1. Learning from discovering (or not) The Scalar

2. Plenty of scalars at this meeting….
BUT…
so far, Nature does not seem
to like elementary scalars
and the composite ones are never
„unnaturally” light

3. PIONS:
Goldstone bosons of the spontaneously broken chiral
(global) symmetry of QCD
New mass scale at < 4f ( mass) where  interactions
become strong
The Scalar in QCD (accompanying SSB)
-  meson (radial excitation)-
has the mass of the order of the  mass
Small pion mass and the  meson mass are fully „natural” (in quantum field theory)

4. Are we going to face a new situation concerning scalars
or, if new ones exist, are they similarly „natural” ?
A firm „reference” point for this question-
we need an EWSB sector
Subtitles of this talk:
What if the EWSB sector will be the only source
of information on BSM physics (hopefull not!)?
Can we understand EWSB without any direct exp information on BSM physics (e.g. like new particles)?

5. Crucial for the Brout-Englert-Higgs mechanism in electroweak theory:
spontaneous breaking of a global symmetry, at least
SU(2)xU(1) or better (for =1)
SU(2)xSU(2)SU(2)
of some sector coupled to the weak gauge
bosons as the origin of their masses
The BEH mechanism:
Goldstone bosons become the longitudinal
modes of the gauge bosons W, Z which
acquire masses.
The Scalar(s) are „by-product” of S (global) SB

6. Simplest dynamical sector with chiral symmetry (to be spontaneously broken) – self interacting scalar field
Virtue - renormalizability; also easy description
of fermion masses;
Prediction: ELEMENTARY scalar h as The Scalar;
hWW, hqq couplings are known;

7. Matching of the couplings 
h unitarizes the WLWL amplitude (WL   )
mh serves as a cut-off

8. We can predict the production cross sections and
the decay rates as a function of The Scalar mass
mh=?
Precision data:

9. Well known drawbacks of the SM The Scalar
(highly unnatural, if it exists in isolation)
Basic concepts to make EWSB „natural”:
supersymmetry
new strong interactions
extra dimensions
All of them give (or at least are consistent with) a light
The Scalar (not necessarily an elementary one)
Can we distinguish it from the SM The Scalar?
What can we learn about the BSM dynamics from the scalar
sector? (First question: does the BSM dynamics exit at all?)

10. Generic characteristics of the scalar sector in (perturbative or non-perturbative) extensions of the SM with elementary ( 2HDM (sorry, Francois), supersymmetry)
or composite scalars
often more than one scalar and/or vectors coupled to WW
none of the scalars couple to WW and to fermions
exactly like the SM The Scalar (because of the mixing
between them)
Looks like good news but… how big effects can
we expect?

11. In non-linear parametrization (W = a)
typically
Interpretation of
the scale f depends
on BSM

12. Implications (with perturbative or non-perturbative
BSM physics)
WW scattering amplitude is not fully unitarized
by a single scalar;
other scalars (elementary or composite) or
vectors must be active in unitarization
production cross sections for h and its decay rates
are modified ( usually more difficult to discover )
Unfortunately, the departures from the SM
The Scalar are likely to be tiny- take e.g. f=1 TeV
(but not necessarily!),
particularly with the limits on BSM particles
coming from the LHC

13. Partial unitarization of the WW scattering by
the lightest scalar S, S,

14. Effects on the precision tests (Slava et al.)
The cutoff scale may have different interpretations (e.g.
the mass of the next scalar)
Light but non-SM- like The Scalar also destroys the fit;
New contributions needed-good news

15. The closer to the SM the lightest The Scalar is
the easier to discover
but, unfortunately, more difficult to distinguish
various scenarios
Extreme non-SM case: The Scalar does not play
any important role in the unitarization of WW scattering
(no- The Scalar scenario)

16. New exclusion limits: SM The Scalar is excluded
at 95% CL in the range GeV.
Very interesting but not surprising in view of the
precision fits
Open windows for the SM The Scalar : GeV
> 460 GeV
Exclusion limits as a function of the scalar couplings?
Let’s assume a light The Scalar scenario (not necessarily
with exactly SM scalar) or no-The Scalar scenario

17. The Higgs boson mass in supersymmetric models
(of the lightest one/closest to the SM Higgs):
MSSM (Haber,Hempling ’91,….)

18. Several options for larger mh with no excesive fine-tuning
e.g additional singlet(s)
(Espinosa, Quiros 92, Gunion, Ellwanger, …Kolda) various versions
Even for  small enough to remain perturbative up to MGUT ,
mh ~ 140 GeV is accessible either for low tan  or for large
tan  with large mix
Larger  (Barbieri et al..)  mh up to 300 GeV
(for perturbative theory up to 10 TeV)
Given the present exclusion limits – no strong motivation

19. SUSY search
Quite constraining for „simple” models (CMSSM etc)
but … too early for any more general conclusions
on the fate of supersymmetry

20. For instance, flavour-motivated „inverted hierarchy” spectrum
3rd generation light, 1st and 2nd heavy
Dudas et al. 95
Cohen et al.. 96
Nelson and Wright 97
Arkani-Hamed and Murayama 97
Lavignac et al.. 05
Barbieri et al.. 07
is much weaker constrained

21. For instance, in models based on horizontal U(1) symmetry
to explain the fermion mass hierarchy,
X= Q, U, D
qXA – the respective horizontal charges
 - Cabibbo angle
- gravity mediation contribution
inverted hierarchy for q3 = 0, q1,2 > 0

22. correlated with
in a model dependent way
e.g.
etc

23. Inverted hirerarchy and LHC searches

24. with a light scalar (more „flexible” than supersymmetric models)
STRONG EWSB
with a light scalar (more „flexible” than supersymmetric
models)
as a radial excitation in technicolour-like theories
(QCD -like) ( this meeting: Sannino, Skiba)
gauge-Higgs unification in extra dim (this meeting: Hosotani)
Higgs doublet as a (pseudo)-Goldstone boson
(this meeting: Grojean)
No-The Scalar models

25. Modeling strong interactions:
resonance saturation approximation, with
perturbative gv couplings; controlled by
chiral symmetry (techniques developed for QCD,
e.g. vector bosons as hidden gauge symmetry bosons)

26. Falkowski, Grojean, Kaminska, SP, Weiler

27. CONCLUSIONS
A light The Scalar scenario looks more plausible but,
paradoxically, the no-scalar one would select more uniquely
the direction for extending the SM
A light scalar, particularly one similar to the SM The Scalar, will leave several options for BSM physics open; more experimental findings or/and high precision measurements in the EWSB sector will be needed for focusing on one of them
A universal, unique laboratory for full understanding
of the EWSB is the WW scattering (elastic and inelastic)

28. END

29. Strongly coupled theories with Higgs doublets
as Golstone bosons (composite Higgs boson models)
SO(5)  SO(4) = SUL(2) x SUR(2) by a vev of
and doublet H remains as Goldstone boson;
Vev of H (to break EW) is then obtained from some explicit breaking of SO(5) (e.g. top quark Yukawa)

30. After SO(5) breaking
Eventually, we assume, H gets a vev v << f (from v) and
Ga are Goldstone bosons eaten by W and Z

31. The electroweak scale is
The Higgs coupling to the „eaten” Goldstones is supressed
Reason: h partially in S

32. Striking experimental signatures related to the
presence of three physical scales:
<H> = v, <> = f,  ~ 4f
breaks SU(2)xU(1) breaks SO(5) cut-off to perturbative physics
v/f  10 for v to be natural
New fermions – to protect Goldstone nature
of H above scale f
heavy top quark T, mT ~ O(f )

33. In summary, three questions about the electroweak symmetry breaking:
1) What is the dynamical origin of the electroweak scale?
2) What stabilises the electroweak scale ?
(where the scale M comes from?)
3) What unitarizes the WW scattering amplitude?
massive W  A ~ GF E2~ s/v2
Related but not identical questions: for instance, in the SM WW is unitarized by an elementary scalar (Higgs boson) but we have no idea what is the origin of GF and what stabilises the Fermi scale.
The LHC should give us some answer to (2) and (3)
but not necessarily to (1)

37. Unitarity of WLWL(ZL) scattering amplitude SM:

38. NON-LINEAR STRUCTURE MORE IMORTANT FOR SMALLER f;
E.G. FOR f=350 GeV  30% efect on the hWW coupling
SINCE FINE-TUNING IN THE EWSB SECTOR RISES LIKE (f/v)^2, ONE COULD HOPE FOR AN INTERESTING EXPERIMENTAL SIGNATURE
BUT, UNORTUNATELY, FOR MODELS WITH A STRONGLY INTERACTING SECTOR RESPONSIBLE FOR THE GLOBAL SYMMETRY BREAKING, FOR LOW f THERE IS GENERICALLY SOME TENSION WITH PRECISION ELECTROWEAK DATA

41. 2) Partial unitarization of the WW scattering by
the light Higgs boson
3) Higgs boson couplings to fermions

42. Crucial for Brout-Englert-Higgs mechanism:
spontaneous breaking of chiral symmetry (global)
SU(2)xSU(2)SU(2)
of some sector coupled to the weak gauge
bosons is the origin of their masses

46. Crucial for Brout-Englert-Higgs mechanism:
ORIGIN OF THE ELECTROWEAK VACUUM
Crucial for Brout-Englert-Higgs mechanism:
spontaneous breaking of chiral symmetry (global)
SU(2)xSU(2)SU(2)
with an order parameter v
of some interactions whose currents are coupled to the electroweak weak gauge bosons is the origin of the gauge boson masses; 3 Goldstone bosons are „eaten up” by gauge bosons