1. Using Subsystem MT2 for Complete Mass Determinations in Decay Chains with Missing Energy @ Hadron Colliders. Myeonghun Park University of Florida In collaboration with M.Burns, K.C.Kong, K.Matchev: Based on :arXiv:0810.5576 KEK

2. Contents Definition of MT2 Subsystem MT2 Detail structure of Subsystem MT2 Application of Subsystem MT2 Summary KEK

3. Definition of MT2 Based on transverse measurement technique Based on transverse measurement technique Use the transverse mass distribution KEK W e

4. Definition of MT2 A pair of semi-invisibly decaying particles If and are obtainable : But since we don’t get them, at most we can do : KEK Lester,Summers 99 Barr,Lester,Stephens 03 W e W  The Best thing that we have : Missing ET constraint

5. Where does Sub-MT2 come from Where does Sub-MT2 come from ? (I) We had an analytic equations for MT2 without (or negligible) ISR / Upstream Transverse Momentum KEK

6. Where does Sub-MT2 come from Where does Sub-MT2 come from ? (II) If we admit ISR (UTM) effects : Since ISRs are arbitrary, what can we get from MT2 ? KEKUTM(ISR)

7. Where does Sub-MT2 come from Where does Sub-MT2 come from ? (III) What are the sources of UTM ? (1) ISR : arbitrary KEK Our consideration UTM X i :(1≤ I ≤ n ) BSM particles which appear as promptly decaying, onshell intermediate resonances. x i : corresponding SM decay products, which are all visible in detector X 0 : Invisible BSM particle

8. Where does Sub-MT2 come from Where does Sub-MT2 come from ? (IV) What are the sources of UTM ? (2) Visible particles before parents particle production : Have an information about “grand parent” and “parent” KEK UTM Our consideration

9. Subsystem MT2 : Various choices MT2 subsystem analysis We can cut whatever we want for MT2(n,p,c) KEK N : The total length of decay chain P : Starting point of our MT2 analysis (Parent) C : Ending point of MT2 analysis (Child)

10. How many measurements ? Sub MT2 n : Length of decay chain N P : Number of unknowns N m : Number of measurements For Sub MT2: N P = number of BSM particles = n+1 N m = Since for fixed p, there are p-possible choices for child And (n-p+1) possible production of grand parent

11. How many measurements ? Sub MT2 n : Length of decay chain Polynomial

12. FLFL FRFR More detail structure of SUB MT2 There are two branches for MT2 max function KEK

13. More detail structure of SUB MT2 1. (composite) Visible particles’ mass running : FLFL FRFR M (x1,···, x2) F L = MT2 when M(x1,x2) = 0 F R = MT2 when M(x1,x2) = Mmax

14. KEK More detail structure of SUB MT2 2. UTM effect : FLFL FRFR UTM(From G, or ISR) F L = MT2 when F R = MT2 when

15. UTM(From G, or ISR) More detail structure of SUB MT2 Composite effect FLFL FRFR M (x1,···, x2) F L = MT2 when M(x1,x2) = 0 & F R = MT2 when M(x1,x2) = M & @ Back to Back boosted frame(BB) so that each mother particle is at rest at that frame M is the mass s.t LSP can have smallest momentum in BB frame

16. Mass spectrum measurement (I) KEK t t e e W W b b M T2 (210) Where Mass reconstruction MT2(2,1,0) doesn’t suffer from the combinatorics problem, Just clear lepton signals !!!

17. Mass spectrum measurement (II) Combination of subsystem of MT2 : KEK t t e e W W b b M T2 (220)

18. Mass spectrum measurement (II) Combination of subsystem of MT2 : KEK t t e e W W b b M T2 (221)

19. Mass spectrum measurement (II) KEK Combination of subsystem of MT2 : t t e e W W b b M T2 (210)

20. KEK Mass spectrum measurement (II) Subsystem of MT2 measurement: KEK W W e e M T2 (110)

21. Mass spectrum measurement (II) KEK

22. Mass spectrum measurement (III) Hybrid : Invariant mass Sub-MT2 KEK t t e e W W b b M (bl)max = Correct bl pairs

23. Another interesting case 3 step -decay using subsystem MT2 (work in progress with CMS) KEK MT2(3,3,0) MT2(2,2,0) MT2(1,1,0) MT2(3,3,2) MT2(2,2,1) MT2(3,3,1) MT2(2,1,0) MT2(3,2,0) MT2(3,2,1) MT2(3,1,0) But, some of them are linearly dependent For example, E(2,1,0) 2 = E220 (E220 – E221) Need to find the good measurements through real detector simulations

24. Summary: For n≤ 2, using only invariant mass, polynomial (or hybrid from both) can’t do the job → we need to listen to MT2 what she talks to us. But also using only MT2 we can determine mass spectrum a) UTM(Upstream Transverse Momentum) from grandparents : Information of G and P particles b) Subsystem MT2 gives us various choices to focus on specific signals : MT2(2,1,0) (example: We can use only lepton parts) KEK

25. Conclusion: For n≤ 2, there exist 8 different measurements from SUB MT2 Even More constraint : Hybrid as our (III) example KEK MT2(1,1,0)(0) MT2(2,2,1)(0) MT2(2,2,0)(0) + MT2(2,2,0)(Eb)+MT2(2,2,0)(Eb ’ ) MT2(2,1,0)(0) + MT2(2,1,0)(Eb)+MT2(2,1,0)(Eb ’ )