SUSY-Yukawa Sum Rule at the LHC

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1 SUSY-Yukawa Sum Rule at the LHC David Curtin bla arxiv: , arxiv:xxxx.xxxx In Collaboration with Maxim Perelstein, Monika Blanke bla Cornell Institute for High Energy Phenomenology SUSY 2010 Parallel Talk Bonn, Germany Monday August 23, 2010

2 Outline 1. Introducing the SUSY-Yukawa Sum Rule 2. How can we use it at the LHC? 3. A Simple LHC Case Study Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 1 / 16

3 Introducing the SUSY-Yukawa Sum Rule

4 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 SUSY-Yukawa Sum Rule at the LHC 2 / 16

5 How to probe the Quartic Higgs Coupling? M 2 t i t j = [ M 2 L + ˆm t 2 + g ul ˆm Z 2 c 2β m t (A t + µ cot β) m t (A t + µ cot β) MT 2 + ˆm2 t + g ur ˆm Z 2 c 2β = [ m 2 t1 ct 2 + mt2 2 s2 t c t s t (mt1 2 m2 t2 ) ] c t s t (mt1 2 m2 t2 ) m2 t1 s2 t + mt2 2 c2 t ] Extract this contribution to diagonal sfermion mass terms! Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 3 / 16

6 SUSY-Yukawa Sum Rule Consider 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 + m 2 t2 s2 t m 2 b1 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. Testing this sum rule at a collider would constitute a highly nontrivial check on SUSY. Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 4 / 16

7 How to test the sum rule? SUSY-Yukawa Sum Rule: ˆm 2 t ˆm 2 b = m2 t1 c2 t + m2 t2 s2 t m2 b1 c2 b m2 b2 s2 b ˆm2 Z cos2 θ w cos 2β Define an observable Υ for which the sum rule gives a definite prediction: Υ 1 v 2 (m 2 t1 c2 t + m 2 t2 s2 t m 2 b1 c2 b m2 b2 s2 b ) Tree-Level Prediction for Υ from SUSY-Yukawa Sum Rule Υ tree SUSY = 1 ( ) ˆm 2 v 2 t ˆm b 2 + m2 Z cos2 θ W cos 2β { 0.39 for tan β = 1 = 0.28 for tan β (converges quickly for tan β > 5) Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 5 / 16

8 Radiative Corrections Radiative Corrections wash out SUSY tree-level prediction for Υ MSSM Parameter Scan with SuSpect for M SUSY < 2 TeV: Υ tree SUSY 0.3 Υ SUSY < 1 (For comparison, the generic perturbative theory prediction is Υ < 16π 2.) Sidenote: R.C. can be constrained by measuring additional parameters. Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 6 / 16

9 Upshot Introduce the SUSY-Yukawa Sum Rule, ˆm 2 t ˆm 2 b = m2 t1 c2 t + m 2 t2 s2 t m 2 b1 c2 b m2 b2 s2 b ˆm2 Z cos2 θ w cos 2β which relies on the same coupling relations that cancel contributions from stop & top loops to the higgs coupling. Introduce new observable which can be measured at a collider: Υ 1 ) (m 2 v 2 t1 c2 t + mt2 2 s2 t mb1 2 c2 b m2 b2 s2 b SUSY-Yukawa Sum Rule Υ < 1 Measuring Υ constitutes a powerful nontrivial check that SUSY is the solution to the hierarchy problem. Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 7 / 16

10 How can we use the SUSY-Yukawa Sum Rule at the LHC?

11 SUSY-Yukawa Sum Rule at the LHC To measure every ingredient of Υ (especially θ b ) we probably need a lepton collider. What good is the sum rule at the LHC? Use SUSY-prediction for Υ to constrain unmeasurable parameters! Which parts can we measure? Often m t1, m b1 are the lightest two masses. ) Υ = 1 (m 2 v 2 t1 m2 b1 }{{} Υ ( ) v 2 mt2 2 m2 t1 }{{} Υ t + s2 t We can try to measure Υ at the LHC. ( ) v 2 mb2 2 m2 b1 }{{} Υ b s2 b Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 8 / 16

12 What does Υ tell us? Υ = Υ + s2 ( ) t v 2 mt2 2 m2 t1 s2 ( ) b v 2 mb2 2 m2 b1 Υ 0 RH t 1 Υ 0 LH t 1, b 1 Υ 0 RH b 1 Even a rough measurement of Υ gives strong constraints on the stop and/or sbottom mixing angles! Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 9 / 16

13 A Simple LHC Case Study

14 Measuring Υ at the LHC Want to demonstrate that the SUSY-Yukawa Sum Rule can be used to measure stop & sbottom mixing angles at the LHC. Choose a particular MSSM Benchmark Point with light t 1, b 1 and small mixing: Parameters: 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 Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 10 / 16

15 Outline of Measurement We will measure Υ = 1 v 2 (m 2 t1 m2 b1 ) Parton-level Analysis with gaussian momentum smearing. (More realistic analysis in progress.) Gluino pair production = m b1 (Bonus: m g and m χ 0 1 ) Stop pair production = m t1 g g b b χ 0 1 t 1 b1 b1 χ 0 1 t 1 b b t t χ 0 1 χ 0 1 Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 11 / 16

16 (I) Gluino Pair Production Analyze the process 1 g g 2 b 1 + 2b 4b + 2 χ 0 1. σ g g 11.6 s = 14 TeV. g g b b χ 0 1 b1 b1 b b χ 0 1 Impose basic p T, MET-cuts and require 4 b-tags. No SUSY-BG. SM-BG suppressed by b-tag requirement. Use L = 10 fb 1. After cuts we are left with 4800 signal events. Even with parton-level pure signal, full mass extraction is challenging! 1 MadGraph/Madevent & BRIDGE Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 12 / 16

17 Edge Extraction & Mass Measurement To measure masses at hadron colliders with invisible massive particles in the final state, we go Edge Hunting! Distributions of M T 2 -subsystem-variables 2 and M bb show edges which tell us mass combinations. Big Problem: Combinatorial Error (especially for M T 2 s). We are able to successfully measure M bb, M 210 T2 (0) and (0) edges M 220 T2 mass th. 68 % c.l. m b1 341 (316, 356) m g 525 (508, 552) m χ (45, 115) 2 Barr, Lester, Stephens, 2003; Cho, Choi, Kim, Park 2008; Burns, Kang, Matchev, Park 2009 LEP bound Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 13 / 16

18 (II) Stop Pair Production Analyze the process t 1 t 1 t t + 2 χ 0 1. σ t 1 t 1 2 s = 14 TeV. t 1 t χ 0 1 Impose standard cuts & use hadronic tops 3. t 1 t χ 0 1 Use L = 100 fb 1. After cuts: 1481 signal and 105 BG events. Easy to extract M max T 2 edge = Gives m t1(m χ 0 1 ) Combine with (I) th. 68 % c.l. m t1 371 (356, 414) 3 Meade, Reece 2006 Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 14 / 16

19 Υ Measurement and SUSY-prediction for Υ Putting all these measurements together, we get th. meas. Υ Υ Unless there is a strong accidental cancelation, such a small Υ measurement implies that both stop and sbottom mixing angles are small, < 0.2. Compare to actual values: s t = s b = Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 15 / 16

20 Conclusions

21 Summary & Conclusions Confirmation of the SUSY-Yukawa Sum Rule ˆm 2 t ˆm 2 b = m2 t1 c2 t + m 2 t2 s2 t m 2 b1 c2 b m2 b2 s2 b ˆm2 Z cos2 θ w cos 2β (probably at a lepton collider) would be strong support for TeV-scale SUSY as the solution for hierarchy problem. At the LHC, the sum rule provides powerful constraints on stop and sbottom mixing angles (hard to come by otherwise) using only a mass measurement. We developed new techniques for reducing M T 2 -combinatorial background, allowing us to measure t 1, b 1, g, χ 0 1 masses at our benchmark point. Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 16 / 16

22 Backup Slides

23 Gluino Pair Production: 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 dropping largest M bb s per event. M bb max meas = 395 ± 15 GeV Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 17 / 16

24 Gluino Pair Production: M T 2 -subsystem Edges The distributions of M T 2 subsystem variables 4 also have edges we can measure. Look at 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. One way to reduce CB: Drop largest 2 MT s per event 4 Barr, Lester, Stephens, 2003; Cho, Choi, Kim, Park 2008; Burns, Kang, Matchev, Park 2009 Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 18 / 16

25 Gluino Pair Production: M T 2 -subsystem Edges Another way to reduce CB: For edge measurement, require two methods to agree! edge th. measurement M bb ± 15 MT (0) ± 13 GeV (0) ± 14 GeV M 220 T 2 = 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 SUSY-Yukawa Sum Rule at the LHC 19 / 16

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