The Quest for SUSY :

issues for collider physics and cosmology S. Kraml (CERN) 1-3 Dec 2006

Supersymmetry (SUSY)

is the leading candidate for physics beyond the Standard Model (SM).

Symmetry between fermions and bosons

Q a |fermion> = |boson> This combines the relativistic “external” symmetries (such as Lorentz unique extension of relativistic symmetries of space-time!

recall Arkani Hamed‘s comments on the unification of space and time...

... predicts a partner particle for every SM state ________________________________________________________ The motivations for TeV-scale SUSY include  the solution of the gauge hierachy problem  the cancellation of quadratic divergences  gauge coupling unification  a viable dark matter candidate ________________________________________________________

The search for SUSY is hence one of the primary objectives of the CERN Large Hadron Colider and a future int. e + e _ linear collider!

This talk

1.

2.

3.

SM problems and SUSY cures   Naturalness and hierachy problems Gauge coupling unification The minimal supersymmetric standard model  Particle spectrum  Collider searches: LHC, ILC The cosmology connection  Dark matter  EW phase transition and baryon asymmetry

SM problems and SUSY cures

The hierachy and naturalness problems

 To break the electroweak symmetry and give masses to the SM particles, some scalar field must acquire a non-zero VEV.

 In the SM, this field is elementary, leading to an elementary scalar `Higgs' boson of mass m H . However, where L is the scale (= cut-off ) up to which the theory is valid.

These large corrections to the SM Higgs boson mass, which should be m H =

O

(m W ), raise problems at two levels:  to arrange for m H to be many orders smaller than other fundamental mass scales, such as the GUT or the Planck scale ― the hierarchy problem ,  to avoid corrections d m H 2 than m H 2 which are much larger itself ― the naturalness problem .

The supersymmetric solution

XXX XXX

A light Higgs

XXXX XXXX XXXX c.f. talk by W. Hollik

c 2 fit of the Higgs boson mass from EW precision data as of Summer 2006

Radiative electroweak symmetry breaking

Heavy top effect, drives m H 2 < 0 EW scale GUT scale

Grand unification

.

 GUTs attempt to embed the SM gauge group SU(3)xSU(2)xU(1) into a larger simple group G with only one single gauge coupling constant g.

 Moreover, the matter particles (quarks leptons) should be combined into common multiplet representations of G.

 Prediction: Unification of the strong, weak and electro magnetic interactions into one single force g at M X . NB: If M X is too low → problems with proton decay

1-loop renormalization group evolution of gauge couplings:  SM:  MSSM:

One can also re-write this as

XX Can also be turned into a prediction of the weak mixing angle .....

The MSSM

Minimal supersymmetric model

MSSM = minimal supersymmetric standard model SM particles quarks leptons gauge bosons Higgs bosons

spin

1/2 1/2 1 0 Superpartners squarks sleptons gauginos higgsinos

spin

0 0 1/2 1/2 1 superpartner for each d.o.f.: ~ L,R and l ~ L,R higgsinos L-R mixing

mix to

~Yukawas 2 charginos + 4 neutralinos 2 Higgs doublets → 5 physical Higgs bosons: neutral states: scalar h, H; pseudoscalar A charged states: H + , H -

XXXX

gluinos, squarks Heavy top effect, drives m H 2 < 0 charginos, neutralinos, sleptons Minimal supergravity (mSUGRA)

Universal boundary conditions @ GUT scale

univ. gaugino mass univ. scalar mass

Recall: Light Higgs

XXXX XXXX XXXX c.f. talk by W. Hollik

_

R parity:

symmetry under which SM particles are even and SUSY particles are odd If R parity is conserved  SUSY particles can only be produced in pairs  Sparticles always decay to an odd number of sparticles  the lightest SUSY particle (LSP) is stable  any SUSY decay chain ends in the LSP, which is a dark matter candidate

The scale of SUSY breaking

Goldstino and Gravitino

Gravitino mass

SUSY @ colliders

L

arge

H

adron

C

ollider

 New accelerator currently built at CERN, scheduled to go in operation in 2007  pp collisions at 14 TeV  Searches for Higgs and new physics beyond the Standard Model  „discovery machine“,  typ. precisions O(few%)

SUSY searches at LHC

Spectacular and large signal

Events for 10 fb -1 Events for 10 fb -1 signal background  Tevatron reach E T (j 1 ) > 80 GeV E T miss > 80 GeV ATLAS M eff  E T miss  i 4   1 p T (jet i ) (GeV) From M eff peak  M eff  E T miss  i 4   1 first/fast measurement of SUSY mass scale to  p T (jet i 20% ) (GeV) (10 fb -1 , mSUGRA) Caution: also other BSM models lead to missing energy signature → need spin determination

Compare with Higgs search c.f. talk by G. Dissertori

Mass measurements: cascade decays

Mass reconstruction through kinematic endpoints [Allanach et al., hep-ph/0007009] Typical precisions: (a) few % [ATLAS, G. Polesello]

I

nternational

L

inear

C

ollider

 e+e- collisions at 0.5-1 TeV  Tunable beam energy and polarization  Clean experimental env.

 Precision measurements of O(0.1%), c.f. LEP  Global initiative, next big accelerator after LHC?

ILC

: Precision measurements with tunable beam energy and polarization [TESLA TDR]

can reach O(0.1%) precision see talk by H.-U. Martyn

High-scale parameter determination

c.f. talk by W. Porod

Higgs?

SUSY?

The cosmology connection • dark matter • dark energy • baryon asymmetry • inflation • ....

1 GeV ~ 1.3 * 10 13 K

What is the Universe made of?

 Cosmological data:  4% ±0.4% baryonic matter  23% ±4% dark matter  73% ±4% dark energy  Particle physics:  SM is incomplete; expect new physics at the TeV scale  Hope that this new physics also provides the dark matter  Discovery at LHC, precision measurements at ILC ?

WIMPs

(weakly interacting massive particles)  DM should be stable, electrically neutral, weakly and gravitationally interacting  WIMPs are predicted by most theories beyond the Standard Model (BSM)  Stable as result of discrete symmetries  Thermal relic of the Big Bang  Testable at colliders!

Neutralino, gravitino, axion, axino, LKP, T-odd Little Higgs, branons, etc., ...

BSM dark matter

Relic density of WIMPs

(weakly interacting massive particles) (1) (2) (3) Early Universe dense and hot; WIMPs in thermal equilibrium Universe expands and cools; WIMP density is reduced through pair annihilation; Boltzmann suppression:

n~e -m/T

Temperature and density too low for WIMP annihilation to keep up with expansion rate → freeze out Final dark matter density: W h 2 ~ 1/ < s

v

> Thermally avaraged cross section of all annihilation channels

Neutralino LSP as dark matter candidate

Neutralino system

Gaugino m ´s

Neutralino mass eigenstates

Higgsino mass → LSP

Neutralino relic density

c 0 LSP as thermal relic: relic density computed as thermally avaraged cross section of all annihilation channels → W h 2 ~ 1/

<

s

v>

W

h 2 = 0.1

with 10% acc. puts strong bounds on the parameter space

Annihilation into gauge bosons

 cc → WW / ZZ mainly through t-channel chargino / neutralino exchange; typically also some annihilation into Zh, hh  Does not occur for pure bino; LSP needs to be mixed bino-higgsino (or bino-wino)  Pure wino or higgsino LSP :  neutral and charged states are a mass-degenerate triplet,  (co)annihilation too efficient  Right relic density for  ( |m| -M 1 )/M 1 ~ 0.3

,  (M 2 -M 1 )/M 1 ~ 0.1

[hep-ph/0604150]

Coannihilations

 Occur for small mass differences between LSP and next-to-lightest sparticle(s); efficient channel for a bino-like LSP  Typical case: coann. with staus  Key parameter is the mass difference DM = m NLSP −m LSP  Other possibilities: Coannihilation with stops ( DM ~20-30GeV), coann. with chargino and the 2nd neutralino (in non-unified models)

mSUGRA parameter space

 GUT-scale boundary conditions: m 0 , m 1/2 , A 0 [plus tan b , sgn( m )]  4 regions with right W h 2    bulk (excl. by m h from LEP) co-annihilation Higgs funnel (tan b ~ 50)  focus point (higgsino scenario)

Prediction of

W

h

2

from colliders:

Requires precise measurements of  LSP mass and decomposition bino, wino, higgsino admixture  Sfermion masses (bulk, coannhilation) or at least lower limits on them  Higgs masses and widths: h,H,A  tan b Required precisions investigated in, e.g. Allanach et al, hep-ph/0410091 and Baltz et al., hep-ph/0602187 c.f. talks by H.U. Martyn & B. Allanach NB: determination of < s v> also gives a prediction of the (in)direct detection rates

For a precise prediction of

W

h

2

we need precision measurements of most of the SUSY spectrum (masses and couplings)

LHC WMAP

→ LHC+ILC ←

ILC

Gravitinos

Recall:  If m 3/2 > m LSP , the gravitino does not play any role in collider phenomenology  However, it is possible that the gravitino is the LSP Phenomenology as before, BUT all SUSY particles will cascade decay to the next-to-lightest sparticle (NLSP), which then decays to the gravitino LSP.

 Note 1: the NLSP may be charged  Note 2: since the couplings to the gravitino are very weak, the NLSP can moreover be long-lived → Gravitino as dark matter candidate → Collider pheno characterized by the nature and lifetime of the NLSP

Implications from cosmology

 The most popular model for explaining the apparent baryon asymmetry of the Universe is LEPTOGENESIS → out-of-equilibrium decays of heavy singlet neutrinos   Leptogenesis requires a reheating temperature T R > 10 9 GeV At high T R ~ an unstable G is severely constrained by BBN ► Leptogenesis is OK if the gravitino is the LSP [Buchmüller et al]

Gravitino dark matter

• Neutralino NLSP is excluded by BBN • Best studied alternative: stau NLSP • Need to confirm spin-3/2 [L. Covi et al] c.f. talk by H.-U. Martyn

instead of conclusions ...

„Since its discovery some ten years ago, supersymmetry has fascinated many physicists“ Hans-Peter Nilles, Phys. Rept. 110 (1984)

„The discovery of supersymmetry is tantamount to the discovery of quantum dimensions of space time“ David Gross, CERN Colloq., 2004

whether or not it is SUSY ....

The exploration of the TEV energy scale at the LHC and a future ILC will lead to fundamental new insights on physics at both the smallest and the largest scales.

PS: SUSY phenomenology is extremly rich, and this talk could only scratch on the surface.

SUSY at this meeting:  MSSM predictions  Charginos at the ILC  Parameter determination  SUSY CP violation  Neutrino masses  SUSY breaking  SUSY dark matter W. Hollik T. Robens H.-U. Martyn, W. Porod T. Kernreiter, K. Rolbiecki F. Deppisch N. Uekusa A. Provenza , B. Allanach

backups

Assume we have found SUSY with a neutralino LSP and made very precise measurements of all relevant parameters:

What if the inferred

W

h

2

is too high?

Solution 1:

Dark matter is superWIMP

e.g. gravitino or axino

Solution 2:

R-parity is violated after all

 RPV on long time scales  Late decays of neutralino LSP reduce the number density; actual CDM is something else  Very hard to test at colliders  Astrophysics constraints?

Solution 3:

Cosmological assumptions are wrong

 Our picture of dark matter as a thermal relic from the big bang may be to simple  Universe after Inflation radiation dominated?

 Non-thermal production?

 Assumptions in WMAP data ↔ W h 2 ?