Full Mass Determination from M T 2 with Combinatorial Background

Transcription

1 Full Mass Determination from M T 2 with Combinatorial Background David Curtin bla arxiv: , arxiv:xxxx.xxxx In Collaboration with Maxim Perelstein, Monika Blanke bla Cornell Institute for High Energy Phenomenology CU-CMS Meeting Thursday, May

2 Outline This talk will be composed of three parts: 1 M T 2 Review 2 Introduction of SUSY-Yukawa Sum Rule 3 M T 2 -subsystem analysis of g g 2b 1 + 2b 4b + 2 χ 0 1 Main M T 2 references: Barr, Lester, Stephens 03 [hep-ph/ ] (old-skool M T 2 review) Cho, Choi, Kim, Park 07 [ ] (analytical expressions for M T 2 event-by-event without ISR, M T 2 -edges) Burns, Kong, Matchev, Park 08 [ ] (definition of M T 2 -subsystem variables, analytical expressions for endpoints & kinks w. & w.o. ISR) Konar, Kong, Matchev, Park 09 [ ] (Definition of M T 2 to project out ISR-dependence) Cornell University David Curtin Full Mass Determination from M T 2 with Comb. BG 1/ 18

3 M T 2 Review

4 Warm-up: W-mass measurement Want to measure m W from W lν. We can reconstruct p ν T and hence calculate m T (l, ν), assuming m ν = 0. Can measure m W from edge in m T -distribution! m max T = m W Could we use a similar method for SUSY-like decays? Two generalizations. LSP is - massive - always produced in pairs Cornell University David Curtin Full Mass Determination from M T 2 with Comb. BG 2/ 18

5 Classical M T 2 Variable M T 2 ( p T t1, p T t2, χ) = min q T 1 + qt 2 = /p T { [ ( max m T pt1 T, q t T, χ ) (, m T pt1 T, q t T, χ )]} If pn1 T, pt N2 were known, this chain 1 t would give us a lower bound on m X However, we only know total /p T minimize wrt all possible splittings, get worst but not incorrect lower bound on m X. p p X X chain 2 t N N We don t even know the invisible mass m N! Insert a testmass χ. For the correct testmass, M max T 2 = m X Effectively get m X (m N ). Cornell University David Curtin Full Mass Determination from M T 2 with Comb. BG 3/ 18

6 Simple Application: Stop Pair Production For each choice of testmass χ, plot M T 2 distribution and find endpoint (edge with BG) = Obtain stop mass as a function of LSP mass! Cornell University David Curtin Full Mass Determination from M T 2 with Comb. BG 4/ 18

7 Longer chains: M T 2 -Subsystem Variables Can generalize M T 2 -idea to sub-chains of larger decay chains (even multi-step subchains). Require knowledge of positions in decay chain. Interpretation of endpoints more involved. There are analytical expressions relating the endpoints to the unknown masses. Good: Only need to measure edge for one testmass. Bad: The expressions also depend on p ISR T! (Same for classical M T 2, but there we didn t really need the analytical expressions.) Cornell University David Curtin Full Mass Determination from M T 2 with Comb. BG 5/ 18

8 ISR Dependence To use analytical expressions for edges, we must divide events into pt ISR-bins and find M T 2 edge for each bin. Low Statistics per bin! Some attempts to use pt ISR -dependence to extract additional information (not very successful). It would be great to project out pt ISR -dependence event-by-event! Then we could extract the edges with full statistics. Solution: Define new variable M T 2. For each event, M T 2 is evaluated exactly like M T 2, except p T p T (component to p ISR T ). Endpoints same as M T 2 with p ISR T = 0. (We re hoping this also works for M T 2 -subsystem variables with different topologies from classical M T 2.) Cornell University David Curtin Full Mass Determination from M T 2 with Comb. BG 6/ 18

9 Upshot: We can use the classical M T 2 variable for 1-step decays to find one of the masses as a function of the other. t 1 t χ 0 1 t 1 t χ 0 1 For 2-step or longer chains, the M T 2 -subsystem variables could allow complete mass determination. g g b b χ 0 1 b1 b1 b b χ 0 1 Cornell University David Curtin Full Mass Determination from M T 2 with Comb. BG 7/ 18

10 SUSY-Yukawa Sum Rule

11 Introduction Hierarchy problem: In the SM, Higgs mass receives quadratically divergent corrections, most importantly from the top quark In SUSY, top contribution cancelled by stop t t L,R (a) h y t y t h (b) h y 2 t h This relies on both particle content and coupling relations. We want to test the coupling relations. Cornell University David Curtin Full Mass Determination from M T 2 with Comb. BG 8/ 18

12 SUSY-Yukawa Sum Rule Look at stop/sbottom LL mass terms at tree level: M 2 t L t L = ML 2 + ˆm2 t + g ul ˆm Z 2 cos 2β = m2 t1 c2 t + mt2 2 s2 t (1) M 2 bl bl = ML 2 + ˆm2 b + g bl ˆm2 Z cos 2β = m2 b1 c2 b + m2 b2 s2 b (2) Soft masses Higgs Quartic Coupling D-term contributions measurable (1) (2) eliminates the soft mass: ˆm t 2 ˆm b 2 = m2 t1 c2 t + mt2 2 s2 t mb1 2 c2 b m2 b2 s2 b ˆm2 Z cos2 θ w cos 2β We call this the SUSY-Yukawa Sum Rule: It has its origins in the same coupling relations that cancel higgs mass corrections. We want to test this sum rule at a collider! First step: measure m t1, m LHC Cornell University David Curtin Full Mass Determination from M T 2 with Comb. BG 9/ 18

13 M T 2 -subsystem analysis of g g b b χ 0 1 b1 b1 b b χ 0 1 to measure b 1 mass

14 Benchmark Point Aim: Measure b 1 mass. Benchmark Point: tan β M 1 M 2 M 3 µ M A M Q3L M tr A t Spectrum: (GeV) m t1 m t2 s t m b1 m b2 s b m g m χ All other sfermions at 1 TeV. This sets Br( g g 2 b 1 + 2b 4b + 2 χ 0 1 ) = 100% and eliminates SUSY background. Cornell University David Curtin Full Mass Determination from M T 2 with Comb. BG 10/ 18

15 Monte Carlo Simulate g g 2 b 1 + 2b 4b + 2 χ 0 1 with MadGraph/MadEvent and BRIDGE at parton-level. σ g g 11.6 s = 14 TeV. Use L = 10 fb 1. Signal: 4b + MET. We impose the following Cuts: - 4 b-tags - p b jet T > 40 GeV, pt max > 100 GeV - MET > 200 GeV σ Signal = 480 fb after cuts 4800 signal events. Backgrounds: - no SUSY background due to choice of BP - SM backgrounds 1 suppressed by b-tag requirement σ BG 30 fb after cuts: Ignore! 1 MGME & ALPGEN Cornell University David Curtin Full Mass Determination from M T 2 with Comb. BG 11/ 18

16 Kinematic Edge M max bb = (m 2 g m2 b1 )(m2 b1 m2 χ 0 1 ) m 2 b1 With known decay chain assignments get (M b1 b 2, M b3 b 4 ) for each event, plot M bb -distribution edge at 382 GeV. Main problem: Combinatorial Background! Can reduce CB with R cuts and by dropping largest M bb s per event. M bb max meas = 395 ± 15 GeV Cornell University David Curtin Full Mass Determination from M T 2 with Comb. BG 12/ 18

17 M T 2 -subsystem Edges We need more edge measurements to fix all masses in this decay. Use M T 2 subsystem variables 2. Example: MT (0). Combinatorial Background is more dangerous. - To calculate MT 210 2, have to divide 4b into an upstream and downstream pair: 6 possibilities. - The M T 2 -distribution for wrong pairings is more featured than M bb. We will reduce Combinatorial Background in two independent ways. Cornell University David Curtin Full Mass Determination from M T 2 with Comb. BG 13/ 18

18 Method 1: Min-Method For each event, have 6 possibilities for M 210 T 1 (0). 2 are particularly bad: if b s from the same chain are assigned up/down-stream, the corresponding M T 2 -distribution extends far beyond the correct edge. Simple way to eliminate those maximally bad combinations: Drop the largest 2 M T 2 s per event. Cornell University David Curtin Full Mass Determination from M T 2 with Comb. BG 14/ 18

19 Method 2: Kinematic-Edge-Method We ve already measured the M bb -edge. Recall: For a given event with 4 b s there are three possible decay chain assignments: (M 12, M 34 ), (M 13, M 24 ), (M 14, M 23 ) For 30% of events, situation like Can deduce correct decay chain assignments! With this information we can reduce the number of possible M T 2 s for that event. Cornell University David Curtin Full Mass Determination from M T 2 with Comb. BG 15/ 18

20 Procedure for extracting M T 2 -Edges For each M T 2 -subsystem variable: 1 Construct M T 2 distributions using both the Min-Method and the Kinematic-Edge-Method. 2 For each distribution, do unbinned ML fits using a linear kink trial PDF over many possible domains. 3 Only accept an edge measurement if Both distributions have the same edge. For each distribution, the edge-fit is stable under change of fit-domain. This double-check method is vital for rejecting artifacts & fake edges due to low statistics! Cornell University David Curtin Full Mass Determination from M T 2 with Comb. BG 16/ 18

21 M T 2 Edge Measurements Using this procedure, two M T 2 -edges are recoverable. edge th. measurement M bb ± 15 MT (0) ± 13 GeV (0) ± 14 GeV M 220 T 2 This allows us to determine all the masses: mass th. 68 % c.l. m b1 341 (316, 356) m g 525 (508, 552) m χ (45, 115) (Imposed m χ 0 1 > 45 GeV bound from LEP measurement of invisible Z decay width.) Cornell University David Curtin Full Mass Determination from M T 2 with Comb. BG 17/ 18

22 Conclusion M T 2 and its variants are powerful tools for mass determination at hadron colliders for theories with invisible (massive) particles in the final state. We also proposed the SUSY-Yukawa Sum Rule, which represents a powerful check on SUSY as the solution as the hierarchy problem. We have shown that complete mass determination using M T 2 -subsystem variables is possible even with combinatorial background. Cornell University David Curtin Full Mass Determination from M T 2 with Comb. BG 18/ 18