pp

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MET events: experimentalist’s view

• What is going on here?

This is why I am interested in MET!

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Why MET signatures are important to study

• WIMP dark matter? Perhaps, but see J. Feng’s talk for counterexamples.

• Challenging – need to understand the detector very well.

• Guaranteed physics in the early LHC (late Tevatron) data!

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This talk is being given• by a “theorist”

The experimentalist asks: The theorist answers:

Are there any well motivatedsuch models? You bet. Let me tell you about

those. Actually I have a paper…

No.

Is it possible to have a theory model which gives signature X?

Yes.

Is there any Monte Carlo which can simulate those models?

No. But I’m the wrong person to ask anyway.

MC4BSM workshops: http://theory.fnal.gov/mc4bsm/

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• Pair production of new particles (conserved R, KK, T parity)• Motivated by dark matter + SUSY, UED, LHT

– How do you tell the difference? (Cheng, KM, Schmaltz 2002)

• SM particles xi seen in the detector, originate from two chains– How well can I identify the two chains? Should I even try?

• What about ISR jets versus jets from particle decays?

• “WIMPs” X0 are invisible, momenta unknown, except pT sum – How well can I reconstruct the WIMP momenta? Should I even try?

• What about SM neutrinos among the xi’s?

MET events: theorist’s view

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In place of a summary

Missing

momenta reconstruction?

Mass measurements Spin measurements

Inclusive 2 symmetric chains

None Inv. mass endpoints

and boundary lines

Inv. mass shapes

Meff,Mest,HT Wedgebox

Approximate Smin, MTgen MT2, M2C, M3C,

MCT, MT2(n,p,c)As usual

(MAOS)

Exact ? Polynomial method

As usual

op

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ism

optimism

pessimism

pes

sim

ism

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Tuesday: invariant mass studies

• Study the invariant mass distributions of the visible particles on one side of the event

• Does not rely on the MET measurement• Can be applied to asymmetric events, e.g.

– No visible SM products on the other side– Small leptonic BR on the other side

• Well tested, will be done anyway.

MET

Hinchliffe et al. 1997

Allanach et al. 2000

Nojiri et al. 2000

Gjelsten et al. 2004

ATLAS TDR 1999

KM,Moortgat,Pape,Park 2009

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Thursday: spin measurements• Separate the spin dependence from all the rest

– Parameterize conveniently the effect from “all the rest”

• Measure both the spin (S) as well as all the rest:

)()()()( 2;

2;

2;

2;2

mFmFmFmFdm

dNSSSS

S

Burns, Kong, KM, Park 08

,,

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In place of a summary

Missing

momenta reconstruction?

Mass measurements Spin measurements

Inclusive 2 symmetric chains

None Inv. mass endpoints

and boundary lines

Inv. mass shapes

Meff,Mest,HT Wedgebox

Approximate Smin, MTgen MT2, M2C, M3C,

MCT, MT2(n,p,c)As usual

(MAOS)

Exact ? Polynomial method

As usual

op

tim

ism

optimism

pessimism

pes

sim

ism

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Wednesday: Meff (HT) and Smin

F. Paige hep-ph/9609373

Konar, Kong, KM 2008

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In place of a summary

Missing

momenta reconstruction?

Mass measurements Spin measurements

Inclusive 2 symmetric chains

None Inv. mass endpoints

and boundary lines

Inv. mass shapes

Meff,Mest,HT Wedgebox

Approximate Smin, MTgen MT2, M2C, M3C,

MCT, MT2(n,p,c)As usual

(MAOS)

Exact ? Polynomial method

As usual

op

tim

ism

optimism

pessimism

pes

sim

ism

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The “Cambridge” mT2 variable

• A. Barr, C. Lester and P. Stephens, “mT2 : the truth behind the glamour”– hep-ph/0304226

• C. Lester and D. Summers, “Measuring masses of semiinvisibly decaying particles pair produced at hadron colliders”– hep-ph/9906349

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Mass measurements

• Single semi-invisibly decaying particle

• Use the transverse mass distribution

2222 ),( TeTTeTTW ppppemM

We

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Mass measurements

• A pair of semi-invisibly decaying particles

• Use the “stransverse” mass (mT2)

2222 ),( TeTTeTTW ppppemM

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Kong, KM 04

• This formula is valid for m=0.

Lester,Summers 99Barr,Lester,Stephens 03

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Definition of MT2• A pair of semi-invisibly decaying particles

• If and were known:• But since unknown, the best one can do :

Lester,Summers 99Barr,Lester,Stephens 03

We

W

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What is mWhat is mT2T2 good for? good for?• Provides a relation between the two unknown

masses of the parent (slepton) and child (LSP)

– Vary the child (LSP) mass, read the endpoint of mmT2T2

• So what? We still don’t know exactly the LSP mass

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LSP mass measurement from kinksLSP mass measurement from kinks

• Include pT recoil due to ISR

ISR with some PISR with some PTT

• A kink appears at the true masses of the parent and the child

Varying PT

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How big is this kink?• It depends on the hardness of the ISR and

the mass spectra

FL

FR

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TP

M

0

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M

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FL

FR

Origin of the MT2 “kink”

• A kink may arise due to– “Composite” particle on each side

– ISR recoils

– Heavy particle decays

Cho, Choi, Kim, Park 2007

Barr, Gripaios, Lester 2007

Burns, Kong, KM, Park 2008

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Subsystem MT2

• Generalize the MT2 concept to MT2(n,p,c)– “Grandparents” (n): The total length of decay chain

– “Parents” (p): Starting point of MT2 analysis

– “Children” (c): End point of MT2 analysis

Burns, Kong, KM, Park 2008

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Mass determination: Subsystem MT2

Sub MT2

n : Length of decay chain

NP : Number of unknownsNm : Number of measurements

NP= number of BSM particles = n+1

Nm=

How many undetermined parameters (masses) are left?

Burns, Kong, KM, Park 2008

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Opening a parenthetical remark

(

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In place of a summary

Missing

momenta reconstruction?

Mass measurements Spin measurements

Inclusive 2 symmetric chains

None Inv. mass endpoints

and boundary lines

Inv. mass shapes

Meff,Mest,HT Wedgebox

Approximate Smin, MTgen MT2, M2C, M3C,

MCT, MT2(n,p,c)As usual

(MAOS)

Exact ? Polynomial method

As usual

op

tim

ism

optimism

pessimism

pes

sim

ism

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Mass determination – polynomial method

Sub MT2

n : Length of decay chain

Cheng,Gunion,Han,Marandella, McElrath, 2007

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Closing the remark

...)

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Subsystem MT2 applied to top pairs

• Don’t assume prior knowledge of the W and neutrino masses

• Traditional MT2 variable: MT2(2,2,0)

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MT2(220)

Combinatorial problem!

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Subsystem MT2 applied to top pairs

• Genuine subsystem variable: MT2(2,1,0)

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MT2(210)

No combinatorial problem!

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Subsystem MT2 applied to top pairs

• Another genuine subsystem variable: MT2(2,2,1)

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MT2(221)

No combinatorial problem!

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Mass measurements in the TTbar system

• We have just measured three MT2 endpoints which are known functions of the hypothesized Top, W and neutrino masses.– MT2(2,2,0)– MT2(2,1,0)– MT2(2,2,1)

• Problem: they are not independent, need an additional measurement– MT2(1,1,0)– Endpoint of the lepton+b-jet inv. mass distribution

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MT2 applied to W pairs

• Yet another MT2 variable: MT2(1,1,0)

W

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MT2(110)

No combinatorial problem!

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Full T, W, Nu mass determination

• Hybrid method: Inv. mass Subsystem MT2

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Correct bl pairs

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On a positive note• MT2 can be used for background suppression

• The dominant background to SUSY is TTbar• For illustration, let us choose a very challenging

example with an identical signature– Stop pair production, with decays to chargino and LSP.

Barr, Gwenlan 2009

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LSP

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Top-Stop separation• What do we know about the stop sample?

– Absolutely nothing.• What do we know about TTbar?

– The endpoints of the subsystem MT2 variables that we just saw. All TTbar events fall below these endpoints, and there are none above!

KM, Park preliminary

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Combination MT2 cut• Accept the event if it is beyond at least one of the

three subsystem MT2 endpoints.

• This greatly enhances the signal acceptance, compared to a single MT2 cut, or an HT cut.

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BACKUPS

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Wedgebox technique• Scatter plot of the invariant masses of the

visible decay products on both sides

Bisset,Kersting,Li,Moortgat,Moretti,Xie 2005

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MTgen

• Inclusive application of MT2: minimize MT2 over all possible partitions of the visible decay products between two chains– Brute force way to deal

with combinatorial issue– Preserves the endpoint,

provides a measure of the scale

– Endpoint smeared in the presence of ISR

– Does not measure the LSP mass

– Difficult to interpret when many processes contribute

Lester,Barr 2008

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Polynomial methodCheng,Gunion,Han,Marandella,McElrath 2007Cheng,Engelhardt,Gunion,Han,McElrath 2007

Cheng,Han 2008