1. Superpartner masses from invariant mass distributions D.J. Miller, SUSY 2005, 22 nd 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

2. D J Miller22nd July 20052 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: Dont 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 )

3. D J Miller22nd July 20053 e.g. consider the decay m ll 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. Hinchliffes talk!

4. D J Miller22nd July 20054 3 unknown masses, but only 1 observable, m ll extend chain further to include squark parent: now have: m ll, m ql +, m ql -, m qll 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…]

5. D J Miller22nd July 20055 SPS 1a slope: SPS 1a point [See Allanach et al, Eur.Phys.J.C25 (2002) 113, hep-ph/0202233] W e examined this decay chain for benchmark SPS 1a at ATLAS using PYTHIA and ATLFAST. Cuts to remove backgrounds: At least 3 jets, with p T > 150, 100, 50 GeV E T, miss > max(100 GeV, 0.2 M eff ) with 2 isolated opposite-sign same-flavour leptons (e, ) with p T > 20,10 GeV Remove remaining uncorrelated lepton background using different-flavour-subtraction

6. D J Miller22nd July 20056 Theory curve End result Z peak (correlated leptons) Distribution for m ll after cuts

7. D J Miller22nd July 20057 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

8. D J Miller22nd July 20058 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

9. D J Miller22nd July 20059 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

10. D J Miller22nd July 200510 Problem 3 One set of mass endpoints can be fit by more than one set of masses! 2 causes: Endpoints themselves depend on mass hierarchy e.g. This splits the mass-space into different regions

11. D J Miller22nd July 200511 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

12. D J Miller22nd July 200512 second mass solutions - at Sps 1a this is caused by

13. D J Miller22nd July 200513 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

14. D J Miller22nd July 200514 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

15. D J Miller22nd July 200515 Feet and drops These become dangerous if the height of the last end structure is small compared to the total height. m ql (low) m ql (high) So now we know when invariant mass distributions have dangerous endpoints, and can correct for them. Problem 2 solved

16. D J Miller22nd July 200516 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.

17. D J Miller22nd July 200517 Compare our anaytic results with the parton level of PYTHIA, with no other effects. Works very well – only deviations are statistical

18. D J Miller22nd July 200518 Parton level with cuts previously defined Cuts cause a decrease in events for low invariant mass, but dont affect the high invariant mass edge.

19. D J Miller22nd July 200519 Its fairly obvious why this is: Only the cut on lepton P T is dangerous, but low lepton P T means low invariant masses

20. D J Miller22nd July 200520 With cuts and FSR FSR causes a shift of the entire distribution to lower mass.

21. D J Miller22nd July 200521 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)

22. D J Miller22nd July 200522 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.

23. D J Miller22nd July 200523 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!

24. D J Miller22nd July 200524 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

25. D J Miller22nd July 200525 UNIVERSITY of GLASGOW DEPARTMENT OF PHYSICS AND ASTRONOMY RESEARCH/ACADEMIC FELLOWSHIP (RCUK) IN THEORETICAL PARTICLE PHYSICS £19,460 - £29,128 per annum REF 11457/HRL/A3 Under the Research Councils UK Academic Fellowship scheme the University of Glasgow is offering a Research/Academic Fellowship in Physical Sciences that will provide for the translation of an active young researcher into a permanent academic position within the University (for more details, including duties, see http://www.rcuk.ac.uk/acfellow/). You will be expected to develop an independent research programme with international impact as part of the theoretical particle physics group and make a progressive input over the period of the Fellowship to the teaching activities of the Department.http://www.rcuk.ac.uk/acfellow/ Your research interests and experience should both broaden and strengthen existing research in theoretical particle physics in the area of phenomenology and Beyond the Standard Model physics (http://www.physics.gla.ac.uk/ppt/). There are extensive opportunities to collaborate with other theorists and experimentalists in Scotland under the auspices of the Scottish Universities Physics Alliance (http://www.supa.ac.uk/). You should be able to teach undergraduate physics, and possibly astronomy, at all levels and postgraduate theoretical particle physics.http://www.physics.gla.ac.uk/ppt/http://www.supa.ac.uk/ Informal enquiries can be made to Professor Christine Davies, +44 (0)141 330 4710, e-mail: c.davies@physics.gla.ac.uk. c.davies@physics.gla.ac.uk For an application pack, please see our website at www.gla.ac.uk or write quoting Ref 11457/HRL/A3 to the Recruitment Section, Human Resources Department, University of Glasgow, Glasgow G12 8QQ. Closing date: 7 October 2005.