superpartner masses from invariant mass distributions d.j. miller, susy 2005, 22 nd july masses from...
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Superpartner masses from invariant mass distributions
D.J. Miller, SUSY 2005, 22nd July
Masses from endpoints of invariant mass distributions:• The method• problems:
Using shapes instead of endpoints:• How do shapes cure these problems?• Incorporating extra effects: cuts, FSR, and detector effects
non-linear edges feet and drops multiple solutions
B. K. Gjelsten, D. J. Miller, P. Osland, JHEP 0412 (2004) 003, hep-ph/0410303
B.K. Gjelsten, D.J. Miller, P. Osland, hep-ph/0501033
D.J. Miller, A.Raklev, P. Osland, in preparation
D J Miller 22nd July 2005 2
Masses from endpoints of invariant mass distributions
If we find Supersymmetry at the LHC, we must measure the masses of the supersymmetric partners, the sleptons, squarks, neutralinos, charginos, and gluino.
But, there are 2 problems with measuring masses at the LHC:
• Don’t know centre of mass energy of collision √s• R-parity conserved (to prevent proton decay)
LSP stable
Cannot use traditional method of peaks in invariant mass distributions
to measure SUSY masses
escapes detector
Instead measure endpoint of invariant mass distributions
Missing energy/momentum )
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e.g. consider the decay
mll is maximised when leptons are back-to-back in slepton rest frame
angle between leptons
This method should already be familiar to you from I. Hinchliffe’s talk!
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3 unknown masses, but only 1 observable, mll
extend chain further to include squark parent:
now have: mll, mql+, mql-, mqll
4 unknown masses, but now have 4 observables
) can measure masses from endpoints
[Hinchliffe, Paige, Shapiro, Soderqvist and Yao, Phys. Rev D 55 (1997) 5520, Allanach, Lester, Parker, Webber, JHEP 0009 (2000) 004, and many others…]
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SPS 1a slope:
SPS 1a point
[See Allanach et al, Eur.Phys.J.C25 (2002) 113, hep-ph/0202233]
We examined this decay chain for benchmark SPS 1a at ATLAS using PYTHIA and ATLFAST.
Cuts to remove backgrounds:
At least 3 jets, with pT > 150, 100, 50 GeV
ET, miss > max(100 GeV, 0.2 Meff) with
2 isolated opposite-sign same-flavour leptons (e,) with pT > 20,10 GeV
Remove remaining uncorrelated lepton background using different-flavour-subtraction
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‘Theory’ curve
End result
Z peak (correlated leptons)
Distribution for mll after cuts
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Use these endpoints to fit for the superpartner masses:
mass differences much better measured – could be exploited by measuring one of
the masses at an e+e- linear collider I will explain these blue curves later
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Problem 1
We used a Gaussian smeared straight line to find endpoints, but can we really trust a linear fit?
Problem 2
The invariant mass distributions often have strange behaviours near the endpoints which may be obscured by remaining backgrounds
- ‘feet’ and ‘drops’
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Notice the ‘foot’ here
5 different mass scenarios:(theory curves)
Here we have a sudden drop of the differential cross-section to zero
Extrapolation to endpoint is not always linear
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Problem 3
One set of mass endpoints can be fit by more than one set of masses!
2 causes:
Endpoints themselves depend on mass hierarchye.g.
This splits the mass-space into different regions
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If the nominal masses are near a boundary, over-constraining the system with another measurement, or simply having large enough errors on the endpoints, can create multiple local minima of the 2 distribution in different regions.
model point
false solution
region boundary
Nominal endpoints Endpoints with errors
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second mass solutions - at Sps 1a this is caused by
D J Miller 22nd July 2005 13
Using shapes instead of endpoints
If we fit the entire shape of the invariant mass distribution, we should get around all of these problems
Problem 1 (non-linear extrapolation to endpoint)
Our analytic expression for the shape should tell us exactly the behaviour of the invariant mass distribution near the endpoint.
Problem 2 (feet and drops)
With an analytic expression we will know about any anomalous structures even if they are hidden by backgrounds
Problem 3 (multiple solutions)
Other features of the shape will serve to the distinguish different mass regions
Additionally, we can use a larger proportion of events, i.e. not just the events near the endpoints
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An example invariant mass distribution
Consider
This invariant mass is not easily measurable (just a simple example) but shows the non-linear edge
Problem 1 solved
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Feet and drops
These become dangerous if the height of the last ‘end structure’ is small compared to the total height.
mql (low) mql (high)
So now we know when invariant mass distributions have dangerous endpoints, and can correct for them. Problem 2 solved
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Problem 3 agiain (multiple solutions)
We can distinguish different mass solutions from the different behaviour of the entire distribution. Although they have the same endpoints, they do not have the same shape.
However, our analytic shapes are parton level so we must ask if the features of the shape are preserved when we include cuts, hadronisation, FSR, detector effects etc.
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Compare our anaytic results with the parton level of PYTHIA, with no other effects.
Works very well – only deviations are statistical
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Parton level with cuts previously defined
Cuts cause a decrease in events for low invariant mass, but don’t affect the high invariant mass edge.
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Its fairly obvious why this is:
Only the cut on lepton PT is dangerous, but low lepton PT means low invariant masses
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With cuts and FSR
FSR causes a shift of the entire distribution to lower mass.
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Detector Level (ATLFAST)
At detector level we have to do better:
We need to remove b-quarks, so make use of b-tagging.
Also need to remove combinotoric backgrounds (where we get the wrong quark for the distribution)
We do this with an “inconsistency cut”
Take some very conservative upper bound for the endpoints (e.g. 20 GeV above the naively measured endpoint) and reject events where more than choice of quark gives consistent endpoints.
(This is actually rather wasteful of events since many good events are discarded, but is good at removing the combinotoric background)
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Some combinotoric background remains because we were very conservative
Here we used extra cuts of lepton P_T to try and distinguish the two leptons.
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Using the shapes to extract masses
These shapes can be used in two ways:
1. As a guide to the measurement of endpoints. • Use the functions derived for extrapolation of the edge of the
distribution to its endpoint. • Use the expressions to identify if you have any dangerous feet
or drops. • Discard any extra solutions which are not compatible with the
gross features of the shape.
2. As a fit function to be compared with the observed differential distributions and used to extract masses directly.
[or a combination of the two]
Unfortunately, this is still a work in progress, so no results to show you today….but hopefully soon!
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Conclusions and Summary
Missing energy/momentum from the LSP in minimal SUSY makes traditional methods for measuring masses difficult.
We can instead use endpoints of invariant mass distributions.
However, this introduces a number of problems:
We can solve these problems by analyzing the entire invariant mass distributions.
We have derived analytic forms for these distributions and compared them to realistic simulations.
We find good agreement and hope to now use these functions to fit for the superpartner masses at the LHC.
non-linear edges feet and drops multiple solutions
D J Miller 22nd July 2005 25
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