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Transverse Mass Kink

Transverse Mass Kink. Yeong Gyun Kim (KAIST). In collaboration with W.S.Cho, K.Choi, C.B.Park. Contents. Introduction Cambridge m T2 variable ‘Gluino’ m T2 variable Conclusion. LHC Commissioning with beam. Started on 10th September 2008 .

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Transverse Mass Kink

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

  2. Contents • Introduction • Cambridge mT2 variable • ‘Gluino’ mT2 variable • Conclusion

  3. LHC Commissioning with beam Started on 10th September 2008. Initial beam commissioning progressed well. 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 ~50 pb for m_gluino~500 GeV ~ 1 pb for m_gluino~1000 GeV (Baer etal. 1995)

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

  7. Characteristic signals of SUSY with Rp • 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. Discovery potential 5s 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) T. Lari INFN Milano

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

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

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

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

  13. Several approaches (and variants) of mass measurements proposed • Invariant massEdge method Hinchliffe, Paige, Shapiro, Soderqvist, Yao ; Allanach, Lester, Parker, Webber … • Mass relation method Kawagoe, Nojiri, Polesello ; Cheng, Gunion, Han, Marandellea, McElrath • Transverse mass (MT2 ) kink method Cho, Choi, YGK, Park ; Barr, Lester, Gripaios ; Ross, Serna; Nojiri, Shimizu, Okada, Kawagoe

  14. Invariant mass edge method Hinchliffe, Paige, etal. (1997) • 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

  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. Consider the following cascade decay chain • (4 step two-body decays) Mass relation method 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 Kawagoe, Nojiri, Polesello (2004) In this case, each event corresponds to a different line in plane 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) Gluino mass distribution with event pair analysis

  20. Both the Edge method and the Mass relation method • rely on a long decay chain to determine sparticle masses • What if we don’t have long enough decay chain but only short one ? • In such case, MT2 variable would be useful to get information on sparticle masses

  21. Cambridge mT2 variable (Stransverse Mass) Lester, Summers (1999) Barr, Lester, Stephens (2003)

  22. For the decay, ( ) • Cambridge mT2 (Lester and Summers, 1999) Massive particles pair produced Each decays to one visible and one invisible particle. For example,

  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. ( with ) • MT2 distribution for LHC point 5, with 30 fb-1, Endpoint measurement of mT2 distribution determines the mother particle mass (Lester and Summers, 1999)

  25. The LSP mass is needed as an input for mT2 calculation. However, it might not be known in advance. Introduce atrial LSP mass for MT2 calculation. Now mT2 depends not only on visible momenta but also on the trial LSP mass. The maximum of mT2 can be considered as a function of the trial LSP mass.

  26. Varying “”… (Taken from Lester’s talk in the LHC focus week at IPMU) Does not just translate … Shape may also change … more on this later. mT2() mB mA

  27. (Lester and Summers, 1999) Maximum of mT2 as a function of the trial LSP mass The correlation from a numerical calculation can be expressed by an analytic formula in terms of true sparticle masses

  28. The maximum of the squark mT2as a function of (Cho, Choi, YGK and Park, 2007) Well described by the above Analytic expression with true Squark mass and true LSP mass • Squark mass and LSP mass • are Not determined separately

  29. ‘Gluino’ mT2 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 mT2 (stransverse mass) A new observable, which is an application of mT2 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. : Mass and transverse momentum of qq system : Trial mass and transverse momentum of the LSP • For each gluino decay, • the following transverse mass can be constructed • With two such gluino decays in each event, • the gluino mT2 is defined as (minimization over all possible trial LSP momenta)

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

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

  34. 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

  35. 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

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

  37. 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

  38. The gluino mT2 distribution with the trial LSP mass mx = 90 GeV Fitting with a linear function with a linear background, We get the endpoints mT2 (max) = The blue histogram : SM background

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

  40. Some Remarks • 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.

  41. m2qq max = Therefore, • For case of two body cascade decay ,

  42. For three body decay For two body cascade decay

  43. M2C (A Variant of ‘gluino’ mT2) • Ross and Serna (arXiv:0712.0943 [hep-ph]) A Variant of ‘gluino’ mT2 with explicit constraint from the endpoint of ‘diquark’ invariant mass (M2C) • MTGen vs. Hemisphere analysis • Barr, Gripaios and Lester (arXiv:0711.4008 [hep-ph]) Instead of jet-paring with hemisphere analysis, we may calculate mT2 for all possible divisions of a given event into two sets, and then minimize mT2

  44. Inclusive mT2 • Nojiri, Shimizu, Okada and Kawagoe (arXiv:0802.2412) Even without specifying the decay channel, mT2 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

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

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

  47. Yes! M.A.O.S(MT2-Assissted On-Shell) reconstruction of WIMP momentum. PT MT2 solution PZ On-Shell condition See W.S.Cho’s Talk This lunch time ! • Is there any other usefulness of MT2, after determining new particle masses ?

  48. 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 masscan 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 !

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

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