1. 1 The latest and greatest tricks in studying missing energy events Konstantin Matchev With: M. Burns, P. Konar, K. Kong, F. Moortgat, L. Pape, M. Park arXiv:0808.2472 [hep-ph], arXiv:0810.5576 [hep-ph], arXiv:0812.1042 [hep-ph], arXiv:0903.4371 [hep-ph], arXiv:0906.2417 [hep-ph], arXiv:090?.???? [hep-ph] Fermilab, LPC August 10-14, 2009

2. 2 MET events: experimentalist’s view What is going on here?

3. 3 Pair production of new particles (conserved R, KK, T parity) Today: imagine very complex topologies –For example, fully hadronic: 10 jets and missing energy SM particles x i seen in the detector, originate from two chains –How well can I identify the two chains? Should I even try? What about ISR jets versus jets from particle decays? “WIMPs” X 0 are invisible, momenta unknown, except p T sum –How well can I reconstruct the WIMP momenta? Should I even try? What about SM neutrinos among the x i ’s? MET events: theorist’s view NO! NO; or TAKE A GUESS…

4. 4 In place of an outline Missing momenta reconstruction? Mass measurementsSpin measurements Inclusive2 symmetric chains NoneInv. mass endpoints and boundary lines Inv. mass shapes M eff, M est,H T Wedgebox ApproximateS min, M Tgen M T2, M 2C, M 3C, M CT, M T2 (n,p,c) As usual Exact?Polynomial method As usual optimism pessimism

5. 5 Outline Historical interlude: comparative discussion of –M eff –M est –H eff –H T What is the problem with measuring the mass scale and how one should deal with it. What is S min ? What is S min good for? Some recent applications

6. 6 M eff Defined by Frank E. Paige at 1996 Snowmass (hep-ph/9609373). What is it? It’s neither a mass, nor very effective. ~M gluino

7. 7 M est Proposed by Dan Tovey in hep-ph/0006276 You measure M est and interpret it as M eff (M susy,M chi ) The relation is very model-dependent:

8. 8 Adding to the confusion Later people started calling M est by the name M eff as well F. Paige hep-ph/0211017

9. 9 H eff and H T Conclusion: M eff, M est,, H eff, H T are all essentially the same! We use calorimeter H T : Look here!

10. 10 Difference in Philosophy What is the problem with measuring the mass scale? –Anything you try to measure will depend on both the mass of the parent particles (M susy ) as well as the LSP mass M chi How should one deal with it? 2 approaches: –Define an experimental observable which does not depend on the unknown LSP mass M chi and then interpret it in terms of some function of both M susy and M chi. Example: M est =M eff (M susy,M chi ) –Define an experimental observable which does depend on the unknown LSP mass M chi and then interpret it in terms of M susy. Cambridge variable: M T2 max (M chi )=M susy, Gator variable: S min (M chi )=(2M susy ) 2 The second option is clearly better!

11. 11 What is S min ? The minimum value of the Mandelstam variable consistent with the measured values of the total energy E and total visible momentum (P x,P y,P z ) Advantages: –Uses all available information (not just transverse quantities) –Model-independent: no need for any event reconstruction –Inclusive –Global –Clear physical meaning

12. 12 What is S min good for? As an approximation to the true value of S:

13. 13 What is S min good for? One can measure SUSY masses in terms of the LSP mass:

14. 14 What is S min good for? Gluino pair production Gluino-LSP assoc. production One can measure SUSY masses in terms of the LSP mass:

15. 15 Subsystem (S min ) 1/2 versus M T true S min introduced as a measure of the energy scale of interest Whenever the ISR contribution can be identified (e.g. leptonic signatures) the proper S min is given by M T true introduced as a measure of the Higgs mass in h- >WW->2leptons+MET Konar,Kong,Matchev 0812.1042 Konar,Kong,Matchev,Park Lester,Gripaios,Barr 0902.4864

16. 16 Comparison of S min and M T true M h =315 GeV The two variables are identical. Both exhibit an endpoint at the Higgs mass. Konar,Kong,Matchev,Park

17. 17 Application to H->WW Craig Group says: –I can use this now in my fancy neural net! Lester,Gripaios,Barr 0902.4864