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 )

D J Miller 22nd July 2005 3

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!

D J Miller 22nd July 2005 4

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…]

D J Miller 22nd July 2005 5

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

D J Miller 22nd July 2005 6

‘Theory’ curve

End result

Z peak (correlated leptons)

Distribution for mll after cuts

D J Miller 22nd July 2005 7

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

D J Miller 22nd July 2005 8

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’

D J Miller 22nd July 2005 9

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

D J Miller 22nd July 2005 12

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

D J Miller 22nd July 2005 14

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

D J Miller 22nd July 2005 16

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.

D J Miller 22nd July 2005 17

Compare our anaytic results with the parton level of PYTHIA, with no other effects.

Works very well – only deviations are statistical

D J Miller 22nd July 2005 18

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.

D J Miller 22nd July 2005 19

Its fairly obvious why this is:

Only the cut on lepton PT is dangerous, but low lepton PT means low invariant masses

D J Miller 22nd July 2005 20

With cuts and FSR

FSR causes a shift of the entire distribution to lower mass.

D J Miller 22nd July 2005 21

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)

D J Miller 22nd July 2005 22

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.

D J Miller 22nd July 2005 23

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!

D J Miller 22nd July 2005 24

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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