1. The measurement of SUSY masses in cascade decays at the LHC Based on: B. K. Gjelsten, D. J. Miller, P. Osland ATL-PHYS-2004-029 hep-ph/0410303 B.K. Gjelsten, E. Lytken, D.J. Miller, P. Osland, G. Polesello, LHC/LC Study Group Working Document. ATL-PHYS-2004-007 D. J. Miller

2. November 10, 2004D.J. Miller2 Contents Introduction How applicable is this method? The SPS 1a point(s) and slope Cascade decays at ATLAS Summary and conclusions

3. November 10, 2004D.J. Miller3 Introduction Low energy supersymmetry presents an exciting and plausible extension to the Standard Model. It has many advantages: Extends the Poincarré 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 ( ) Supersymmetry may be discovered at the LHC (switch on in 2007) 0101 ~

4. November 10, 2004D.J. Miller4 Supersymmetry predicts many new particles Scalars: squarks & sleptons Spin ½: gauginos & higgsinos (neutralinos) Predicts SUSY particles have same mass as SM partners – wrong! SUSY must be broken, but how is not clear MSSM: break supersymmetry by hand by adding masses for each SUSY particle Supergravity: break SUSY via gravity GMSB:SUSY is broken by new gauge interactions AMSB:SUSY is broken by anomalies Which, if any, of these is true?

5. November 10, 2004D.J. Miller5 SUSY breaking models predict masses at high energy Evolved to EW scale using (logarithmic) Renormalisation Group Equations Need very accurate measurements of SUSY masses [Zerwas et al, hep-ph/0211076] Uncertainties in masses at low energy magnified by RGE running

6. November 10, 2004D.J. Miller6 2 problems with measuring masses at the LHC: Dont know centre of mass energy of collision s R-parity conserved (to prevent proton decay) P = (-1) R 3B-3L+2s SM particles have P = +1 R R SUSY partners have P = - 1 R-parity Lightest SUSY Particle (LSP) does not decay All decays of SUSY particle have missing energy/momentum This cannot be recovered by using conservation of momentum

7. November 10, 2004D.J. Miller7 Measure masses using endpoints of invariant mass distributions e.g. consider the decay m ll is maximised when leptons are back-to-back in slepton rest frame angle between leptons

8. November 10, 2004D.J. Miller8 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 et al, Phys. Rev D 55 (1997) 5520, and many others…]

9. November 10, 2004D.J. Miller9 How applicable is this method? To make this work we need The correct mass hierarchy to allow i.e. A large enough cross-section and branching ratio Examine mSUGRA scenarios to see if this is likely (if it isnt we would have to study a different decay)

10. November 10, 2004D.J. Miller10 In mSUGRA models have universal boundary conditions at GUT scale (10 16 GeV) SUSY scalar mass: m 0 SUSY fermion mass: m 1/2 Common triple coupling: A 0 Higgs vacuum expectation values:tan, >0 Run down from GUT scale: QCD interaction push up mass of squarks and gluino unification at GUT scale pushes up masses compared to Also Quarks and gluons tend to be heavy LSP is usually B-like: ~ Consequently:

11. November 10, 2004D.J. Miller11 Snowmass benchmark model slope SPS 1a: A 0 = -m 0, tan = 10, >0 lighter green is where

12. November 10, 2004D.J. Miller12 A 0 = -m 0, tan = 10 A 0 = 0, tan = 10 A 0 = 0, tan = 30 A 0 = -1000GeV, tan = 5 0)

13. November 10, 2004D.J. Miller13 Squark decay branching ratios: W-like ~ B-like ~ ( ¼ SU(2) singlet)

14. November 10, 2004D.J. Miller14 bottom squarks are mixtures of left and right handed states both decay to

15. November 10, 2004D.J. Miller15 2 0 decay branching ratios ~ 2 0 - 1 0 ) independent of m 0 ~~

16. November 10, 2004D.J. Miller16 A large part of interesting parameter space has the decay Constraints from WMAP: A 0 = 0 2 exclusion [Ellis et al, hep-ph/0303043]

17. November 10, 2004D.J. Miller17 The SPS 1a slope and point(s) SPS 1a slope: SPS 1a point Standard point SPS 1a point Extra point, with smaller cross-sections Defined as low energy (TeV scale) parameters (masses, couplings etc) as evolved by version 7.58 of the program ISAJET from the GUT scale parameters: Snowmass points and slopes are benchmark scenarios for SUSY studies [See Allanach et al, Eur.Phys.J.C25 (2002) 113, hep-ph/0202233]

18. November 10, 2004D.J. Miller18 masses widths NB: instabilities due to inaccuracy in ISAJET, and thus inherent to definition ααββ

19. November 10, 2004D.J. Miller19 Parent gluino/squark production cross-sections in pb: [not useful] These are not yet the relevant numbers for our analysis; it doesnt matter where the parent squark comes from αβ

20. November 10, 2004D.J. Miller20 βα 2 0 branching ratios: ~ Maybe we could use or at point β?

21. November 10, 2004D.J. Miller21 Cannot normally distinguish the two leptons is Majorana particle: Must instead define m ql (high) and m ql (low) ? Do we have Endpoints are not always linearly independent Four endpoints not always sufficient to find the masses Introduce a new distribution m qll ( > /2) identical to m qll except enforce the constraint > /2 It is the minimum of this distribution which is interesting Some extra difficulties:

22. November 10, 2004D.J. Miller22 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 m ql

23. November 10, 2004D.J. Miller23 Without spin correlations: With spin correlations: [Barr, Phys.Lett. B596 (2004) 205] Recall, cannot distinguish ql + and ql - must average over them Spin correlations cancel when we sum over lepton charges Pythia OK

24. November 10, 2004D.J. Miller24 Cascade decays at ATLAS

25. November 10, 2004D.J. Miller25 Generate simulated data using PYTHIA 6.2 (with CTEQ 5L) Pass events through ATLFAST 2.53, a fast simulation of ATLAS. Acceptance requirements: ATLFAST has no lepton identification efficiency – include 90% efficiency per lepton by hand ATLFAST has no pile-up, or jets misidentified as leptons – not included here

26. November 10, 2004D.J. Miller26 Initial (untuned) cuts to remove backgrounds: 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 After these cuts, remaining background is mainly and other SUSY processes Split remaining background into two categories: Correlated leptons (e.g. Z e + e - ) - processes where the leptons are of the Same Flavour (SF) Uncorrelated leptons (e.g. leptons from different decay branches) - processes where the leptons need not be SF

27. November 10, 2004D.J. Miller27 Uncorrelated backgrounds have the same number of events with SF leptons (a background to the signal) as events with Different Flavour (DF) leptons Can remove SF events by Different Flavour (DF) subtraction Theory curve End result of DF subtraction Z peak (correlated leptons)

28. November 10, 2004D.J. Miller28 When distribution includes a quark have an extra problem - which quark to pick? This will give a combinotoric background Estimate this background with mixed events Combine the lepton pair with a jet from a different event to mimic choosing the wrong jet gives dashed curve Here we have chosen the jet (from the two highest p T jets) which minimises m qll

29. November 10, 2004D.J. Miller29 Fit m ll endpoint to Gaussian smeared triangle Fit other distributions to a Gaussian smeared straight line where indicated It is not clear that this is the best thing to do!

30. November 10, 2004D.J. Miller30 Theory curves can we really trust a linear fit? something to improve in the future…? notice the foot here - this can be easily hidden by backgrounds

31. November 10, 2004D.J. Miller31 Point β: much more difficult due to lower cross-sections

32. November 10, 2004D.J. Miller32 Energy scale error: 1% for jets, 0.1% for leptons

33. November 10, 2004D.J. Miller33 From endpoints to masses Can (in principle) extract the masses in two ways: 1.Analytically invert endpoint formulae for masses Endpoints in terms of masses are already complicated, with 9 different physical mass regions. m qll( > /2) particularly complicated to invert Not very flexible Not all endpoints should be given the same weight, e.g. m ll is much better measured. see over

34. November 10, 2004D.J. Miller34

35. November 10, 2004D.J. Miller35 Consider 10,0000 gedanken ATLAS experiments, with measured endpoints smeared from the nominal value by a Gaussian of width given by the statistical & energy scale error with A i and B i picked from Gaussian distribution Use analytic expressions to find a starting point for the fit 2. Fit masses to these endpoints using method of least squares Problem: the multi-region nature of the endpoint formulae often lead to 2 consistent solutions for the masses. Usually these are sufficiently different that we can distinguish them from the real masses by some other means and/or the wrong mass spectrum has a much lower likelihood.

36. November 10, 2004D.J. Miller36 SPS 1a (α) results second mass solutions - at α this is caused by Note mass differences much better measured – could be exploited by measuring one of the masses at an e + e - linear collider

37. November 10, 2004D.J. Miller37 second solution

38. November 10, 2004D.J. Miller38 SPS 1a (β) results much worse than SPS 1a (α) additionally have extra solutions – at β caused by

39. November 10, 2004D.J. Miller39 Conclusions and summary It will be important to accurately measure SUSY masses at the LHC R-parity conservation and unknown CME makes measuring masses difficult Can measure masses using endpoints of invariant mass distributions in cascade decays We have studied the decay at ATLAS for the Snowmass benchmark SPS 1a This decay is applicable over much of the allowed parameter space as long as m 0 is not too large compared with m 1/2 We examined a second point on the SPS 1a line which has less optimistic cross-sections

40. November 10, 2004D.J. Miller40 Simulated data using PYTHIA and ATLFAST Remove real and combinotoric backgrounds using DF subtraction and mixed events Fit straight lines to edges of distributions to find endpoints – it is not clear whether this is a good idea Use method of least squares to fit for the masses Often find multiple solution (though correct solution is always favoured) This method provides reasonable mass measurements, but even better measurements of mass differences