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  • SUSY-Sumrules and MT2 Combinatorics

    David Curtinbla

    arXiv:1004.5350, arXiv:1102(?).????In Collaboration with Maxim Perelstein, Monika Blanke

    bla

    Cornell Institute for High Energy Phenomenology

    Theory SeminarUniversity of Syracuse

    Monday, December 6 2010

  • Outline

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

    2. MT 2 Review

    3. Collider Physics Investigation(i) Objective: measure

    (ii) Measuring all the masses in 2 g 2b1 + 2b 4b + 201(iii) Measuring t1 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 quadraticallydivergent corrections, most importantly from the top quarkIn SUSY, top contribution cancelled by stop

    hh

    t

    (a) (b)ythh

    tL,R

    yt y2t

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

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

  • How to probe the Quartic Higgs Coupling?

    M2ti tj =[

    M2L + m2t + guLm

    2Z c2 mt (At + cot)

    mt (At + cot) M2T + m2t + guRm

    2Z c2

    ]

    =

    [m2t1c

    2t + m

    2t2s

    2t ctst (m

    2t1 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:

    M2tL tL

    = M2L + m2t + guLm

    2Z cos 2 = m

    2t1c

    2t + m

    2t2s

    2t (1)

    M2bLbL

    = M2L + m2b + gbLm

    2Z cos 2 = m

    2b1c

    2b + m

    2b2s

    2b (2)

    Soft masses Higgs Quartic Coupling D-term contributions measurable

    (1) (2) eliminates the soft mass:

    m2t m2b = m2t1c2t + m2t2s2t m2b1c2b m2b2s2b m2Z cos2 w cos 2

    We call this the SUSY-Yukawa Sum Rule: It has its origins in thesame coupling relations that cancel higgs mass corrections.

    Testing this sum rule at a collider wouldconstitute 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:

    m2t m2b = m2t1c2t + m2t2s2t m2b1c2b m2b2s2b m2Z cos2 w cos 2

    Define an observable for which the sum rule gives a definiteprediction:

    1v2(

    m2t1c2t + m

    2t2s

    2t m2b1c2b m2b2s2b

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

    treeSUSY =1v2(

    m2t m2b + m2Z cos2 W cos 2)

    =

    {0.39 for tan = 10.28 for tan (converges quickly for tan > 5)

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

  • Caveat: Radiative Corrections!

    Radiative Corrections wash out SUSY tree-level prediction for

    measSUSY =1v2

    physical stop, sbottom masses & mixings (m2t1c

    2t + m

    2t2s

    2t m2b1c2b m2b2s2b

    )= treeSUSY

    0.3

    +loopSUSY(mti , t ,mg , tan, . . .) = ?

    Properties of loop:Kicks in at energies below Msoft .is a function of many SUSY-parameters, so could be theoreticallyconstrained by measurements of those parameters.is very complicated1, but one can try to numerically estimatepossible range with parameter scans.

    1Pierce, Bagger, Matchev, Zhang 1996Cornell 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 experimentalconstraints other than MSUSY < 2 TeV and Neutralino LSP:

    treeSUSY 0.3 |SUSY|

  • Upshot

    Introduce the SUSY-Yukawa Sum Rule,

    m2t m2b = m2t1c2t + m2t2s2t m2b1c2b m2b2s2bm2Z cos2 w cos 2

    which relies on the same coupling relations that cancelcontributions from stop & top loops to the higgs coupling.

    Introduce new observable which can be measured at a collider:

    1v2(

    m2t1c2t + m

    2t2s

    2t m2b1c2b m2b2s2b

    )SUSY-Yukawa Sum Rule ||

  • How can we use the

    SUSY-Yukawa Sum Rule

    at the LHC?

  • SUSY-Yukawa Sum Rule at the LHC

    To measure every ingredient of (especially b) we probablyneed a lepton collider.

    What good is the sum rule at the LHC? Use SUSY-predictionfor to constrain unmeasurable parameters!

    Which parts can we measure? Often t2, b2 are too heavy for theLHC.

    known

    =1v2(

    m2t1 m2b1)

    (maybe measurable)

    +s2tv2(

    m2t2 m2t1)

    s2bv2(

    m2b2 m2b1)

    unknown

    We can try to measure at the LHC.

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

  • What does tell us?

    = +s2tv2(

    m2t2 m2t1)

    s2bv2(

    m2b2 m2b1)

    0 RH t1 0 LH t1, b1 0 RH b1

    Even a rough measurement of gives strong constraints onthe stop and/or sbottom mixing angles!

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

  • This gives us motivation tomeasure mt1, mb1

    .

    Lets 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 MT2event-by-event without ISR, MT2-edges)

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

    Konar, Kong, Matchev, Park 09 [0910.3679] (Definition of MT2 to project outISR-dependence)

  • Warm-up: W-mass measurement

    Want to measure mW fromW `.

    We can reconstruct pT andhence calculate mT (`, ),assuming m = 0.

    Can measure mW from edge inmT -distribution! mmaxT = mW

    0

    100

    200

    300

    400

    500

    600

    700

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

    num

    ber

    of e

    vent

    s

    2/dof = 79.5/60KS 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, ~pTt2, mN) =

    min~qT1 +~q

    T2 =

    ~/pT

    {max

    [mT

    (~pTt1, ~q

    Tt , mN

    ),mT

    (~pTt1, ~q

    Tt , mN

    )]}

    p

    p

    t

    t

    N

    N

    X

    X

    chain 1

    chain 2

    If pTN1, pTN2 were known, this

    would give us a lower bound on mX

    However, we only know total ~/pT

    minimize wrt all possible splittings,get worst but not incorrect lowerbound on mX .We dont even know the invisiblemass mN ! Insert a testmass mN .

    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

    340

    360

    380

    400

    mXMT2

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

    MmaxT 2 (mN) = +2 + m2N , where =

    m2Xm2N

    2mX

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

  • Simple Example: Stop Pair Production without ISR

    t1

    t1

    t

    t01

    01

    Find edge for zero testmass:

    MmaxT2 (0) =m2

    tm2mt

    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 ontestmass & ISR more in-teresting each containsunique 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 findone of the masses as a function of the other.

    t1

    t1

    t

    t01

    01

    For 2-step or longer chains, the MT2-subsystem variables couldallow complete mass determination.

    g

    g

    b b

    b b 01

    01

    b1b1

    Cornell University David Curtin SUSY-Sumrules and MT2 Combinatorics 17 / 42

  • Remarks

    1 We have not discussed what happens in realistic measurementswith ISR. This is well understoood. (Maybe say more later.)

    2 There are two types of combinatorics problems when using MT 2:

    (a) Distinguishing ISR from hard process final state (depends on theprocess).

    (b) For subsystem variables: correctly placing each particle at itscorrect place in the long decay chain.

    We will later discuss some strategies for addressing (b).

    Cornell University David Curtin SUSY-Sumrules and MT2 Combinatorics 18 / 42

  • Collider Physics Investigation

  • Measuring = (m2t1 m2b1)/v2 at the LHC

    Want to demonstrate that the SUSY-Yukawa Sum Rule can beused to measure stop & sbottom mixing angles at the LHC.

    Choose a particular MSSM Benchmark Point with light t1, b1 andsmall mixing:

    Parameters:tan M1 M2 M3 MA MQ3L MtR At10 100 450 450 400 600 310.6 778.1 392.6

    Spectrum: (GeV)

    mt1 mt2 st mb1 mb2 sb mg m01371 800 -0.095 341