slac summer institute 2009

New Physics Scenarios

Jay WackerSLAC

SLAC Summer InstituteAugust 5&6, 2009

Any minute now!When’s the revolution?

An unprecedented moment

What is a “New Physics Scenario”?

“New Physics”:

A structural change to the Standard Model Lagrangian

“Scenario”:

“A sequence of events especially when imagined”

Why New Physics?Four Paradigms


Experiment doesn’t match theoretical predictionsBest motivation



Parameters are “Unnatural”Well defined and have good theoretical motivation




Reduce/Explain the multitude of parametersTypically has limited success, frequently untestable




Reduce/Explain the multitude of parametersTypically has limited success, frequently untestable

To know what is possibleLet’s us know what we can look for in experiments

Limited only by creativity and taste

The PlanBeyond the SM Physics is 30+ years old

There is no one leading candidate for new physics

New physics models draw upon all corners of the SM

In 2 hours there will be a sketch some principlesused in a half dozen paradigmsthat created hundreds of models

and spawned thousands of papers

Outline

The Standard Model

Motivation for Physics Beyond the SM

Organizing Principles for New Physics

New Physics ScenariosSupersymmetry

Extra DimensionsStrong Dynamics

Standard Model: a story of economysymmetry unification!

15 Particles, 12 Force carriers! 2700 !V !! Couplings

Standard Model: a story of economy

!eL eL eR uL uR dRdLuLuL uRuR dL dL dR dR

symmetry unification!15 Particles, 12 Force carriers! 2700 !V !! Couplings



! e q u d

5 Particles 3 Couplings

symmetry unification!15 Particles, 12 Force carriers! 2700 !V !! Couplings



! e q u d

5 Particles 3 Couplings

symmetry unification!

4 forces, 20 particles, 20 parameters

x 3

Mystery of Generations:

15 Particles, 12 Force carriers! 2700 !V !! Couplings

The Standard Model... where we stand today

LSM = LGauge + LFermion + LHiggs + LYukawa



LGauge = !14Bµ!

2 ! 14W a

µ!2 ! 1

4GA

µ!2



LGauge = !14Bµ!

2 ! 14W a

µ!2 ! 1

4GA

µ!2

LFermion = QiiD! Qi + U ci iD! U c

i + Dci iD! Dc

i + LiiD! Li + Eci iD! Ec

i



LGauge = !14Bµ!

2 ! 14W a

µ!2 ! 1

4GA

µ!2


i + Dci iD! Dc


i

LHiggs = |DµH|2 ! !(|H|2 ! v2/2)2



LGauge = !14Bµ!

2 ! 14W a

µ!2 ! 1

4GA

µ!2


i + Dci iD! Dc


i

LHiggs = |DµH|2 ! !(|H|2 ! v2/2)2

LYuk = yiju QiU

cj H + yij

d QiDcjH

! + yije LiE

cjH

!

Q

U c

Dc

Ec

L

3

331

1

11

1

2

2

+16

!23

+13

!12

+1

Field Color Weak Hypercharge

Standard Model Charges

Motivations for Physics Beyond the Standard Model

The Hierarchy Problem

Dark Matter

Exploration

The Hierarchy ProblemThe SM suffers from a stability crisis

!µ2

!3y2t !2

t

16!2

+34g2!2

W

16!2

+14g!2!2

B

16!2

+!!2

H

16"2

Higgs vev determined by effective mass, not bare massMany contributions that must add up to -(100 GeV)2

=

A recasting of the problem:

Why is gravity so weak?GN

GF= 10!32

Explain how to make GF large (i.e. v small)

Explain why GN is so small (i.e. MPl large)

1998: Large Extra Dimensions (Arkani-Hamed, Dimopoulos, Dvali)

High scale is a “mirage”Gravity is strong at the weak scale

Need to explain how gravity is weakened

MPlanckMWeak

!

2001: Universal Extra Dimensions (Appelquist, Cheng, Dobrescu)

1978: Technicolor(Weinberg, Susskind)

1999: Warped Gravity(Randall, Sundrum)

2001: Little Higgs(Arkani-Hamed, Cohen, Georgi)

The Higgs is composite

h

Resolve substructure at small distances

!M2Composite

Why hadrons are lighter than Planck Scale

A New Symmetryµ2 = 0 not specialUV dynamics at

A New Symmetry

Scalar

Fermion

!

! Supersymmetry

!! "#Scalar Mass related to Fermion Mass

µ2 = 0 not specialUV dynamics at

A New Symmetry

Scalar

Fermion

!

! Supersymmetry


!

Scalar

Scalar

!Shift Symmetry

!! ! + "Scalar Mass forbidden


A New Symmetry

Scalar

Fermion

!

! Supersymmetry


!

Scalar

Scalar

!Shift Symmetry

!! ! + "Scalar Mass forbidden

1981: Supersymmetric Standard Model(Dimopoulos, Georgi)

2001: Little Higgs(Arkani-Hamed, Cohen, Georgi)

1974: Higgs as Goldstone Boson(Georgi, Pais)


Dark Matter85% of the mass of the Universe is not described by the SM

There must be physics beyond the Standard Model

Cold dark matterElectrically & Color Neutral

Cold/SlowRelatively small self interactions

Interacts very little with SM particles

No SM particle fits the bill

The WIMP Miracle DM was in equilibrium with SM in the Early Universe

1 3 10 30 100 300 1000!20

!15

!10

!5

0

log

Y(x

)/Y

(x=

0)

x ! m/T

!!Annv"

Incr

easi

ng


T ! mDM

1 3 10 30 100 300 1000!20

!15

!10

!5

0

log

Y(x

)/Y

(x=

0)

x ! m/T

!!Annv"

Incr

easi

ng


T ! mDM

T ! mDMReverse process energetically disfavored

1 3 10 30 100 300 1000!20

!15

!10

!5

0

log

Y(x

)/Y

(x=

0)

x ! m/T

!!Annv"

Incr

easi

ng


T ! mDM

T ! mDM

DM too dilute to find each other


1 3 10 30 100 300 1000!20

!15

!10

!5

0

log

Y(x

)/Y

(x=

0)

x ! m/T

!!Annv"

Incr

easi

ng


T ! mDM

T ! mDM

DM too dilute to find each other


Relic density is “frozen in”

1 3 10 30 100 300 1000!20

!15

!10

!5

0

log

Y(x

)/Y

(x=

0)

x ! m/T

!!Annv"

Incr

easi

ng

Boltzmann Equation Solves for

! = "DM/"baryon ! 6

Frozen out when nDM !v ! H!ann =


! = "DM/"baryon ! 6


H ! T 2/MPlnDM = !

mp

mDM"s

s ! T 3 TFO ! mDM


! = "DM/"baryon ! 6

!v =1

"mpMPl#! 3" 10!26cm3/s


H ! T 2/MPlnDM = !

mp

mDM"s

s ! T 3 TFO ! mDM


! = "DM/"baryon ! 6

!v =1

"mpMPl#! 3" 10!26cm3/s

Frozen out when

mDM ! !" 20 TeV! ! "2

m2DM

=!

nDM !v ! H!ann =

H ! T 2/MPlnDM = !

mp

mDM"s

s ! T 3 TFO ! mDM

We want to see what’s there!

Muon, Strange particles, Tau leptonnot predicted before discovery

Serendipity favors the prepared!

Exploration

Chirality

Anomaly Cancellation

Flavor Symmetries

Gauge Coupling Unification

Effective Field Theory

Organizing Principlesfor going beyond the SM

ChiralityA symmetry acting a fermions that forbids masses

! =!

ffc

"M!! = M(ff c + f fc)


! =!

ffc

"M!! = M(ff c + f fc)

f ! ei!f fc ! ei!c

fc

Can do independent phase rotations


! =!

ffc

"M!! = M(ff c + f fc)

! = !!cVector symmetry

Allows mass

JµV = !!µ!

f ! ei!f fc ! ei!c

fc



! =!

ffc

"M!! = M(ff c + f fc)

! = !!cVector symmetry

Allows mass

JµV = !!µ!

! = !cAxial symmetry

Forbids mass

JµA = !!5!

µ!

f ! ei!f fc ! ei!c

fc


The Standard Model is a Gauged Chiral Theory

All masses are forbidden by a gauge symmetry

15 different bilinears all forbidden

QU c ! (1, 2)! 12 QEc ! (3, 2) 7

6

DcEc ! (3, 1) 43

U cL ! (3, 2)! 53

EcEc ! (1, 1)+2

LL ! (1, 1)!1QQ ! (3, 3) 1

3

DcDc ! (3, 1) 23

DcL ! (3, 2)! 16

etc...

The Standard Model force carriers forbid fermion masses

Electroweak Symmetry BreakingBreaking of Chiral Symmetry

SU(2)L ! U(1)Y " U(1)EM!H" #!

0v

"V (H) = !|H|4 ! µ2|H|2

LYuk = yiju QiU

cj H + yij

d QiDcjH

! + yije LiE

cjH

!

Q =!

UD

"L =

!!E

"

LYuk = miju UiU

cj + mij

d DiDcj + mij

e EiEcj

Fermions pick up Dirac Masses


Take a theory with light and heavy particlesLFull = Llight(!) + Lheavy(!,!)

If we only can ask questions in the range!

s" !cut o!<#M"

!cut o!

!s

m!

M!


Take a theory with light and heavy particlesLFull = Llight(!) + Lheavy(!,!)

If we only can ask questions in the range!

s" !cut o!<#M"

!cut o!

!s

m!

M!

with n > 0

Dynamics of light fields described by

Lfull(!) = Llight(!) + "L(!) !L ! O(")/!ncut o!

Only contribute as !" !! "

s

!cut o!

"n

known as “irrelevant operators”

Nonrenomalizable

We have only tested the SM to certain precision

How do we know that there aren’t those effects?

We know the SM isn’t the final theory of nature

We should view any theory we test asan “Effective Theory” that describes the dynamics

Shouldn’t be constrained by renormalizability

One way of looking for new physics is bylooking for these nonrenormalizable operators

Limits on Non-Renormalizable Operators


Baryon Number Violation QQQL/!2

! >! 1016 GeV



! >! 1016 GeV

Lepton Number Violation (LH)2/!! ! 1015 GeV



! >! 1016 GeV


Flavor Violation H†(L2!µ!Ec

1)Bµ!/!2Dc

1Dc1D

c2D

c2/!2

! >! 106 GeV ! >! 106 GeV



! >! 1016 GeV



1)Bµ!/!2Dc

1Dc1D

c2D

c2/!2

! >! 106 GeV ! >! 106 GeV

CP Violation iH†(L1!µ!Ec

1)Bµ!/!2

! >! 106 GeV



! >! 1016 GeV



1)Bµ!/!2Dc

1Dc1D

c2D

c2/!2

! >! 106 GeV ! >! 106 GeV


1)Bµ!/!2

! >! 106 GeVPrecision Electroweak |H†DµH|2/!2

! >! 3" 103 GeV



! >! 1016 GeV



1)Bµ!/!2Dc

1Dc1D

c2D

c2/!2

! >! 106 GeV ! >! 106 GeV


1)Bµ!/!2


! >! 3" 103 GeV

Contact Operators (L1L1)2/!2

! >! 3" 103 GeV



! >! 1016 GeV



1)Bµ!/!2Dc

1Dc1D

c2D

c2/!2

! >! 106 GeV ! >! 106 GeV


1)Bµ!/!2


! >! 3" 103 GeV

Contact Operators (L1L1)2/!2

! >! 3" 103 GeV

Generic Operators Gµ!G!"Gµ"/!2

! >! 3" 102 GeV

Flavor SymmetriesSymmetries that interchange fermions

Turn off all the interactions of the SM = Free Theory

L = !i i"! !i !i ! U ji !j U(N) symmetry



Q,U c, Dc, L,Ec = 15 Fermions/Generation

45 Total fermions that look the same in the free theoryglobal symmetry! U(45)




Q,U c, Dc, L,Ec = 15 Fermions/Generation

45 Total fermions that look the same in the free theoryglobal symmetry! U(45)

Gauge interactions destroy most of this symmetry

U(3)5 = U(3)Q ! U(3)Uc ! U(3)Dc ! U(3)L ! U(3)Ec

Yukawa couplings break the rest...but they are the only source of U(3)5 breaking


Prevents Flavor Changing Neutral CurrentsImagine two scalars with two sources of flavor breaking

LYuk = yijH!i!cj + "ij#!i!

cj

H = v + h mij = yijv



cj


Can diagonalize mass matrix with unitary transformations!i ! U j

i !j !ci ! V j

i !cj mij ! (UT mV )ij = Mi!

ij

LYuk !Mi!ij"i"

cj(1 + h/v) + (UT #V )ij$"i"j



cj


Higgs doesn’t change flavor, but other scalar field is a disaster

K0K0

d s

sd

!

! ! yUnless m!

!>! 100 TeVor

Can diagonalize mass matrix with unitary transformations!i ! U j

i !j !ci ! V j

i !cj mij ! (UT mV )ij = Mi!

ij

LYuk !Mi!ij"i"

cj(1 + h/v) + (UT #V )ij$"i"j

Anomaly CancellationQuantum violation of current conservation

!µJaµ ! Tr T aT bT c (F bF c)

T a

T b

T c

!

An anomaly leads to a mass for a gauge boson

m2 =!

g2

16!2

"3

!2

Anomaly cancellation:

One easy way: only vector-like gauge couplings

!, !c

(+1)3 + (!1)3 = 0


but the Standard Model is chiral


!, !c

(+1)3 + (!1)3 = 0


but the Standard Model is chiral


!, !c

(+1)3 + (!1)3 = 0

SU(3)SU(3)

SU(3)

U(1)U(1)

U(1)

U(1)SU(3)

SU(3)

6!

16

"3

+ 3!!2

3

"3

+ 3!

13

"3

+ 2!!1

2

"3

+ (1)3 = 0

2(1)3 + (!1)3 + (!1)3 + 0 + 0 = 0

2!

16

"+

!!2

3

"+

!13

"+ 0 + 0 = 0

Q U c Dc L Ec

It works, but is a big constraint!

Gauge coupling unification: Our Microscope

!!1

E103 106 109 1012 1015

(GeV)

30

40

20

10

sin2 !w

1

2

3

EGUT

d

dt!!1 =

b0

2"Counts charged matter


!!1

E103 106 109 1012 1015

(GeV)

30

40

20

10

sin2 !w

1

2

3

EGUT

!!13 (t) = !!1

3 (t") +b3 0

2"(t! t")

!!12 (t) = !!1

2 (t") +b2 0

2"(t! t")

!!11 (t) = !!1

1 (t") +b1 0

2"(t! t")

d

dt!!1 =

b0



!!1

E103 106 109 1012 1015

(GeV)

30

40

20

10

sin2 !w

1

2

3

EGUT

!!13 (t) = !!1

3 (t") +b3 0

2"(t! t")

!!12 (t) = !!1

2 (t") +b2 0

2"(t! t")

!!11 (t) = !!1

1 (t") +b1 0

2"(t! t")

d

dt!!1 =

b0


A3221 = 0.714

!!13 (t)! !!1

2 (t)!!1

2 (t)! !!11 (t)

=b3 0 ! b2 0

b2 0 ! b1 0

Weak scale measurementHigh scale particle contentB32

21 = 0.528


Grand Unification

! e q u d SU(3)! SU(2)! U(1)

Gauge coupling unification indicates forces arise from single entity


Grand Unification

! e q u d

5 10 SU(5)

SU(3)! SU(2)! U(1)



Grand Unification

! e q u d

5 10 SU(5)

!eR

! SO(10)

SU(3)! SU(2)! U(1)


Standard Model Summary

The Standard Model is chiral gauge theory

It is an effective field theory

It is anomaly free & anomaly cancellationrestricts new charged particles

Making sure that there is no new sourcesof flavor violation ensures that new theories are

not horribly excluded

SM Fermions fit into GUT multiplets,but gauge coupling unification doesn’t quite work

The Scenarios

Supersymmetry

Little Higgs Theories

Extra Dimensions

Technicolor

SupersymmetryDoubles Standard Model particles

Q,U c, Dc, L,Ec

Q, U c, Dc, L, Ec

H

Hu,Hd

Hu, Hd

g,W,B

g, W , B

Dirac pair of Higgsinos GauginosSfermions

Squarks, Sleptons Gluino, Wino, Bino

Fermions Higgs Gauge

(1, 2) 12

(1, 2)! 12

Susy Taxonomy

Needed for anomaly cancellation

Susy Gauge Coupling Unification

A3221 = 0.714

!!13 (t)! !!1

2 (t)!!1

2 (t)! !!11 (t)

=b3 0 ! b2 0

b2 0 ! b1 0

B3221 =

4285

= 0.714

Too good!(Two loop beta functions, etc)

But significantly better than SM or any other BSM theory

Only need to add in particles that contribute to the relative runningGauge Bosons, Gauginos, Higgs & Higgsinos

SUSY Interactions

Rule of thumb: take 2 and flip spins

q

qq

q

gg

Q

U c

U c

HH

Q

SUSY BreakingSUSY is not an exact symmetry

We don’t know how SUSY is broken, butSUSY breaking effects can be parameterized in the Lagrangian

Lsoft = Lm20+ Lm 1

2+ LA + LB



Lsoft = Lm20+ Lm 1

2+ LA + LB

Lm20

= m2!

ij !†

i !j

+m2Hu

|Hu|2 + m2Hd

|Hd|2! ! Q,U c, Dc, L,Ec



Lsoft = Lm20+ Lm 1

2+ LA + LB

Lm 12

= m1BB + m2WW + m3gg

Lm20

= m2!

ij !†

i !j

+m2Hu

|Hu|2 + m2Hd




Lsoft = Lm20+ Lm 1

2+ LA + LB

Lm 12


LA = aiju QiU

cj Hu + aij

d QiDcjHd + aij

e LiEcjHd

Lm20

= m2!

ij !†

i !j

+m2Hu

|Hu|2 + m2Hd




Lsoft = Lm20+ Lm 1

2+ LA + LB

Lm 12


LA = aiju QiU

cj Hu + aij

d QiDcjHd + aij

e LiEcjHd

LB = Bµ HuHd

Lm20

= m2!

ij !†

i !j

+m2Hu

|Hu|2 + m2Hd


Problem with Parameterized SUSY Breaking

There are over 100 parameters onceSupersymmetry no longer constrains interactions

Most of these are new flavor violation parametersor CP violating phases

Horribly excluded

Susy breaking is not generic!

m2ijQ

†i Q

j Qi ! U ji Qj

gs g Q†iQ

i ! gs g Q†i (U

†U)ijQ

j

Soft Susy Breaking

i.e. Super-GIM mechanismUniversality of soft terms

d

d s

s

g gd, s, b

d, s, b

K0 K0

Soft Susy Breaking

i.e. Super-GIM mechanismUniversality of soft terms

d

d s

s

g gd, s, b

d, s, b

K0 K0

Need to be Flavor Universal Couplings

A ! 11m2

0 ! 11Scalar MassesTrilinear A-Terms

Approximate degeneracy of scalars

Proton StabilityNew particles ⇒ new ways to mediate proton decay

Dangerous couplings

Prot

on Pionu u

u

d

d

u

e+

LRPV = !BU cDcDc + !LQLDc

Supersymmetric couplings that violate SM symmetries

A new symmetry forbids these couplings: (!1)3B+L+2s


Lightest Supersymmetric Particle is stable

Dangerous couplings

Prot

on Pionu u

u

d

d

u

e+





Lightest Supersymmetric Particle is stable

Dangerous couplings

Must be neutral and colorless -- Dark Matter

Prot

on Pionu u

u

d

d

u

e+




Mediation of Susy Breaking

MSSM PrimoridalSusy BreakingMediation

Susy breaking doesn’t occur inside the MSSMFelt through interactions of intermediate particles

Studied to reduce the number of parametersGauge Mediation

Universal “Gravity” MediationAnomaly Mediation

Usually only 4 or 5 parameters...but for phenomenology, these are too restrictive

The Phenomenological MSSMThe set of parameters that are:

Not strongly constrainedEasily visible at colliders

First 2 generation sfermions are degenerate

3rd generation sfermions in independent

Gaugino masses are free

Independent A-terms proportional to Yukawas

Higgs Masses are Free

55334

20 Total Parameters

Charginos & NeutralinosThe Higgsinos, Winos and Binos

Hu ! 2 12" 0,+1 Hd ! 2! 1

2" 0,#1 W ! 30 " 0,+1,#1 B ! 10 " 0

After EWSB: 2 Charge +1 Dirac Fermions

4 Charge 0 Majorana Fermions

L = µHuHd + m2WW + m1BB

+(H†uHu + H†

dHd)(gW + g!B)

(2)

All mix together, but typically mixture is small

Tend find charginos next to their neutralino brethren

Neutralinos are good DM candidates

Elementary Phenomenology

Neutralinos Charginos Sleptons Squarks Gluinos

Mas

s

Collider signatures

q

q

!0

!0

!02

!+1

!

!!

!

!

!

Trileptons+MET: If sleptons are availableN

eutra

linos

Cha

rgin

os

Slep

tons

Mas

s

3 Leptons + MET

Collider signatures

9 RESULTS AND LIMITS 13

)2Chargino Mass (GeV/c100 110 120 130 140 150 160 170

3l)

(p

b)

!± 1"#

0 2" ~

BR

($

%

0

0.2

0.4

0.6

0.8

1

1.2

-1CDF Run II Preliminary, 3.2 fb

)2Chargino Mass (GeV/c

LEP 2 direct

limit

BR$ NLO

%Theory

% 1 ±Expected Limit % 2 ±Expected Limit

95% CL Upper Limit: expected

Observed Limit

) > 0µ=0, (0

=3, A&=60, tan 0

mSugra M

Figure 6: Expected and observed limit for the mSugra model M0 =60, tan! = 3, A0 = 0, (µ) > 0. In red is the theoretical " ! BR and inblack is our expected limit with one and two " errors. We expect to set alimit of about 156 GeV/c2, and observe a limit of 164 GeV/c2.

q

q

!0

!0

!02

!+1

!

!!

!

!

!

Trileptons+MET: If sleptons are availableN

eutra

linos

Cha

rgin

os

Slep

tons

Mas

s

3 Leptons + MET

Collider signaturesTrileptons+MET

Without sleptons in the decay chainN

eutra

linos

Cha

rgin

os

Slep

tons

Mas

s q

q

!0

!0

!02

!+1 !

!!!W+

Z0

30% leptonic Br of W, 10% leptonic Br of Z3% Total Branching Rate

7

Cro

ss S

ecti

on [p

b]

]2 [GeV/cg~

M]2 [GeV/cq~

M

2 = 230 GeV/cg~

M

q~ = M

g~M

2 = 370 GeV/cq~

M

2 = 460 GeV/cq~

M

Theoretical uncertainties not included in the calculation of the limit

<0µ = 5, ! = 0, tan0A -1L = 2.0 fb

NLO Prospino Ren.)"syst. uncert. (PDF

expected limit 95% C.L.

observed limit 95% C.L.

-110

1

10

210

-110

1

10

210

300 400 500

-210

-110

1

10

300 400 500

-210

-110

1

10

200 300 400 500200 300 400 500

FIG. 2: Observed (solid lines) and expected (dashed lines)95% C.L. upper limits on the inclusive squark and gluinoproduction cross sections as a function of M!q (left) and

M!g (right) in di!erent regions of the squark-gluino mass

plane, compared to NLO mSUGRA predictions (dashed-dotted lines). The shaded bands denote the total uncertaintyon the theory.

0 100 200 300 400 500 6000

100

200

300

400

500

600

no mSUGRA

solution

LEP

UA

1

UA

2

g~

= M

q~M

0 100 200 300 400 500 6000

100

200

300

400

500

600

observed limit 95% C.L.

expected limit

FNAL Run I

)-1

<0 (L=2.0fbµ=5, !=0, tan0A

]2

[GeV/cg~M

]2 [G

eV/c

q~M

FIG. 3: Exclusion plane at 95 % C.L. as a function of squarkand gluino masses in an mSUGRA scenario with A0 = 0,µ < 0 and tan! = 5. The observed (solid line) and expected(dashed line) upper limits are compared to previous resultsfrom SPS [30] and LEP [31] experiments at CERN (shadedbands), and from the Run I at the Tevatron [2] (dashed-dottedline). The hatched area indicates the region in the plane withno mSUGRA solution.

Japan; the Natural Sciences and Engineering ResearchCouncil of Canada; the National Science Council of theRepublic of China; the Swiss National Science Founda-tion; the A.P. Sloan Foundation; the Bundesministeriumfur Bildung und Forschung, Germany; the Korean Sci-ence and Engineering Foundation and the Korean Re-search Foundation; the Science and Technology FacilitiesCouncil and the Royal Society, UK; the Institut Nationalde Physique Nucleaire et Physique des Particules/CNRS;the Russian Foundation for Basic Research; the Ministe-rio de Ciencia e Innovacion, and Programa Consolider-Ingenio 2010, Spain; the Slovak R&D Agency; and the

Academy of Finland.

[1] H. E. Haber and G. L. Kane, Phys. Rep. 117, 75 (1985).[2] T. A!older et al. (CDF Collaboration), Phys. Rev. Lett.

88, 041801 (2002); S. Abachi et al. (D0 Collaboration),ibid. 75, 618 (1995).

[3] V.M. Abazov et al. (D0 Collaboration), Phys. Lett. B660, 449 (2008).

[4] H. P. Nilles, Phys. Rep. 110, 1 (1984).[5] CDF uses a cylindrical coordinate system about the beam

axis with polar angle " and azimuthal angle #. We definetransverse energy ET = E sin", transverse momentumpT = p sin", pseudorapidity $ = !ln(tan( !

2 )), and rapid-

ity y = 12 ln(E+pz

E!pz

). The missing transverse energy E/T is

defined as the norm of !"

iEi

·%ni, where %ni is the com-ponent in the azimuthal plane of the unit vector pointingfrom the interaction point to the i-th calorimeter tower.

[6] D. Acosta et al. (CDF Collaboration), Phys. Rev. D 71,032001 (2005).

[7] D. Acosta et al., Nucl. Instrum. Methods, A 494, 57(2002).

[8] T. Sjostrand et al., Comp. Phys. Comm. 135, 238 (2001).[9] T. A!older et al. (CDF Collaboration), Phys. Rev. D 65,

092002 (2002).[10] M. Cacciari et al., J. High Energy Phys. 0404, 068

(2004).[11] J. M.Campbell and R. K. Ellis, Phys. Rev. D60, 113006

(1999).[12] M.L. Mangano et al., J. High Energy Phys. 07, 001

(2003).[13] A Abulencia et al. (CDF Collaboration), J. Phys. G:

Nucl. Part. Phys. 34, 2457 (2007).[14] F. Maltoni and T. Stelzer, J. High Energy Phys. 02, 027

(2003).[15] B. W. Harris et al., Phys. Rev. D66, 054024 (2002).[16] B. C. Allanach et al., Eur. Phys. J. C25, 113 (2002).[17] W. Beenakker et al., Nucl. Phys. B492, 51 (1997).[18] F. Paige and S. Protopopescu, in Supercollider Physics,

p. 41, ed. D. Soper (World Scientific, 1986).[19] J. Pumplin et al., J. High Energy Phys. 0207, 012 (2002).[20] Pole masses are considered. The squark mass is averaged

over the first two squark generations.[21] R. Brun et al., Tech. Rep. CERN-DD/EE/84-1, 1987.[22] G. Grindhammer, M. Rudowicz, and S. Peters, Nucl. In-

strum. Methods A 290, 469 (1990).[23] F. Abe et al. (CDF Collaboration), Phys. Rev. D 45,

1448 (1992).[24] A. Bhatti et al., Nucl. Instrum. Methods A 566, 375

(2006).[25] Charge conjugation is implied throughout the paper.[26] The sum runs over the selected jets. In the four-jets case,

the first three leading jets are considered.[27] X. Portell, Ph.D. Thesis, U.A.B., Barcelona (2007).[28] G. De Lorenzo, Master Thesis, U.A.B., Barcelona (2008).[29] R. Cousins, Am. J. Phys. 63, 398 (1995).[30] C. Albajar et al. (UA1 Collaboration), Phys. Lett. B198,

261 (1987); J. Alitti et al. (UA2 Collaboration), ibid.B235, 363 (1990).

[31] LEPSUSYWG/02-06.2, http://lepsusy.web.cern.ch/lepsusy/.

Collider signaturesGluino Pairs: 4j +MET Squark Pairs: 2j +MET Squark-Gluino Pairs: 3j +MET

q

q

g

g

q

q

q

q

!0

!0

q

q

q

q

q q

!0

!0

q

q

q

qq gq

g

!0

!0

q

qq

mSUGRA Searchm3 : m2 : m1 = 6 : 2 : 1

Away from mSUGRA Gluino Search

Out[27]=

XX

100 200 300 400 5000

50

100

150

Gluino Mass !GeV"

BinoMass!GeV

"mg ! 130 GeVmg ! 120 GeV

g ! qqB

g ! qqW ! qqBW

The Higgs Mass ProblemVHiggs = !|H|4 + µ2|H|2m2

h0 = 2!v2 = !2µ2

The Higgs Mass ProblemVHiggs = !|H|4 + µ2|H|2m2

h0 = 2!v2 = !2µ2

mh0 !MZ0!susy =18

!g2 + g!2" cos2 2"

Need a susy copy of quartic coupling, only gauge coupling works in MSSM

The Higgs Mass Problemm2

h0 = 2!v2 = !2µ2

H

t t

H

!" =3y4

top

8#2log

mstop

mtop

mh0 !MZ0!susy =18

!g2 + g!2" cos2 2"


The Higgs Mass Problem

!µ2 = !3y2

top

8"2m2

stopH t tH

m2h0 = 2!v2 = !2µ2

H

t t

H

!" =3y4

top

8#2log

mstop

mtop

mh0 !MZ0!susy =18

!g2 + g!2" cos2 2"


The Higgs Mass Problem

!µ2 = !3y2

top

8"2m2

stopH t tH

Higgs mass gain is only logFine tuning loss is quadratic

Difficult to make the Higgs heavier than 125 GeV in MSSM

FT !m2

h0

!µ2

m2h0 = 2!v2 = !2µ2

H

t t

H

!" =3y4

top

8#2log

mstop

mtop

mh0 !MZ0!susy =18

!g2 + g!2" cos2 2"


Susy is the leading candidate for BSM Physics

Dark Matter candidate

Gauge Coupling Unification

Compelling structure

Become the standard lamppost

Basic Susy Signatures away from mSUGRAare still being explored

A lot of the qualitative signatures of Susyappear in other models

Extra Dimensions Taxonomy

Large TeV Small

Flat Curved

UEDs RS Models GUT ModelsADD Models

Kaluza-Klein ModesThe general method to analyze higher dimensional theories

S =!

d4x

!dy |!M"(x, y)|2 !M2|"(x, y)|2

y

xµ


S =!

d4x

!dy |!M"(x, y)|2 !M2|"(x, y)|2

y

xµ

(!µ!µ ! !25 + M2)"(x, y) = 0

Equations of Motion


S =!

d4x

!dy |!M"(x, y)|2 !M2|"(x, y)|2

y

xµ

(!µ!µ ! !25 + M2)"(x, y) = 0

Equations of Motion

!(x, y) =!

n

!n(x)fn(y)!

!µ!µ + M2 +"

2"n

R

#2$

#n(x) = 0

One 5D field = tower of 4D fields

fn(y) =e2!iny/R

!2!R

Large Extra Dimensions

GravitySM

Integrate out extra dimension

S4+n =!

d4x

!dny!

g M2+n! R4+n + !n(y)LSM

S4 e! =!

d4x!

g M4+n! Ln R4 + LSM


GravitySM


S4+n =!

d4x

!dny!


S4 e! =!

d4x!

g M4+n! Ln R4 + LSM

M2Pl = M2+n

! Ln

Identify new Planck Mass


GravitySM


S4+n =!

d4x

!dny!


S4 e! =!

d4x!

g M4+n! Ln R4 + LSM

M2Pl = M2+n

! Ln

Identify new Planck Massn L1 1010 km

2 1 mm

3 10nm

4 10-2nm

5 100fm

6 1fmM! ! 1 TeVSet

If fundamental Planck mass is weakscale, there is no hierarchy problem!

Large Extra Dimension Signatures

Monophoton+MET

6

Background EventsZ ! !! 388 ± 30W ! "! 187 ± 14W ! µ! 117 ± 9W ! e! 58 ± 4Z ! ## 8 ± 1

Multi-jet 23 ± 20$+jet 17 ± 5

Non-collision 10 ± 10Total predicted 808 ± 62Data observed 809

TABLE II: Number of observed events and expected SM back-grounds in the jet + E/T candidate sample.

mates and the number of observed events are shown inTable II, and a comparison of the expected and observedleading jet ET distributions is shown in Fig. 2.

(GeV)TLeading Jet E100 150 200 250 300 350 400

Eve

nts

/ 1

0 G

eV

0

50

100

150

200

250

300

Data

SM Prediction

=1TeV)DSM + LED (n=2,M

)-1

CDF II ( 1.1 fb

FIG. 2: Predicted and observed leading jet ET distributionsfor the jet + E/T candidate sample. The expected LED signalcontribution for the case of n = 2 and MD = 1.0 TeV is alsoshown.

Based on the observed agreement with the SM expecta-tion in both the ! + E/T and jet + E/T candidate samples,we proceed to set lower limits on MD for the LED model.The limits are obtained solely from the total number ofobserved events in each of the samples (no kinematicshape information is incorporated). In order to estimateour sensitivity to the ADD model we simulate expectedsignals in both final states using the pythia [12] eventgenerator in conjunction with a geant [13] based de-tector simulation. For each extra dimension scenario wesimulate event samples for MD ranging between 0.7 and2 TeV. In the case of the ! + E/T analysis, the final kine-matic selection requirements for the candidate sampleare determined by optimizing the expected cross sectionlimit without looking at the data. The jet + E/T anal-ysis was done as a generic search for new physics usingthree sets of kinematic cuts, the most sensitive of which isused here. To compute the expected 95% C.L. cross sec-tion upper limits we combine the predicted ADD signal

$ + E/T Jet + E/T Combinedn % Mobs

D % MobsD Mobs

D

2 7.2 1080 9.9 1310 14003 7.2 1000 11.1 1080 11504 7.6 970 12.6 980 10405 7.3 930 12.1 910 9806 7.2 900 12.3 880 940

TABLE III: Percentage of signal events passing the candidatesample selection criteria (%) and observed 95% C.L. lowerlimits on the e!ective Planck scale in the ADD model (Mobs

D )in GeV/c2 as a function of the number of extra dimensions inthe model (n) for both individual and the combined analysis.

Number of Extra Dimensions2 3 4 5 6

Lo

we

r L

imit (

Te

V)

DM

0.6

0.8

1

1.2

1.4

1.6

Number of Extra Dimensions2 3 4 5 6

Lo

we

r L

imit (

Te

V)

DM

0.6

0.8

1

1.2

1.4

1.6

TE + !CDF II Jet/

)-1

(2.0 fbTE + !CDF II

)-1

(1.1 fbTECDF II Jet +

LEP Combined

FIG. 3: 95 % C.L. lower limits on MD in the ADD model asa function of the number of extra dimensions in the model.

and background estimates with systematic uncertaintieson the acceptance using a Bayesian method with a flatprior [14]. The acceptance is found to be almost indepen-dent (within 2%) of the mass MD. The total systematicuncertainties on the number of expected signal events are5.7% and 12.4% for the ! + E/T and jet + E/T candidatesamples respectively. The largest systematic uncertain-ties arise from modeling of initial/final state radiationconvoluted with jet veto requirements, choice of renor-malization and factorization scales, modeling of partondistribution functions, modeling of the jet energy scale(jet + E/T sample only), and the luminosity measurement.

Since the underlying graviton production mechanismis equivalent for both final states, the combination of theindependent limits obtained from the two candidate sam-ples is based on the predicted relative contributions ofthe four graviton production processes. Systematic un-certainties on the signal acceptances are treated as 100%correlated, while uncertainties on background estimates,obtained in most cases from data, are considered to beuncorrelated. The 95% C.L. lower limits on MD fromeach candidate sample and the combined limits are givenin Table III and plotted with LEP limits [15] in Fig. 3.

In conclusion, the CDF experiment has recently com-pleted searches for new physics in the ! + E/T and jet +E/T final states using data corresponding to 2.0 fb!1 and

q

q

!

G

Large Extra Dimension SignaturesBlack Holes at the LHC

Topology Total Cross Section (fb)

n = 2 62, 000

5 TeV black hole n = 4 37, 000

n = 6 34, 000

n = 2 580

8 TeV black hole n = 4 310

n = 6 270

n = 2 6.7

10 TeV black hole n = 4 3.4

n = 6 2.9

Table 1: The black hole production cross sections at the LHC for MPL = 1 TeV as given byCHARYBDIS. Note that CHARYBDIS does not include the form factors mentioned in section 7.

in order for our analyses to be as widely applicable as possible. In this section we review

these uncertainties.

4.1 Production cross section

The process of black hole production in hadron collisions is subject to a number of basic

uncertainties. The order of magnitude of the parton-level cross section should be given by

equation 2.1, but the form factor relating the left- and right-hand sides is uncertain and

would be expected to be n-dependent. Classical numerical simulations [26] suggest values

in the range 0.5–2, increasing with n. These values are not included in the CHARYBDIS

generator, but we take them into account when cross section data are used in our analysis

(in sections 7 and 8).

More fundamentally, the transition from the parton-level to the hadron-level cross

section is based on the factorization formula

!(S) =

!

dx1 dx2 f(x1)f(x2)!(s = x1x2S) (4.1)

where f(x) is the parton distribution function (PDF) summed over parton flavours. The

validity of this formula in the trans-Planckian energy region is unclear. Even if factoriza-

tion remains valid, the extrapolation of the PDFs into this region based on Standard Model

evolution from present energies is questionable. Also, comparison to Standard Model pro-

cesses in the trans-Planckian regime would be di!cult since perturbative physics would be

suppressed.

4.2 The first stages of decay

CHARYBDIS does not model the initial balding or spin-down phases of the black hole decay.

The amount of energy emitted from the black hole during these phases is expected to be

small [8] so such an omission should not be significant. However, it is probable that the

energy spectrum will be modified at low energies.

– 5 –

Rs(!

s) = M!1"

!!s

M"

" 1n+1!

s"M!for !BH ! R2s

BHs decaythermally, violating all

global conservation laws

High multiplicity eventswith lots of energy

qq

Universal Extra Dimensions

+GravitySM

Standard Model has KK modes

S5D =!

d5x F 2MN + !iD! ! + · · ·

!12R " x5 "

12R

All fields go in the bulk

R!1 >! 500 GeV

Universal Extra Dimensions

+GravitySM

Standard Model has KK modes

S5D =!

d5x F 2MN + !iD! ! + · · ·

!12R " x5 "

12R

All fields go in the bulkM

ass

g W B Q U c Dc L Ec H

n = 1

n = 2n = 3· · ·

n = 0

f(x5)

1

sin(x5/R)

cos(2x5/R)sin(3x5/R)

Impose Dirichlet Boundary Conditions

R!1 >! 500 GeV

UED KK Spectra

FIG. 6: The spectrum of the first KK level at (a) tree level and (b) one-loop, for R!1 = 500 GeV,

!R = 20, mh = 120 GeV, m2H = 0, and assuming vanishing boundary terms at the cut-o" scale !.

R!1 = 500 GeV, !R = 20, mh = 120 GeV, m2H = 0 and assumed vanishing boundary

terms at the cut-o" scale !. We see that the KK “photon” receives the smallest corrections

and is the lightest state at each KK level. Unbroken KK parity (!1)KK implies that the

lightest KK particle (LKP) at level one is stable. Hence the “photon” LKP !1 provides an

interesting dark matter candidate. The corrections to the masses of the other first level KK

states are generally large enough that they will have prompt cascade decays down to !1.3

Therefore KK production at colliders results in generic missing energy signatures, similar

to supersymmetric models with stable neutralino LSP. Collider searches for this scenario

appear to be rather challenging because of the KK mass degeneracy and will be discussed

in a separate publication [13].

V. CONCLUSIONS

Loop corrections to the masses of Kaluza-Klein excitations can play an important role

in the phenomenology of extra dimensional theories. This is because KK states of a given

level are all nearly degenerate, so that small corrections can determine which states decay

and which are stable.

3 The first level graviton G1 (or right-handed neutrino N1 if the theory includes right handed neutrinos N0)

could also be the LKP. However, the decay lifetime of !1 to G1 or N1 would be comparable to cosmo-

logical scales. Therefore, G1 and N1 are irrelevant for collider phenomenology but may have interesting

consequences for cosmology.

20

Levels are degenerate at tree level

All masses within 30% of each other!(This is a widely spaced example!)

KK Parityx5 ! "x5

All odd-leveled KK modes are oddSM and even-leveled KK modes are even

KK Parityx5 ! "x5


LKP is stable!

Usually KK partner of Hypercharge Gauge boson

g0,0,1 !! R/2

!R/2dx5 f0(x5)f0(x5)f1(x5) "

!dx5 1 · 1 · sin(!x5/R)

KK Parityx5 ! "x5


Looks like a degenerate Supersymmetry spectrumuntil you can see 2nd KK level

LKP is stable!

Usually KK partner of Hypercharge Gauge boson

g0,0,1 !! R/2

!R/2dx5 f0(x5)f0(x5)f1(x5) "

!dx5 1 · 1 · sin(!x5/R)

Typical UED EventPair produce colored 1st KK level

Each side decays separately













V. CONCLUSIONS









20













V. CONCLUSIONS









20















V. CONCLUSIONS









20













V. CONCLUSIONS









20

g1 ! q1q















V. CONCLUSIONS









20













V. CONCLUSIONS









20

q1 ! B1q

g1 ! q1q















V. CONCLUSIONS









20













V. CONCLUSIONS









20

q1 ! B1q

g1 ! q1q

2j + ET!















V. CONCLUSIONS









20













V. CONCLUSIONS









20

g1 ! q1q

q1 ! B1q

g1 ! q1q

2j + ET!















V. CONCLUSIONS









20













V. CONCLUSIONS









20

g1 ! q1q

q1 ! B1q

g1 ! q1q

q1 !W 31 q

2j + ET!















V. CONCLUSIONS









20













V. CONCLUSIONS









20

g1 ! q1q

q1 ! B1q

g1 ! q1q

q1 !W 31 q

W 31 ! !1!

2j + ET!















V. CONCLUSIONS









20













V. CONCLUSIONS









20

g1 ! q1q

q1 ! B1q

g1 ! q1q

q1 !W 31 q

W 31 ! !1!

!1 ! !B1

2j + ET!















V. CONCLUSIONS









20













V. CONCLUSIONS









20

g1 ! q1q

q1 ! B1q

g1 ! q1q

q1 !W 31 q

W 31 ! !1!

!1 ! !B1

2j + ET! 2j + ! + ! + ET!















V. CONCLUSIONS









20













V. CONCLUSIONS









20

g1 ! q1q

q1 ! B1q

g1 ! q1q

q1 !W 31 q

W 31 ! !1!

!1 ! !B1

2j + ET! 2j + ! + ! + ET!

Difficult is in Soft Spectra

Randall Sundrum ModelsTeV Scale Curved Extra Dimensions

ds2 = e!2kydx24 ! dy2

Warp factor

UV Brane IR Brane

y

0 ! y ! y0

At each point of the 5th dimension,there is a different normalization of 4D lengths

Effects of the Warping

S5 =!

d4xdy!

g5 !(y " y0)"gµ!5 "µ#"!# + m2#2 + g#3 + $#4

#

gµ!5 = e2ky0!µ!!

g5 = e!4ky0

An IR brane scalar


S5 =!

d4xdy!

g5 !(y " y0)"gµ!5 "µ#"!# + m2#2 + g#3 + $#4

#

gµ!5 = e2ky0!µ!!

g5 = e!4ky0

S4 =!

d4x e!4ky0"e2ky0(!")2 + m2"2 + g"3 + #"4

#

Need to go to canonical normalization !! eky0!

An IR brane scalar


S5 =!

d4xdy!

g5 !(y " y0)"gµ!5 "µ#"!# + m2#2 + g#3 + $#4

#

gµ!5 = e2ky0!µ!!

g5 = e!4ky0

S4 =!

d4x e!4ky0"e2ky0(!")2 + m2"2 + g"3 + #"4

#

Need to go to canonical normalization !! eky0!

S4 =!

d4x (!")2 + m2e!2ky0"2 + ge!ky0"3 + #"4

All mass scales on IR brane got crunched by warp factor

Super-heavy IR brane Higgs becomes light!

An IR brane scalar

Can put all fields on IR brane...but just like low dimension operators get

scrunched, high dimension operators get enlarged!

Motivated putting SM fields in bulk except for the Higgs

UV Brane IR Brane

SM Gauge + Fermions

Higgs boson

Now have SM KK modes, but no KK parityResonances not evenly spaced either

Get light KK copies of right-handed top

Tonnes of Theory & Pheno and Models for RS Models!

AdS/CFTTheories in Anti-de Sitter space (RS metric)

Equivalent to 4D theories that are conformal (scale invariant)

5D description is way of mocking up complicated 4D physics!

Warping is Dimensional Transmutation

IR Brane is breaking of conformal symmetry

!IR = e!ky0!UV

!QCD = e!2!"!1

3 (MGUT)b0 MGUT

Technicolor TheoriesImagine there was no Higgs

QCD still gets strong and quarks condense

!QQc" #= 0 Qc = (U c, Dc)

QQc ! (1, 2) 12

Condensate has SM gauge quantum numbers

Like the Higgs!QCD confinement/chiral symmetry breaking

breaks electroweak symmetry

Technicolor is a scaled-up version of QCDRS Models are the modern versions of Technicolor

In Technicolor theoriesNot necessarily a Higgs boson

Technirhos usually first resonance

OS =H†Wµ!HBµ!

!2

Mediate contributions to

! >! 3 TeVwithW±, Z0

!T

!T

90 GeV

800 GeV

etcNeed to be lighter than 1 TeV

In Technicolor theoriesNot necessarily a Higgs boson

Technirhos usually first resonance

OS =H†Wµ!HBµ!

!2

Mediate contributions to

! >! 3 TeVwithW±, Z0

!T

!T

90 GeV

800 GeV

etcNeed to be lighter than 1 TeV

W±, Z0

!T!T

90 GeV

3 TeV

etc

Can push off the Technirhosusually a scalar resonance becomes narrow

600 GeV !T

!T starts playing the role of the HiggsRequires assumptions about

technicolor dynamics

Would like to get scalars lightwithout dynamical assumptions

Higgs as a Goldstone boson!T !" "T

Higgs boson is a technipion

Pions are light because the areGoldstone bosons of approximate symmetries

V (!T ) ! m2f2 cos !T /f

f set by Technicolor scale

!!T " = 0,!f

Goldstone bosons only have periodic potentials

Little Higgs TheoriesSpecial type of symmetry breaking

V (!T ) ! f4 sin4 !T /f + m2f2 cos !T /f

Looks like normal “Mexican hat” potential

Lots of group theory to get specific examples

Little Higgs TheoriesSpecial type of symmetry breaking

V (!T ) ! f4 sin4 !T /f + m2f2 cos !T /f

Looks like normal “Mexican hat” potential

Lots of group theory to get specific examples

[SU(3)! SU(3)/SU(3)]4SU(5)/SO(5)

SU(6)/Sp(6) [SO(5)! SO(5)/SO(5)]4

[SU(4)/SU(3)]4SU(9)/SU(8)

SO(9)/SO(5)! SO(4)

All have some similar features

New gauge sectors

Vector-like copies of the top quarksQ3 & Qc

3 U c3 & U3

There are extended Higgs sectors SU(2)L singlets, doublets & triplets

Conclusion

Beyond the Standard Model Physics is rich and diverse

Within the diversity there are many similar themes

These lectures were just an entry way into the phenomenology of new physics

We’ll soon know which parts of these theorieshave something to do with the weak scale

References

S. P. Martin

hep-ph/9709356

C. Csaki et al

“Supersymmetry Primer”

“TASI lectures on electroweak symmetry breaking from extra dimensions”hep-ph/0510275

M. Schmaltz, D. Tucker-Smith“Little Higgs Review”

hep-ph/0502182

I. Rothstein

hep-ph/0308286“TASI Lectures on Effective Field Theory”

G. Kribs“TASI 2004 Lectures on the pheomenology of extra dimensions”

hep-ph/0605325

J. Wells

hep-ph/0512342“TASI Lecture Notes: Introduction to Precision Electroweak Analysis”

R. Sundrum“TASI 2004: To the Fifth Dimension and Back”

hep-ph/0508134

slac summer institute 2009

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