Transcript Document

Using mass distributions to improve SUSY mass
measurements at the LHC
D.J. Miller, DESY, 3rd February 2006
Part I: Edges and endpoints
Part II: Problems with the endpoint method
Part III: Using shapes instead of endpoints
B. K. Gjelsten, D. J. Miller, P. Osland, JHEP 0412 (2004) 003, hep-ph/0410303
D.J. Miller, A.Raklev, P. Osland, hep-ph/0510356
PART I: Edges and endpoints
Introduction
Low energy supersymmetry is an exciting and plausible extension to the
Standard Model.
It has many advantages:
• Extends the Poincaré algebra of space-time
• Solves the Hierarchy Problem
• More amenable to gauge unification
• Provides a natural mechanism for generating the Higgs potential
• Provides a good Dark Matter candidate ( )
Lots of exciting new phenomenology at the LHC:
squarks, sleptons, neutralinos, charginos, Higgs bosons….
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But: The MSSM has 105 extra parameters compared to the Standard Model!
This is a parameterisation of our ignorance of supersymmetry breaking.
If supersymmetry is discovered, the next question to ask is ‘How is it broken?’
Supergravity?
GMSB?
AMSB?
broken by gravity
broken by new gauge interactions
broken by anomalies
or something else….?
To answer this question,
Measure soft supersymmetry breaking parameters at the LHC
Run them up to the GUT scale and compare with susy breaking models
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The uncertainties in masses/parameters at low energy magnified by RGE running
Not so bad for the sleptons, but is
very difficult for the squarks and Higgs
bosons.
Need very accurate measurements
of SUSY masses
Supersymmetry Parameter Analysis:
SPA Convention and Project
J.A. Aguilar-Saavedra et al, hep-ph/0511344
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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)
Lightest SUSY Particle
(LSP) stable
Missing energy/momentum )
escapes detector
Cannot use traditional method of
peaks in invariant mass distributions
to measure SUSY masses
Instead measure endpoint of invariant mass distributions
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Measure masses using endpoints of invariant mass distributions
e.g. consider the decay
mll is maximised when leptons are
back-to-back in slepton rest frame
angle between leptons
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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
[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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For the chain
we need:
This is possible over a wide range of parameter space.
If this chain is not open, the method is still valid, but we need to look at
other decay chains.
In this talk I will consider only the decay chain above.
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Example mSUGRA inspired scenario:
[See Allanach et al, Eur.Phys.J.C25 (2002) 113, hep-ph/0202233]
OurDark
decay
chain
doesn’t work,
matter
constraints
others
areout
possible.
rule this
Thebut
hatched
area
is amenable
to this method in some form.
Its pretty
hard to do
lighter
green
is where
This area
doesn’t
change much
anything with this!
for other mSUGRA inspired
scenarios.
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Some extra difficulties:
Cannot normally distinguish the two leptons since
is a Majorana particle
Do we have
OR
?
Must instead define mql (high) and mql (low)
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Endpoints are not always linearly independent
e.g. if
and
then the endpoints are
Four endpoints not always sufficient to find the masses
angle between
leptons in slepton
rest frame
Introduce new distribution mqll >/2 identical to mqll except require >/2
It is the minimum of this distribution which is interesting
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Spin correlations
PYTHIA does not include spin correlations (HERWIG does)
OK for decays of scalars, but may give wrong results for fermions
PYTHIA ‘forgets’
spin
This could be a problem for mql
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Without spin correlations:
With spin correlations:
Recall, cannot distinguish ql+ and ql) must average over them
Spin correlations cancel when we
sum over lepton charges
) Pythia OK for our purposes
[Barr, Phys.Lett. B596 (2004) 205]
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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
After these cuts the remaining background is mainly
Remove this background using different-flavour-subtraction
Leptons in the signal are correlated (the same)
Leptons in the
background are uncorrelated
By subtracting the
sample with same-flavour leptons we remove the
different-flavour lepton background
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Distribution for mll after cuts
End result
‘Theory’ curve
Z peak (correlated leptons)
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Combinatoric backgrounds
Generally there will be 2 squarks in each event
there are extra jets not associated with our decay chain
If we choose the wrong jet to construct the invariant masses we will mess up our endpoints
We can cure this problem in 2 ways:
1. Inconsistency cuts: For many events, choosing the wrong jet results in one invariant
mass, e.g. mql high being unreasonable. If we only use events where this is the case, we
are guaranteed to choose the correct jet. We use a very conservative cut (e.g. 20GeV
above the first endpoint guess).
2. Mixed Events: We can simulate the combinatoric background by deliberately pairing
the leptons with the wrong jet, e.g. from a different event. Subtracting off this simulated
background removes the combinatoric background.
Both these methods use only data (no theory input).
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Inconsistency cut:
Mixed events:
The final result has been rescaled to
allow comparison with the theory
curve. About ¼ of the events survive.
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This seems to work much better.
Notice that beyond the kinematic
maximum, the background is very
well predicted.
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Procedure to extract endpoints and masses:
Make a (Gaussian smeared) linear extrapolation of the edge to find the endpoint
measured set of endpoints with errors
Generate 10,000 sample ‘endpoint sets’ Eexp using these values and errors
Use method of least squares to fit the masses to these endpoints:
[If the endpoints were uncorrelated, W would be
diagonal and this would become a simple 2 fit]
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We can do this “blind” (i.e. input masses into the Monte Carlo only and don’t look at
them again until we are done) and see what we get
Input mass
(GeV)
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Measured
Error (GeV)
mass (GeV)
96.1
96.3
3.8
143.0
143.2
3.8
176.8
177.0
3.7
537.2
537.5
6.1
491.9
492.4
13.4
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However, the kinematic endpoints depend strongly on mass differences
e.g.
) the mass measurements are very strongly correlated
Thus mass differences are much better measured, e.g.
Synergy between the LHC and ILC: if the ILC measures
all the mass measurements improve.
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precisely (e.g. 50MeV) then
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Widths here are error widths, not real widths
mass differences much better measured
– could be exploited by measuring one of
the masses at an e+e- linear collider
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I will explain these
blue curves later
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PART II: Problems with the endpoint method
Problem 1:
We used a Gaussian smeared straight line to find endpoints,
but can we really trust a linear fit?
Look at some other non-SPS1a points.
linear fit
lower part of
plot obscured
by background
endpoint
mismeasured
For SPS 1a, this isn’t such a problem because the edges are almost linear and the
backgrounds are not large compared to the signal.
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Problem 2:
The invariant mass distributions often have strange
behaviours near the endpoints which may be obscured by
remaining backgrounds
Notice a “foot” here. This caused us to
underestimate this endpoint by 9 GeV!
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Here, there is a
sudden drop to zero
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Quantify this by asking how large the final ‘feature’
is compared to the total height of the distribution.
Many parameter scenarios have dangerous “feet”
or “drops”.
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e.g.
b
a
r=a/b
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Problem 3:
One set of mass endpoints can be fit by more than one set of masses!
This has 2 causes:
Endpoints themselves depend on the mass hierarchy
e.g.
This splits the mass-space into different regions, each of which may contain a mass
solution which fits the measured endpoint.
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For example, in SPS 1a, using values of mqll, mql high, mql low and mll with no errors,
fitting to the LSP mass returns a second solution at around 80 GeV.
region boundary
true mass
false mass
In this case, the false mass is far enough away that this should not be a problem.
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Region boundaries:
If the nominal masses are near a region 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.
Endpoints with errors
Nominal endpoints
model point
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region boundary
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second mass solutions - at SPS 1a this is caused by
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PART III: Using shapes instead of endpoints
All of these problems are associated with using only endpoints of distributions.
If we fit the entire shape of the invariant mass distribution, we should avoid them.
In principle, this could be done numerically:
Use PYTHIA to produce sample data sets for lots of different mass spectra and
compare the invariant mass distributions of these sets with the real data to see
which mass spectra is best.
Allows you to include hadronization and detector effects directly into the sample
data set.
In practice, it is better to do this analytically:
Numerical generation of data sets is very slow, and impractical
Analytic solutions allow one to easily examine features of the distributions which
you might otherwise miss.
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Using analytic formula for the differential mass distributions:
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, giving us a good fit function.
Problem 2 (feet and drops)
With an analytic expression we will know about any anomalous structures even if
they are hidden by backgrounds, and be able to correct for them.
Problem 3 (multiple solutions)
Other features of the shape will serve to the distinguish the different solutions
which were obtained by the endpoint method.
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
since we cannot tell which lepton is lf, but is
a simple example of the method we use.
For simplicity, lets also assume that
and
are
scalars. This amounts to neglecting spin correlations (like
PYTHIA). It is actually OK for our purposes, but is easily
corrected later anyway.
I will be interested in:
angle between q and ln in the
rest frame of
angle between q and lf in the
rest frame of
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Our assumption that the intermediate particles are scalars means that the differential
rate cannot depend on u or v, but obviously we still need to keep 0 < (u,v) < 1.
So
The quantity we want to investigate is
energy/momentum
conservation
)
with
We can now change variables from u, v to
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So far, this was all very easy.
The “difficult” part is integrating out v, not because the integration itself is hard, but we
have to get the correct integration limits.
for
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Finally
The multi-function form of this is coming from the question “can
maximum opening angle or not”?
reach its
Of course, this was the simplest (non-trivial) case. The more physical expressions
are much harder to derive because the limits become very complicated.
To include spin correlations, all we need to do is change modify the distribution in
u and v:
e.g.
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In this derivation we have completely ignored the widths of the particles
In principle, in every event, each particle has a definite p2 which plays the role of m2
in our derivation.
So our derivation is OK is we now smear p2 around m2.
derived distribution with no widths
new distribution
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We calculate mqll, mql high, mql low and mll in this way (but not mqll >/2).
We now know the analytic form of the edges which lead down to the endpoints. They
are all simple logarithms + polynomials, which can be easily fit to the edges.
Problem 1 solved

We have an analytic expression for “r”, the quantity that tells us when we have a foot
or a drop.
In the example we derived r=1 always, which
is a bit dull…
…. but we can now perform detailed
scans to see which areas are dangerous, and
correct for them.
Problem 2 solved 
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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.
Problem 3 solved 
We can now use the data from (almost) the entire distribution, not just the edge, so
statistical error will get better too.
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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Step 1: compare our analytic results with the parton level of PYTHIA, with no other effects.
(SPS 1a)
Works very well – only deviations are statistical
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Step 2: Compare with 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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Step 3: compare with PYTHIA with cuts and FSR
FSR causes a slight shift of the entire distribution to lower mass.
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Step 4: compare with detector level
We used AcerDet with
(a simplified version of ATLFAST)
[E. Richter-Was, hep-ph/0207355]
As well as previous cuts, use a b-tag to remove events with b-squarks
Remove combinatoric backgrounds with an inconsistency cut
parton level
analytic distribution
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Some combinatoric background remains because we
were very conservative with our inconsistency cut
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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]
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Things to do
1. So far, we have only simulated with AcerDet and
Need to do proper experimental simulations with high luminosity
(e.g. 300 fb-1) and fit the masses to this data.
How much of an improvement to the measured masses does using shapes give?
Both ATLAS and CMS are interested in doing this.
2. Investigate distributions like mqll >/2
Helps set overall scale with endpoints. Is it so useful for shapes?
>/2 was arbitrary. Can we do better?
Need to derive the distribution for whatever function we come up with (hard?)
3. Investigate other decay chains
This decay chain is only a portion of the parameter space. Can we use the same
methods for other decay chains? How well can we do?
The derivations of the shapes was model independent. Can we use this method
for other physics, e.g. extra dimensions, little Higgs models etc?
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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:
non-linear edges
feet and drops
multiple solutions
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.
Lots still to do!
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