Lecture 8 - PowerPoint Presentation

Slide1

Lecture 8

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Overview

Final lecture today! Can cover the following topics today:

Sfermion

, chargino and neutralino massesFine Tuning What this really means, how we may quantify it.How LHC squark, gluino and Higgs searches affect this Changing universality assumptions Relaxing some constraints Using different breaking scheme inspired constraints Non-minimal Supersymmetry Extend the chiral superfield contentExtend the gauge structure

Can give overview of all or focus on one or

two?Slide3

MSSM

Chiral

Superfield

ContentLeft handed quark chiral superfieldsNote: left handed fermions are described by chiral superfields, right handed fermions by anti-chiral superfields. Superpotential is a function of chiral superfields only so we include right handed fermions by taking the conjugate, which transforms as a left handed

superfield

!

Conjugate

of right handed quark

superfields Slide4

MSSM

Lagragngian

density

Superpotential

With the gauge structure, superfield content and Superpotential now specified we can construct the MSSM Lagrangian. Slide5
Slide6

EWSB conditions

For successful EWSB:

With: Slide7

Higgs Masses

Goldstone bosons

CP-even Higgs bosons

Charged Higgs boson

CP-odd Higgs bosonSlide8

Sfermion

masses

Softmass

:

Flavour

diagonal postulate

F-terms

D-termsSlide9

Sfermion

masses

Home exercise:

find all the mistakes on the previous slide, then write in matrix form below and

diagonalise.Slide10

Chargino

and

Neutralino

masses

Soft masses:

Superpotential

:

Kahler

potential:

VEVs

(Home exercise)

Hints:Slide11

Chargino

and

Neutralino

massesSlide12

Chargino

and

Neutralino

massesSlide13

Chargino

and

Neutralino

massesSlide14
Slide15
Slide16

parameter space

volume restricted by,

Parameter space point,

Tuning

:

`` ``

Compare dimensionless variations

in

:

ALL parameters

vs

ALL observables

Our Approach

PA &

D.J.Millier

PRD 76,

075010 (2007) Slide17

parameter space

volume restricted by,

Parameter space point,

Tuning

:

`` ``

Compare dimensionless variations

in

:

parameters

vs

observables

Our Approach

PA &

D.J.Millier

PRD 76,

075010 (2007)

Probability of random point

from lying

in :

But remember any parameter space point is incredibly unlikely if all equally likely (flat prior)!

Fine tuning is when a special qualitative feature ( ) is far less likely that other typical case ( )Slide18

Any G

<<

F

parameter space volume restricted by,

Parameter space point,

Tuning

:

`` ``

Compare dimensionless variations

in

:

parameters

vs

observables

Our Approach

PA &

D.J.Millier

PRD 76,

075010 (2007)

Probability of random point

from lying

in :

But what if :

l

arge for all points (or all values of

O

)

Global sensitivity (Anderson &

Castano

1995) Slide19

Any G

<<

F

parameter space volume restricted by,

Parameter space point,

Tuning

:

`` ``

Compare dimensionless variations

in

:

parameters

vs

observables

Our Approach

PA &

D.J.Millier

PRD 76,

075010 (2007)

Probability of random point

from lying

in :

But what if :

l

arge for all points (or all values of

O

)

Rescale to our expectation for

Slide20
Slide21

Regardless of measure details, fine tuning is increased when searches increase mass limits on

squarks

and

gluinos:

Search pushes up. Larger cancellation required!Slide22

What about the Higgs?

Heavy stops

Large soft masses

a

nd large one loop corrections

A relatively heavy Higgs requires heavy stops

Break

cMSSM

link between stop masses and light

squarks

and evade fine tuning

LEP bound

Tuning?

Tentative LHC Higgs signalSlide23

Fine Tuning Summary

Most important consideration at the LHC (by far) is what do we

seec

Higgs? Beyond the standard model (BSM) signal?

If BSM signal is observed initially all efforts on understanding new physics.Eventually will know if new physics solves Hierachy ProblemResidual tuning may also be a hint about highscale physicsIf no SUSY signal? Where does that leave us? Subjective question, depends on tuning measure, but also prejudice Conventional wisdom: no observation ) SUSY is fine tuned! Motivation for low energy SUSY weakened (doesn’t remove fine tuning).No BSM signal at allHierarchy Problem motivated BSM models have tuning too.Nature is fine tuned?

SM true up to Planck scale?

Or we need some great new ideaSlide24

Beyond the CMSSM

(Relaxing high scale constraints)

Non-universal Higgs MSSM (NUHM)

Motivated since Higgs bosons do not fit into the same SU(5) or SO(10) GUT

multiplets: 105*+

1

+

16

10

5

5

*

Color triplets

+Slide25

Beyond the CMSSM

(Relaxing high scale constraints)

Non-universal Higgs MSSM (NUHM)

Impact: Higgs masses not linked to other scalar masses so strongly

easier to fit EWSB constraints and other observables Motivated since Higgs bosons do not fit into the same SU(5) or SO(10) GUT multiplets

:

Very mild modification to the CMSSMSlide26

Beyond the CMSSM

(Relaxing high scale constraints)

Non-universal

Gaugino

masses For universal

gauginos

we have a (one loop)

relation:

Testable predictions for

gaugino

universality!

Breaks ratio get different

gaugino

mass patterns:

One can also ignore the universality more parameters to consider the model with less prejudice, e.g.

pMSSMSlide27

In gauge mediated symmetry breaking

the SUSY breaking is transmitted from the hidden sector via SM

gauge interactions of heavy

messenger fields.Chiral Messenger fields couple to Hidden sector SUSY breaking in messenger spectrumSM Gauge interactions couple them to visible sectorLoops from gauge interactions with virtual messengers flavour diagonal soft masses.

Non-universal soft

gaugino

masses since they depend on gauge interactions!

Soft mass relations imposed at messenger scale

Gauge Mediation

More details and a more general definition given in Steve Abel’s lectures

Loop diagram:Slide28

Minimal

G

auge

Mediated

SUSY Breaking (mGMSB)Messenger fields form Complete SU(5) representations

From EWSB as in CMSSM

Number of SU(5)

multiplets

Messenger scaleSlide29

Beyond the MSSM

Non-minimal

Supersymmetry

The fundamental motivations for

Supersymmetry are: - The hierarchy problem (fine tuning) - Gauge Coupling Unification - Dark matterNone of these require Supersymmetry to be realised in a minimal form.MSSM is not the only model we can consider!Slide30

The MSSM

superpotential

is written down before EWSB or SUSY breaking:

The

 problem What mass should we use?The natural choices would be 0 or MPlanck (or MGUT)) it should know nothing about the EW scale

.

Phenomenological Constraints

)

¹

¼

0.1 -1

TeV

(

¹

-parameter has the dimension of mass!

The

superpotential

contains a mass scale!

)

Scale of origin

Forbidden by symmetry

)

Slide31

Solve the



-problem by introducing an extra singlet

[Another way is to use the

Giudice-Masiero mechanism, which I won’t talk about here.]Introduce a new iso-singlet neutral colorless chiral superfield , coupling together the usual two Higgs doublet superfields. If S gains a vacuum expectation value we generate an effective -term, automatically of oder the electroweak scale

with

We must also modify the

supersymmetry breaking terms

to reflect the new structureSlide32

Yukawa terms

effective



-

termSo our superpotential so far isBut this too has a problem – it has an extra U(1) Peccei-Quinn symmetry

Lagrangian

invariant under the (global) transformation:

This extra U(1) is broken with electroweak symmetry breaking (by the effective



-term)

massless

axion

!Slide33

Yukawa terms

effective



-

termPQ breaking termNMSSM Chiral

Superfield

Content

massless

axion

!Slide34

The superpotential of the

N

ext-to-

Minimal S

upersymmetric Standard Model (NMSSM) isYukawa termseffective -termPQ breaking term

We also need

new soft

supersymmetry

breaking terms in the

Lagrangian

:

[Dine, Fischler and Srednicki]

[Ellis, Gunion, Haber, Roszkowski, Zwirner]

Modified Higgs sector: 3 CP-even Higgs, 2 CP-odd Higgs (new real and

imagnary

scalar S)

“

Neutralino

sector: 5

neutralinos

(new

fermion

component of S) Slide35

Parameters:

The MSSM limit is



! 0,  ! 0, keeping / and  fixed.  and  are forced to be reasonably small due to renormalisation group running.Top left entry of CP-odd mass matrix. Becomes MSSM M

A

in MSSM limit.

minimisation conditions

Finally:Slide36

Supersymmetric

Models

M

inimal

Supersymmetric Standard Model (MSSM)Next to Minimal Supersymmetric Standard Model (NMSSM)

[Dine,

Fischler

and

Srednicki

] [

Ellis,

Gunion

, Haber,

Roszkowski

,

Zwirner

]

Decouple the axion PQSNMSSM

Alternative solution to

Peccei

–Quinn

symmetry :

Linear S term

nMSSM

Eat the

axion

Z

0

models (e.g

. USSM,

E

6

SSM)

In the latter we extend the gauge group of the SM with an extra gauged U(1)

0

!

When U(1)

0

is broken as S gets a

vev

,

Z

0

eats the

masless

axion

to become massive vector boson! Slide37

Supersymmetric

Models

M

inimal

Supersymmetric Standard Model (MSSM)Next to Minimal Supersymmetric Standard Model (NMSSM)Other variants: nmMSSM, PQSNMSSM.U(1) extended

S

upersymmetric

S

tandard

Model (USSM)Exceptional

S

upersymmetric

S

tandard

M

odel (

E

6

SSM

)

[Dine,

Fischler

and

Srednicki

]

[Ellis,

Gunion

, Haber,

Roszkowski

,

Zwirner

]

[S.F. King, S.

Moretti

, R.

Nevzrov

,

Phys.Rev

. D73 (2006) 035009]Slide38

Yukawa terms

effective



-

termUSSM Chiral Superfield ContentProblem: to avoid gauge anomalies Slide39

Yukawa terms

effective



-

termUSSM Chiral Superfield ContentProblem: to avoid gauge anomalies

Charges not specified in the definition of the USSMSlide40

U

(1) extended

S

upersymmetric S

tandard Model (USSM)Yukawa termseffective -termModified Higgs sector: 3 CP-even Higgs, 2 CP-odd Higgs (new real and imagnary scalar S)

Modified

Neutralino

sector: 6

neutralinos

:

(new singlino + Zprimino )

Modified Gauge sector, new Z

0Slide41

Disclaimer:

I work on the

E

6

SSM Final part included for vanitySlide42

For anomaly cancelation, one can use complete E

6

matter

multiplets

New U(1)

0

from

E

6

E

6

inspired models

Matter from

3

complete generations

of

E

6

)

automatic cancellation of gauge anomalies!

In the E

6

SSM

)

right-handed neutrino is a gauge singletSlide43

All the SM matter fields are contained in one 27-plet of E

6

per generation.

27

10, 1 5*, 2 5*, - 35,

- 2

1,

0

+

+

+

+

U(1)

N

charge

SU(5) reps.

1,

5

+

singlets

right handed neutrino

3 generations of “Higgs”

exotic quarks

E

xceptional

S

upersymmetric

S

tandard

M

odel

(

E

6

SSM

)

[

Phys.Rev

. D73 (2006) 035009 ,

Phys.Lett

. B634 (2006) 278-284

S.F.King

,

S.Moretti

& R.

Nevzorov

]Slide44

E

6

SSM

Chiral Superfield ContentNote: In it’s usual form there are also two extra SU(2) doublets included for single step gauge coupling unification, but these are negleected here for simplicity.Slide45

SUSY Theory space

Gauge group

(vector

superfields

)Chiral superfieldsMinimalsuperfieldsComplete E6 multiplets

E

6

SSM

MSSM

NMSSM

USSMSlide46

Thank you for listening

End of

Supersymmetry

Lecture courseSlide47

Sfermion

masses