Physics Beyond the Standard Model?

Physics Beyond the Standard Model? Shrihari Gopalakrishna

Institute of Mathematical Sciences (IMSc), Chennai

IX EHEP SERC School 2013 IIT Madras

Dec 2013

Motivation for BSM Physics Observational What is the observed Dark Matter? What generates the neutrino masses? What generates the Baryon Asymmetry of the Universe (BAU)?

Theoretical SM hierarchy problem (Higgs sector): MEW MPl SM flavor problem: me mt Explained by new dynamics? Extra dimensions (Warped (AdS), Flat) Supersymmetry Strong dynamics Little Higgs

Outline (Supersymmetry)

Supersymmetry (SUSY) Basics SUSY invariant theory SUSY breaking Minimal Supersymmetric Standard Model (MSSM) SUSY preserving Lagrangian and soft-breaking terms R-parity Superpartner Mixing Implications Dark Matter 125 GeV Higgs

Outline (Extra Dimensions)

Aspects of Extra Dimensional Theories Large Extra Dimensions (LED) (aka ADD) Universal Extra Dimensions (UED) Warped Extra Dimensions (WED) Kaluza-Klein (KK) expansion LHC Signatures

Outline (Dark Matter)

BSM DM Candidates DM Detection Direct detection Indirect detection At colliders

Supersymmetry Basics

SUPERSYMMETRY Reviews: [Wess & Bagger] [Martin] [Drees] [Drees, Godbole, Roy] [Baer, Tata]


Supersymmetry (SUSY)

Reviews: [Wess & Bagger]

Symmetry: Fermions ⇔ Bosons Q |Φi = |Ψi

;

Q |Ψi = |Φi

Qα is a spinorial charge

SUSY algebra: n o ¯ ˙ Qα , Q β

µ

= 2σ ˙ Pµ n αβ o ¯ α˙ , Q ¯ ˙ =0 Qα , Qβ = Q β ¯ α˙ = 0 [P µ , Qα ] = P µ , Q


SUSY invariant theory Under a SUSY transformation √ δξ φ = 2ξψ √ √ ¯ m φ + 2ξF δξ ψ =i 2σ m ξ∂ √ ¯σ m ∂m ψ δξ F =i 2ξ¯

δξ Amn =i

¯ + ξ¯ ¯σ n ∂m λ − (n ↔ m) ξσ n ∂m λ

δξ λ =iξD + σ mn ξAmn ¯σ m ∂m λ − ξσ m ∂m λ ¯ δξ D =ξ¯


SUSY invariant theory Under a SUSY transformation √ δξ φ = 2ξψ √ √ ¯ m φ + 2ξF δξ ψ =i 2σ m ξ∂ √ ¯σ m ∂m ψ δξ F =i 2ξ¯

δξ Amn =i

A SUSY invariant action: S =

¯ + ξ¯ ¯σ n ∂m λ − (n ↔ m) ξσ n ∂m λ

δξ λ =iξD + σ mn ξAmn ¯σ m ∂m λ − ξσ m ∂m λ ¯ δξ D =ξ¯

R

d 4x L

√ † L =|Dµ φi |2 − i ψ¯i σµ D µ ψi − g 2 φ∗i T a ψi λa + λa ψ † T a φi ∂W(φi ) 2 1 ∂ 2 W(φi ) ψj ψk + h.c. − − 2 ∂φj ∂φk ∂φj † 1 a µν 1 X ∗ a 2 − Fµν Fa − g φi Tij φj − iλa σ ¯µ D µ λa 4 2 a

W(φi ) : Superpotential, a holomorphic function of the fields


Consequences Solution to gauge hierarchy problem tL , tR

h −i √yt

2

h

t˜L, t˜R

+

= 0 h

2

−i y2t

h

Λ2 divergence cancelled

[Romesh Kaul, ’81, ’82] [Witten]

˜ (Similarly W ± , Z divergences cancelled by λ)


Consequences Solution to gauge hierarchy problem tL , tR

h −i √yt

2

h

t˜L, t˜R

+

= 0 h

2

−i y2t

h

Λ2 divergence cancelled

[Romesh Kaul, ’81, ’82] [Witten]

˜ (Similarly W ± , Z divergences cancelled by λ)

Lightest SUSY Particle (LSP) stable dark matter (if Rp conserved) Gauge Coupling Unification - SUSY SO(10) GUT Includes νR ⇒ Neutrino mass via seesaw

Supersymmetry SUSY breaking

SUSY breaking Exact SUSY =⇒ Mψ = Mφ

;

MA = Mλ˜

So experiment =⇒ SUSY must be broken SUSY broken if and only if h0|H|0i > 0 Spontaneous SUSY breaking O’Raifeartaigh F -term breaking Fayet-Iliopoulos D-term breaking STr (M 2 ) = 0 superfield

=⇒

cannot break SUSY spontaneously using SM

Hidden sector breaking

←→ Communicated to SM Mediation

Spectrum depends on Mediation type + RGE In effective low-energy theory Explicit soft-breaking terms, i.e., with dimensionful parameters

Supersymmetry MSSM

MSSM

The Minimal Supersymmetric Standard Model (MSSM) Reviews: [Martin] [Drees] [Drees,Godbole,Roy] [Baer,Tata]

Supersymmetry MSSM

MSSM fields To every SM particle, add a superpartner (spin differs by 1/2) Matter fields (Chiral Superfields) (SU(3), SU(2))U(1)

Components

Q

(3, 2)1/6

(˜ qL , qL , FQ ) ;

Uc

(¯ 3, 1)−2/3

∗ c (˜ uR , uR , FU )

(¯ 3, 1)1/3

(d˜R∗ , dRc , FD )

L

(1, 2)−1/2

(`˜L , `L , FL ) ;

Ec

(1, 1)1

∗ c (˜ eR , eR , FE )

c

(1, 1)0

∗ c (ν ˜R , νR , FN )

D

c

(N ) Gauge fields (Vector Superfields)

(gµ , g˜ , D3 )

SU(2)

˜ , D2 ) (Wµ , W

U(1)

˜ D1 ) (Bµ , B,

`˜L =

u ˜L d˜L

ν ˜L e˜L

uL ; qL = dL

; `L =

νL eL

Higgs fields (Chiral Superfields)

Components SU(3)

q ˜L =

(SU(3), SU(2))U(1) Hu

(1, 2)1/2

Hd

(1, 2)−1/2

Components + hu ; hu0 ! hd0 ˜ (hd , hd , FH ) ; hd = ; d hd− ˜u , FH ) ; hu = (hu , h u

+ ˜ h u ˜0 h u ! ˜ hd0 ˜d = h − ˜ h ˜u = h

d

Supersymmetry MSSM

MSSM Superpotential

Write most general W consistent with SU(3)c ⊗ SU(2)L ⊗ U(1)Y W = U c yu QHu − D c yd QHd − E c ye LHd + µHu Hd + (N c yn LHu ) W∆L = LHu + LE c L + QD c L ;

W∆B = U c D c D c

W∆L + W∆B induce proton decay :

τp ∼ 10−10 s for m ˜ ∼ 1 TeV

Supersymmetry MSSM

MSSM Superpotential

Write most general W consistent with SU(3)c ⊗ SU(2)L ⊗ U(1)Y W = U c yu QHu − D c yd QHd − E c ye LHd + µHu Hd + (N c yn LHu ) W∆L = LHu + LE c L + QD c L ;

W∆B = U c D c D c

W∆L + W∆B induce proton decay :

τp ∼ 10−10 s for m ˜ ∼ 1 TeV

So impose Matter Parity RM = (−1)3(B−L) to forbid ∆L and ∆B terms For components =⇒ R-parity Rp = (−1)3(B−L)+2s Rp (particle) = +1 ,

Rp (sparticle) = −1

Consequence : The Lightest SUSY Particle (LSP) is stable Cosmologically stable Dark Matter Missing Energy at Colliders

Supersymmetry MSSM

Soft SUSY breaking Effective parametrization with explicit soft-SUSY-breaking terms 2 ˜ 2 ˜† ˜Q ˜† m ˜ − e˜† m Lsoft Q −u ˜R† m ˜ u2 u ˜R − d˜R† m ˜ d2 d˜R − L ˜ L2 L ˜R − (˜ νR† m ˜ ν2 ν˜R ) SUSY Br ⊃ −Q m R ˜ee 1 ˜B ˜ − 1 M2 W ˜W ˜ − 1 M3 g˜ g˜ + h.c. − M1 B 2 2 2 ˜ u ) + h.c. ˜ d − (ν˜c Aν LH ˜ u + d˜c Ad QH ˜ d + e˜c Ae LH − u˜c Au QH

− mH2 u Hu† Hu − mH2 d Hd† Hd − (BµHu Hd + h.c.)

Supersymmetry MSSM

Soft SUSY breaking Effective parametrization with explicit soft-SUSY-breaking terms 2 ˜ 2 ˜† ˜Q ˜† m ˜ − e˜† m Lsoft Q −u ˜R† m ˜ u2 u ˜R − d˜R† m ˜ d2 d˜R − L ˜ L2 L ˜R − (˜ νR† m ˜ ν2 ν˜R ) SUSY Br ⊃ −Q m R ˜ee 1 ˜B ˜ − 1 M2 W ˜W ˜ − 1 M3 g˜ g˜ + h.c. − M1 B 2 2 2 ˜ u ) + h.c. ˜ d − (ν˜c Aν LH ˜ u + d˜c Ad QH ˜ d + e˜c Ae LH − u˜c Au QH

− mH2 u Hu† Hu − mH2 d Hd† Hd − (BµHu Hd + h.c.) UV SUSY breaking and mediation dynamics will set these parameters Eg: Gravity Mediation (MSUGRA, CMSSM) Inputs m ˜ 0 ,M1/2 , A0 , tan β, sign(µ) at GUT scale TeV scale values determined by RGE

Supersymmetry MSSM

Electroweak symmetry breaking (EWSB)

hHu i =

√1 2

0 vu

;

hHd i =

√1 2

Physical Higgses: h0 , H 0 , A0 , H ±

vd ; 0

v 2 = vu2 + vd2 ;

tan β ≡

vu vd

;

Supersymmetry MSSM


hHu i =

√1 2

0 vu

;

hHd i =

√1 2

vd ; 0

v 2 = vu2 + vd2 ;

tan β ≡

vu vd

;

Physical Higgses: h0 , H 0 , A0 , H ± 2 )|h |2 +(|µ|2 +m2 )|h |2 −(b h h +h.c.)+ 1 (g 2 +g 02 )(|h |2 −|h |2 )2 V = (|µ|2 +mH u u µ u d d d H 8 u d

Minimization and EWSB sin(2β) =

2bµ 2 +m2 +2|µ|2 mH H u

d

and

2 |m2 −mH |

H mZ2 = √ d

d

1−sin2 (2β)

2 − m2 − 2|µ|2 − mH H u d

Supersymmetry MSSM


hHu i =

√1 2

0 vu

hHd i =

;

√1 2

vd ; 0

v 2 = vu2 + vd2 ;

tan β ≡

vu vd

;

Physical Higgses: h0 , H 0 , A0 , H ± 2 )|h |2 +(|µ|2 +m2 )|h |2 −(b h h +h.c.)+ 1 (g 2 +g 02 )(|h |2 −|h |2 )2 V = (|µ|2 +mH u u µ u d d d H 8 u d

Minimization and EWSB sin(2β) =

2bµ 2 +m2 +2|µ|2 mH H u

and

2 |m2 −mH |

H mZ2 = √ d

d

2

d

1−sin2 (2β) 2

2 − m2 − 2|µ|2 − mH H u d

So we need µ (SUSY preserving param) ∼ m (SUSY br param)! Why? This is called the µ-problem

Supersymmetry MSSM

125 GeV Higgs

At 1-loop mh2 ≈ mZ2 cos2 (2β) +

3g22 mt4 2 8π 2 mW

h m m ˜1 ˜t2 + ln tm 2 t

Xt2 m˜t m˜t 1

1−

[Haber, Hempfling, Hoang ,1997] i Xt2 12m˜t m˜t 1

2

2

where Xt = At − µ cot β

mh = 125 GeV needs sizable loop contribution Hard! Needs large m˜t1 m˜t2 or large Xt2 h m m ˜1 ˜t2 3g 2 m4 X2 But δmH2 u ≈ 8π22m2t ln tm + 2m˜ tm˜ 1 − 2 W

t

t1

t2

So fine-tuning necessary to keep mZ2 correct (cf “Little hierarchy problem”

Xt2 6m˜t m˜t 1

i

2

previous EWSB relation)

Supersymmetry MSSM

Neutralino mixing

˜ W ˜ 3, H ˜ u0 , H ˜ 0 ) : Majorana Neutralino: Neutral EW gauginos (B, d states L ⊃ − 21

  ˜  B M1 0 −cβ sW mZ sβ sW mZ   W ˜ 3 0 M c c m −s c m 2 W Z W Z β β 3 0 0   ˜W ˜ H ˜u H ˜  B d  −c s m  H ˜ u0  0 −µ β W Z cβ cW mZ 0 ˜ sβ sW mZ −sβ cW mZ −µ 0 H d

 ˜   0 B χ ˜1 ˜ 3 W χ ˜0     Diagonalizing this  ˜ 0  →  20  : the mass eigenstates χ ˜3  Hu 0 0 ˜d χ ˜4 H

Supersymmetry MSSM

Chargino mixing

˜ ±, H ˜ ± ), W˜ ± = W˜ 1 ± i W˜ 2 Chargino: Charged EW gauginos (W + ˜u α ˜+ ˜ + = H− ˜ + = W−αα˙ ; H Form Dirac states W ˜ α˙ ˜ H W d

˜+ L⊃− W

W ˜+ † + ˜ M P + M P χ H χ R L ˜ + + h.c. H where Mχ =

Diagonalizing this

˜+ W ˜+ H

→

χ ˜+ 1 χ ˜+ 2

√

M2 2 cos β mW

: the mass eigenstates

√

2 sin β mW µ

Supersymmetry MSSM

Scalar mixing

Eg. stop sector (˜tL , ˜tR ) L ⊃ − ˜tL∗ ˜tR∗

2 + m2 + ∆ m ˜ LL (vu At − µ∗ cot β mt )∗ L t 2 + m2 + ∆ (vu At − µ∗ cot β mt ) m ˜ RR R t

˜tL ˜tR

2 ) cos(2β) m2 where ∆ = (T3 − QsW Z

Diagonalizing this

˜tL ˜tR

→

˜t1 ˜t2

: the mass eigenstates

Supersymmetry MSSM

Flavor Probes FCNC (Mixing, Rare decays) and Precision probes Kaon observable, B-factories (BaBar, Belle) (g − 2)µ , EDM, ... Flavor Problem In general m ˜ ij can have arbitrary flavor structure and phases (MSSM has 9 new phases + 1 CKM phase)

FCNC & EDM experiments severely constrain these some deeper reason (in SUSY br mediation)? Minimal Flavor Violation (MFV) Only CKM phase Need experimental guidance

Extra Dimension

Details of the Models

EXTRA DIMENSION(S)

LHC Phenomenology

Extra Dimension


LHC Phenomenology

Large Extra Dimensions (LED, ADD) [Arkani-Hamed, Dimopoulos, Dvali (ADD), 1998]

n (compact) space extra dims with Radius R (in addition to the usual 3+1 dims) Example: 5-D : (x µ , y ) Extra Dim

Only fundamental scale M∗ ∼ 1 TeV 2 Mpl

=

M∗2+n Vn

Vn ∼

Rn

Gravity in bulk, SMh on brane S=

R

d 4x d ny

LBulk + δ(y ) LBrane

Gravitational potential modified to V (r ) ∼ 1/r n+1

xµ

y

i

Gravity Our 4D Brane

Extra Dimension


LHC Phenomenology

Large Extra Dimensions (LED, ADD) [Arkani-Hamed, Dimopoulos, Dvali (ADD), 1998]

n (compact) space extra dims with Radius R (in addition to the usual 3+1 dims) Example: 5-D : (x µ , y ) Extra Dim

Only fundamental scale M∗ ∼ 1 TeV 2 Mpl

=

M∗2+n Vn

Vn ∼

Rn

Gravity in bulk, SMh on brane S=

R

d 4x d ny

LBulk + δ(y ) LBrane

xµ

y

i

Gravitational potential modified to V (r ) ∼ 1/r n+1 Some implications for n = 1 , R = 1011 m excluded by solar system tests! for n = 2 , R ∼ 100 µm Cavendish type experiments limit M∗ > 4 TeV

Gravity Our 4D Brane

Extra Dimension


LHC Phenomenology

Universal Extra Dimensions (UED)

[Appelquist, Cheng, Dobrescu] [Cheng, Matchev, Schmaltz] [Datta, Kong, Matchev]

All SM fields propagate in Extra Dimension(s) No solution to the hierarchy problem KK parity conserved Relaxed constraints since no tree level contribution to EW precision obs

MKK & 400 GeV LKP stable! Dark Matter Missing energy at Colliders

[Servant, Tait]

Extra Dimension


LHC Phenomenology

Warped Extra Dimensions (WED, RS) SM in background 5D warped AdS space

[Randall, Sundrum 99]

ds 2 = e −2k|y | (ηµν dx µ dx ν ) + dy 2 Z2 orbifold fixed points:

y

Planck (UV) Brane

0

πR

TeV (IR) Brane R : radius of Ex. Dim. k : AdS curvature scale (k . Mpl )

y=0 UV

Hierarchy prob soln: IR localized Higgs :

MEW ∼ ke −kπR : Choose kπR ∼ 34

CFT dual is a composite Higgs model

y=πR IR

Extra Dimension


LHC Phenomenology

Explaining SM (gauge & mass) hierarchies (WED) Bulk Fermions explain SM mass hierarchy S (5) ⊃

R

d 4 x dy

n

[Gherghetta, Pomarol 00][Grossman, Neubert 00]

cψ k Ψ(x, y ) Ψ(x, y )

o

Fermion bulk mass (cψ parameter) controls f ψ (y ) localization h χ

tR

f1

q3 f0

RS-GIM keeps FCNC under control For details, see our review: [Davoudiasl, SG, Ponton, Santiago, New J.Phys.12:075011,2010. arXiv:0908.1968 [hep-ph]]

Extra Dimension


LHC Phenomenology

AdS/CFT

AdS/CFT Correspondence AdS/CFT Correspondence

[Maldacena, 1997]

A classical supergravity theory in AdS5 × S5 at weak coupling is dual to a 4D large-N CFT at strong coupling The CFT is at the boundary of AdS [Witten 1998; Gubser, Klebanov, Polyakov 1998] ZCFT [φ0 ] = e −ΓAdS [φ0 ]

S⊃

R

d 4 x OCFT (x) φ0 (x)

Eg: hO(x1 ) O(x2 )i =

δ 2 ZCFT [φ0 ] δφ0 (x1 )δ(x2 )

with ZCFT given by the RHS

ΓAdS [φ] supergravity eff. action φ(y , x) is a solution of the EOM (δΓ = 0) for given bndry value φ0 (x) = φ(y = y0 , x)

Extra Dimension


LHC Phenomenology

AdS/CFT

4D Duals of Warped Models [Arkani-Hamed, Porrati, Randall, 2000; Rattazzi, Zaffaroni, 2001]

Dual of Randall-Sundrum model RS1 (SM on IR Brane) Planck brane =⇒ UV Cutoff; Dynamical gravity in the 4D CFT TeV (IR) brane =⇒ IR Cutoff; Conformal invariance broken below a TeV All SM fields are composites of the CFT

Dual of Warped Models with Bulk SM UV localized fields are elementary IR localized fields (Higgs) are composite 4D dual is Composite Higgs model Shares many features with Walking Extended Technicolor

Partial Compositeness AdS dual is weakly coupled and hence calculable!

KK states are dual to composite resonances

[Georgi, Kaplan 1984]

Extra Dimension


LHC Phenomenology

KK Decomposition

Kaluza-Klein (KK) expansion Eg: 5-Dimensional theory : Bulk fields : S= δS (5) = 0

R

d 4 x dy L(5)

;

Φ(x, y ) = {AM , φ, Ψ, , ...}

(5)

2 φ† φ Lφ ⊃ ∂ M φ† ∂M φ − mφ

(5) δL(5) = ∂M δ∂ =⇒ Euler-Lagrange Equations of Motion (EOM) : δL δΦ MΦ

Extra Dimension


LHC Phenomenology

KK Decomposition


R

d 4 x dy L(5)

;

Φ(x, y ) = {AM , φ, Ψ, , ...}

(5)

2 φ† φ Lφ ⊃ ∂ M φ† ∂M φ − mφ


KK expansion: expand in a complete set of states fn (y ) Φ(x, y ) =

P∞

n=0

φ(n) (x) f (n) (y ) with

R

dy f (n) (y ) f (m) (y ) = δnm

Extra Dimension


LHC Phenomenology

KK Decomposition


R

d 4 x dy L(5)

;

Φ(x, y ) = {AM , φ, Ψ, , ...}

(5)

2 φ† φ Lφ ⊃ ∂ M φ† ∂M φ − mφ


KK expansion: expand in a complete set of states fn (y ) Φ(x, y ) =

P∞

n=0

φ(n) (x) f (n) (y ) with h

R

dy f (n) (y ) f (m) (y ) = δnm

i

ˆ 2 f(n) (y ) = mn2 fn (y ) Plug into EOM, y dependent piece is −∂y2 + M Φ

The solution is f(n) (y ) =

1 imn y e Nn

;

mn =

n R

Plug in the KK expansion into 5D action and integrate over y i hP R ∞ µ (n)∗ ∂µ φ(n) − mn2 φ(n)∗ φ(n) S = d 4x n=−∞ ∂ φ Is the equivalent 4D theory with an infinite tower of states (the KK states)

Extra Dimension


LHC Phenomenology

KK Decomposition

Equivalent 4D theory (with interactions) Similar procedure for interactions also S (4) ⊃

PR

(nml)

d 4 x mn2 φ(n) φ(n) + g4D

φ(n) →KK tower with mass mn

(nm)

;

Denote φ(1) ≡ φ0 ;

(for WED)

Some 4D couplings ψ ψ = λ5D dy f0 L f0 R f H Yukawas: λ(00) 4D R (001) ψ ψ = g5D dy f0 f0 f1A Gauge couplings: g4D

R

(n)

(m)

ψ (n) ψ (m) A(l) + λ4D ψL ψR

H

m1 ≡ mKK ∼TeV

Extra Dimension


LHC Phenomenology

KK Decomposition

Equivalent 4D theory (with interactions) Similar procedure for interactions also S (4) ⊃

PR

(nml)

d 4 x mn2 φ(n) φ(n) + g4D

φ(n) →KK tower with mass mn

(nm)

(n)

(m)

ψ (n) ψ (m) A(l) + λ4D ψL ψR

;

Denote φ(1) ≡ φ0 ;

H

m1 ≡ mKK ∼TeV

(for WED)

Some 4D couplings ψ ψ = λ5D dy f0 L f0 R f H Yukawas: λ(00) 4D R (001) ψ ψ = g5D dy f0 f0 f1A Gauge couplings: g4D

R

In summary 5D (compact) field ↔ “Infinite” tower of 4D fields Look for this tower at the LHC Example: b

2nd KK

W+

t

q′

1st KK

W+

SM

q¯

(1)

¯b

ν

ℓ+

Extra Dimension


LHC Phenomenology

UED

UED Spectrum All KK states degenerate at leading order Loop corrections split this

[Cheng, Matchev, Schmaltz]

LHC SUSY ↔ UED confusion!

[Cheng, Matchev, Schmaltz: 2002]

Extra Dimension


LHC Phenomenology

Warped Extra Dimensions

4-D KK couplings in WED

ξ≡ Compare to SM couplings: ξ enhanced: tR tR A0 , hhA0 , φφA0 1/ξ suppressed: SM strength:

ψlight ψlight A0++ tL tL A0

√

kπR ≈ 5

(Equivalence Theorem ⇒ Note:

φ ↔ AL )

ψlight ψlight A0−+ = 0

Extra Dimension


LHC Phenomenology


4-D KK couplings in WED

ξ≡ Compare to SM couplings: ξ enhanced: tR tR A0 , hhA0 , φφA0 1/ξ suppressed: SM strength: Effective coupling L

4D

ψlight ψlight A0++ tL tL A0

√

kπR ≈ 5

(Equivalence Theorem ⇒ Note:

φ ↔ AL )

ψlight ψlight A0−+ = 0

(Eg: Z 0 ):

h i ¯L,R γ µ eQIA1 µ + gZ T 3 − s 2 TQ IZ1 µ + g 0 T 3 − s 02 TY IZX µ ψL,R ⊃ψ 1 L W R Z

Extra Dimension


LHC Phenomenology


Challenge I : Precision EW Constraints in WED

W, Z, γ

¯ Precision Electroweak Constraints (S, T, Zbb)

Bulk gauge symm - SU(2)L × U(1) (SM ψ, H on TeV Brane) T parameter ∼ ( Mv )2 (kπR) KK S parameter also (kπR) enhanced

AdS bulk gauge symm SU(2)R

[Csaki, Erlich, Terning 02]

⇔ CFT Custodial Symm [Agashe, Delgado, May, Sundrum 03]

T parameter - Protected 1 for light bulk fermions S parameter - kπR ¯ Problem: Zb b shifted

3rd gen quarks (2,2)

[Agashe, Contino, DaRold, Pomarol 06]

¯ coupling - Protected Zb b Precision EW constraints ⇒ MKK & 2 − 3 TeV [Carena, Ponton, Santiago, Wagner 06,07] [Bouchart, Moreau-08] [Djouadi, Moreau, Richard 06]

Extra Dimension


LHC Phenomenology


WED Bulk Gauge Group

[Agashe, Delgado, May, Sundrum 03]

Bulk gauge group : SU(3)QCD ⊗ SU(2)L ⊗ SU(2)R ⊗ U(1)X 8 gluons 3 neutral EW (WL3 , WR3 , X ) 2 charged EW (WL± , WR± )

Extra Dimension


LHC Phenomenology


WED Bulk Gauge Group

[Agashe, Delgado, May, Sundrum 03]

Bulk gauge group : SU(3)QCD ⊗ SU(2)L ⊗ SU(2)R ⊗ U(1)X 8 gluons 3 neutral EW (WL3 , WR3 , X ) 2 charged EW (WL± , WR± )

Gauge Symmetry breaking: By Boundary Condition (BC):

A−+ (x, y ) BC: A|y =0 = 0 ; ∂y A |y =πR = 0

SU(2)R × U(1)X → U(1)Y By VEV of TeV brane Higgs SU(2)L × U(1)Y → U(1)EM

Higgs Σ = (2, 2)

Extra Dimension


LHC Phenomenology


Fermion representation : Zb b¯ not protected

[Agashe, Delgado, May, Sundrum ‘03]

Complete SU(2)R multiplet : Doublet tR (DT) model QL ≡ (2, 1)1/6 = (tL , bL ) ψtR ≡ (1, 2)1/6 = (tR , b 0 ) ψbR ≡ (1, 2)1/6 = (t 0 , bR ) “Project-out” b 0 , t 0 zero-modes by (−, +) B.C. New ψVL : b 0 , t 0

b ↔ b 0 mixing ¯ coupling shifted Zbb So LEP constraint quite severe

Extra Dimension


LHC Phenomenology


Fermion representation : Zb b¯ protected

QL = (2, 2)2/3 =

tL χ bL t 0

[Agashe, Contino, DaRold, Pomarol ‘06]

ZbL bL protected by custodial SU(2)L+R ⊗ PLR invariance WtL bL , ZtL tL not protected, so shifts

Extra Dimension


LHC Phenomenology


Fermion representation : Zb b¯ protected

QL = (2, 2)2/3 =

tL χ bL t 0

[Agashe, Contino, DaRold, Pomarol ‘06]

ZbL bL protected by custodial SU(2)L+R ⊗ PLR invariance WtL bL , ZtL tL not protected, so shifts Two tR possibilities: 1

Singlet tR (ST) :

2

Triplet tR (TT) :

(1, 1)2/3 = tR

0

(1, 3)2/3 ⊕ (3, 1)2/3 = ψtR ⊕

New ψVL : χ, t 0

 00   t  00 t R √ χ0  √2 χ  2   ψtR = ⊕ 00  t b 0 − √R t b 00 − √ 2 2 New ψVL : χ, t 0 , χ0 , 00

b 0 , χ00 , t 00 , b 00

Extra Dimension


LHC Phenomenology


Flavor structure

[Agashe, Perez, Soni, 04]

¯ i iΓµ Dµ Ψi + Mij Ψ ¯ i Ψj + yij5D H Ψ ¯ i Ψj + h.c. L⊃Ψ Basis choice: Mij diagonal ≡ Mi All flavor violation from yij5D KK decompose and go to mass basis ¯ i(n) Wµ(k) Ψj off-diagonal in flavor =⇒ g Ψ (m) (due to non-degenerate f i i.e. M i ) 5D fermion Ψ is vector-like Mij is independent of hHi = v But zero-mode made chiral (SM)

Extra Dimension


LHC Phenomenology


FCNC couplings µν h(0) ψ(0) ψ(0) : diagonal A(0) , g(0) ψ(0) ψ(0) : diagonal (unbroken gauge symmetry) Z(0) , Zx(0) ψ(0) ψ(0) : almost diagonal (non-diagonal due to EWSB effect) h ψ(0) ψ(0) : diagonal (only source of mass is hhi = v )

µν h(1) ψ(0) ψ(0) : off-diagonal A(1) , g(1) ψ(0) ψ(0) : off-diagonal Z(1) , Zx(1) ψ(0) ψ(0) : off-diagonal

(i=1,2 almost diagonal)

µν ψ(0) ψ(1) : 0 h(0) A(0) , g(0) ψ(0) ψ(1) : 0 (unbroken gauge symmetry) Z(0) , Zx(0) ψ(0) ψ(1) : off-diagonal (EWSB effect) h ψ(0) ψ(1) : off-diagonal (since Mψ is extra source of mass)

ψ(0) ↔ ψ(1) mixing due to EWSB

Extra Dimension



FCCC couplings

j ij ± i WL(0) ψ(0) ψ(0) : g VCKM

o n ± ± , WR(1) ψ(0) ψ(0) : g V100 [fW (1) fψ fψ ] WL(1)

[...] suppressed for i = 1, 2; (Not suppr for bL , tL , tR ) ± WL(0) ψ(0) ψ(1) : g V001 fW (1) fψ fψ(1)

LHC Phenomenology

Extra Dimension


LHC Phenomenology


Challenge II : Flavor Constraints in WED ¯ 0 mixing: K 0K Tree-level FCNC vertex g(1) d s ∝

VLd†

g(1) d d 0 VLd 0 g(1) s s

b → sγ : No tree-level contribution to helicity flip dipole operator So 1-loop with g(1) b s(1) OR φ± b s(1) b → s `+ `− ,

b → s s ¯s ,

K → πν ν¯ :

Tree level FCNC vertex Z s d

Bound : mKK & few TeV

[Agashe et al][Buras et al][Neubert et al][Csaki et al]

Relaxed with flavor alignment : MFV, NMFV, flavor symmetries, ... [Fitzpatrick et al][Agashe et al]

[SG, A.Iyer, S.Vempati Ongoing]

Extra Dimension


LHC Phenomenology

LHC Phenomenology

Extra Dimension


LHC Phenomenology

LHC Signatures

LED KK Graviton @ LHC

[Giudice, Rattazzi, Wells 1998][Hewett 1998] [Han, Lykken, Zhang 1998] (n)

Look for KK Gravitons (hµν ) : Missing energy (MET) Small KK spacing : sum over huge number of states Cutoff dependence

Final state Gravitons : pp → γ h(n) , j h(n) Virtual Gravitons : pp → h(n) → `+ `− , · · ·

Extra Dimension


LHC Signatures

(n)

LED LHC Limit pp → hµν → `+ `−

ATLAS : 1211.1150 : 7TeV, 5 fb−1

LHC Phenomenology

Extra Dimension


LHC Phenomenology

LHC Signatures

WED KK Graviton mn = xn ke =kπr xn = 3.83, 7.02, ... ffG (n) ¯ P e =kπr L ⊃ − CΛ T αβ hαβ Λ = M

[Agashe et al, 07] [Fitzpatrick et al, 07]

SM on IR brane CDF & D0 bounds : m1 > 300 − 900 GeV for ATLAS & CMS reach : 3.5 TeV with 100fb-1

SM in Bulk (flavor)

k Mp

=0.01-0.1

gg → h(1) → ZZ → 4` LSM ->ZZDHfbL Σ@HggLRS ,Hqq 100

Η 1.6 TeV @ 95% CL

Extra Dimension


LHC Phenomenology

LHC Signatures

WED KK Fermions @ LHC

SM fermions : (+, +) BC → zero-mode “Exotic” fermions : (−, +) BC → No zero-mode

1st KK vectorlike fermion 2.00 1.50

[Choi, Kim, 2002] [Agashe, Delgado, May, Sundrum, 03] [Agashe, Perez, Soni, 04] [Agashe, Servant 04]

Look for it at the LHC

MΨ

c : Fermion bulk mass parameter

M KK

Typical ctR , ctL : (−, +) top-partners “light”

1.00 0.70 0.50 0.30 0.20 0.15 0.10 - 0.4 - 0.2 0.0

0.2

0.4

0.6

c [Dennis et al, ‘07] [Carena et al, ‘07] [Contino, Servant, ‘08] [Atre et al, ‘09, ‘11] [Aguilar-Saavedra, ‘09] [Mrazek, Wulzer, ‘09] [SG, Moreau, Singh, ‘10] [SG, Mandal, Mitra, Tibrewala, ‘11] [SG, Mandal, Mitra, Moreau : ’13]

0.8

1.0

Extra Dimension


LHC Signatures

CMS Resonances Limits (Moriond 2013)

LHC Phenomenology

Extra Dimension


LHC Signatures

ATLAS Extra Dimensions Limits (Moriond 2013)

LHC Phenomenology

Dark Matter

Dark Matter Candidates from BSM

Dark Matter

Observations tell us

Dark Matter


Flat on large scales Expansion is Accelerating 95% is unknown dark matter + dark energy What is it??

Dark Matter


Flat on large scales Expansion is Accelerating 95% is unknown dark matter + dark energy What is it??

The DARK SIDE rules!

Dark Matter

What is the dark sector?

Dark Matter Astrophysical objects? (Disfavoured) MAssive Compact Halo Objects (MACHO) or Black Holes or . . .

Particle dark matter? More on this... Hot or Warm or Cold Dark Matter (CDM)

Dark Matter

What is the dark sector?

Dark Matter Astrophysical objects? (Disfavoured) MAssive Compact Halo Objects (MACHO) or Black Holes or . . .

Particle dark matter? More on this... Hot or Warm or Cold Dark Matter (CDM)

Dark energy

Dark Matter Particle DM Candidates

Particle DM Requirements

Should be around for a long long long time ... Absolutely stable : Conserved quantum number e, p are stable, but not “dark”! So not possible Active νL , disfavored. Sterile νR , possible BSM particle with Z2 symmetry

Decays, but with very very very long life-time Very very very tiny coupling to other SM states


Particle Dark Matter

Thermal Relic In thermal equilibrium in early universe Details of its origin do NOT matter So most studied

Nonthermal Relic Never in thermal equilibrium Details of its origin do matter


Particle DM Possibilities

LSP - Lightest Supersymmetric Particle χ ˜01 Neutralino (SUSY partner of neutral gauge boson) ν˜ Sneutrino (SUSY partner of neutrino) SuperWIMP - Gravitino (SUSY partner of graviton) E-WIMP - Right-handed sneutrino (partner of neutrino) WIMPzilla - Extremely massive particle LKP - Lightest Kaluza-Klein Particle - Extra space dimensions LTP - Lightest T-odd Particle - Little-higgs theory with Z2 Hidden sector DM


Particle DM Possibilities

LSP - Lightest Supersymmetric Particle χ ˜01 Neutralino (SUSY partner of neutral gauge boson) ν˜ Sneutrino (SUSY partner of neutrino) SuperWIMP - Gravitino (SUSY partner of graviton) E-WIMP - Right-handed sneutrino (partner of neutrino) WIMPzilla - Extremely massive particle LKP - Lightest Kaluza-Klein Particle - Extra space dimensions LTP - Lightest T-odd Particle - Little-higgs theory with Z2 Hidden sector DM

Your candidate here

Dark Matter Computing the Relic Density

Thermal Relic

Thermal history of the Universe Big Bang → Inflation → DM freeze-out→ BBN →γ decouples → Today

Hubble rate: H≡

a˙ ; a

H2 =

8πG ρ 3

√ T2 H = 1.66 g∗ MPl

(Rad Dom)

Dark Matter Computing the Relic Density

Boltzmann Equation d 2 n = −3Hn − hσv iSI n2 − neq − hσv iCI nnφ − neq nφ eq + CΓ dt Thermal equilibrium if hσv iSI nν˜0 > 3H ;

hσv iCI nφ > 3H

Freeze-out 0.01 0.001 0.0001

1

10

100

1000

[Kolb & Turner, Early Universe]

Dark Matter Some BSM DM Candidates

Weakly Interacting Massive Particle (WIMP)

WIMP Cold dark matter - New BSM particle Mass: M ∼ 100 GeV

n M

Ω0 ≡ ρ0 c

≈ 4 × 10−10

GeV−2 hσv i

Interaction strength: g ∼ gEW Example: SUSY WIMP: If conserved Rp , Lightest Supersymmetric Particle (LSP) stable LSP (Eg: Neutralino) can be WIMP DM


Weakly Interacting Massive Particle (WIMP)

WIMP Cold dark matter - New BSM particle Mass: M ∼ 100 GeV

n M

Ω0 ≡ ρ0 c

≈ 4 × 10−10

GeV−2 hσv i

Interaction strength: g ∼ gEW Example: SUSY WIMP: If conserved Rp , Lightest Supersymmetric Particle (LSP) stable LSP (Eg: Neutralino) can be WIMP DM Precisely the scale being explored at colliders! DM at present colliders? (LHC connection)


Hidden sector DM Extend the SM to: SM × U(1)X U(1)X sector : GaugeBoson(Xµ ), Scalar (ΦH ), Fermion(ψ) If stable, can be DM

SM ↔ U(1)X communication

L ⊃ −α |ΦSM |2 |ΦH |2 + Bµ

η 2

Xµν B µν

Xµ

ψ

SM φSM

φH


Hidden Sector Relic Density

Self-annihilation

Supernova Cosmology Project

3 Knop et al. (2003) Spergel et al. (2003) Allen et al. (2002)

No Big Bang

ψ

ψ φH

φSM

φH

SM

Supernovae

1

ψ

φH ψ

CMB

φSM

expands forever lly recollapses eventua

0

clo

se

-1

d

en

op

eV −2 hσv i 4 + O(vrel ) xf ≡ Mψ /Tf

Clusters

t

2 a + b vrel a + b/xf

ΩΛ

fla

Ω0 h2 = 10−29 xf σvrel = hσv i =

2

φSM

≈ 25

0

1

2

3

ΩM

Observations : Ω0 = 0.222 ± 0.02 [PDG ’08] Channels ψψ → b b¯, W + W − , ZZ , hh , t ¯t

Dark Matter DM Detection

Dark Matter Detection

Direct Detection DM directly intereacts with a detector Indirect Detection Look for indirect emmissions from DM Collider Detection DM escapes as missing momentum at colliders


Direct Detection of Hidden sector ΣDirDet 1044 cm2 10.0 5.0 ψ

ψ

2.0

φH

1.0 0.5

φSM

0.2 N

N

0.1 150

200

250

300

350

Mψ = 125 GeV , κ11 = 1.5, sh = 0.25 ¯ coupling ≈ 2 × 10−3 Effective hNN

[Shifman, Vainshtein, Zakharov (1973)]

ψ- Nucleon c.s. : σ (ψN → ψN) ≈

2 ) κ211 sh2 ch2 λ2N (|pψ |2 + mN

8πvrel

(t − mh2 )2

mh


ψ Relic Density + Direct Detection

3.0 0.7

0.1

2.5

0.6 2.0

0.5

1.5

sh

Κ11

0.2 WDM =0.3

0.4

0.1

0.3

0.2

1.0 0.2 0.5 100

200

300 400 500 MΨ HGeVL

600

700

WDM =0.3

0.1 50

100

150

200 250 mh HGeVL

300

350

[SG, S.Lee, J.Wells 2009] Mψ = 250GeV , mh = 120GeV , κ11 = 2.0, sh = 0.25, κ3φ = 1, mH = 1TeV Shaded: σDir & 10−43 cm2 (dark); & 10−44 cm2 (medium); & 10−45 cm2 (light)


Direct Detection Experimental Limits (Old)


Direct Detection Experimental Limits http://dmtools.brown.edu/ Gaitskell,Mandic,Filippini

Cross−section [cm2] (normalised to nucleon)

−38

10

−40

10

−42

10

−44

10

DATA listed top to bottom on plot

−46

10

CoGeNT, 2013, WIMP region of interest, SI

−48

DAMA, 2000, NaI−0 to 4 combined, 58,000kg−days, 3sigma

10

CDMSII−Si (Silicon), c58 95% CL , SI (2013)

CRESST II commissioning run (2009) extended to low mass

10

−50

XENON100, 2012, 225 live days (7650 kg−days), SI 131206083800

1

10

2

10 WIMP Mass [GeV/c2]

DAMA vs. XENON/LUX puzzle What’s going on?

10

3

LUX (2013) 85d 118kg (SI, 95% CL)

LUX (2014/15) 300d projection (SI, 90% CL median expecte Xenon10T, G3 expected sensitivity (2013)


DM at Colliders II

Example: Supersymmetry t˜R , ˜bR , g˜

`+

`+ (YN ) ˜u H

(YN ) ˜u H

˜d H

˜R N t˜R

(Yt )

˜bR bL

LSP leads to “missing momentum”

X

˜R N

(Yb)

tL


Higgs decay to DM Higgs decay and BR If mh > 2Mψ : h → ψψ

Invisible Decay!

¯ , WW , ZZ , t ¯t Decay channels: h → ψ ψ¯ , b b

1.0

ΨΨ

ΨΨ WW

0.6 0.4 0.2 0.0 100

0.1 BR

BR

0.8

ZZ

ΤΤ

0.01

gg

0.001

ΓΓ

tt

bb

10-4

200

300 mh HGeVL

400

Mψ ≈ 59GeV , sh = NB: Relic density not enforced

500

100

200

300 mh HGeVL

0.25, κ11 = 2.0, κ3φ = 1.0, mH = 1TeV

400

500

Dark Matter Neutrino mass

Neutrino Mass Generation Questions What is the scale of mν Is the ν a DIRAC or MAJORANA particle? (Is L# good?) Which mass spectrum? m1,2,3

m2 m1

m3 m2

m3

m1 NORMAL

INVERTED

DEGENERATE

Is there CP violation in the lepton sector?

Dark Matter Neutrino mass

Neutrino Mass Generation Questions What is the scale of mν Is the ν a DIRAC or MAJORANA particle? (Is L# good?) Which mass spectrum? m1,2,3

m2 m1

m3 m2

m3

m1 NORMAL

INVERTED

DEGENERATE

Is there CP violation in the lepton sector?

Possible Answers Dirac ν : Add νR with TINY (10−12 ) Yukawa coupling Type I seesaw: Add νR and a BIG (1011 GeV) mass Type II seesaw: Add SU(2) triplet scalar ξ with TINY (0.1 eV) VEV Type III seesaw: Add SU(2) triplet fermion Ξ Extra dimensions: Add BULK νR with BRANE coupling to νL

Dark Matter Conclusions

Conclusions

Standard Model has shortcomings Theoretical: Gauge (& flavor) hierarchy problem Observational: DM, BAU

Beyond the Standard Model physics can resolve these Supersymmetry, Extra dimension(s), Strong dynamics, Little Higgs, ...

Are any of these ideas realized in Nature? Desperately seeking experimental guidance Experiments poised for discovery? LHC7,8 constraints already nontrivial. LHC14 high luminosity run crucial DM Direct, Indirect detection Flavor and precision probes

BACKUP SLIDES

BACKUP SLIDES

Yukawa Couplings

Yukawa Couplings ¯ protection No Zbb DT

¯ L Σψt + λb Q ¯ L Σψb + h.c. LYuk ⊃ λt Q R R

¯ protection With Zbb ST LYuk ⊃ λt Trh Q¯ L Σ tR i+ h.c. h 00 i 0 0 TT LYuk ⊃ λt Tr Q¯ L ΣψtR + λt Tr Q¯ L ΣψtR + h.c. b Yukawa requires triplet bR  

t

0

 00

χ0b   √b  2   (1, 3)2/3 ⊕ (3, 1)2/3 = ψb ⊕ ψb =  0 ⊕  R R tb bR − √ 2 h h 0 i 0 00 i ¯ L Σψ ¯ L Σψ LYuk ⊃ λb Tr Q + λb Tr Q + h.c. b b 0

00

R

R

cb

R

0

00



tb √ 2

χ00 b   00  tb 00 bb − √ 2

such that new ψb , ψb & 3 TeV, so ignore them

WED pp → g (1) → t ¯t (semi-leptonic)

!!!Warning!!! Very rough estimates! √ S = 14TeV , kπR = 35) ≈ 600 fb √ = 2TeV , S = 14TeV , kπR = 35) = 1.2 fb −1

σ(Mg (1) = 2TeV , L5σ (Mg (1)

σ(g (1) = 2TeV ) falls by a factor of 25 √ = 2TeV , S = 7TeV , kπR = 35) = 30 fb −1

14 TeV → 7TeV : L5σ (Mg (1)

(Assumed : Bkgnd falls with same factor) 5σ

L (Mg (1) = 2TeV ,

√ S = 7TeV , kπR = 7) = 1 fb −1

Bulk EW Gauge Sector Bulk EW Gauge group : SU(2)L × SU(2)R × U(1)X Three neutral gauge bosons: (WL3 , WR3 , X ) Two charged gauge bosons: (WL± , WR± )

Symmetry Breaking: By Boundary Condition (BC): ZX (−, +) means ZX |y =0 = 0 ; ∂y ZX |y =πR = 0

SU(2)R × U(1)X → U(1)Y : (WL3 , WR3 , X ) → (WL3 , B, ZX ) A → (+, +) ; Z → (+, +) ; ZX → (−, +) ZX ≡ √ 21 2 (gR WR3 − gX X ) → (−, +) ; WR± → (−, +) gx +gR

B≡√

1 gx2 +gR2

(gX WR3 + gR X ) → (+, +) ; WL± → (+, +)

Bulk EW Gauge Sector Bulk EW Gauge group : SU(2)L × SU(2)R × U(1)X Three neutral gauge bosons: (WL3 , WR3 , X ) Two charged gauge bosons: (WL± , WR± )

Symmetry Breaking: By Boundary Condition (BC): ZX (−, +) means ZX |y =0 = 0 ; ∂y ZX |y =πR = 0

SU(2)R × U(1)X → U(1)Y : (WL3 , WR3 , X ) → (WL3 , B, ZX ) A → (+, +) ; Z → (+, +) ; ZX → (−, +) ZX ≡ √ 21 2 (gR WR3 − gX X ) → (−, +) ; WR± → (−, +) gx +gR

B≡√

1 gx2 +gR2

(gX WR3 + gR X ) → (+, +) ; WL± → (+, +)

By VEV of TeV brane Higgs SU(2)L × U(1)Y → U(1)EM :

(WL3 , B, ZX ) → (A, Z , ZX )

Gauge EW KK States

Gauge Boson “Zero” modes: A(0) , Z (0) ; WL(0) (1)

First KK modes: A(1) , Z (1) , ZX

EWSB mixes :

→ Z 0 ; WL(1) , WR(1) (1)

(1)

Z (0) ↔ Z (1) ; Z (0) ↔ ZX ; Z (1) ↔ ZX (1) (0) (1) (1) (1) ↔ WL ; WL ↔ WR ; WL ↔ WR

(0) WL

Mass eigenstates : “Zero” modes: A, Z ; W ± First KK modes: A1 , Z˜1 , Z˜X1

→ Z0

;

˜ L ,W ˜R W 1 1

→ W 0±

Z 0 Overlap Integrals Define: ξ ≡

√

kπR = 5.83

Z 0 overlap with Higgs → ξ Z 0 overlap with fermions: I+ I−

QL3 − 1.13 ξ + 0.2ξ ≈ 1 0.2ξ ≈ 1.2

tR + 0.7ξ ≈ 3.9 0.7ξ ≈ 4.1

− 1.13 ξ

other fermions − 1.13 ξ ≈ −0.2 0

Compared to SM Z 0 couplings to h enhanced (also VL - Equivalence Theorem!) Z 0 couplings to tR enhanced Z 0 couplings to χ suppressed

h 2 ψ¯L,R γ µ eQIA1 µ + gZ TL3 − sW TQ IZ1 µ + i gZ 0 TR3 − s 02 TY IZX 1 µ ψL,R

EWSB induced Z 0 W + W − coupling Z (1) V (0) V (0) is zero by orthogonality ... ... but induced after EWSB φ+

Using Goldstone equivalence: Z0 φ−

In Unitary Gauge: W+

W+

W+

W Z0

= W−

Z (1)

Z

Z (1) W−

Even though ξ · ( MvKK )2 suppressed ...

W+

(1) +

Z (1) W−

W (1)

−

W−

Z 0 decays [Agashe, Davoudiasl, SG, Han, Huang, Perez, Si, Soni - arXiv:0709.0007 [hep-ph]]

W+ Z0

W−

t, b, `−

Z Z0

e 2 κ2 MZ 0 5 Γ(A1 → WL WL ) = ; 4 192π mW g 2 c 2 κ2 MZ 0 5 ; Γ(Z˜1 , Z˜X 1 → WL WL ) = L W 4 192π mW

t¯, ¯b, `+

Z0

h

p κ ∝ kπrc κ∝

p

mW MW ± 1

kπrc

p g 2 κ2 Γ(Z˜1 , Z˜X 1 → ZL h) = Z MZ 0 ; κ ∝ kπrc , 192π (e 2 , gZ2 ) 2 0 Γ(Z → f f¯) = κV + κ2A MZ 0 . 12π

!2 ,

mZ (MZ1 , MZX 1 )

2 ,

Widths & BR’s (For MZ 0 = 2TeV)

Z˜1

A1 ¯t t ¯ bb u¯u ¯ dd + − ` ` WL+ WL− ZL h Total

Γ(GeV) 55.8 0.9 0.28 0.07 0.21 45.5 103.3

BR 0.54 8.7 × 10−3 2.7 × 10−3 6.7 × 10−4 2 × 10−3 0.44 -

Γ(GeV) 18.3 0.12 0.2 0.25 0.06 0.88 94 114.6

BR 0.16 10−3 1.7 × 10−3 2.2 × 10−3 5 × 10−4 7.7 × 10−3 0.82

Z˜X 1 Γ(GeV) 55.6 28.5 0.05 0.07 0.02 50.2 2.7 135.6

BR 0.41 0.21 4 × 10−4 5.2 × 10−4 1.2 × 10−4 0.37 0.02

Total Widths

MZ 0 = 2TeV

A1

Z1

ZX 1

Γ (GeV)

103.3

114.6

135.6

pp → Z 0 → W + W − → ` ν j j Meff ≡ pTjj + pT` + p/T

q 2 MTWW ≡ 2 pT2 jj + mW

MWW and MTWW

Diff c.s. [fb/GeV]

0.1 2TeV Z’ MTWW 2TeV Z’ MWW SM MWW 0.01

0.001

1e-04 1000

1500

2000 2500 3000 MWW, MTWW (GeV)

3500

4000

pp → Z 0 → W + W − → ` ν j j

(Boosted W → (jj))

jj opening angle

10

Jet-mass

0.025 2TeV Z’

9 8

Z’ no Smr SM no Smr Z’ w/ Smr SM w/ Smr

0.02

7 6

0.015

5 4

0.01

3 2

0.005

1 0

0 0

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 ∆θjj

0

50

100 Mjet (GeV)

150

200

j j Collimation implies forming mW nontrivial : use jet-mass In our study: Jet-mass after Parton shower in Pythia [Thanks to Frank Paige for discussions]

To account for (HCal) expt.√uncert. Smearing by δE = 80%/ E

; δη, δφ = 0.05

Tracker + ECal (2 cores?) have better resolutions

[F. Paige; M. Strassler]

pp → Z 0 → W + W − → ` ν ` ν 2 ν’s ⇒ cannot reconstruct event Di-lepton invariant mass 2TeV Z’ 3TeV Z’ SM WW SM τ τ

1e-04 1e-05 1e-06 1e-07 1e-08

Transverse mass 0.001

Diff c. s. [pb/GeV]

Diff c. s. [pb/GeV]

0.001

1e-09

2TeV Z’ 3TeV Z’ SM WW SM τ τ

1e-04 1e-05 1e-06 1e-07 1e-08 1e-09

0

500

1000 1500 2000 2500 3000 Mll

Meff ≡ pT`1 + pT`2 + p/T

0

1000

MTWW ≡ 2

2000 3000 MT

q 2 pT2 `` + M``

L needed: 100 fb−1 (2 TeV) ; 1000 fb−1 (3 TeV)

4000

5000

pp → Z 0 → W + W − → ` ν ` ν Cross-section (in fb) after cuts: 2 TeV Signal WW ττ

Basic cuts 0.48 82 7.7

|η` | < 2 0.44 52 5.6

Meff > 1 TeV 0.31 0.4 0.045

MT >1.75 TeV 0.26 0.26 0.026

# Evts 26 26 2.6

S/B 0.9

√ S/ B 4.9

3 TeV Signal WW ττ

Basic cuts 0.05 82 7.7

|η` | < 2 0.05 52 5.6

1.5 < Meff < 2.75 0.03 0.08 0.015

2.5 < MT < 5 0.025 0.04 0.003

# Evts 25 40 3

S/B

√ S/ B

0.6

3.8

# events above is for 2 TeV : 100 fb−1 3 TeV : 1000 fb−1

pp → Z 0 → W + W − → ` ν j j Cross-section (in fb) after cuts: MZ 0 = 2 TeV Signal W+1j WW MZ 0 = 3 TeV Signal W+1j WW

pT 4.5 1.5 × 105 1.2 × 103

η`,j 2.40 3.1 × 104 226

Meff 2.37 223.6 2.9

MTWW 1.6 10.5 0.13

Mjet 1.25 3.15 0.1

# Evts 125 315 10

S/B 0.39

√ S/ B 6.9

0.37 1.5 × 105 1.2 × 103

0.24 3.1 × 104 226

0.24 88.5 1.3

0.12 0.68 0.01

-

120 680 10

0.17

4.6


pp → Z 0 → Z h → `+ `− b b¯ (mh = 120 GeV) Z pT

Z h invariant mass 0.001

0.01 2TeV Z’ 3TeV Z’ SM Z b SM Z b B

2TeV Z’ 3TeV Z’ SM Z b SM Z b B

0.001 Diff c.s. [pb/GeV]

Diff c.s. [pb/GeV]

1e-04 1e-05 1e-06 1e-07

1e-04 1e-05 1e-06 1e-07 1e-08 1e-09

1e-08 1000

1e-10 1500

2000

2500 3000 MZh (GeV)

3500

4000

500

How well can we tag high pT b’s ?

For b = 0.4, expect Rj ≈20 – 50; Rc = 5

Two b’s close : ∆Rbb ∼ 0.16

L needed: 200 fb−1 (2 TeV) ; 1000 fb−1 (3 TeV)

1000 1500 pTZ (GeV)

2000

2500

pp → Z 0 → Z h → `+ `− b b¯ (mh = 120 GeV) Cross-section (in fb) after cuts: MZ 0 = 2 TeV ¯ `` Z 0 → hZ → b b SM Z + b ¯ SM Z + b b SM Z + ql SM Z + g SM Z + c MZ 0 = 3 TeV ¯ `` Z 0 → hZ → b b SM Z + b ¯ SM Z + b b SM Z + ql SM Z + g SM Z + c

Basic

pT , η

cos θZh

Minv

b-tag

# Evts

S/B

√ S/ B

0.81 157 13.5 2720 505.4 184

0.73 1.6 0.15 48 11.2 1.9

0.43 0.9 0.05 22.4 5.8 1.1

0.34 0.04 0.01 1.5 0.5 0.05

0.14 0.016 0.004 0.08 0.025 0.01

27 3 0.8 15 5 2

1.1

5.3

0.81 157 13.5 2720 505.4 183.5

0.12 0.002 0.018 1.1 0.3 0.03

0.05 0.001 0.014 0.7 0.2 0.02

0.04 3 × 10−4 0.002 0.1 0.03 0.002

0.016 1.2 × 10−4 0.001 0.005 0.0015 4 × 10−4

16 0.12 1 5 1.5 0.4

2

5.7


pp → Z 0 → Z h : (mh = 150 GeV)

Z → j j ; h → W +W − → j j ` ν

Minv and MT

MTZh ≡

1e-04 2TeV Z’ Minv 2TeV Z’ MT 3TeV Z’ Minv 3TeV Z’ MT

Diff c.s. [pb/GeV]

1e-05 1e-06

q

pT2 Z + mZ2 +

q

pT2 h + mh2

1e-07 1e-08 1e-09 1e-10 1000

1500

2000 2500 3000 Minv , MT (GeV)

MZ 0 = 2 TeV

3500

mh = 150 GeV

0

Z → hZ → ` E /T (jj) (jj) SM W j j SM W Z j SM W W j MZ 0 = 3 TeV

4000

Basic

pT , η

cos θ

MT

Mjet

# Evts

S/B

√ S/ B

2.4 3 × 104 184 712

1.6 35.5 0.45 0.54

0.88 12.7 0.15 0.2

0.7 0.62 0.02 0.02

0.54 0.19 0.02 0.01

54 19 2 1

2.5

11.5

0.26 3 × 104

0.2

0.14 4.1

0.06 0.05

− −

18 15

1.2

4.7

mh = 150 GeV

Z 0 → hZ → ` E /T (jj) (jj) SM W j j # events above is for 2 TeV : 100 fb−1 3 TeV : 300 fb−1

pp → Z 0 → `+ `−

MZ 0 = 2 TeV

Basic

pT `

M``

# Evts

S/B

√ S/ B

Signal SM `` SM WW

0.1 3 × 104 295

0.09 5.4 0.03

0.06 0.2 0.002

60 200 2

0.3

4.2

# events above is for 2 TeV : 1000 fb−1

Experimentally clean, but needs a LOT of luminosity

pp → Z 0 → t ¯t Top pT

t t invariant mass

10

1 2TeV Z’ 3TeV Z’ SM tt

1

2TeV Z’ 3TeV Z’ SM tt

0.1 Diff c.s. [pb/GeV]

Diff c.s. [pb/GeV]

0.1 0.01 0.001 1e-04 1e-05

0.01 0.001 1e-04 1e-05

1e-06 1e-06

1e-07 1e-08 500

1000 1500 pTt (GeV)

2000

1e-07 1000 1500 2000 2500 3000 3500 4000 4500 5000 Mtt (GeV)

2500

MZ 0 = 2 TeV

Basic

pT > 800

1900 < Mtt < 2100

Signal SM t ¯t

17 1.9 × 105

7.2 31.1

5.6 19.1

MZ 0 = 3 TeV

Basic

pT > 1250

2850 < Mtt < 310

Signal SM t ¯t

1.7 1.9 × 105

0.56 4.1

0.45 1.1

W 0 ± width

+ W’ → X X

1100 1000 900

Width [GeV]

800

~ WL + (i) ~ 1 WR + (i) ~ 1 WL + (ii) ~ 1 WR + (ii) 1

700 600 500 400 300 200 100 1000

1500

2000

2500 M

3000 3500 [GeV]

4000

4500

5000

W 0 ± BR

~ BR(WL

+

1

~ BR(WR

→ X X)

νe e

→ X X)

TL b χL tL + ZW tL b W+ h ud

+

+

νe e

1

1

0.1

0.1

0.01

0.01

0.001

0.001

0.0001 1000 1500 2000 2500 3000 3500 4000 4500 5000 MW’ [GeV]

+

1

tL b + W h TL b χL tL Z W+ ud

0.0001 1000 1500 2000 2500 3000 3500 4000 4500 5000 MW’ [GeV]

W 0 ± → t b → `νb b Signal c.s. ∼ 1fb Bkgnd is single top + QCD W b b .... AND ... t ¯t : hadronically decaying top can fake a b b-jet Event Jet Cluster (diff)

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0-1

t-jet Event Jet Cluster (diff) b Evt 2

pTi/pTtot

t Evt 4

pTi/pTtot

0

-0.5 dEta

0

0.5

-0.5

1 0.5 dPhi

0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0-1

dEta

1 -1

b-jet Event Jet Cluster (diff)

0

0.5

-0.5

t-jet Event Jet Cluster (diff) t Evt 3

pTi/pTtot

0

-0.5 dEta

0

0.5

-0.5 1 -1

1 0.5 dPhi

1 -1

b Evt 4

pTi/pTtot 0.3 0.25 0.2 0.15 0.1 0.05 0-1

0

-0.5

1 0.5 dPhi

0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0-1

0

-0.5 dEta

0

0.5

-0.5 1 -1

1 0.5 dPhi

W 0 ± → t b → `νb b Jet Mass : ConSiz=0.4, VetoFrac=0.25

Jet Mass : ConSiz=1.0, VetoFrac=0.2 : 2 TeV

0.014

0.018 b-jet t-jet

0.012

b-jet t-jet

0.016 0.014

0.01

0.012

0.008

0.01

0.006

0.008 0.006

0.004

0.004 0.002

0.002

0

0 0

50

100 150 Jet Mass (GeV)

200

250

0

50

100 150 Jet Mass (GeV)

200

Jet-mass cut: cone size 1.0 and 0 < jM < 75 ⇒0.4% of top fakes b L needed: 100 fb−1 (2 TeV)

250

W 0 ± → Z W and W h W 0± → Z W :

Fully leptonic → L : 100 fb−1 (2 TeV) ; 1000 fb−1 (3 TeV) Semi leptonic →L : 300 fb−1 (2 TeV) (SM W /Z + 1j large)

W 0 ± → Z W and W h W 0± → Z W :

Fully leptonic → L : 100 fb−1 (2 TeV) ; 1000 fb−1 (3 TeV) Semi leptonic →L : 300 fb−1 (2 TeV) (SM W /Z + 1j large)

W 0 ± → W h:

mh ≈ 120 : h → b b

What is b-tagging eff?

mh ≈ 150 : h → W W

Use W jet-mass to reject light jet

L needed: 100 fb−1 (2TeV) ;

300 fb−1 (3TeV)

Warped States

Warped (RS) model Heavy EW gauge bosons : 3 neutral (Z 0 ) & 2 charged (W 0 ± ) Precision electroweak observables require MZ 0 , MW ± &2 TeV 1

Makes discovery challenging at the LHC