The measurement of SUSY masses in cascade decays at the LHC

1. The measurement of SUSY masses in cascade decays at the LHC D. J. Miller 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

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

3. 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) ~ 0 1 D.J. Miller

4. 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? D.J. Miller

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

6. 3B-3L+2s P= (-1) R • 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) SM particles have P = +1 R SUSY partners have P = - 1 R 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 D.J. Miller

7. Measure masses using endpoints of invariant mass distributions e.g. consider the decay mll is maximised when leptons are back-to-back in slepton rest frame angle between leptons D.J. Miller

8. )can(?) measure masses from endpoints 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 [Hinchliffe et al, Phys. Rev D 55 (1997) 5520, and many others…] D.J. Miller

9. 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 isn’t we would have to study a different decay) D.J. Miller

10. Run down from GUT scale: • QCD interaction push up mass of squarks and gluino • unification at GUT scale pushes up masses compared to Consequently: Quarks and gluons tend to be heavy LSP is usually ‘B-like’: ~ In mSUGRA models have universal boundary conditions at GUT scale (1016 GeV) SUSY scalar mass: m0 SUSY fermion mass: m1/2 Common triple coupling: A0 Higgs vacuum expectation values: tan,>0 Also D.J. Miller

11. lighter green is where Snowmass benchmark model ‘slope’ SPS 1a: A0 = -m0, tan = 10, >0 D.J. Miller

12. A0 = 0, tan = 30 A0 = 0, tan = 10 A0 = -1000GeV, tan = 5 (>0) A0 = -m0, tan = 10 D.J. Miller

13. ~ ~ ‘W-like’ ‘B-like’ Squark decay branching ratios: (¼ SU(2) singlet) D.J. Miller

14.  both decay to bottom squarks are mixtures of left and right handed states D.J. Miller

15. ~ 20 decay branching ratios ~ ~ (20 - 10) independent of m0 D.J. Miller

16. A0 = 0 2 exclusion Constraints from WMAP: [Ellis et al, hep-ph/0303043] A large part of ‘interesting’ parameter space has the decay D.J. Miller

17. Standard point SPS 1a point : SPS 1a point b: Extra point, with smaller cross-sections The SPS 1a slope and point(s) Snowmass ‘points and slopes’ are benchmark scenarios for SUSY studies [See Allanach et al, Eur.Phys.J.C25 (2002) 113, hep-ph/0202233] 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: SPS 1a slope: D.J. Miller

18. widths masses α β α β NB: instabilities due to inaccuracy in ISAJET, and thus inherent to definition D.J. Miller

19. Parent gluino/squark production cross-sections in pb: α β [not useful] These are not yet the relevant numbers for our analysis; it doesn’t matterwhere the parent squark comes from D.J. Miller

20. α β Maybe we could use or at point β? ~ 20 branching ratios: D.J. Miller

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

22. PYTHIA ‘forgets’ spin Spin correlations PYTHIA does not include spin correlations (HERWIG does!) OK for decays of scalars, but may give wrong results for fermions This could be a problem for mql D.J. Miller

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

24. Cascade decays at ATLAS D.J. Miller

25. 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 D.J. Miller

26. After these cuts, remaining background is mainly and other SUSY processes • Initial (untuned) cuts to remove backgrounds: • ≥ 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 • 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 D.J. Miller

27. 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’ End result of DF subtraction ‘Theory’ curve Z peak (correlated leptons) D.J. Miller

28. 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 pT jets) which minimises mqll D.J. Miller

29. Fit mll 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! D.J. Miller

30. 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 D.J. Miller

31. Point β: much more difficult due to lower cross-sections D.J. Miller

32. Energy scale error: 1% for jets, 0.1% for leptons D.J. Miller

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

34. D.J. Miller

35. 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 Ai and Bi picked from Gaussian distribution 2. Fit masses to these endpoints using method of least squares Use analytic expressions to find a starting point for the fit 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. D.J. Miller

36. 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 SPS 1a (α) results D.J. Miller

37. second solution D.J. Miller

38. much worse than SPS 1a (α) additionally have extra solutions – at β caused by SPS 1a (β) results D.J. Miller

39. 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 m0 is not too large compared with m1/2 We examined a second point on the SPS 1a line which has less optimistic cross-sections D.J. Miller

40. 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 D.J. Miller