1. Transverse Mass Kink Yeong Gyun Kim (KAIST) In collaboration with W.S.Cho, K.Choi, C.B.Park

2. Introduction Cambridge m T2 variable ‘Gluino’ m T2 variable Conclusion Contents

3. Started on 10th September 2008.10th September 2008 Initial beam commissioning progressed well. LHC Commissioning with beam An incident : a helium leak into the LHC tunnel. The LHC is able to restart in 2009.

4. We are entering exciting period in particle physics. The LHC is about to explore for the first time the TeV energy scale. The origin of EWSB ? The nature of dark matter ? Supersymmetry ? Extra dimensions ?

5. General features for SUSY at the LHC  SUSY production is dominated by gluinos and squarks, unless they are too heavy Squark and gluino production rates -determined by strong interaction, and the squark and gluino masses, -do not depend on the details of model (Baer etal. 1995) ~50 pb for m_gluino~500 GeV ~ 1 pb for m_gluino~1000 GeV

6.  The gluinos and squarks cascade down, generally in several steps, to the final states including multi-jets (and/or leptons) and two invisible LSPs

7.  Characteristic signals of SUSY with R p  Invisible LSPs  Large Missing Transverse Energy  Decays of squarks and gluinos  Large multiplicity of hadronic jets and/or  Decays of sleptons and gauginos  Isolated leptons

8. Supersymmetry searches LHC focus week Tokyo 24/6/2008 T. Lari INFN Milano Discovery potential 5  evidence after 1 fb -1 (including systematics) expected if squarks lighter than 1300 GeV 0-lepton and 1-lepton best modes for mSUGRA No attempt to combine channels yet ~ ~ preliminary (Taken from T.Lari’s talk in LHC focus week at IPMU)

9. Discovery of Supersymmetry Mass measurements Measurements of spin, couplings

10.  Precise measurement of SUSY masses  Reconstruction of SUSY theory (SUSY breaking sector)  Weighing Dark Matter with collider M1: M2: M3 = 1 : 2 : 6 mSUGRA pattern 3.3 : 1 : 9 AMSB pattern etc.

11.  Distinguishing SUSY from other models The rate of KK-gluon vs. gluino (Datta, Kane,Toharia 2007 ) Mass (GeV)

12.  SUSY events always contain two invisible LSPs  No masses can be reconstructed directly  Final state momentum in beam direction is unknown a priori, due to our ignorance of initial partonic center of mass frame The Mass measurement is Not an easy task at the LHC !

13. Several approaches (and variants) of mass measurements proposed  Invariant mass Edge method Hinchliffe, Paige, Shapiro, Soderqvist, Yao ; Allanach, Lester, Parker, Webber …  Mass relation method Kawagoe, Nojiri, Polesello ; Cheng, Gunion, Han, Marandellea, McElrath  Transverse mass (M T2 ) kink method Cho, Choi, YGK, Park ; Barr, Lester, Gripaios ; Ross, Serna; Nojiri, Shimizu, Okada, Kawagoe

14.  Basic idea  Identify a particular long decay chain and measure kinematic endpoints of various invariant mass distributions of visible particles  The endpoints are given by functions of SUSY particle masses Invariant mass edge method Hinchliffe, Paige, etal. (1997)

15. If a long enough decay chain is identified, It would be possible to measure sparticle masses in a model independent way 3 step two-body decays

16.  Invariant mass edges In total, five endpoint measurements Four invovled sparticle masses can be obtained for SPS1a point

17. Mass relation method  Consider the following cascade decay chain (4 step two-body decays) Kawagoe, Nojiri, Polesello (2004)  Completely solve the kinematics of the cascade decay by using mass shell conditions of the sparticles

18.  One can write five mass shell conditions which contain 4 unknown d.o.f of LSP momentum  Each event describes a 4-dim. hypersurface in 5-dim. mass space, and the hypersurfcae differs event by event  Many events determine a solution for masses through intersections of hypersurfaces

19.  Measurements of gluino and sbottom masses (assuming that the masses of two neutralinos and slepton are already known) in SPS 1a point In this case, each event corresponds to a different line in plane Gluino mass distribution with event pair analysis Two events are enough to solve the gluino and sbottom masses altogether Build all possible event pairs (with some conditions) m_gluino ~ 592 GeV (300 fb -1 ) Kawagoe, Nojiri, Polesello (2004)

20. Both the Edge method and the Mass relation method rely on a long decay chain to determine sparticle masses W hat if we don’t have long enough decay chain but only short one ? In such case, M T2 variable would be useful to get information on sparticle masses

21. (Stransverse Mass) Cambridge m T2 variable Lester, Summers (1999) Barr, Lester, Stephens (2003)

22. Cambridge m T2 (Lester and Summers, 1999) Massive particles pair produced Each decays to one visible and one invisible particle. For example, For the decay, ()

23. ( : total MET vector in the event ) However, not knowing the form of the MET vector splitting, the best we can say is that : with minimization over all possible trial LSP momenta

24.  M T2 distribution for LHC point 5, with 30 fb -1, (Lester and Summers, 1999) Endpoint measurement of m T2 distribution determines the mother particle mass ( with )

25. The LSP mass is needed as an input for m T2 calculation. However, it might not be known in advance. Introduce a trial LSP mass for MT2 calculation. Now m T2 depends not only on visible momenta but also on the trial LSP mass. The maximum of m T2 can be considered as a function of the trial LSP mass.

26. Varying “  ” … m T2 (  ) mBmB mAmA Does not just translate … Shape may also change … more on this later. (Taken from Lester’s talk in the LHC focus week at IPMU)

27. Maximum of m T2 as a function of the trial LSP mass (Lester and Summers, 1999) The correlation from a numerical calculation can be expressed by an analytic formula in terms of true sparticle masses

28. Well described by the above Analytic expression with true Squark mass and true LSP mass  The maximum of the squark m T2 as a function of (Cho, Choi, YGK and Park, 2007) Squark mass and LSP mass are Not determined separately

29. ‘Gluino’ m T2 variable W.S.Cho, K.Choi, Y.G.Kim, C.B.Park Ref) PRL 100 (2008) 171801 [arXiv:0709.0288], JHEP 02 (2008) 035 [arXiv:0711.4526].

30. Gluino m T2 (stransverse mass) A new observable, which is an application of m T2 variable to the process Gluinos are pair produced in proton-proton collision Each gluino decays into two quarks and one LSP through three body decay (off-shell squark) or two body cascade decay (on-shell squark)

31.  For each gluino decay, the following transverse mass can be constructed : Mass and transverse momentum of qq system : Trial mass and transverse momentum of the LSP  With two such gluino decays in each event, the gluino m T2 is defined as (minimization over all possible trial LSP momenta)

32. m qq value for three body gluino decay Each mother particle produces one invisible LSP and more than one visible particle

33.  MT2 maximum as a function of trial LSP mass depends on di-quark invariant mass (mqq) mqq=minimum mqq=mqq mqq=maximum Trial LSP mass MT2 maximum (Assume mqq (1) = mqq (2), for simplicity )

35.  If the function can be constructed from experimental data, which identify the KINK, one will be able to determine the gluino mass and the LSP mass simultaneously. A numerical example and a few TeV masses for sfermions

36. Experimental feasibility An example (a point in mAMSB) with a few TeV sfermion masses (gluino undergoes three body decay) Wino LSP We have generated a MC sample of SUSY events by PYTHIA, which corresponds to 300 fb -1 The generated events further processed with PGS detector simulation, which approximates an ATLAS or CMS-like detector

37.  Event selection cuts  At least 4 jets with  Missing transverse energy  Transverse sphericity  No b-jets and no-leptons GeV

38.  The four leading jets are divided into two groups of dijets by hemisphere analysis Seeding : The leading jet and the other jet which has the largest with respect to the leading jet are chosen as two ‘seed’ jets for the division Association : Each of the remaining jets is associated to the seed jet making a smaller opening angle If this procedure fail to choose two groups of jet pairs, We discarded the event

39. The gluino m T2 distribution with the trial LSP mass m x = 90 GeV Fitting with a linear function with a linear background, We get the endpoints m T2 (max) = The blue histogram : SM background

40. as a function of the trial LSP mass for a benchmark point Fitting the data points with the above two theoretical curves, we obtain The true values are GeV

41.  The above results DO NOT include systematic uncertainties associated with, for example, fit function, fit range and binning of the histogram etc. to determine the endpoint of mT2 distribution.  SM backgrounds are generated by PYTHIA. It may underestimate the SM backgrounds. Some Remarks

42. For case of two body cascade decay m 2 qq max = Therefore,,

43. For three body decayFor two body cascade decay

44.  Barr, Gripaios and Lester (arXiv:0711.4008 [hep-ph]) Instead of jet-paring with hemisphere analysis, we may calculate m T2 for all possible divisions of a given event into two sets, and then minimize m T2 M TGen vs. Hemisphere analysis M 2C (A Variant of ‘gluino’ mT2)  Ross and Serna (arXiv:0712.0943 [hep-ph]) A Variant of ‘gluino’ m T2 with explicit constraint from the endpoint of ‘diquark’ invariant mass (M 2C )

45.  Nojiri, Shimizu, Okada and Kawagoe (arXiv:0802.2412) Even without specifying the decay channel, m T2 variable still shows a kink structure in some cases. This might help to determine the sparticle masses at the early stage of the LHC experiment Inclusive m T2

46. (Cho,Choi, YGK, Park, arXiv:0804.2185) Standard Candle for MT2 study Top quark mT2 distribution with m_nu = 0 With 10 fb -1, 2 b jets, 2 leptons, Large missing ET for input mt=170.9 GeV Without systematic uncertainty

47. Standard Candle for MT2 study mT2 max vs. trial neutrino mass Shape of mT2 distribution The di-leptonic channel will provide a good playground for mT2 excercise

48. Is there any other usefulness of MT2, after determining new particle masses ? Yes! M.A.O.S (M T2 -Assissted On-Shell) reconstruction of WIMP momentum. P T  M T2 solution P Z  On-Shell condition See W.S.Cho’s Talk This lunch time !

49. Conclusion  Maximum of gluino MT2 as a function of trial LSP mass shows a kink structure at true LSP mass from which gluino mass and LSP mass can be determined altogether.  Top-quark MT2 provides an independent way of measuring the top-quark mass and can serve as a Standard Candle for general MT2 analysis.  MAOS reconstruction of WIMP momentum may open a new window for investigating New physics structures  See W.S.Cho’ Talk Today !

50. The Horror of the Heights Arther Conan Doyle (1913)

51. The Horror of the Heights(2008-) Nothing new in the TeV scale….

52. “ There are jungles of the upper air, and there are worse things than tigers which inhabit them. I believe in time they will map these jungles accurately out “ - Armstrong in ‘the Horror of the Height’ The Hope of the Heights (2008-) SUSY jungle (sps1a)