1. Generalized MT2 for mass determinations in decay chains with missing PT at LHC Myeonghun Park University of Florida In collaboration with M.Burns, K.C.Kong, K.Matchev: Based on : arXiv:0810.5576arXiv:0810.5576 PHENO 09 : Myeonghun Park

2. Contents Definition of MT2 Subsystem MT2 Detail structure of Subsystem MT2 Application of Subsystem MT2 Summary PHENO 09 : Myeonghun Park

3. Expected signals at LHC We want to have MET (missing transverse Energy) signals from LHC PHENO 09 : Myeonghun Park : Pair production and ends up with stable BSM particles like R-parity from SUSY Thus information we have is 1. The visible sector from each decay chain 2. The amount of MET

4. Spectrum Measurements If we can reconstruct the production particles, then like as Z - particle mass measurement: If we can’t reconstruct the particles from resonance, then PHENO 09 : Myeonghun Park Z f F Using the invariant mass of two visible particles : W e

5. Using the transverse information PHENO 09 : Myeonghun Park A pair of semi-invisibly decaying particles If and are obtainable : But since we don’t get them, at most we can do : Also, since we don’t know the LSP(or Missing particles)’ mass, we need to guess LSP’s mass to formulate each Lester,Summers 99 Barr,Lester,Stephens 03 W e W  The Best thing that we have : MET constraint

6. PHENO 09 : Myeonghun Park Using the transverse information MT2 is a function of test mass. And MT2(True LSP) give the True “Mother particle” s mass.UTM(ISR) Since, true mass doesn’t depend on PT boost, MT2(true LSP) is independent of ISR(PT), but the false endpoints shift to different values. (actually become large) Burns, Kc Kong, Matchev, M Park : arXiv:0810.5576arXiv:0810.5576 Kink : arXiv:0711.4526 Won Sang Cho, Kiwoon Choi, Yeong Gyun Kim, Chan Beom Park. arXiv:0711.4008 Alan J. Barr, Ben Gripaios, Christopher G. LesterarXiv:0711.4526 arXiv:0711.4008

7. Validity to use Kink “Kink” depends on hardness of ISR and mass spectraUTM(ISR) FLFL FRFR

8. PHENO 09 : Myeonghun Park UTM(From G, or ISR) FLFL FRFR M (x1,···, x2) F L = MT2 when M(x1,x2) = 0 & F R = MT2 when M(x1,x2) = M & Burns, Kc Kong, Matchev, M Park : arXiv:0810.5576arXiv:0810.5576 Analytical behavior of MT2 variable

9. MT2 with Controlled PT boost PHENO 09 : Myeonghun Park If PT boost is controlled by the kinematics of decay chain: Visible particles before parents particle production have information about “grand parent” and “parent” UTM (Upstream Transverse Momentum) Our consideration n : The total length of decay chain p : Starting point of our MT2 analysis (Parent) c : Ending point of MT2 analysis (Child) Burns, Kc Kong, Matchev, M Park : arXiv:0810.5576arXiv:0810.5576

10. PHENO 09 : Myeonghun Park Application to Top mass measurement 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 !!! Burns, Kc Kong, Matchev, M Park : arXiv:0810.5576arXiv:0810.5576 FLFL FRFR

11. PHENO 09 : Myeonghun Park Combination of subsystem of MT2 : t t e e W W b b M T2 (210) Burns, Kc Kong, Matchev, M Park : arXiv:0810.5576arXiv:0810.5576 Application to Top mass measurement

12. PHENO 09 : Myeonghun Park Combination of subsystem of MT2 : t t e e W W b b M T2 (220) Burns, Kc Kong, Matchev, M Park : arXiv:0810.5576arXiv:0810.5576

13. PHENO 09 : Myeonghun Park Application to Top mass measurement Combination of subsystem of MT2 : t t e e W W b b M T2 (221) Burns, Kc Kong, Matchev, M Park : arXiv:0810.5576arXiv:0810.5576

14. PHENO 09 : Myeonghun Park Application to Top mass measurement Subsystem of MT2 measurement: W W e e M T2 (110) Burns, Kc Kong, Matchev, M Park : arXiv:0810.5576arXiv:0810.5576

15. Hybrid : Invariant mass Sub-MT2 PHENO 09 : Myeonghun Park t t e e W W b b M (bl)max = Correct bl pairs Application to Top mass measurement

16. Summary: For short decay channel (eg: n≤ 2), → Not enough information to pin down mass spectra There is method using Kink structure but the ability to use “kink” depends on event topology and mass spectra. Subsystem MT2, we don’t need to rely on kink. But still we can determine mass spectra a) UTM(Upstream Transverse Momentum) from grandparents : Information about G and P particles b) Subsystem MT2 gives us various choices to focus on specific signals : 1. We can use those subsystem MT2s to cross check each other 2. we can choose more clear signals, for example MT2(2,1,0) (example: We can use only lepton parts) PHENO 09 : Myeonghun Park

17. Backup Notes How many measurements Analytical behavior Equation for mass spectra PHENO 09 : Myeonghun Park

18. How many measurements ?(BACK UP) 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

19. Sub MT2 n : Length of decay chain Polynomial How many measurements ?(BACK UP)

20. Analytical behavior of MT2 variable PHENO 09 : Myeonghun Park 1. (composite) Visible particles’ mass running : 2. UTM effect FLFL FRFR F L = MT2 when M(x1,x2) = 0 F R = MT2 when M(x1,x2) = Mmax M (x1,···, x2) UTM(From G, or ISR) F L = MT2 when F R = MT2 when

21. PHENO 09 : Myeonghun Park Application on Top mass measurement Burns, Kc Kong, Matchev, M Park : JHEP 0903.143,2009