Post on 19-Jan-2016
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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: