The latest and greatest tricks in studying missing energy events Konstantin MatchevWith: 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

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, ParkUsing subsystem MT2 for complete mass determinations in decay chains with missing energy at hadron colliders, JHEP (2009)Burns, Kong, KM, Parks1/2min a global inclusive variable for determining the mass scale of new physics in events with missing energy at hadron colliders, JHEP (2009).Konar, Kong, KMUsing kinematic boundary lines for particle mass measurements and disambiguation in SUSY-like events with missing energy, JHEP (2009)Burns, KM, ParkPrecise reconstruction of sparticle masses without ambiguities, JHEP (200?)KM, Moortgat, Pape, Park

MET events: experimentalists viewWhat is going on here?This is why I am interested in MET!

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 particlesResonant mass peak. Example: Z. EASYUnstable, decays semi-visibly to SM particlesJacobian peak (endpoint). Example: W. EASYStable, charged CHAMPs. Examples in J. Fengs talk. EASYStable, neutralMissing energy. Examples: LSP in SUSY, LKP in UED, DIFFICULT!Theory: Typically 2 missing particles per event, unknown massExperiment: MET is a challenging signatureSociology: Dont even try masses/spins at LHC, go to ILC.

Why MET signatures are important to studyDark matter? Perhaps, but see J. Fengs talk for counterexamples.Challenging need to understand the detector very well.Guaranteed physics in the early LHC data!

This talk is being givenby a theorist

Ask the theorist!Feel free to ask me questions on any topicSome 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?

MET events: experimentalists viewWhat is going on here?

MET events: theorists viewPair production of new particles (conserved R, KK, T parity)Motivated by dark matter + SUSY, UED, LHTHow do you tell the difference? (Cheng, KM, Schmaltz 2002)SM particles xi seen in the detector, originate from two chainsHow 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 xis?

In place of an outlineoptimismoptimismpessimismpessimism

Today: invariant mass studiesStudy the invariant mass distributions of the visible particles on one side of the event Does not rely on the MET measurementCan be applied to asymmetric events, e.g.No visible SM products on the other sideSmall leptonic BR on the other sideWell tested, will be done anyway.Hinchliffe et al. 1997Allanach et al. 2000Nojiri et al. 2000Gjelsten et al. 2004ATLAS TDR 1999

The classic endpoint methodIdentify a sub-chain as shown. Combinatorics problem?Form all possible invariant mass distributionsMll, Mjll, Mjl(lo), Mjl(hi) Measure the endpoints and solve for the masses of A,B,C,D4 measurements, 4 unknowns. Should be sufficient.Not so fast! The measurements may not be independentPiecewise defined functions -> multiple solutions?The ATLAS approach

Combinatorics problemsLepton combinatoricsSolution: OF subtractionJet combinatoricsSolution: Mixed Event subtraction

Example: dilepton invariant massMLLMBMC-MA

Jet-lepton-lepton invariant massThere are 6 different cases to consider: (Njll,-)MJLL

Jet-lepton invariant massMJLBut which is near and which is far?Define low and high pairs as:Allanach et al. 2000

Low jet-lepton pair invariant massMJL(lo)4 additional cases: (-,Njl)

High jet-lepton pair invariant massThe same 4 cases as low jet-lepton pair: (-,Njl)

RecapSo far we measured the upper kinematic endpoints of four invariant mass distributionsMll, Mjll, Mjl(lo), Mjl(hi) They depend on 4 input masses: MA, MB, MC, MD4 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?

How many solutions?The endpoints are piecewise functions of the masses11 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

An alternative to MJLLThe MJLL(>/2) invariant mass thresholdMJLLin the rest frame of C L LMJLL(>/2)Nojiri et al, 2000, Allanach et al. 2000

MJLL versus MLL scatter plot,,Bounded by a hyperbola OWS and a line UVLester,Parker,White 06Burns, KM, Park (2009)

Posing the LHC inverse problemFind the spectrum of A,B,C,D, given the 4 endpointsNjll not used: we have reduced the number of cases to four:Njl=1, Region R1Njl=2, Region R2Njl=3, Region R3Njl=4, Region R4May cross-check the solution with

(Njll,Njl) regions

Solving the LHC inverse problemFind the four masses of A, B, C, D, given the 4 endpoints

Solution:

Burns, KM, Park (2009)

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)

Mass ambiguitiesExact spectrum duplication in (3,1), (3,2) and (2,3)Burns, KM, Park (2009)

What have we learned so far?How the classic (ATLAS) endpoint method worksThe inverse problem can be solved analytically5 endpoint measurements may not be enough to uniquely determine 4 massesGood news: in theory, at most 2-fold ambiguityBad 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!

oldnew

One fresh new ideaPretty 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 distributionInstead of looking for endpoints in 1D histograms, look at boundary lines in 2D scatter plotsFor convenience, plot versus mass2 instead of massThe shape of the scatter plot reveals the region RiSome special points provide additional measurements

R1R2R3Burns, KM, Park (2009) Costanzo, Tovey (2009)

JL scatter plots resolve the ambiguityR1 versus R3R2 versus R3DropFootBurns, KM, Park (2009)

Precision problemGjelsten, Miller, Osland (2004) Lester (2006) In theory OK, butscatter plots require more statisticsthe MJLL(>/2) threshold is hard to read

Back to the drawing boardRedesign the classic endpoint methoddo not use distributions whose endpoints are piecewise-defined functions: Mjll, Mjl(lo) or Mjl(hi)do not use the poorly measured MJLL(>/2) thresholddo not use scatter plotsderive the shapes of all differential distributions Sounds impossible? Must introduce new observable distributions.KM, Moortgat, Pape, Park (2009)

New jet-lepton distributionsBut which is near and which is far?ATLAS: define low and high as:Allanach et al. 2000

The combined jet-lepton distributionSimply plot near and far togetherKM, Moortgat, Pape, Park (2009) Read the two endpointsThese two are not piecewise defined

The generalized sumsPlot the combinationAlpha is a continuous parameter: infinitely many possibilities!Alpha=1 is not piecewise defined:

KM, Moortgat, Pape, Park (2009)

The product and the differenceUnfortunately, both endpoints piecewise defined

The bottom lineIf we use only the 4 unambiguous endpointsThe masses are found fromDespite the 2-fold near-far confusion, the answers for A, C and D are unique!Remember that there are (infinitely) many more endpoint measurementsAllow measurement of MBImprove precisionKM, Moortgat, Pape, Park (2009)

SummaryThere now exists a CMS version of the invariant mass endpoint method.It uses a different set of (in principle, infinitely many) invariant mass distributionsIt avoids multiple solution ambiguities(Allegedly) it leads to better precisionmore measurementsbetter measured endpoints

BACKUPS

Mathematics of duplicationCompose the two mapsApply to each pair of different regions e.g. R2 and R1 This pair is safe!Only boundary effect due to the finite experimental precision

Bad news!Examples of real duplicationRegions 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 helpPart of region R3 is safe

Understanding shapesLets start with near versus far JL pairs (unobservable)The shape is a right-angle trapezoid ONPFNotice the correspondence between regions and point PNotice available measurements: n, f, p, perhaps also q

From near-far to low-highThis reordering is simply origami: a 45 degree fold

The four basic JL shapes

Animation: Region R1Green dot: Mjln endpointBlue dot: Mjlf endpointRed dot: point PEndpoints given by (Low,High)=(Near,Far)

Animation: Region R2Green dot: Mjln endpointBlue dot: Mjlf endpointRed dot: point PBlack dot: Equal endpointEndpoints given by (Low,High)=(Equal,Far)

Animation: Region R3Green dot: Mjln endpointBlue dot: Mjlf endpointRed dot: point PBlack dot: Equal endpointEndpoints given by (Low,High)=(Equal,Near)

Animation: Region R4 (off-shell) The shape is fixed: always a triangleLow and High endpoints are related:

Scatter plots resolve the ambiguityR1 versus R3R2 versus R3DropFoot

MJLL versus MLL scatter plot,,Bounded by a hyperbola OWS and a line UVLester,Parker,White 06The MJLL(>/2) invariant mass threshold

Animation: MJLL versus MLL scatter plotRegion (1, - )Region (2, - ) , (3, - ) Region (4, - )

Invariant mass summaryInverse LHC problem solved analyticallyIdentified dangerous regions of parameter space with exact spectrum duplicationAdvertisement: 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: