Supersymmetry and the LHC: an Introduction

Supersymmetry and the LHC: An Introduction

Brent D. Nelson Northeastern University

8/11/2009 Some History... 1

1974 The free world discovers “supergauge transformations” 1979 Technicolor as a theory of BSM physics is born Some History... 1

1974 The free world discovers “supergauge transformations” 1979 Technicolor as a theory of BSM physics is born 1981 The MSSM is born 1983 W ± and Z bosons discovered 1983 SSC proposed 1986 Low-energy SUSY emerges as a likely outcome of 4D string theories 1987 Tevatron begins Some History... 1

1989 SUSY loop corrections to mh computed ⇒ Surprise! They’re substantial! 1991 Construction of SSC begins (“no lose machine for EWSB”) 1992 Electroweak precision measurements from LEP ﬁrmly establish SUSY over technicolor as the world’s favorite BSM model Some History... 1

1. Why do we need to look beyond the Standard Model?

2. What is supersymmetry? What is the MSSM?

3. What are the selling points for supersymmetry?

4. SUSY breaking and superpartner masses

5. Minimal supergravity: the simplest SUSY model

6. Signatures of SUSY at hadron colliders

References: S. Martin’s SUSY Primer, Chung et al. Physics Reports 407 (2005) 1 (hep-ph/0312378), Branson et al. High pT -physics at the LHC (hep-ph/0110021) The Standard Model in One Page! 3

⇒ The SM gauge symmetry is SU(3)c × SU(2)L × U(1)Y

a=1,...,8 i=1,2,3 a=1,...,8 + − gµ ,Wµ ,Bµ → EWSB → gµ ,Wµ Wµ Zµ,Aµ

⇒ Matter content involves three generations of quarks and leptons

u ν , u , d ; , e , ν → 16 of SO(10) d R R e R R L L

⇒ The Higgs sector consists of a single doublet of SU(2)L which performs two crucial roles: EWSB and fermion mass generation

φ+ L 3 D φ†Dµφ + Qφu + Qφ†d + ... φ = ; µ R R φ 0 L Dµ = ∂µ + gAµ + ...

⇒ Total SM Lagrangian contains 19 undetermined parameters

⇒ Has (thus far) provided a good-to-excellent description of almost all accelerator/particle physics data ever collected!! So Why Did we Build the LHC? 4

⇒ Well...we still haven’t found the Higgs ﬁeld

⇒ Even if we did, scalars have problems

λ2 m2 ' m2 + Λ2 + ... h 0 16π2 uv

• Technicolor • “Little Higgs” Models • Composite Higgs Models • Large Extra Dimensions • Supersymmetry • ...

⇒ Three things the Standard Model cannot explain

• Baryogenesis • Dark matter • Dark energy The Building Blocks of Supersymmetry 5

⇒ What is meant by a “supermultiplet”?

• Irreducible multiplet of the supersymmetry algebra • Fields of the same quantum number(s), but different spin n o ? Chiral supermultiplet: F = f,e f,Ff The Building Blocks of Supersymmetry 5

⇒ What is meant by a “supermultiplet”?

• Irreducible multiplet of the supersymmetry algebra • Fields of the same quantum number(s), but different spin n o ? Chiral supermultiplet: F = f,e f,Ff n o ? Vector supermultiplet: Aa = λea, (Aµ)a,Da n o ? Gravity supermultiplet: G = gµν, ψeµ, bµ,M The Building Blocks of Supersymmetry 5

⇒ What is meant by a “supermultiplet”?

⇒ Auxiliary ﬁelds F , D, M, bµ

• NOT dynamical – no kinetic terms in the component Lagrangian • Required for SUSY algebra to close “off-shell” • Solve EOM ∂L/∂Φ = 0 for auxiliary ﬁelds to eliminate them (more later) The Building Blocks of Supersymmetry 5

⇒ What is meant by a “supermultiplet”?

⇒ Auxiliary ﬁelds F , D, M, bµ

Names spin 0 spin 1/2 SU(3)C,SU(2)L,U(1)Y 1 squarks, quarks Q (ueL deL) (uL dL) ( 3, 2 , 6) ∗ † 2 (×3 families) u¯ ueR uR ( 3, 1, −3) ¯ ∗ † 1 d deR dR ( 3, 1, 3) 1 sleptons, leptons L (νe eL) (ν eL) ( 1, 2 , −2) ∗ † (×3 families) e¯ eR eR ( 1, 1, 1) + 0 + 0 1 Higgs, higgsinos Hu (Hu Hu) (χu χu) ( 1, 2 , +2) 0 − 0 − 1 Hd (Hd Hd ) (χd χd ) ( 1, 2 , −2) The MSSM I: Field Content 6 ⇒ Fields of the MSSM

0 ± Gauginos: B,e Wf , Wf , ge The MSSM I: Field Content 6 ⇒ Fields of the MSSM

0 ± Gauginos: B,e Wf , Wf , ge ⇒ Why two Higgs doublets? • One Higgs doublet of scalars OK for anomalies • New fermions create triangle anomalies, e.g. Tr Y 3 6= 0 • Need opposite hypercharge fermion The MSSM I: Field Content 6 ⇒ Fields of the MSSM

⇒ A supersymmetric Lagrangian is deﬁned by a superpotential W

• A superpotential W must itself be a chiral (holomorphic) object

• This is ensured by making it a product of chiral supermultiplets only

• But how to ﬁnd the component expression? Tensor calculus From “Superspace” to Real Space 7

⇒ A supersymmetric Lagrangian is deﬁned by a superpotential W

• A superpotential W must itself be a chiral (holomorphic) object

• This is ensured by making it a product of chiral supermultiplets only

• But how to ﬁnd the component expression? Tensor calculus

⇒ To make accounting easier, the superﬁeld was invented       h+ χ+ F + c c c 2 u u 2 Hu uR =u ˜R + θuR + θ Fu Hu =   + θ   + θ   h0 χ0 F 0 u u Hu From “Superspace” to Real Space 7

⇒ A supersymmetric Lagrangian is deﬁned by a superpotential W

• A superpotential W must itself be a chiral (holomorphic) object

• This is ensured by making it a product of chiral supermultiplets only

• But how to ﬁnd the component expression? Tensor calculus

⇒ To make accounting easier, the superﬁeld was invented       h+ χ+ F + c c c 2 u u 2 Hu uR =u ˜R + θuR + θ Fu Hu =   + θ   + θ   h0 χ0 F 0 u u Hu

• Tensor calculus made simple: every term must have two thetas

c † 0 c 0 † ˜ † + W 3 λuQuRHu → λuu˜LuRχu + λuuLu˜Rχu + λuuLuRh0 + λudLuRχu + ··· The MSSM II: Superpotential 8

⇒ Most general gauge-invariant, renormalizable superpotential

W = WMSSM + WR

c c c c WMSSM = λuQuRHu + λdQdRHd + λeLeRHd + λνLνRHu + µHuHd 0 c 00 c c c 000 c 0 WR = λ QdRL + λ dRdRuR + λ LLeR + µ LHu

⇒ The second set of terms are allowed, but dangerous!

• Higgs states can mix with leptons The MSSM II: Superpotential 8

⇒ Most general gauge-invariant, renormalizable superpotential

W = WMSSM + WR

c c c c WMSSM = λuQuRHu + λdQdRHd + λeLeRHd + λνLνRHu + µHuHd 0 c 00 c c c 000 c 0 WR = λ QdRL + λ dRdRuR + λ LLeR + µ LHu

⇒ The second set of terms are allowed, but dangerous!

• Higgs states can mix with leptons

• New contributions to FCNC’s at loop level → λ ∼ 0.05 The MSSM II: Superpotential 8

⇒ Most general gauge-invariant, renormalizable superpotential

W = WMSSM + WR

c c c c WMSSM = λuQuRHu + λdQdRHd + λeLeRHd + λνLνRHu + µHuHd 0 c 00 c c c 000 c 0 WR = λ QdRL + λ dRdRuR + λ LLeR + µ LHu

⇒ The second set of terms are allowed, but dangerous!

• Higgs states can mix with leptons

• New contributions to FCNC’s at loop level → λ ∼ 0.05

• Products of operators can allow rapid proton decay (τp ' τn)

+ 0 0 00 −30 e.g. p → ` π via seR,ebR exchange → λ λ ∼ 10 The MSSM III: R-Parity 9

3(B−L)+2s ⇒ So we introduce R-parity : Rp = (−1) • Without 2s we have “matter parity”

PM (Q, u, d, L, e) = −1 PM (Hu,Hd) = +1

• With spin it instead separates SM from superpartners

0 0 + 0 − 0 Rp(q, `; hu, hd;(Aµ)a) = +1 RP (q,e `e; χu , χu, χd , χd; λa) = −1

⇒ Require each term in component Lagrangian have Rp = +1 The MSSM III: R-Parity 9

3(B−L)+2s ⇒ So we introduce R-parity : Rp = (−1) • Without 2s we have “matter parity”

PM (Q, u, d, L, e) = −1 PM (Hu,Hd) = +1

• With spin it instead separates SM from superpartners

0 0 + 0 − 0 Rp(q, `; hu, hd;(Aµ)a) = +1 RP (q,e `e; χu , χu, χd , χd; λa) = −1

⇒ Require each term in component Lagrangian have Rp = +1

• Immediately forbids all of WR The MSSM III: R-Parity 9

3(B−L)+2s ⇒ So we introduce R-parity : Rp = (−1) • Without 2s we have “matter parity”

PM (Q, u, d, L, e) = −1 PM (Hu,Hd) = +1

• With spin it instead separates SM from superpartners

0 0 + 0 − 0 Rp(q, `; hu, hd;(Aµ)a) = +1 RP (q,e `e; χu , χu, χd , χd; λa) = −1

⇒ Require each term in component Lagrangian have Rp = +1

• Immediately forbids all of WR • The “two superpartner” rule The MSSM III: R-Parity 9

3(B−L)+2s ⇒ So we introduce R-parity : Rp = (−1) • Without 2s we have “matter parity”

PM (Q, u, d, L, e) = −1 PM (Hu,Hd) = +1

• With spin it instead separates SM from superpartners

0 0 + 0 − 0 Rp(q, `; hu, hd;(Aµ)a) = +1 RP (q,e `e; χu , χu, χd , χd; λa) = −1

⇒ Require each term in component Lagrangian have Rp = +1

• Immediately forbids all of WR • The “two superpartner” rule • All superpartners must decay into Lightest Supersymmetric Particle (LSP) ? Stable ? Neutral and weakly-interacting → cold dark matter? ? Signature implication: missing energy Feynman Diagrams with Superpartners 10

⇒ Example: scalar ﬁeld decays

⇒ Example: Top Yukawa (superpotential) interactions OK... So Why Supersymmetry? (I) 11

⇒ It provides a solution to the so-called “hierarchy problem”

2 2 2 • Consider corrections to SM mH via ∆V = −λS|H| |s|

2 2 |λf | 2 2 δm = −2Λ + 6m ln(λuv/mf ) H f 16π2 uv f 2 λs 2 2 δm = Λ − 2m ln(λuv/ms) H s 16π2 uv s

• Scalars will diverge like fermions (logarithmically) provided OK... So Why Supersymmetry? (I) 11

⇒ It provides a solution to the so-called “hierarchy problem”

2 2 2 • Consider corrections to SM mH via ∆V = −λS|H| |s|

2 2 |λf | 2 2 δm = −2Λ + 6m ln(λuv/mf ) H f 16π2 uv f 2 λs 2 2 δm = Λ − 2m ln(λuv/ms) H s 16π2 uv s

• Scalars will diverge like fermions (logarithmically) provided ? 2 scalars per every (Weyl) fermion OK... So Why Supersymmetry? (I) 11

⇒ It provides a solution to the so-called “hierarchy problem”

2 2 2 • Consider corrections to SM mH via ∆V = −λS|H| |s|

2 2 |λf | 2 2 δm = −2Λ + 6m ln(λuv/mf ) H f 16π2 uv f 2 λs 2 2 δm = Λ − 2m ln(λuv/ms) H s 16π2 uv s

• Scalars will diverge like fermions (logarithmically) provided

? 2 scalars per every (Weyl) fermion X 2 ? The couplings satisfy λS = |λF | OK... So Why Supersymmetry? (I) 11

⇒ It provides a solution to the so-called “hierarchy problem”

2 2 2 • Consider corrections to SM mH via ∆V = −λS|H| |s|

2 2 |λf | 2 2 δm = −2Λ + 6m ln(λuv/mf ) H f 16π2 uv f 2 λs 2 2 δm = Λ − 2m ln(λuv/ms) H s 16π2 uv s

• Scalars will diverge like fermions (logarithmically) provided

? 2 scalars per every (Weyl) fermion X 2 ? The couplings satisfy λS = |λF | X ? The scalar and fermion masses are similar 2 α 2 2 δm ∼ (m − m ) ln (Λuv/m) H f+s 16π2 f s

2 2 < • Hence the desire that (mf − ms) ∼ 1 TeV OK... So Why Supersymmetry? (II) 12 • Dark matter

? LSP is Rp-odd → nothing to decay into → stable! ? Interacts weakly with itself and with SM → perfect CDM candidate! • Baryogenesis ? SM has only one (small phase); MSSM has 40 of them! ? Phase transition for EWSB strongly ﬁrst-order in MSSM, but not in SM • Gauge coupling uniﬁcation Gaugino Masses I 13

1 Lsoft 3 −2Maλaλa ⇒ Gluinos (M3)

• Only s = 1/2, SU(3) adjoint-valued ﬁelds → no mixing

• Adjoint irrep.’s → self-conjugate → “LH” and “RH” components identical Gaugino Masses I 13

1 Lsoft 3 −2Maλaλa ⇒ Gluinos (M3)

• Only s = 1/2, SU(3) adjoint-valued ﬁelds → no mixing

• Adjoint irrep.’s → self-conjugate → “LH” and “RH” components identical

⇒ Charginos (M2 and µ)

+ − • Four 2-component spinors: Higgsinos (χu , χd ) and W-inos (λe1, λe2)

± + + − − ψ = Wf , χu , Wf , χd

• Charged → can be grouped into two Dirac spinors (Ce1, Ce2)

• Mass terms in 4 × 4 notation: L 3 −1 (ψ±)T M (ψ±) +c.c. 2 Ce     T iϕ 0 X M2e 2 g2vu MC =   X =   e iϕµ X 0 g2vd µe Gaugino Masses II – EM Neutral Sector 14

⇒ Neutralinos (M1, M2 and µ) 0 0 0 • Four 2-comp. spinors: Higgsinos (χu, χd), W-ino λe3 = Wf and B-ino Be 0 0 0 0 ψ = B,e Wf , χd, χu

• Neutral → can be organized into four Majorana spinors Nei Gaugino Masses II – EM Neutral Sector 14

⇒ Neutralinos (M1, M2 and µ) 0 0 0 • Four 2-comp. spinors: Higgsinos (χu, χd), W-ino λe3 = Wf and B-ino Be 0 0 0 0 ψ = B,e Wf , χd, χu

• Neutral → can be organized into four Majorana spinors Nei T • Mass terms in 4 × 4 notation: L 3 −1 ψ0 M ψ0 +c.c. 2 Ne √ √  iϕ1 0 0  M1e 0 −g vd/√ 2 g vu/ √2  0 M eiϕ2 g0v / 2 −g0v / 2  M =  √ 2 √ d u  Ne  0 0 iϕµ   −g vd/√ 2 g vd/ √2 0 −µe  0 0 iϕµ g vu/ 2 −g vu/ 2 −µe 0

< ⇒ Typical eigenstates if M1 ∼ M2 µ

m ' M1; m ' m ' M2; m ' m ' m ' µ Ne1 Ne2 Ce1 Ne3 Ne4 Ce1 0 Ne1 ∼ Be; Ne2 ∼ Wf ; Ne3, Ne4 ∼ He ± ± Ce1 ∼ Wf ; Ce2 ∼ He The µ parameter 15

⇒ A supersymmetric mass term

αβ W 3 µHuHd = µ(Hu)α(Hd)β + − 0 0 2 0 2 0 2 + 2 − 2 → µ(χu χd − χuχd) + |µ| |hu| + |hd| + |hu | + |hd |

• Non-vanishing µ needed to give Higgsinos mass The µ parameter 15

⇒ A supersymmetric mass term

αβ W 3 µHuHd = µ(Hu)α(Hd)β + − 0 0 2 0 2 0 2 + 2 − 2 → µ(χu χd − χuχd) + |µ| |hu| + |hd| + |hu | + |hd |

• Non-vanishing µ needed to give Higgsinos mass

2 2 4 2 • But if VH ∼ mH|h| + λ|h| , need mH < 0 if we want hhi= 6 0 The µ parameter 15

⇒ A supersymmetric mass term

αβ W 3 µHuHd = µ(Hu)α(Hd)β + − 0 0 2 0 2 0 2 + 2 − 2 → µ(χu χd − χuχd) + |µ| |hu| + |hd| + |hu | + |hd |

• Non-vanishing µ needed to give Higgsinos mass

2 2 4 2 • But if VH ∼ mH|h| + λ|h| , need mH < 0 if we want hhi= 6 0

• So we need |µ|2 < m2 ∼ (1 TeV)2 ∼ fe

⇒ But not tied to SUSY breaking, so no need to be EW scale! Higgs Sector I: EWSB scalar potential 16

⇒ Assume that only Higgs ﬁelds obtain vevs at minimum

+ − • Minimum can always be found such that hhu i = hd = 0 • Phase rotations on remaining two Higgs states can make potential real and 0 0 hu = vu, hd = vd real and positive

V = |µ|2 + m2 |h0 |2 + |µ|2 + m2 |h0|2 Hu u Hd d 1 −(bh0 h0 + c.c.) + (g2 + g02)(|h0 |2 − |h0|2)2 u d 8 u d Higgs Sector I: EWSB scalar potential 16

⇒ Assume that only Higgs ﬁelds obtain vevs at minimum

+ − • Minimum can always be found such that hhu i = hd = 0 • Phase rotations on remaining two Higgs states can make potential real and 0 0 hu = vu, hd = vd real and positive

V = |µ|2 + m2 |h0 |2 + |µ|2 + m2 |h0|2 Hu u Hd d 1 −(bh0 h0 + c.c.) + (g2 + g02)(|h0 |2 − |h0|2)2 u d 8 u d

0 0 ⇒ Two minimization conditions ∂V/∂hu, hd = 0 m2 − m2 tan2 β 1 µ2 = Hd Hu − M 2; 2b = (m2 + m2 + 2µ2) sin 2β tan2 β − 1 2 z Hd Hu

• Here we have introduced the parameter tan β = vu/vd

2 2 2 2 2 v2 5 0 2 2 • Note that v = vu + vd ' (174 GeV) and Mz = 2 (3(g ) + g2) Higgs Sector II: Mass Eigenstates 17

⇒ Two doublets → 8 d.o.f. - 3 d.o.f. (eaten) = 5 Higgs eigenstates

0 0 A ∼ sin β Im(hd) + cos β Im(hu) + + − ∗ H ∼ cos β hu + sin β (hd )       0 0 h √ cos α − sin α Re[h ] − vu ∼ 2 u  0     0  H sin α cos α Re[hd] − vd Higgs Sector II: Mass Eigenstates 17

⇒ Two doublets → 8 d.o.f. - 3 d.o.f. (eaten) = 5 Higgs eigenstates

0 0 A ∼ sin β Im(hd) + cos β Im(hu) + + − ∗ H ∼ cos β hu + sin β (hd )       0 0 h √ cos α − sin α Re[h ] − vu ∼ 2 u  0     0  H sin α cos α Re[hd] − vd

⇒ Masses of these are given by 2 2 2 2 mA = 2b/ sin 2β; mH± = mA + mW 1 q m2 = m2 + M 2 ∓ (m2 + M 2)2 − 4M 2m2 cos2 2β h0,H0 2 A z A z z A

⇒ Parameterizing the Higgs sector: minimization conditions allow swap of µ, b for Mz, tan β Breaking SUSY, Generally 18

⇒ What is a hidden sector ? • No tree-level (renormalizable) interaction of MSSM ﬁelds to SUSY breaking order parameters hF i, hDi, hMi

• Thus hDY i= 6 0 and FHu,Hd 6= 0 can’t be dominant source of SUSY breaking Breaking SUSY, Generally 18

⇒ What is a hidden sector ? • No tree-level (renormalizable) interaction of MSSM ﬁelds to SUSY breaking order parameters hF i, hDi, hMi

• Thus hDY i= 6 0 and FHu,Hd 6= 0 can’t be dominant source of SUSY breaking

2 2 i ∗ j • Instead, expect terms like hFX/MXi λaλa or |FX| /MX kij(φ ) φ • That is, SUSY breaking is spontaneous in the hidden sector, but appears explicitly in our sector Breaking SUSY, Generally 18

⇒ What is a hidden sector ? • No tree-level (renormalizable) interaction of MSSM ﬁelds to SUSY breaking order parameters hF i, hDi, hMi

• Thus hDY i= 6 0 and FHu,Hd 6= 0 can’t be dominant source of SUSY breaking

2 2 i ∗ j • Instead, expect terms like hFX/MXi λaλa or |FX| /MX kij(φ ) φ • That is, SUSY breaking is spontaneous in the hidden sector, but appears explicitly in our sector

⇒ Why must we break SUSY in one?

• If no hidden sector, then at least some scalars lighter than fermions!

• Spontaneous breaking in our sector can only be through hDY ,D3i= 6 0 and

FHu,Hd 6= 0

2 2 m ∼ m ± (aDY + bD3) et t Gravity Mediation 19

As a result of putting SUSY breaking in a hidden sector that models are classifed more by how SUSY breaking is transmitted to our sector than how it was actually broken in the ﬁrst place. Gravity Mediation 19

As a result of putting SUSY breaking in a hidden sector that models are classifed more by how SUSY breaking is transmitted to our sector than how it was actually broken in the ﬁrst place.

⇒ Sterile (gauge-singlet) chiral superﬁeld as spurion

• Imagine soft Lagrangian given by

FG P FS 2 P f i ∗ j 1 FB FA P α i j k − λaλa − | | k (φ ) φ − µHuHd − λ φ φ φ MG a MS f ij ef ef 2 MB MA α ijk e e e

• Mi are the scales of the mediation ﬁelds (what’s been integrated out)

• If we take Mi = Mpl we have gravity mediation Gravity Mediation 19

As a result of putting SUSY breaking in a hidden sector that models are classifed more by how SUSY breaking is transmitted to our sector than how it was actually broken in the ﬁrst place.

⇒ Sterile (gauge-singlet) chiral superﬁeld as spurion

• Imagine soft Lagrangian given by

FG P FS 2 P f i ∗ j 1 FB FA P α i j k − λaλa − | | k (φ ) φ − µHuHd − λ φ φ φ MG a MS f ij ef ef 2 MB MA α ijk e e e

• Mi are the scales of the mediation ﬁelds (what’s been integrated out)

• If we take Mi = Mpl we have gravity mediation

⇒ Resulting soft terms

FG 2 FS 2 α α FA FB m1/2 = , m = | | , a = λ , b = µ MG 0 MS ijk ijk MA MB Minimal Supergravity (mSUGRA) 20

Deﬁned by parameter set: m1/2, m0,A0, tan β, sgn(µ) mSUGRA Sample Spectrum A 21 mSUGRA Sample Spectrum B 22 Overview of Classic SUSY Signatures 23

⇒ Break up into channels by n jets + m leptons + E/T

• 0 leptons + ≥ 2 jets + E/T (“multijet”channel)

• 1 lepton + ≥ 2 jets + E/T

• 2 leptons + E/T ? Same Sign (SS) vs. Opposite Sign (OS) sub-samples ? Can be “clean”(no jets) or with ≥ 2 jets

• Trilpetons, clean or ≥ 2 jets, + E/T

⇒ Remember: invisible, stable LSP means no mass peaks! Jets plus Missing Energy 24

⇒ Squark, gluino production rate ∼ SM jet production at similar Q2

⇒ Multijet signal via quark decays 0 ± ge → qq¯Nei , ge → tet, qeL → qCei , etc. [and subsequent cascades] ⇒ The ultimate inclusive signature

• Just count events – does not matter what the original particles were

• Look for excess over (known) SM rate Jets plus Missing Energy 24

⇒ Squark, gluino production rate ∼ SM jet production at similar Q2

⇒ Multijet signal via quark decays 0 ± ge → qq¯Nei , ge → tet, qeL → qCei , etc. [and subsequent cascades] ⇒ The ultimate inclusive signature

• Just count events – does not matter what the original particles were

• Look for excess over (known) SM rate

P jet ⇒ Kinematic variable Meﬀ ≡ E/T + i(pT )i can be useful in SUSY discovery

• Claim: peak in M distribution proportional to M ≡ min(M ,M ) eﬀ susy ge qe

• This channel alone can find SUSY for squarks/gluinos up to 1 TeV with 1 fb−1 – 2.5-3 TeV for 300 fb−1 Meff and Kinematic Distributions 25 • SM backgrounds ? QCD (gg → gg, etc.) with extra jets from parton showers ? Heavy flavor production ? Z + multijets with Z → ττ or Z → νν ? W + multijets with W → τν or W → `ν

• A typical set of cuts jet ? ET ≥ 100, 50, 50, 50 GeV ? No isolated lepton with pT > 20 GeV ? Transverse sphericity ST > 0.2 ? Transverse plane angle o o 30 < ∆φ(E/T , j) < 90 ? E/T > 0.2 Meﬀ Multilepton Events: OS dileptons 26

⇒ Multi-lepton signals are comparable in reach/discovery to multijets with 100 fb−1 data

⇒ OS Dilepton events (inclusive)

± • Many paths to this signature in SUSY: Ce1 pair production, 0 ± ∓ 0 + − 0 0 + − Ne2 → `e ` → Ne1 ` ` , qeL → Ne2 q → Ne1 ` ` q, etc. • Main SM background is tt¯production • Inclusive OS and same ﬂavor can be a SUSY discovery mode Multilepton Events: OS dileptons 26

⇒ Multi-lepton signals are comparable in reach/discovery to multijets with 100 fb−1 data

⇒ OS Dilepton events (inclusive)

• Veto Z → `` via invariant mass cut M`` 6= MZ ± 10 GeV

• Off shell γ and Z decays to taus reduced by ∆φ(``) ≤ 150o Multilepton Events: OS dileptons 27 Multilepton Events: SS Dileptons & Trileptons 28

⇒ SS dilepton events often said to be “truly SUSY” signature

• SS usually seen as gluino-driven; result of Majorana nature

0 ± 0 ± 0 ge → qqe → qq Ce1 → qq W Ne1

• Signature is E/T + jets + pair of same-sign dileptons • SM background very low and easy to control for... Multilepton Events: SS Dileptons & Trileptons 28

⇒ SS dilepton events often said to be “truly SUSY” signature

• SS usually seen as gluino-driven; result of Majorana nature

0 ± 0 ± 0 ge → qqe → qq Ce1 → qq W Ne1

• Signature is E/T + jets + pair of same-sign dileptons • SM background very low and easy to control for...

⇒ “Clean” Trilepton Events: the Gold-Plated Signature

• Lack of jets tends to mean chargino/neutralino production

± 0 0 0 pp → Ce1 Ne2 → Ne1 `` Ne1 `ν

± 0 • Separation of production mechanism (i.e. isolation of Ce1 Ne2 sample) seems possible with cuts

• Various kinematic distributions can be formed m`i`j Information from Lepton Distributions 29

⇒ Endpoint of effective mass distribution of the two leptons carries information.....but on what?

0 0 + − max Ne2 → Ne1 ` ` then M`` = M 0 − M 0 Ne2 Ne1 q N 0 → `±`∓ → N 0`+`− then M max = 1 (M 2 − M 2)(M − M 2 ) e2 e e1 `` M 0 è2 0 è Ne2 è Ne1 ⇒ Shape of distribution is supposed to tell them apart Some Words of Caution 30

Rule of thumb: SUSY “discovery” can be done with inclusive, model-independent observations – parameter extraction requires exclusive, model-dependent techniques

⇒ The background to SUSY is more SUSY! Some Words of Caution 30

Rule of thumb: SUSY “discovery” can be done with inclusive, model-independent observations – parameter extraction requires exclusive, model-dependent techniques

⇒ The background to SUSY is more SUSY!

Lots of distribution features will be extracted...to what end?

• Example: trilepton + 2 jets allows all sorts of pairings. Do they have information content if you don’t know the spectrum? Can you separate chargino/neutralino sources from squark/gluino sources?

• Example: SS dileptons can come from gluinos, but also from

¯ − + pp → ebLebLX → tCe1 tCe1 X

Endpoint value measures something different here!

⇒ Need to use strict cuts to separate multiple channels leading to same inclusive topology...reduction in signal and signiﬁcance Concluding Thoughts 31

⇒ We are passing from theory-rich era of SUSY to data-rich era! ⇒ Analysis Approach and Synthesis Approach will likely both be needed Concluding Thoughts 31

⇒ We are passing from theory-rich era of SUSY to data-rich era! ⇒ Analysis Approach and Synthesis Approach will likely both be needed • Synthesis direction ? Enlarge the set of inclusive signatures ? Improve SM baseline determination ? Study ability to separate regions with a model’s parameter space – and models from one another • Analysis direction ? Enlarge toolbox using non-SUGRA cases ? Robustness analysis: from points to lines to footprints Concluding Thoughts 31

⇒ Towards a decision tree style strategy 1. Organize analysis tools by needed inputs/model dependence 2. Use least dependent tools with global ﬁts to paradigms 3. Cross check promising paradigms against other analysis measurements 4. Organize ﬂow chart as function of integrated luminosity Supporting Slides Some Words of Caution: II 1

Examples of exclusive analysis: separating contributions to Meﬀ and m`` In multijet channel, how do you know what fraction of the sample is from production of gluino pairs and what fraction from squark pairs? • Jet multiplicity: assume for ﬁrst/second generation squarks “R” and “L” produced more or less equally 0 • BR(qeR → qNe1 ) nearly 100% → one jet per decay ± ± • qeL and ge have different decays such as ge → qq¯Cei and ge → qq¯Nei → usually more jets per decay

In SS dilepton + jets sample, how do you separate gluino from squark contributions? Some Words of Caution: II 1

In SS dilepton + jets sample, how do you separate gluino from squark contributions? • Charge asymmetry: initial state at LHC is pp

• Cascade decays from geqe and qeqe events leads to a larger cross section for positive SS pairs than for negative ones

• This asymmetry is sensitive to m /m ge qe Some Words of Caution: III 2

⇒ Many such algorithms known, but all are devised within limited model regimes (all mSUGRA)

0 • BR(qeR → qNe1 ) nearly 100% artifact of LSP being 99% B-ino • Obtaining m /m from charge asymmetry in SS dileptons really requires ge qe outside knowledge of m to work well ge • Gluino mass measurement algorithm based on mSUGRA point where 2 m ' M 0M 0 – by no means a general result `eR Ne2 Ne1 Some Words of Caution: III 2

⇒ Many such algorithms known, but all are devised within limited model regimes (all mSUGRA)

⇒ Even once exclusive samples are prepared, information from distributions may be misleading because of phases

• Can shift peak of Meﬀ distributions by signiﬁcant amount • Can change the shape of kinematic distributions and location of endpoint • Can effect cross-sections for gaugino production [clean trilepton signal] by 30-40% • Relation between mass eigenstates and soft Lagrangian parameters becomes more complicated