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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