Download ppt

Martin White – Cambridge ATLAS
UK ATLAS Physics Meeting, May 2004
The WMAP Experiment
The WMAP experiment:
• measures anisotropies in the Cosmic Microwave Background
• is able to determine the cosmological parameters with greater accuracy than ever
before
The goal of modern CMB measurements is to accurately measure the power spectrum
of the fluctuations in the microwave background (i.e. fluctuation amplitude vs angular
scale).
• theories make definite predictions about the power
spectrum
• these theories can potentially reveal a wealth of detail
about the early universe
Martin White – Cambridge ATLAS
UK ATLAS Physics Meeting, May 2004
WMAP Analysis
The WMAP team have considered a flat Universe with radiation, baryons, cold dark
matter and cosmological constant, with a power law spectrum of adiabatic primordial
fluctuations.
The model provides a very good description of the data with just 6 parameters. The
most relevant three are:
• the hubble constant h
• the matter density wm = mh2
• the baryon density wb = bh2
Values of these parameters are obtained
using a Monte Carlo Markov Chain to
explore the probability distribution in the
parameter space.
Still need information from other
experiments, since some parameter
combinations are degenerate.
Martin White – Cambridge ATLAS
UK ATLAS Physics Meeting, May 2004
WMAP Results
Fitting to a combination of WMAP and other data gives the best fit values:
 m h 2  0.13500..008
009
b h 2  0.0224  0.0009
Can assume the difference gives the CDM relic density, and further assume that
this is entirely comprised of the LSP of an R-parity conserving SUSY model.
Hence:
This result allows us to constrain SUSY models.
For any given model (e.g. mSUGRA is used here),
one can plot the regions of parameter space
consistent with the above relic density. I have been
investigating a point shown on the right, positioned
in the coannihilation region.
Martin White – Cambridge ATLAS
UK ATLAS Physics Meeting, May 2004
Coannihilation Point
The mSUGRA model is characterised by 5 parameters: m1/2 ,m0 , ,tan , A0
• The point studied here has m1/2 = 350 GeV, m0 = 70 GeV, A0 = 0,  > 0, tan = 10
• LSP’s coannihilate with sleptons, reducing the relic density to within the limits
allowed by WMAP
• The mass spectrum at the weak scale is generated from the above parameters using
ISAJET, with events subsequently generated using HERWIG before reconstruction
with the ATLFAST simulation.
• The small mass difference between the 2 and the eL and
between the 1 and the eR leads to soft leptons, which present a
potential problem in the ATLFAST simulation (this is not
parameterised properly for leptons with PT less than ≈ 6 GeV)
The ATLFAST analysis presented here is
due to be repeated later in the year with
fully reconstructed events.
Martin White – Cambridge ATLAS
UK ATLAS Physics Meeting, May 2004
Analysis of SUSY Events
Previous ATLAS studies (e.g. TDR) have documented the procedure of isolating
exclusive decay processes and looking for kinematic edges in the various invariant
mass distributions associated with the chosen events.
• An analysis is performed here using the
squark decay chain shown on the left.
• The two OSSF leptons give a clear
signature, which can be combined with
missing PT to isolate the chain.
• Kinematic edges are theoretically obtainable in the invariant mass distributions mll,
mllq and mlq (two edges), and one can also look for a threshold in the mllq
distribution.
• Each edge position is given by an function of the four (squared) masses involved
in the decay chain.
 Can solve for the masses in the chain
Martin White – Cambridge ATLAS
UK ATLAS Physics Meeting, May 2004
ll Invariant Mass Plot
All the plots that follow are based on 100 fb-1 of signal events.
The dilepton plot is subject to the cuts:
• ETmiss > 300 GeV
• exactly two OS leptons with pT > 5 GeV
and || <2.5
• at least two jets with pT > 150 GeV
• in addition, the plot is flavour subtracted
A kinematic edge is expected at 58 GeV,
resulting from eL decay.
This is clearly visible, and the
corresponding eR edge is also visible at 98
GeV.
Martin White – Cambridge ATLAS
UK ATLAS Physics Meeting, May 2004
llq Invariant Mass Plot
The llq invariant mass is worked out with each of
the two highest pT jets in the event, and the
lowest combination is plotted in the histogram
(i.e. the lowest should be below the endpoint).
Cuts:
• ETmiss > max(100 GeV, 0.2Meff), where
Meff > 400 GeV
• exactly two OS leptons with pT > 5 GeV
and || <2.5
• at least 4 jets with pT,1 > 100 GeV and
pT,2,3,4 > 50 GeV
• in addition, the plot is flavour subtracted
An edge is expected at 600 GeV, and again this is clearly observed.
Martin White – Cambridge ATLAS
UK ATLAS Physics Meeting, May 2004
llq Invariant Mass Threshold Plot
A threshold can be observed in the llq invariant mass plot if one chooses the subset of
events for which the angle between the two lepton momenta exceeds /2 in the
slepton rest frame (corresponding to m / 2  m  m ).
edge
ll
ll
edge
ll
Reduced statistics
 plot is not flavour subtracted
Additional cuts:
• ETmiss > 300 GeV
• exactly two OSSF leptons with pT > 5
GeV and || <2.5
• at least 2 jets with pT > 150 GeV
Threshold expected at 134 GeV. The
position of the observed threshold is
unclear (need to fit some kind of function,
yet form of function unknown at present)
Martin White – Cambridge ATLAS
UK ATLAS Physics Meeting, May 2004
lq High Invariant Mass Plot
If one forms the llq mass with the two hardest pT jets in the each event and takes the
jet that gives the lower llq mass, one can form two lq invariant masses.]
• get an edge in the plot containing the highest of these two lq masses
• get an additional edge in the plot containing the lowest of these two masses.
Additional cuts:
• ETmiss > 300 GeV
• exactly two OSSF leptons with pT > 5
GeV and || <2.5
• at least 2 jets with pT > 150 GeV
• one of the llq masses formed with the two
hardest pT jets must be above the llq
endpoint, the other must be below
Edge expected at 592 GeV- seen very clearly.
Martin White – Cambridge ATLAS
UK ATLAS Physics Meeting, May 2004
lq Low Invariant Mass Plot
Cuts same as previous page, except:
• dilepton invariant mass must be less than
the dilepton endpoint
An edge is expected at 182 GeV, and this is
clearly observable.
Martin White – Cambridge ATLAS
UK ATLAS Physics Meeting, May 2004
Summary of Edge Analysis
• Have observed 5 edges
 5 equations in 4 unknowns
 can solve for sparticle masses
• It appears that the soft leptons have not hindered the ATLFAST analysis, although
the generally poor statistics observed reflect that fact that in many events one of the
soft leptons is not picked up
• Still need to fit edges/determine edge errors more precisely (the above errors are
‘by eye’!)
Martin White – Cambridge ATLAS
UK ATLAS Physics Meeting, May 2004
Mass Reconstruction
There are several ways of reconstructing the masses from the edge equations.
I have been using Bayesian techniques:
• A sampler picks a point in the 4D mass space defined by the four masses in the
decay chain
• A probability weight is assigned to the point, by evaluating prob(masses|edges)
• The sampler picks other points (based on a Metropolis algorithm), ensuring that
regions of higher probability are sampled more frequently
• The sampled points are histogrammed, giving a visual description of the likelihood
surface
The resulting 4D likelihood plot can be projected onto pairs of axes. The result shows
the regions of parameter space favoured by the data.
More information  better constrained region
Martin White – Cambridge ATLAS
UK ATLAS Physics Meeting, May 2004
Favoured regions - results
Martin White – Cambridge ATLAS
UK ATLAS Physics Meeting, May 2004
Favoured regions - results
Martin White – Cambridge ATLAS
UK ATLAS Physics Meeting, May 2004
Further constraints?
The regions are not currently very well constrained. However, there are a wealth of
other measurements that could be obtained to rule out certain regions. Examples:
• there are other theoretical kinematic edges that, if observed, could provide more
equations, and hence further constrain the problem. (Poor statistics have made these
hard to find however)
• a lot of the parameter space can be ruled out due to the fact that it gives the wrong
relic density
• if the cross-section for SUSY production can be measured accurately, this could be
used to remove regions from the parameter space in which the cross-section is wrong
The problem is how to relate the excluded parameters at the SUSY scale to the
weak scale sparticle masses.
Martin White – Cambridge ATLAS
UK ATLAS Physics Meeting, May 2004
Inclusive Measurements
One approach to the wider problem of excluding SUSY models in a model
independent way is to use inclusive measurements. e.g.
• Measure the cross-section of events with missing pT bigger than 500 GeV
• Compare this with the cross-section predicted by a given model to determine the
probability of the model (Bayesian techniques will again prove useful)
• A whole list of inclusive measurements can be searched for, and an effective 2
obtained by comparison with the prediction of each model
• Plot on the left shows the variation in
the cross-section of events with missing
pT bigger than 500 GeV as you move
along the co-annihilation region
• There is sufficient variation in the
cross-section to make it a viable way of
discriminating between models that
otherwise satisfy the relic density
constraints in this region
Martin White – Cambridge ATLAS
UK ATLAS Physics Meeting, May 2004
Conclusions
• An analysis has been performed here on a mSUGRA point in the coannihilation
region.
• Existing analysis based on kinematic edges has produced good results, and
demonstrates that existing techniques are still applicable in this region
• Mass reconstruction has been attempted using Bayesian techniques, highlighting
the regions of mass parameter space consistent with the data. These need to be
further constrained with extra information
• I have started looking at inclusive measurements to both provide the extra
information required above, and also develop more model independent ways of
performing SUSY analysis
Martin White – Cambridge ATLAS
UK ATLAS Physics Meeting, May 2004