F. ZwirnerUniversity & INFN, Padova

LPT-ENS, CNRS, Paris

Why Supersymmetry and/orNew Physics in the LHC Era?

High Energy Physics in the LHC EraParis, 13 November 2006

PreambleThis talk: (possible) new physics at the TeV scale,to be directly explored by experiments the LHC

Other interesting new physics accessible toexperiment, not directly related to LHC scale:

•Neutrino masses and oscillations•Dark matter candidates (e.g. axions)•Dark energy models (e.g. quintessence)•Modifications of gravity (e.g. sub-mm distances)•Models of inflation (e.g. within unified theories)•…

Some of these topics discussed in other talksSome may be linked to LHC-scale new physics!

Plan

1. New physics at the LHC scale?

2. Supersymmetry at the LHC scale

3. Other new physics at the LHC scale?

4. Conclusions

1. Why new physics at the LHC scale? Why new physics? #1 answer:

to reconcile gravity and quantum mechanics

string theory unifies all interactions may give predictions for LHC physics

present understanding: “plausible scenarios”(or, according to some, a landscape of vacua) new physics at LHC: phenomenologicalapproach, mixing theoretical motivationswith hints coming from experimental data

A critical look at the Standard ModelOnly part of SM still under discussion

symmetry-breaking sectorrealized by elementary scalar doublet

Spontaneous breaking of the gauge symmetry

Explicit breaking of the global flavour symmetry

Picture confirmed so far with impressive precisionMissing particle (parameter): Higgs boson H (mH)

LEP direct searches: mH > 114.4 GeV (95% c.l.)

Precision tests of EW breaking [LEPEWWG, Summer 2006]

Recent improvement: mt = 171.4 ± 2.1 GeV (CDF & D0)

i) SM still fits well at such high precision!ii) Indication for (too?) light Higgs in SM

+39mH=85 GeV -28

What prefers a light Higgs?

[P.Gambino]

Correlations: MtopmH MWmH s2wlmH

• MW points to a light Higgs, with good accuracy• Some tension in leptonic vs. hadronic asymmetries

Precision tests of flavour breakingImpressive recent progress, and:

no significant deviation from SM (GIM,CKM) found

The unitarity triangle Some recent examples:

CDF (& D0)

CP-violation in B systemRare B decays

UT from tree-level processes(Belle, BABAR)

(Belle)

(NA48)

and some older ones:

The SM as an effective theory= effective UV cutoff (not necessarily universal)= the scale of some (unspecified) new physics

[triviality and (meta-)stability bounds not very constrainingwith present values of the top and Higgs boson masses]

Naturalness [‘t Hooft; …]

coefficients small only because of symmetries

electron mass me in QED naturally smallchiral symmetry no linear dependence on cutoff

could have been used in NR theory to predict positron

4-fermion FCNC “box diagram” with 3 light quarks

Natural solution: GIM mechanism! New physics: charm!

Another example: charged/neutral pion mass difference

Naturalness works!

Naturalness problem of the SMHiggs mass term (weak scale): gauge hierarchy problem

No quantum SM symmetry recovered for mH 0SM unnatural unless New Physics at the LHC scale

The lighter the Higgs, the lower the scale of New Physics!

A worse naturalness problem (when gravity is included) is thevacuum energy (10-3eV scale): cosmological constant problem

No natural solution found so far, but not excluded either:modifications of gravity at sub-mm scales still possibleeven if bound considerably improved in the last years

Today’s puzzle[stressed, e.g., by Barbieri and Strumia: little hierarchy problem]

SM with light Higgs is in precise agreement with dataNaturalness pushes for a low scale of new physics:

Precision tests push for a high scale of new physics:

Conflict avoided with weakly coupled new physicsaffecting low-energy observables only via loops

(and decoupled from flavour-violating operators)

2. Supersymmetry at the LHC scale

•In most general symmetry of local relativistic Q.F.T.•Linearly realized, it gives a rationale for elementary scalars, living in N=1 multiplets with chiral fermions•Local version, supergravity, fits naturally in strings exactperturbative stability of flat Minkowski space

However, in any realistic model it must be broken[O(10^2 GeV) lower bounds on charged sparticles]

none of above arguments points to LHC scaleas preferred scale for superparticle masses

Why supersymmetry?

Why at the LHC scale?SUSY can solve the gauge hierarchy problem

[Weinberg; Maiani; Veltman; Witten; …]

thanks to its special renormalization properties[Wess-Zumino; Iliopoulos-Zumino; Ferrara-Girardello-Palumbo; Grisaru et al;…]

In (many) supersymmetric extensions of the SM:

Power-dependence on SUSY-breaking massesonly mild logarithmic dependence on cutoff

Naturalness preserved up to very high scalesif superparticle masses are at the weak scale

[qualitative here,more details below]

The prototype: MSSM [Fayet; Dimopoulos-Georgi; …]

• Gauge group SU(3) x SU(2) x U(1)

• 3 SM generations, 2 Higgs doublets

• R-parity conserving superpotential

• Explicit soft supersymmetry breaking

(more on possible variations later)

(the source of many troubles: # parameters, flavour)[see talks by Djouadi, Ellis, Polesello for phenomenology]

Two important bonuses•Effective unification of gauge coupling constants (at a scale MU~2×1016 GeV not very far from MP)•A natural candidate for dark matter, the LSP typically lightest neutralino (gaugino/higgsino)

Two features so appealing that some proposed to keep them without solving the hierarchy problem, sending all the scalars but SM Higgs to very high mass scales:

SPLIT SUPERSYMMETRY [ArkaniHamed-Dimopoulos, Giudice-Romanino,…]

A limiting case of the MSSM worth exploring(for those who feel ready to throw naturalness away)

Advantage: no flavour problemsLHC signature: long-lived gluino

MSSM post-LEP tensionconcrete MSSM realization poses some tuning problems,especially when extrapolating the MSSM to high scales

Things are made worse by the upper bound on the Higgs mass[Ellis, Ridolfi, FZ; Okada,Yamaguchi,Yanagida; Haber,Hempfling; …]

There are ways to do better, e.g. adding a singlet (NMSSM)

O(few%) fine-tuning required without further theoretical input(might be explained in dynamical models of mass generation)

naturalness suggests light SUSY:

An empirical measure of fine-tuning

lightestHiggsmass(GeV)

lightest chargino mass (GeV)

After LEP-1

After LEP-2

Beyond the MSSM [see talks by Binetruy, Derendinger, Savoy]

Taking the MSSM at face value, its appealing properties

•Solution of “big” hierarchy problem•Effective unification of gauge couplings•Natural candidate for dark matter

come with a number of unanswered questions

•Special flavour structure of soft terms•Relative scale of different soft terms•Absolute scale of soft terms•Little hierarchy problem•Vacuum energy problem

To answer, study spontaneous breaking in the microscopictheory (for the first two issues, enough to know mediationmechanism from the susy-breaking sector to the MSSM)

The need for supergravity

spin-2 GRAVITINOspin-3/2 gauge fermion of SUGRA

Minimal framework for spontaneous breaking in localSUSY (supergravity) : MSSM + goldstino multiplet +

gravitationalmultiplet

A crucial difference with global supersymmetry:

no sparticle observed

limits on vacuum energy

phenomenology gravitational effects crucial for vacuum selection

(only afterwards we can take the global limit)if not, we implicitly accept anthropic attitude…

only inSUGRA

SUSY-breaking scale, m3/2 and phenomenologyAssuming sparticles with masses at the LHC scale does

not fix gravitino mass and supersymmetry-breaking scale:

Irrespectively of models, two broad scenariosfor the effective theory valid at the LHC scaleo Heavy gravitino (weak scale mass)• MSSM + soft terms with cutoff O(MP)• MSSM LSP stable (WIMP dark matter)• Fits well with gauge coupling unificationo Light gravitino (mass < keV)• MSSM + goldstino multiplet• Effective cutoff << MP (“messengers”)• MSSM LSP particle + (goldstino)

No-scale modelsHierarchy problems of generic N=1 supergravity:

• Vacuum energy (classical and quantum level)• (m3/2/MP) hierarchy (generation and stability)

No-scale models have special classical properties:[Cremmer, Ferrara, Kounnas, Nanopoulos]

• Classically flat potential with zero vacuum energy• Broken supersymmetry with sliding gravitino mass

Assuming no terms O[(m3/2MP)2] in Veff = Vcl + ∆V mayallow for a dynamical generation of the hierarchy m3/2<<MPfrom interplay of gauge vs. Yukawa renormalization effects[Ellis-Lahanas-Nanopoulos-Tamvakis; Ellis-Kounnas-Nanopoulos; Kounnas-Pavel, FZ]

With more assumptions, may explain little hierarchy[Barbieri-Strumia]

No-scale model arise in string compactifications,important to explore more their quantum properties

3. Other new physics at the LHC scale?What if naturalness fails for the weak scale?(as it may fail for the vacuum energy scale)

A logical possibility, although not my favourite

Light SM Higgs boson and nothing else at the LHC(called by some supersplit supersymmetry)

•A triumph for the SM•A triumph for the LHC Experiments•A failure for many theorists

Before such possibility, rather consider solutions to the SMnaturalness problem, alternative/complementary to SUSY,

they also predict testable new physics at the LHC scale

Briefly, since most interesting ones covered by other talks

Extra dimensions

Naturally predicted by string theory, but no predictionabout their size (mass scale mKK of first KK excitations)

Relevant at LHC for mKK ~ TeV (or less: ADD models)

Can be combined with susy broken in the compactification

Dynamical problem: understand origin & stability of mKK

Richer possibilities if warped [Randall-Sundrum] (“holography”)

[see talks by Antoniadis, Pomarol, Quiros]

Some variants:•Higgsless models [Csaki, Grojean, Murayama, Pilo, Terning;…]: delayunitarity bound on mh via KK states; problems with EWPT

•Gauge-Higgs unification [Manton; … ]: mH protected by D>4gauge symmetry; problems with EWPT, mh, mKK, flavour

A strongly interacting EW-breaking sector?

Higgs as a bound state of new strong interactions

Traditional implementation (technicolor) stronglydisfavoured by precision tests (and our limitedunderstanding of non-perturbative dynamics)

Now being revived with some modern tools:light Higgs as pseudo-Goldstone boson

holographic gauge/gravity correspondence

Promising results on naturalness and precision tests:technicolor strikes back?

[see talk by Pomarol]

Higgs as pseudo-Goldstone boson (Little Higgs)

Minimal natural models?[see talk by Barbieri]

Minimalistic approach to little hierarchy problem:raise the natural cutoff scale of (MS)SM by raising the

Higgs mass, with another ingredient to pass EWPT

•Higgs mass protected by a global shift symmetry (GB)•Broken explicitly (PGB) for quartic and Yukawa couplings•Collective symmetry breaking mass only at two loops•Typical models predict new particles at the LHC scale•Problems with precision tests (T-parity+complications)

[Georgi-Pais; ArkaniHamed-Cohen-Georgi; …]

4. (My temporary) conclusions•Naturalness can still be used as a guiding principle•It unambiguously predicts new physics at the LHC scale•Precision tests: new physics must have special properties•Supersymmetry still the most plausible candidate, even if we would have expected it to have been found already•We may be missing important aspects of susy breaking•Healthy to have alternatives for new physics at the LHC, some may merge with supersymmetry at a deeper level (e.g. extra dimensions & strongly interacting EW sector)

and, most importantly:THE ERA OF SPECULATIONS ON WEAK SCALEIS AT ITS END: THE LHC VERDICT IS COMING!