martin white – cambridge atlas uk atlas physics meeting, may 2004

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


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.


WMAP Results

Fitting to a combination of WMAP and other data gives the best fit values:

008.0009.0

2 135.0 hm 0009.00224.02 hb

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.


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.


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


ll Invariant Mass Plot

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.

All the plots that follow are based on 100 fb-1 of signal events.

The dilepton plot is subject to the cuts:

• > 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

missTE


llq Invariant Mass Plot

Cuts:

• > 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

missTE

An edge is expected at 600 GeV, and again this is clearly observed.

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).


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 ).edge

lllledgell mmm 2/

Reduced statistics

plot is not flavour subtracted

Additional cuts:

• > 300 GeV

• exactly two OSSF leptons with pT > 5 GeV and || <2.5

• at least 2 jets with pT > 150 GeV

missTE

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)


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:

• > 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

missTE

Edge expected at 592 GeV- seen very clearly.


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.


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’!)


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


Favoured regions - results


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.


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


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

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