SUSY-Yukawa Sum Rule at the LHC David Curtin bla arXiv:1004.5350, arXiv:XXXX.XXXX In Collaboration with Maxim Perelstein, Monika Blanke bla Cornell Institute for High Energy Phenomenology Phenomenology 2010 Symposium Madison, Wisconsin Monday, May 10 2010
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 L,R t ( a ) h h ( b ) y t y t y 2 t h 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 1 / 12
How to probe the Quartic Higgs Coupling? ˜ ˜ h t t h × ˜ ˜ h t t × ˜ ˜ t t × Look at diagonal sfermion mass terms! Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 2 / 12
SUSY-Yukawa Sum Rule Look at stop/sbottom LL mass terms at tree level: M 2 M 2 m 2 m 2 Z cos 2 β = m 2 t 1 c 2 t + m 2 t 2 s 2 L + ˆ t + g uL ˆ = ( 1 ) t L ˜ ˜ t t L M 2 M 2 m 2 m 2 Z cos 2 β = m 2 b 1 c 2 b + m 2 b 2 s 2 L + ˆ b + g bL ˆ = ( 2 ) b L ˜ ˜ b b L Soft masses Higgs Quartic Coupling D-term contributions measurable ( 1 ) − ( 2 ) eliminates the soft mass: Z cos 2 θ w cos 2 β m 2 m 2 b = m 2 t 1 c 2 t + m 2 t 2 s 2 t − m 2 b 1 c 2 b − m 2 b 2 s 2 m 2 ˆ t − ˆ b − ˆ 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! Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 3 / 12
Defining an observable to test the Sum Rule � � ˜ t L , ˜ , ˜ t R , ˜ Assume SUSY-like particle content b L b R but not the SUSY coupling relations. � M 2 � M 2 � � M 2 , M 2 L L Before EWSB, t = b = M 2 M 2 ˜ ˜ t b After EWSB, can parameterize quartic higgs coupling ‘model-independently’: ( M 2 t ) 11 → M 2 L + v 2 Y t ( M 2 b ) 11 → M 2 L + v 2 Y b , ˜ 11 ˜ 11 Define a new observable to probe the quartic higgs coupling: 1 � � m 2 t 1 c 2 t + m 2 t 2 s 2 t − m 2 b 1 c 2 b − m 2 b 2 s 2 Υ ≡ b v 2 Y t 11 − Y b = 11 at tree level Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 4 / 12
SUSY prediction for Υ & Radiative Corrections Tree-Level Prediction for Υ from SUSY-Yukawa Sum Rule 1 � � Z cos 2 θ W cos 2 β m 2 m 2 b + m 2 Υ tree ˆ t − ˆ = SUSY v 2 � 0 . 39 for tan β = 1 = for tan β → ∞ (converges quickly for tan β > 0 . 28 ∼ 5) TeV-scale SUSY: | Υ | < ∼ 1. In a generic theory, only ‘requirement’ is | Υ | < ∼ 16 π . Radiative Corrections wash out SUSY tree-level prediction for Υ . Worst case scenario ( SuSpect ) → Can narrow predicted range with more measurements (see later). Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 5 / 12
Prospects at the LHC Fully measuring Υ requires lepton collider. Can make some progress at LHC in favorable regions of MSSM parameter space. ⇒ Could then use Υ to constrain stop/sbottom parameters. Demonstrate feasibility of partial Υ -measurement with a particular Benchmark Point: Parameters: tan β M 1 M 2 M 3 µ M A M Q 3 L M tR A t 10 100 450 450 400 600 310.6 778.1 392.6 Spectrum: (GeV) m t 1 m t 2 s t m b 1 m b 2 s b m ˜ m ˜ g χ 0 1 371 800 -0.095 341 1000 -0.011 525 98 Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 6 / 12
Measuring part of Υ Small mixing angles and light ˜ t 1 , ˜ b 1 = ⇒ rewrite − s 2 + s 2 � � � � � � Υ = 1 m 2 t 1 − m 2 t m 2 t 2 − m 2 b m 2 b 2 − m 2 b 1 t 1 b 1 v 2 v 2 v 2 � �� � � �� � � �� � Υ ′ ∆Υ t ∆Υ b Most of Υ = 0 . 423 comes from Υ ′ = 0 . 350. ∆Υ t � O ( 0 . 1 ) can be estimated 1 . ∆Υ b can’t be measured at LHC. We will measure Υ ′ - Need to determine m t 1 , m b 1 b b ˜ t χ 0 χ 0 ˜ ˜ g ˜ t 1 1 - Analyse gluino & stop pair production & decay ˜ 1 b 1 ˜ b 1 ˜ g χ 0 ˜ - Extract kinematic- and M T 2 -edges to ˜ χ 0 ˜ t 1 1 1 b b get all the masses ⇒ Υ ′ t 1MP , Weiler 2008 Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 7 / 12
(I) Gluino Pair Production Analyze the process 2 b ˜ b χ 0 g → 2 ˜ χ 0 g ˜ ˜ ˜ b 1 + 2 b → 4 b + 2 ˜ 1 . g 1 ˜ b 1 ˜ g ≈ 11 . 6 pb @ √ s = 14 TeV . b 1 ˜ g χ 0 ˜ σ ˜ g ˜ 1 b b Impose basic p T , MET -cuts and require 4 b -tags. Use L = 10 fb − 1 . After cuts we are left with 4800 signal events. No SUSY-BG. SM-BG suppressed by b -tag requirement. Even with parton-level pure signal, full mass extraction is challenging! 2MadGraph/Madevent & BRIDGE Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 8 / 12
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 3 and M bb show edges which tell us mass combinations. Big Problem: Combinatorial Error (especially for M T 2 ’s). mass th. 68 % c.l. We are able to successfully m b 1 341 (316, 356) measure M bb , M 210 T2 ( 0 ) and ⇒ m ˜ 525 (508, 552) g M 220 T2 ( 0 ) edges m ˜ 98 (45 ∗ , 115) χ 0 1 3Barr, 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 9 / 12
(II) Stop Pair Production Analyze the process ˜ t 1 ˜ 1 → t ¯ χ 0 t ∗ t + 2 ˜ 1 . t χ 0 ˜ ˜ 1 ≈ 2 pb @ √ s = 14 TeV . t 1 1 σ ˜ t 1 ˜ t ∗ ˜ χ 0 ˜ t 1 Impose standard cuts & use hadronic tops 4 . 1 t Use L = 100 fb − 1 . After cuts: 1481 signal and 105 BG events. Easy to extract M max T 2 edge = ⇒ Gives m t 1 ( m ˜ 1 ) χ 0 th. 68 % c.l. Combine with (I) ⇒ m t 1 371 (356, 414) 4Meade, Reece 2006 Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 10 / 12
Υ ′ Measurement and SUSY-prediction for Υ Putting all these measurements together, we get th. meas. 0 . 525 + 0 . 20 Υ ′ 0.350 − 0 . 15 Υ 0.423 — The measurements of the ˜ b 1 , ˜ χ 0 t 1 , ˜ g , ˜ 1 masses also allow us to make the SUSY-prediction for Υ more precise: → Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 11 / 12
Summary & Conclusions Confirmation of SUSY-Yukawa Sum Rule Z cos 2 θ w cos 2 β m 2 m 2 b = m 2 t 1 c 2 t + m 2 t 2 s 2 t − m 2 b 1 c 2 b − m 2 b 2 s 2 m 2 ˆ t − ˆ b − ˆ would be strong support for TeV-scale SUSY as the solution for hierarchy problem. Full measurement will have to wait for Lepton Collider. Can make significant progress at LHC in some regions of parameter space. We developed new techniques for reducing M T 2 -combinatorial t 1 , ˜ background, allowing us to measure ˜ χ 0 b 1 , ˜ g , ˜ 1 masses at our benchmark point. Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 12 / 12
Gluino Pair Production: Kinematic Edge � ( m 2 g − m 2 b 1 )( m 2 b 1 − m 2 ) ˜ χ 0 ˜ M max = 1 bb m 2 b 1 With known decay chain assignments get ( M b 1 b 2 , M b 3 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. max M bb meas = 395 ± 15 GeV Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 13 / 12
Gluino Pair Production: M T 2 -subsystem Edges The distributions of M T 2 subsystem variables 5 also have edges we can measure. Look at M 210 T 2 ( 0 ) . Combinatorial Background is more dangerous. - To calculate M 210 T 2 , have to divide 4 b 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 M 210 T 2 ’s per event → 5Barr, Lester, Stephens, 2003; Cho, Choi, Kim, Park 2008; Burns, Kang, Matchev, Park 2009 Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 14 / 12
Gluino Pair Production: M T 2 -subsystem Edges Another way to reduce CB: For edge measurement, require two methods to agree! mass th. 68 % c.l. edge th. measurement m b 1 341 (316, 356) M bb 382 395 ± 15 = ⇒ M 210 m ˜ 525 (508, 552) T 2 ( 0 ) 321 314 ± 13 GeV g M 220 m ˜ 98 (45, 115) T 2 ( 0 ) 507 492 ± 14 GeV χ 0 1 (Imposed m ˜ 1 > 45 GeV bound from LEP measurement of invisible Z decay width.) χ 0 Cornell University David Curtin SUSY-Yukawa Sum Rule at the LHC 15 / 12
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