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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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Q: What do we do for a living?A: Hunt for new particles. How?

• First make it, then detect it. Suppose it is:– Unstable, decays visibly to SM particles

• Resonant mass peak. Example: Z’. EASY

– Unstable, decays semi-visibly to SM particles• Jacobian peak (endpoint). Example: W’. EASY

– Stable, charged • CHAMPs. Examples in J. Feng’s talk. EASY

– Stable, neutral• Missing energy. Examples: LSP in SUSY, LKP in UED, …

DIFFICULT!– Theory: Typically 2 missing particles per event, unknown mass

– Experiment: MET is a challenging signature

– Sociology: Don’t even try masses/spins at LHC, go to ILC.

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Why MET signatures are important to study

• 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 data!

t

t

e

e

W

W

b

bW

W

e

e

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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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Ask the theorist!• Feel free to ask me questions on any topic• Some questions that I anticipate:

– Suppose we discover SUSY. How would we know it is SUSY and not something else?

– Almost all of our SUSY studies are based on LMx study points in MSUGRA. How much model dependence is introduced by the MSUGRA assumptions? Is it possible to design a model-independent SUSY search?

– I see you wrote a paper on MT2. I keep hearing about this MT2 and could never understand what it is god for. Can you explain?

– What are some safe cuts to use in our skims? Is there any magic (model-independent) cut which would cut the SM background yet preserve all of the (SUSY) signal?

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MET events: experimentalist’s view

• What is going on here?

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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 an outline

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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Today: 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

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The classic endpoint method

• Identify a sub-chain as shown. Combinatorics problem?• Form all possible invariant mass distributions

– Mll, Mjll, Mjl(lo), Mjl(hi) • Measure the endpoints and solve for the masses of A,B,C,D• 4 measurements, 4 unknowns. Should be sufficient.• Not so fast!

– The measurements may not be independent– Piecewise defined functions -> multiple solutions?

The “ATLAS” approach

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Combinatorics problems

• Lepton combinatorics• Solution: OF subtraction

• Jet combinatorics• Solution: Mixed Event

subtraction

14MA MC

maxllM

B on-shell

B off-shell

Example: dilepton invariant mass

MLL

MMBB

MC-MA

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Jet-lepton-lepton invariant mass

• There are 6 different cases to consider: (Njll,-)

MJLL

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Jet-lepton invariant mass

MJL• But which is near and

which is far?• Define “low” and “high”

pairs as: Allanach et al. 2000

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“Low” jet-lepton pair invariant mass

MJL(lo)

• 4 additional cases: (-,Njl)

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“High” jet-lepton pair invariant mass• The same 4 cases as “low” jet-lepton pair: (-,Njl)

MJL(hi)

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Recap• So far we measured the upper kinematic endpoints of

four invariant mass distributions– Mll, Mjll, Mjl(lo), Mjl(hi)

• They depend on 4 input masses: MA, MB, MC, MD

• 4 measurements, 4 unknowns. Should be sufficient. Invert and solve for the masses.

• However, 2+1 generic problems:– Piecewise defined functions -> multiple solutions? (next)– These four measurements may not all be independent,

sometimes

– This requires a new measurement. How precise is it?

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How many solutions?

• The endpoints are piecewise functions of the masses

– 11 cases altogether: (Njll,Njl).• It could have been

even worse, but 3 cases are impossible– (2,1), (2,2), (3,3)

• Bad news: in (3,1), (3,2) and (2,3) the measured endpoints are not independent:

(Njll,Njl) regions

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An alternative to MJLL

• The MJLL(Ѳ>π/2) invariant mass “threshold”

MJLL

in the rest frame of C

L L

MJLL(Ѳ>π/2)

Nojiri et al, 2000, Allanach et al. 2000

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MJLL versus MLL scatter plot

, ,

Bounded by a hyperbola OWS and a line UV

Lester,Parker,White 06

The MJLL(Ѳ>π/2) invariant mass “threshold”

Burns, KM, Park (2009)

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Posing the LHC inverse problem

• Find the spectrum of A,B,C,D, given the 4 endpoints

• Njll not used: we have reduced the number of cases to four:

– Njl=1, Region R1

– Njl=2, Region R2

– Njl=3, Region R3

– Njl=4, Region R4

• May cross-check the solution with

(Njll,Njl) regions

R3

R4

R2 R1

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Solving the LHC inverse problem• Find the four masses of A, B, C, D, given the 4 endpoints

• Solution:

Burns, KM, Park (2009)

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Multiple solutions?• Previously multiple solutions arose due to insufficient

experimental precision or using an incomplete data setGjelsten, Miller, Osland (2005); Gjelsten, Miller, Osland, Raklev (2006)

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Mass ambiguities• Exact spectrum duplication in (3,1), (3,2) and (2,3)

Burns, KM, Park (2009)

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What have we learned so far?• How the classic (ATLAS) endpoint method works• The inverse problem can be solved analytically• 5 endpoint measurements may not be enough to

uniquely determine 4 masses– Good news: in theory, at most 2-fold ambiguity– Bad news: will get even worse in the real world (with

error bars)

• What can we do?– Improve precision at the LHC? Does not help.– Extra measurements from ILC? Expensive.– Longer decay chain? Not up to us.– Fresh new ideas? Yes!

old

new

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One fresh new idea• Pretty obvious: a two-dimensional (scatter) plot contains

more information than the two individual one-dimensional histograms. Look at the scatter plot!– There is even more information in the 3D distribution

• Instead of looking for endpoints in 1D histograms, look at boundary lines in 2D scatter plots– For convenience, plot versus mass2 instead of mass

• The shape of the scatter plot reveals the region Ri

• Some special points provide additional measurements

R1 R2 R3

Burns, KM, Park (2009)

Costanzo, Tovey (2009)

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JL scatter plots resolve the ambiguity

(3,1) (2,3)

(3,2) (2,3)

• R1 versus R3

• R2 versus R3

“Drop”

“Foot”

Burns, KM, Park (2009)

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Precision problem

Gjelsten, Miller, Osland (2004) Lester (2006)

• In theory OK, but– scatter plots require more statistics

– the MJLL(Ѳ>π/2) “threshold” is hard to read

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Back to the drawing board

• Redesign the classic endpoint method– do not use distributions whose endpoints are

piecewise-defined functions: Mjll, Mjl(lo) or Mjl(hi)

– do not use the poorly measured MJLL(Ѳ>π/2)

“threshold”– do not use scatter plots– derive the shapes of all differential distributions

• Sounds impossible? Must introduce new observable distributions.

KM, Moortgat, Pape, Park (2009)

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New jet-lepton distributions

• But which is near and which is far?• ATLAS: define “low” and “high” as:

Allanach et al. 2000

Don’t ask, don’t tell: always use the two jet-lepton entries in a symmetric fashion

KM, Moortgat, Pape, Park (2009)

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The combined jet-lepton distribution

• Simply plot “near” and “far” together KM, Moortgat, Pape, Park (2009)

• Read the two endpoints

• These two are not piecewise defined

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The generalized sums

• Plot the combination

• Alpha is a continuous parameter: infinitely many possibilities!

• Alpha=1 is not piecewise defined:

KM, Moortgat, Pape, Park (2009)

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The product and the difference

• Unfortunately, both endpoints piecewise defined

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The bottom line• If we use only the 4 unambiguous endpoints

• The masses are found from• Despite the 2-fold near-far

confusion, the answers for A, C and D are unique!

• Remember that there are (infinitely) many more endpoint measurements– Allow measurement of MB

– Improve precision

KM, Moortgat, Pape, Park (2009)

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Summary

• There now exists a “CMS” version of the invariant mass endpoint method.

• It uses a different set of (in principle, infinitely many) invariant mass distributions

• It avoids multiple solution ambiguities

• (Allegedly) it leads to better precision– more measurements– better measured endpoints

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BACKUPS

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Mathematics of duplication• Compose the two maps

• Apply to each pair of different regions – e.g. R2 and R1

• This pair is safe!• Only “boundary” effect

due to the finite experimental precision

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Bad news!• Examples of “real” duplication

– Regions R1 and R3, namely (3,1) and (2,3)

– Regions R2 and R3, namely (3,2) and (2,3)

• The extra measurement of MJLL does not help

• Part of region R3 is safe

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Understanding shapes• Let’s start with “near” versus “far” JL pairs (unobservable)• The shape is a right-angle trapezoid ONPF• Notice the correspondence between regions and point P

R3 R4

R2R1

• Notice available measurements: n, f, p, perhaps also q

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From “near-far” to “low-high”

• This reordering is simply origami: a 45 degree fold

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The four basic JL shapes

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Animation: Region R1

• Green dot: Mjln endpoint

• Blue dot: Mjlf endpoint

• Red dot: point P• Endpoints given by (Low,High)=(Near,Far)

M2jln

M2 jlf

M2jl(lo)

M2 jl(

hi)

Region R1

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Animation: Region R2

M2jln

M2 jlf

M2jl(lo)

M2 jl(

hi)

Region R2

• Green dot: Mjln endpoint

• Blue dot: Mjlf endpoint

• Red dot: point P• Black dot: “Equal” endpoint• Endpoints given by (Low,High)=(Equal,Far)

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Animation: Region R3

M2jln

M2 jlf

M2jl(lo)

M2 jl(

hi)

Region R3

• Green dot: Mjln endpoint

• Blue dot: Mjlf endpoint

• Red dot: point P• Black dot: “Equal” endpoint• Endpoints given by (Low,High)=(Equal,Near)

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Animation: Region R4 (off-shell)

M2jln

M2 jlf

M2jl(lo)

M2 jl(

hi)

Region R4 (off-shell)

• The shape is fixed: always a triangle• “Low” and “High” endpoints are related:

max2)(

max2)( )(

2

1)( hijllojl mm

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Scatter plots resolve the ambiguity

(3,1) (2,3)

(3,2) (2,3)

• R1 versus R3

• R2 versus R3

“Drop”

“Foot”

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MJLL versus MLL scatter plot

, ,

Bounded by a hyperbola OWS and a line UV

Lester,Parker,White 06

The MJLL(Ѳ>π/2) invariant mass “threshold”

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Animation: MJLL versus MLL scatter plot

M2LL

M2JLL

(5,4)

(6,4)

(1,1)

(3,2)

(1,2

)

(2,3

)

(4,3)

(4,2

)(4,1)

(3,1)

(1,3)

Region (1, - ) Region (2, - ) , (3, - ) Region (4, - )

(5, 4 ) (6, 4 )

Several additional measurements besides the 1D endpoints:

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Invariant mass summary• Inverse LHC problem solved analytically• Identified dangerous regions of parameter space

with exact spectrum duplication• Advertisement: look at scatter plots (in m2)• The shape of the scatter plots determines the

type of region (Njll,Njl), removes the ambiguity

• The boundaries of the scatter plots offer additional measurements, 11 altogether:

as opposed to 5: