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Transcript of SUSY-Sumrules and MT2 curtin/presentations/sumrule... T2 Review 3. Collider Physics Investigation...

  • SUSY-Sumrules and MT2 Combinatorics

    David Curtin bla

    arXiv:1004.5350, arXiv:XXXX.XXXX In Collaboration with Maxim Perelstein, Monika Blanke

    bla

    Cornell Institute for High Energy Phenomenology

    Lunch Seminar University of Michigan

    Wednesday September 15, 2010

  • Outline

    1. Motivation (i) The SUSY-Yukawa Sum Rule→ The Υ Observable (ii) How can we use it at the LHC?→ Υ′

    2. MT 2 Review

    3. Collider Physics Investigation (i) Objective: measure Υ′

    (ii) Measuring all the masses in 2 g̃ → 2b̃1 + 2b → 4b + 2χ̃01 (iii) Measuring t̃1 mass

    Cornell University David Curtin SUSY-Sumrules and MT2 Combinatorics 1 / 42

  • Introducing the

    SUSY-Yukawa Sum Rule

  • 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

    hh

    t

    (a) (b)yt hh

    t̃L,R

    yt y2t

    This relies on both particle content and coupling relations. We want to test the coupling relations.

    Cornell University David Curtin SUSY-Sumrules and MT2 Combinatorics 2 / 42

  • How to probe the Quartic Higgs Coupling?

    M2t̃i t̃j = [

    M2L + m̂ 2 t + guLm̂

    2 Z c2β mt (At + µ cotβ)

    mt (At + µ cotβ) M2T + m̂ 2 t + guRm̂

    2 Z c2β

    ]

    =

    [ m2t1c

    2 t + m

    2 t2s

    2 t ctst (m

    2 t1 −m2t2)

    ctst (m2t1 −m2t2) m2t1s2t + m2t2c2t

    ]

    Extract this contribution to diagonal sfermion mass terms!

    Cornell University David Curtin SUSY-Sumrules and MT2 Combinatorics 3 / 42

  • SUSY-Yukawa Sum Rule

    Consider stop/sbottom LL mass terms at tree level:

    M2 t̃L t̃L

    = M2L + m̂ 2 t + guLm̂

    2 Z cos 2β = m

    2 t1c

    2 t + m

    2 t2s

    2 t (1)

    M2 b̃Lb̃L

    = M2L + m̂ 2 b + gbLm̂

    2 Z cos 2β = m

    2 b1c

    2 b + m

    2 b2s

    2 b (2)

    Soft masses Higgs Quartic Coupling D-term contributions measurable

    (1)− (2) eliminates the soft mass:

    m̂2t − m̂2b = m2t1c2t + m2t2s2t −m2b1c2b −m2b2s2b − m̂2Z cos2 θw 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-Sumrules and MT2 Combinatorics 4 / 42

  • How to test the sum rule?

    SUSY-Yukawa Sum Rule:

    m̂2t − m̂2b = m2t1c2t + m2t2s2t −m2b1c2b −m2b2s2b − m̂2Z cos2 θw cos 2β

    Define an observable Υ for which the sum rule gives a definite prediction:

    Υ ≡ 1 v2 (

    m2t1c 2 t + m

    2 t2s

    2 t −m2b1c2b −m2b2s2b

    ) Tree-Level Prediction for Υ from SUSY-Yukawa Sum Rule

    ΥtreeSUSY = 1 v2 (

    m̂2t − m̂2b + m2Z cos2 θW cos 2β )

    =

    { 0.39 for tanβ = 1 0.28 for tanβ →∞ (converges quickly for tanβ >∼ 5)

    Cornell University David Curtin SUSY-Sumrules and MT2 Combinatorics 5 / 42

  • Caveat: Radiative Corrections!

    Radiative Corrections wash out SUSY tree-level prediction for Υ

    ΥmeasSUSY = 1 v2

    physical stop, sbottom masses & mixings︷ ︸︸ ︷( m2t1c

    2 t + m

    2 t2s

    2 t −m2b1c2b −m2b2s2b

    ) = ΥtreeSUSY︸ ︷︷ ︸

    ≈0.3

    +ΥloopSUSY(mti , θt ,mg̃ , tanβ, . . .) = ?

    Properties of Υloop: is a function of many SUSY-parameters, so could be theoretically constrained by measurements of those parameters. is very complicated1, but one can try to numerically estimate possible range with parameter scans. might depend on SUSY-breaking mechanism.

    1Pierce, Bagger, Matchev, Zhang 1996 Cornell University David Curtin SUSY-Sumrules and MT2 Combinatorics 6 / 42

  • Numerically Estimate Radiative Corrections

    Tool: use SuSpect to do MSSM Parameter Scan

    Examine a ‘Worst-case’ scenario: no BSM experimental constraints other than MSUSY < 2 TeV and Neutralino LSP:

    ΥtreeSUSY ≈ 0.3 −→ |ΥSUSY|

  • Upshot

    Introduce the SUSY-Yukawa Sum Rule,

    m̂2t − m̂2b = m2t1c2t + m2t2s2t −m2b1c2b −m2b2s2b−m̂2Z cos2 θw 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 v2 (

    m2t1c 2 t + m

    2 t2s

    2 t −m2b1c2b −m2b2s2b

    ) SUSY-Yukawa Sum Rule⇒ |Υ|

  • How can we use the

    SUSY-Yukawa Sum Rule

    at the LHC?

  • SUSY-Yukawa Sum Rule at the LHC

    To measure every ingredient of Υ (especially θb) 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 t̃2, b̃2 are too heavy for the LHC.

    Υ︸︷︷︸ ∼ known

    = 1 v2 (

    m2t1 −m2b1 )

    ︸ ︷︷ ︸ Υ′ (maybe measurable)

    + s2t v2 (

    m2t2 −m2t1 ) −

    s2b v2 (

    m2b2 −m2b1 )

    ︸ ︷︷ ︸ unknown

    We can try to measure Υ′ at the LHC.

    Cornell University David Curtin SUSY-Sumrules and MT2 Combinatorics 9 / 42

  • What does Υ′ tell us?

    Υ = Υ′ + s2t v2 (

    m2t2 −m2t1 ) −

    s2b v2 (

    m2b2 −m2b1 )

    Υ′ � 0⇒ RH t̃1 Υ′ ∼ 0⇒ LH t̃1, b̃1 Υ′ � 0⇒ RH b̃1

    Even a rough measurement of Υ′ gives strong constraints on the stop and/or sbottom mixing angles!

    Cornell University David Curtin SUSY-Sumrules and MT2 Combinatorics 10 / 42

  • This gives us motivation to measure mt̃1, mb̃1

    .

    Let’s talk Collider Physics!

  • MT 2 Review

    Main MT2 references used here:

    Barr, Lester, Stephens ’03 [hep-ph/0304226] (old-skool MT2 review)

    Cho, Choi, Kim, Park ’07 [0711.4526] (analytical expressions for MT2 event-by-event without ISR, MT2-edges)

    Burns, Kong, Matchev, Park ’08 [0810.5576] (definition of MT2-subsystem variables, analytical expressions for endpoints & kinks w. & w.o. ISR)

    Konar, Kong, Matchev, Park ’09 [0910.3679] (Definition of MT2⊥ to project out ISR-dependence)

  • Warm-up: W-mass measurement

    Want to measure mW from W → `ν.

    We can reconstruct pνT and hence calculate mT (`, ν), assuming mν = 0.

    Can measure mW from edge in mT -distribution! mmaxT = mW

    0

    100

    200

    300

    400

    500

    600

    700

    50 55 60 65 70 75 80 85 90 95 100 mT (GeV)

    nu m

    be r

    of e

    ve nt

    s

    χ2/dof = 79.5/60 KS Prob = 25%

    Could we use a similar method for SUSY-like decays?

    Two generalizations. LSP is - massive - always produced in pairs

    Image source: D0 website

    Cornell University David Curtin SUSY-Sumrules and MT2 Combinatorics 11 / 42

  • Classical MT 2 Variable

    MT2(~pTt1, ~p T t2, m̃N) =

    min ~qT1 +~q

    T 2 =

    ~/p T

    { max

    [ mT

    ( ~pTt1, ~q

    T t , m̃N

    ) ,mT

    ( ~pTt1, ~q

    T t , m̃N

    )]}

    p

    p

    t

    t

    N

    N

    X

    X

    chain 1

    chain 2

    If pTN1, p T N2 were known, this

    would give us a lower bound on mX

    However, we only know total ~/p T

    ⇒ minimize wrt all possible splittings, get ‘worst’ but not ‘incorrect’ lower bound on mX . We don’t even know the invisible mass mN ! Insert a testmass m̃N .

    For the correct testmass, MmaxT 2 = mX ⇒ Effectively get mX(mN).

    Cornell University David Curtin SUSY-Sumrules and MT2 Combinatorics 12 / 42

  • MmaxT 2 gives us mX as a function of mN

    60 80 100 120 140 160 180 200 Χ

    340

    360

    380

    400

    mX MT2

    maxH ΧL for mN = 98, mX = 341 GeV without ISR

    MmaxT 2 (m̃N) = µ+ √ µ2 + m̃2N , where µ =

    m2X−m 2 N

    2mX

    Cornell University David Curtin SUSY-Sumrules and MT2 Combinatorics 13 / 42

  • Simple Example: Stop Pair Production without ISR

    t̃1

    t̃1

    t

    t χ̃01

    χ̃01

    Find edge for zero testmass:

    MmaxT2 (0) = m2

    t̃ −m2χ mt̃

    ⇒ Obtain stop mass as a function of LSP mass!

    Cornell University David Curtin SUSY-Sumrules and MT2 Combinatorics 14 / 42

  • Longer Chains: MT 2-Subsystem Variables

    Cornell University David Curtin SUSY-Sumrules and MT2 Combinatorics 15 / 42

  • Longer Chains: MT 2-Subsystem Variables

    Cornell University David Curtin SUSY-Sumrules and MT2 Combinatorics 15 / 42

  • Complete Mass Determination

    Dependence of endpoints on testmass & ISR more in- teresting → each contains unique information.

    2+ steps⇒ complete mass determination possible!

    Cornell University David Curtin SUSY-Sumrules and MT2 Combinatorics 16 / 42

  • Upshot:

    We can use the classical MT 2 variable for 1-step decays to find one of the masses as a function of t