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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:0810.5576. Contents. Definition of MT2 Subsystem MT2 Detail structure of Subsystem MT2

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## Generalized MT2 for mass determinations in decay chains with missing PT at LHC

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**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:0810.5576 PHENO 09 : Myeonghun Park**Contents**• Definition of MT2 • Subsystem MT2 • Detail structure of Subsystem MT2 • Application of Subsystem MT2 • Summary PHENO 09 : Myeonghun Park**Expected signals at LHC**• We want to have MET (missing transverse Energy) signals from LHC : 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 PHENO 09 : Myeonghun Park**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 Using the invariant mass of two visible particles : f Z e F W n PHENO 09 : Myeonghun Park**Using the transverse information**• 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 e W Lester,Summers 99 Barr,Lester,Stephens 03 n The Best thing that we have : MET constraint n W m 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) 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. Lester Since, true mass doesn’t depend on PT boost, MT2(true LSP) is independent ofISR(PT), but the false endpoints shift todifferent values. (actually become large) Burns, Kc Kong, Matchev, M Park : arXiv:0810.5576 PHENO 09 : Myeonghun Park**Validity to use Kink**• “Kink” depends on hardness of ISR and mass spectra FR UTM(ISR) FL PHENO 09 : Myeonghun Park**Analytical behavior of MT2 variable**Burns, Kc Kong, Matchev, M Park : arXiv:0810.5576 UTM(From G, or ISR) M(x1,···, x2) FR FL M(x1,···, x2) FL= MT2 when M(x1,x2) = 0 & FR= 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 PHENO 09 : Myeonghun Park**MT2 with Controlled PT boost**Burns, Kc Kong, Matchev, M Park : arXiv:0810.5576 • 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) n : The total length of decay chain p : Starting point of our MT2 analysis (Parent)c : Ending point of MT2 analysis (Child) Our consideration PHENO 09 : Myeonghun Park**Application to Top mass measurement**Burns, Kc Kong, Matchev, M Park : arXiv:0810.5576 FR e b t W n FL MT2(210) Where n W t b e Mass reconstruction MT2(2,1,0) doesn’t suffer from the combinatorics problem, Just clear lepton signals !!! PHENO 09 : Myeonghun Park**Application to Top mass measurement**Burns, Kc Kong, Matchev, M Park : arXiv:0810.5576 • Combination of subsystem of MT2 : MT2(210) e b t W n n W t b e PHENO 09 : Myeonghun Park**Application to Top mass measurement**Burns, Kc Kong, Matchev, M Park : arXiv:0810.5576 • Combination of subsystem of MT2 : MT2(220) e b t W n n W t b e PHENO 09 : Myeonghun Park**Application to Top mass measurement**Burns, Kc Kong, Matchev, M Park : arXiv:0810.5576 • Combination of subsystem of MT2 : MT2(221) e b t W n n W t b e PHENO 09 : Myeonghun Park**Application to Top mass measurement**Burns, Kc Kong, Matchev, M Park : arXiv:0810.5576 • Subsystem of MT2 measurement: e W n W n e MT2(110) PHENO 09 : Myeonghun Park**Application to Top mass measurement**• Hybrid : Invariant mass Sub-MT2 M(bl)max = b e t W n Correct bl pairs W n t b e PHENO 09 : Myeonghun Park**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 rely on kink.But still we can determine mass spectra a) UTM(Upstream Transverse Momentum) from grandparents : Information of G and P particlesb) 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**Backup Notes**• How many measurements • Analytical behavior • Equation for mass spectra PHENO 09 : Myeonghun Park**How many measurements ?(BACK UP)**Sub MT2 NP : Number of unknownsNm : Number of measurements For Sub MT2: NP= number of BSM particles = n+1 Nm= Since for fixed p, there are p-possible choices for child And (n-p+1) possible production of grand parent n : Length of decay chain**How many measurements ?(BACK UP)**Sub MT2 Polynomial n : Length of decay chain**Analytical behavior of MT2 variable**1. (composite) Visible particles’ mass running : 2. UTM effect UTM(From G, or ISR) FR FL= MT2 when M(x1,x2) = 0 FR= MT2 when M(x1,x2) = Mmax M(x1,···, x2) FL M(x1,···, x2) FL= MT2 when FR= MT2 when PHENO 09 : Myeonghun Park**Application on Top mass measurement**Burns, Kc Kong, Matchev, M Park : JHEP 0903.143,2009 PHENO 09 : Myeonghun Park

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