The Post-Model Building Era and

Simplified Models

Jay WackerSLAC

Modeling and the LHCWuppertal, Germany January 28, 2012

How should we motivate LHC searches for signatures of physics beyond the Standard Model?

Question:

300 Trillion Collisions

1 Billion Recorded Collisions

Last Year

The Challenge Facing the LHC

Very hard to make general predictions

Space of experimental signatures is very high

Njets < 12

Nleptons < 5

Nphotons < 4

x 3 ( pT, η, φ)x

x

~600 dimensions

Sparsely populatedCan’t calculate predictions accurately in this full space of signatures

Must reduce dimensionality

What theories/models are for

M2γγ= 2 pT1pT2( cosh(η1-η2) - cos(φ1-φ2) )

Combines 6 variables into 1

But theories have a high dimensional parameter space...

MSSM has ~100 parameters

Allowed parameter space has 19 parameters

mSUGRA has 5, but introduces theory prejudice

“Theory”

Set of rules based upon principlesused for predicting outcomes

Most Model Building is Theory Buildinguse principles to create new theories

(naturalness, supersymmetry, unification)

“Model”

A representation of a system

Not necessarily physical

Mγγ

Nevents f(Mγγ)

Background

Theory vs. Model

Ultimate goal of theoretical physics

Answer any physical question

Complete vs. Incomplete?

Complete Theory

Complete Theories

Is “Complete” a criteria to select out theories?

Complete Theories

Non-renormalizable theories are incomplete

Comes with energy scale Λ

Questions with E> Λ cannot be answered

Λ ~ “Cutoff of Theory”

Questions with E< Λ go as (E/Λ)N << 1

However

Effects are invisible at low energies

Complete Theories

Used to be a criteria to prefer theories

Complete Theories

This was a great simplifying criteria

Type of Theory Number of parameters

Renormalizable

Non-renormalizable

Finite

Infinite

Complete Theories, In Principle

Discover the particles

Only finite number of measurements to fully specify the theory

Complete Theories

“Discover the particles”

Devil is in the details

How?

If EΑΒ<Mφ, can’t discover

φΑ

Β

abcd

How does an undiscovered particle of a complete theory manifest itself?

L (A, B, ... ; φ) L’(A, B, ... )

L’ is a non-renormalizable theory

Λ = Mφ

How do we know we’ve discovered all the particles?

How do we know we’ve discovered all the particles?

We know we haven’t

Dark Matter (80% of the mass of the Universe)

May be not so bad

L (A, B, ... ; φ) L’(A, B, ... )

May be not so bad

L (A, B, ... ; φ) L’(A, B, ... )

Can any non-renormalizable theorybe realized as a

renormalizable theory with more particles?

Basically

Is the backdrop for all theory building

Any theory comes with Cutoff

Above Λ, theory may be arbitrarily complicated

Insensitive to Cutoff scale physics at low energies

Cannot write down complete theory with a straight face

Using hypothetical principles to create new theories

Given that we can’t discover the complete theory of nature,

how do we propose models?

Can parameterize all deviations fromStandard Model

LSM(A, B, ... ) + LNon-Renormalizable (A, B, ... )δ

Given that we can’t discover the complete theory of nature,

how do we propose models?

Can parameterize all deviations fromStandard Model

LSM(A, B, ... ) + LNon-Renormalizable (A, B, ... )δWe usually want to explore

EAB > MφNeed to incorporate φ into model

Modern Vision ofTheories Beyond the Standard Model

SM

φ

Λ Scale theory is no longer valid

New particles to be discovered

What we’ve already seen

Ener

gy

Λ can be low ~ 10 TeV Λ can be high ~ 1016 TeV

Theory Building In Practice

Pick a problem

Build a theory that solves it

Make predictions for experiment

Theory Building In Practice

Argue about which theory is better while waiting

Pick a problem

Build a theory that solves it

Make predictions for experiment

The Hierarchy Problem>50% of motivation for past 35 years

1978Technicolor

The Hierarchy Problem>50% of motivation for past 35 years

1978Technicolor Susy

1981

The Hierarchy Problem>50% of motivation for past 35 years

1978Technicolor Susy

1981

1991

The Hierarchy Problem>50% of motivation for past 35 years

1978Technicolor Susy

1981

1991

Large ED RS Small ED

1998

The Hierarchy Problem>50% of motivation for past 35 years

1978Technicolor Susy

1981

1991

Large ED RS Small ED

1998

LH

2002

2012

The Hierarchy Problem>50% of motivation for past 35 years

1978

1981

1991

1998

2002

2012

Technicolor Susy Large ED RS LHSmall ED

1978

1981

1991

2002

2012

Technicolor Susy Large ED RS LHSmall ED

Could enumerate theories

Implications for Experimental Searches

1998

Lots of effort on the specific theories

2 4 6 8 10 12 14 16 18Log10(Q/1 GeV)

0

100

200

300

400

500

600

Mas

s [G

eV]

m0

m1/2

(µ2+m02)1/2

squarks

sleptons

M1

M2

M3

Hd

Hu

Figure 7.4: RG evolution of scalar and gaugino mass parameters in the MSSM with typical minimalsupergravity-inspired boundary conditions imposed at Q0 = 2.5! 1016 GeV. The parameter µ2 + m2

Hu

runs negative, provoking electroweak symmetry breaking.

a reasonable approximation, the entire mass spectrum in minimal supergravity models is determinedby only five unknown parameters: m2

0, m1/2, A0, tan !, and Arg(µ), while in the simplest gauge-mediated supersymmetry breaking models one can pick parameters !, Mmess, N5, "F #, tan !, andArg(µ). Both frameworks are highly predictive. Of course, it is easy to imagine that the essentialphysics of supersymmetry breaking is not captured by either of these two scenarios in their minimalforms. For example, the anomaly mediated contributions could play a role, perhaps in concert withthe gauge-mediation or Planck-scale mediation mechanisms.

Figure 7.4 shows the RG running of scalar and gaugino masses in a typical model based on theminimal supergravity boundary conditions imposed at Q0 = 2.5 ! 1016 GeV. [The parameter valuesused for this illustration were m0 = 80 GeV, m1/2 = 250 GeV, A0 = $500 GeV, tan ! = 10, andsign(µ)= +.] The running gaugino masses are solid lines labeled by M1, M2, and M3. The dot-dashedlines labeled Hu and Hd are the running values of the quantities (µ2 + m2

Hu)1/2 and (µ2 + m2

Hd)1/2,

which appear in the Higgs potential. The other lines are the running squark and slepton masses,with dashed lines for the square roots of the third family parameters m2

d3, m2

Q3, m2

u3, m2

L3, and m2

e3

(from top to bottom), and solid lines for the first and second family sfermions. Note that µ2 + m2Hu

runs negative because of the e"ects of the large top Yukawa coupling as discussed above, providing forelectroweak symmetry breaking. At the electroweak scale, the values of the Lagrangian soft parameterscan be used to extract the physical masses, cross-sections, and decay widths of the particles, and otherobservables such as dark matter abundances and rare process rates. There are a variety of publiclyavailable programs that do these tasks, including radiative corrections; see for example [204]-[213],[194].

Figure 7.5 shows deliberately qualitative sketches of sample MSSM mass spectrum obtained fromthree di"erent types of models assumptions. The first is the output from a minimal supergravity-inspired model with relatively low m2

0 compared to m21/2 (in fact the same model parameters as used

for fig. 7.4). This model features a near-decoupling limit for the Higgs sector, and a bino-like !N1

LSP, nearly degenerate wino-like !N2, !C1, and higgsino-like !N3, !N4, !C2. The gluino is the heaviest

80

1978

1981

1991

1998

2002

2012

Technicolor Susy Large ED RS LHSmall ED

Drowning in Possibilities

Implications for Experimental Searches

Belief in any single theory or paradigmis at all-time low

time

Ntheories Belief

Just examples of possibilities

Model Building Era successful, but over

Huge pain for experimentalists

Models help motivate where how separate signal from background

Enormous work to test each theory

Want to go to the Post-Model Building Era

Huge pain for experimentalists

Models help motivate where how separate signal from background

Enormous work to test each theory

Want to go to the Post-Model Building Era

Is this theory-ladeness acceptable/necessary?

Need a way of simplifying theories

Theories Models

Simplified Models

Models that are based upon well-established principles

(e.g. local quantum field theories that contain Standard Model)

Purpose: Reduce Theory-Ladeness

Not based upon principlesi.e. there is not explicit physical motivation

to avoid two types of problems

Simplified Models designed

Theory Space

Signature Space

Type 1: Narrowly Focused Searches

ExperimentalSearches

Type 2: Redundant TheoriesTheory Space

Signature Space

ExperimentalSearches

Simplified Models

Start with Standard Model

Postulate relevant particles for a search

Start with 1,2 or 3 new particles

Write down most general theory

Usually small number of parameters

Simplified Models

Can capture essential features of existing models

Notice unexplored corners of theory spacefrom lack of imagination

No burden of top-down motivationNo Principles

Simplified Model Example

g̃

�̃

MASS

color octet majorana fermion (“Gluino”)

neutral majorana fermion (“LSP”)

THREE-BODY DECAY

g̃q̃

q q̄

�01

g̃

g̃

g̃

g

g

q

q

q̄

q̄

�

�

Gluino Pair Production

p

p

g̃

g̃

g̃

g

g

q

q

q̄

q̄

�

�

Gluino Pair Production

p

p

g̃

g̃

g̃

g

g

q

q

q̄

q̄

�

�

j

j

j

jGluino Pair Production

ET�

p

p

g̃

g̃

g̃

g

g

q

q

q̄

q̄

�

�

j

j

j

jGluino Pair Production

ET�

p

p

g̃

g̃

g̃

g

g

q

q

q̄

q̄

�

�

j

j

j

j

Multijets + Missing Energy

Gluino Pair Production

Common Susy Search Strategy

Base searches on mSUGRA Supersymmetry

mg̃ = 7m�0

Not general

Risk Type 1 Failure

Allowed us to place limits on new theorieswith little data

200 pb

300 pb

500 pb

1 nb

2 nb

100 pb

Tevatron

!prod = 3!" NLO-QCD

!prod = !" NLO-QCD

!prod = 0.3 !" NLO-QCD

!prod = 0.1 !" NLO-QCD

mSUGRA

g̃ � �qq̄

Sample theory

LHC 70 nb-1

18

Oneplot

summaryExperiments are in the game now

Has led to more searches

Modified Triggering

More kinematic regions searched

Unfortunately, no discoveries (yet)

Summary of Simplified Models

Represent natural extension ofEffective Field Theory to the LHC

Construct incomplete models to fit data

When incomplete model doesn’t work extend model

In the Discovery Era

Too many theories to search for

Simp. Mods.: axes for decomposing all theories

Reduce theory prejudice

Then construct Theory (understand Principles)

End