# Presentation: 527652

## The Mystery of Mass

-  Marcela Carena
- Theoretical Physics Department
- Fermilab
- Department of Physics, University of Wisconsin
- Madison, November 29, 2006

## Outline

**Introduction**
-     -- The Standard Model (SM) and the quest for electroweak symmetry breaking
**The search for the SM Higgs boson**
-         -- the TeVatron           -- the LHC           -- the prospective ILC
**What does the SM fail to explain?**
-       Conceptual issues:      * The hierarchy problem     * Unification of forces
-       Data driven issues:      * Dark Matter                      * Baryonic asymmetry
**Supersymmetry: a solution to all these problems**
-       An extended Higgs sector   <==>  Flavor changing neutral current effects
-  **The search for the Supersymmetric Higgs bosons**
-       --  At colliders              --Complementarity with direct dark matter searches
**Conclusions**

##                        to explain it in terms of quantum physics which 
                                 governs the microscopic, subatomic world

                    This has revealed an amazing structure and simplicity 

    The basic feature is the occurrence of forces which hold together matter

 At the microscopic level:

                    Elementary particles are the ultimate constituents of matter 
                  Four basic forces act among these elementary matter particles                                                  
                                            gravitation, electromagnetism, 
  the strong and weak nuclear forces

-                                  governs the microscopic, subatomic world
-                     *This has revealed an amazing structure and simplicity** *
*                             *
**    **The basic feature is the occurrence of forces which hold together matter
-  At the microscopic level:
-                     Elementary particles are the ultimate constituents of matter
-                   Four basic forces act among these elementary matter particles **                                                 **
**                                            ****gravitation, electromagnetism, **
**  ****the strong and weak nuclear forces**

_**The role of Particle Physics**_**:  **to discover what the universe is made of and how it works

## Gravitational Force

- Attractive force between 2 massive objects:

- Proportional to product of masses

-   Assumes interaction over a distance d

- ==> comes from properties of space and time

- Is very weak unless one of the masses is huge, like the earth

_**Electromagnetic Force**_

- Electrons interact with protons via quantum
- of e.m. energy : the photons

- Attracts particles of opposite charge

- Forces within atoms and between atoms

- + and - charges bind together
-       and screen each other

-     Modeled by a theory based on
-          U(1) gauge symmetry

- 

## Strong Force

- Atoms are made from protons, neutrons and electrons.

- D. I. S. of electrons with protons or neutrons at high energies shows that
**            ****protons and  neutrons **
**             ****are not fundamental**

**p ******** ****u u**** ****d ****  ****   ****formed by three quarks, bound together by **
**n ******** u**** ****d d****      ****the gluons of the strong interactions**** **

- Very strong at large distances

- confinement

- we see no free quarks  in nature

-  Strong nuclear force binds together
-  protons and neutrons to form nuclei

**demands a novel interaction**

- Observation of Beta decay

- Short range forces exist only inside the protons and neutrons, with massive force carriers:

** ****gauge bosons **** W  and  Z **

-    Explains nuclear fusion in the Sun!
-     and ultimately, Sunlight
**     ****and ultimately****, Sunlight**

- Modeled by

- gauge symmetry

**assigns 2 isospin **
**charges  **

- _Weak Force_

##       The Standard Model 

- A quantum theory that describes how all  known fundamental particles interact
-                                  via the strong, weak and electromagnetic forces** **

- based on a gauge field theory with a symmetry group

- _Matter fields_ :
- 3 families of quarks and leptons with
- the same quantum numbers  under
- the gauge groups

- 12 fundamental gauge  fields:

- 8 gluons,  3       ‘s  and

- and 3 gauge couplings:

- _Force Carriers:_

- There are neutral and charged mediated interactions:
- The charged force carrier -- W boson-- can change the flavor of the quarks: u <==> d

## Matter Fields: 

**3 ****families of quarks and leptons  have**** ****very different masses !**

- How to give mass to             gauge bosons?

- Largest Hierarchies:
- neutrino masses as small as

- _The gauge symmetries of the model do not allow to generate mass at all!_

## What is the origin of Mass of the Fundamental Particles ?orthe source of Electroweak Symmetry Breakdown (EWSB)

- There is a Mystery Field that fills all the Universe
-          -- it does not disturb gravity and electromagnetism but it renders
-              the weak force short-ranged
-          -- it slows down the fundamental particles from the speed of light

-    We know that the electromagnetic and weak
-       forces are unified ==> electroweak theory
-               what breaks the symmetry
-                 ==> the Mystery Field
-  We know EWSB occurs at the electroweak scale
-  New phenomena associated to the Mystery Field
-       should lie in the TeV range or below
-                  within LHC/ILC reach

- HERA ep collider

##                     In the Standard Model:  The Higgs Mechanism

-                     _In the Standard Model_:  The Higgs Mechanism
- a self interacting complex scalar doublet with no trivial quantum numbers under SU(2)L x U(1)Y

##              Discovering the Higgs will put the final piece

-              **Discovering the Higgs will put the final piece**
**                          ****of the Standard Model in place**

**but will present big mysteries of its own!**

-    First evidence of EWSB ==> masses of gauge bosons
- Measuring the WWH and ZZH couplings is essential to identify the Higgs as the agent of EWSB
- without a vacuum expectation value, no such trilinear coupling at tree level
-     ==> we need to detect the Higgs in association with gauge bosons
-  The other particle whose mass is related to the source of EWSB is the top quark
-     -- If there were other particles (Higgs) responsible for the top mass, their v.e.v. will be small
-    (not responsible for W,Z masses)  ==> their couplings to the top would need to be too strong --
-    ==> if the theory remains perturbative, the top mass will mainly come from a
-           Higgs with SM-like couplings to W and Z

## The first step is discovery:  

- Observe one candidate Higgs boson (or more).
_**Next step: determine its basic properties**_** :**
- mass, spin, CP quantum numbers;
- couplings to boson and fermions, total width;
- Higgs self couplings to reconstruct Higgs potential;
- possible rare decay modes
_**Use precision measurement of basic properties to learn about basic model of nature**_:
- Is this scalar a Higgs boson?
- Distinguish between a SM Higgs boson and a SM-like Higgs boson coming from an extended Higgs sector in other models of new physics:
- (Supersymmetry, Extra dimensions, Strongly interacting Higgs models ...)
- Investigate CP violation, beyond the SM, via effects in the Higgs sector
**Both the LHC and the ILC will be crucial in establishing **
** ****the nature of the EWSB mechanism**

## How do we search for the Higgs?

**How do we search for the Higgs?**
- Through  its decays into gauge bosons and fermions

-   Demanding theoretical consistency of the SM
-   ==>
-       Depending on its mass it will decay into
-           different particles. One can define:

-  For

-  Above WW, ZZ thresholds, it decays almost exclusively into these particles,
-    with small admixture of

## Direct Higgs search at the Large Electron-Positron collider (LEP)

Indirect constraints on          from precision tests of the SM
    accuracy at the per mille level from experiments at CERN, Fermilab and SLAC

**Indirect constraints on          from precision tests of the SM**
-     accuracy at the per mille level from experiments at CERN, Fermilab and SLAC

- final LEP result, 2003

- Although the Higgs boson has not been seen and its mass is unknown, it enters via virtual Higgs production in electroweak observables: particle masses, decay rates,etc

- All electroweak parameters have a weak logarithmic dependence on
- Nonetheless, preferred value of           can be determined

**To avoid a light Higgs Boson, must have new phenomena below 1 TeV**

## The TeVatron at Fermilab   (2001-2009) 

-  beams of protons-antiprotons colliding to create
-  a shower of new particles:
- 2 multi-purpose detectors:  D and _CDF_

_**The TeVatron at Fermilab**_**   **(2001-2009)
-                the highest energy accelerator in the world

##  Precision measurements of the top quark and W boson masses may   

**                        ****exclude the SM of nature at/above the TeV scale**
-           SM correlation for  Mt-Mw-mHSM   information on mHSM

- New CDF/D0 top mass (174.1  2.1 GeV)
-  & new LEP W mass (80.392  0.029 GeV)
- Soon, new Tevatron measurement of W mass
- competitive in accuracy with LEP
-  What  will be its central value?

_**Indirect Higgs searches**__ __**at the Tevatron**_

## Direct Higgs searches at the Tevatron

_**Direct Higgs searches at the Tevatron**_

** ****Tevatron  can search for a Higgs in parts**** of the mass range   **
**   ****preferred by precision data **

- Quite challenging! Evidence of a signal will mean that
-       the Higgs has SM-like couplings to the W and Z

- Caveat: at the moment both experiments are working hard to achieve the sensitivity shown above

## The Large Hadron Colliderstarts in 2008, opens a new high-energy frontier for physics

_**The Large Hadron Collider**_starts in 2008, opens a new high-energy frontier** **for physics

- ~ a billion proton-proton collisions per second!
-    2 multi-purpose detectors ATLAS and CMS

- CMS

## The search for SM Higgs at the LHC

_**The search for SM Higgs at the LHC**_

-  **Low mass range** mHSM < 200 GeV

|         Production
DECAY | Inclusive | VBF | WH/ZH | ttH |
| --- | --- | --- | --- | --- |
| H → γγ | YES | YES | YES | YES |
| H → bb |  |  | YES | YES |
| H → ττ |  | YES |  |  |
| H → WW* | YES | YES | YES |  |
| H → ZZ*, Z l+l- | YES |  |  |  |

-  **Intermediate mass range**
- 200 GeV < mHSM< 700 GeV
- Inclusive H ==> ZZ==> 4l

-  **Large mass range**:mHSM> 700 GeV
-   VBF with  H ==> WW ==> lv jj
-                                ZZ ==> ll vv

- Nikitenko, ICHEP06

- With K factors

**Higgs Production processes**

## The LHC potential ==> a SM Higgs cannot escape discovery! 

- _Total sensitivity combining all channels_
- _ __plus two experiments_

- 5     discovery possible over the entire SM Higgs mass range of interest with 5 fb-1 (~ 2010)

-   ==> For mHSM~120 GeV combination of many
-    different channels necessary, hence, requires
-    a good understanding of the detectors.
-    ==> The Tevatron may explore such region

**Higgs mass resolution**:  0.1 to 1%, combining most channels for maximal luminosity
- 300 fb-1  (~2015) and both experiments, using H ==>ZZ ==> 4l or H ==> gamma gamma
**Total Width resolution**: 5-8 %  for mHSM > 300 GeV, ATLAS 300 fb-1, H ==> ZZ ==> 4l
**Measure Higgs Couplings** with 5-20 % accuracy (maximal luminosity, both exp.)
**Measuring  SM-like Higgs couplings to W and Z bosons of order one will be evidence**
**      ****of the Higgs responsible for the EWSB  ==> WW fusion most relevant channel**

## The Standard Model: an effective theory

- The SM is not valid at energies above                          where gravity can no
-           longer be ignored
- SM neutrinos are massless, but neutrino masses have recently been
-           observed to be very small
**                                                                                                                                 **Theories with fundamental scales of order               generate neutrino masses**          **
- Quantum corrections can destabilize the Higgs potential or render the Higgs self coupling to infinity
- Has inelegant mathematical issues: The hierarchy problem ==>
-           ==> quantum corrections make it unnatural to have such huge hierarchy
- 5.      **It does not allow for unification of all forces in nature**
- 6.      **It does not explain: Dark Matter**
**                                           ****The Matter-Antimatter asymmetry  **
**                                           ****The fermion mass hierarchies**

- On its behalf:  it works amazingly well !!  beyond our wildest expectations.

##    SM particles                    SUSY particles

**       **
-         ==> For every fermion there is a boson with equal mass and couplings
-   SUSY is an essential
-   part of String Theory
**                 ****Low energy supersymmetry ==> SUSY particles at the TeV Scale**
-     -- provides a solution to the Higgs mass stability problem
-     -- plays a central role in unification of gauge couplings
-     -- provides a natural candidate for Dark Matter, the neutralino
-     -- provides a solution to the Matter-Antimatter asymmetry of the Universe

**   ****SM particles                    SUSY particles**

**        **New Fermion-boson  Symmetry: **SUPERSYMMETRY ** (SUSY)

*Just as for every particle *
*there exists an antiparticle*

- SUSY must be broken in nature:
- no SUSY partner degenerate in mass with its SM particle has been observed

## Higgs and Supersymmetry

- _Higgs and Supersymmetry_

**Minimal SUSY Standard Model** (MSSM) ==> 2 SU(2) Higgs doublets

- SUSY theories ==> extended Higgs sector with lightest Higgs having (usually)
-                                 SM-like properties and  mh < 200 GeV

-  Exact SUSY: one Higgs doublet couples to down
-   quarks and the other couples to up quarks
- ==> neutral Higgs interactions do not change flavor
-  After quantum corrections <==> SUSY breakdown
-  neutral Higgs induce flavor changing processes
-        ==> important experimental constraints

- after Higgs Mechanism

**stringent test of the MSSM**

**Lightest Higgs mass :**
- important quantum corrections due to incomplete
- cancellation of particles and superparticles loops

## The MSSM HIGGS sector

-   In most of the parameter space:
-   ==> lightest Higgs behaves like SM Higgs and
-           can be searched for similarly at colliders
-          others heavy and roughly degenerate

- Couplings to gauge bosons and fermions     ( normalized to SM values)

-  Quantum corrections affect the couplings relevantly, especially for the heavy Higgses

- (enhanced)

_**LEP MSSM  HIGGS limits:**_

## Heavy MSSM Higgs searches at the Tevatron and the LHC

- ==> robust results under quantum corrections

_**Heavy MSSM Higgs searches at the Tevatron and the LHC**_

**  ****A large region of the full MSSM **
**parameter space can be proved!**

- Enhanced couplings to b quarks and tau-leptons
- ==> enhanced production processes

_**Tevatron reach**_

- Many SUSY Higgs production and decay processes accessible with full LHC potential
**Still regions where only a SM-like Higgs is visible**

_**LHC reach**_

- ATLAS and CMS with 300fb-1

**only h**

## In the SM: Flavor Changing (FC) effects arise from charged currents,
 which mix left- handed up and down quarks:
                                                               where the CKM matrix is almost the identity 
==> transitions between different flavors are suppressed 
The SM Higgs sector and the neutral gauge interactions do not lead to Flavor Changing Effects

B-observables: rare B-meson transitions mediated by charged currents which
                            involve Flavor Changing effects

-  which mix left- handed up and down quarks:
-                                                                where the CKM matrix is almost the identity
- ==> transitions between different flavors are suppressed
- The SM Higgs sector and the neutral gauge interactions do not lead to Flavor Changing Effects
**B-observables**: rare B-meson transitions mediated by charged currents which
-                             involve Flavor Changing effects

- _Indirect searches for MSSM Higgs bosons in B meson observables_

- 1) _Rare decay rate:_

-   Present CDF limit:

- Initial state

- Final state

## 2) Rare decay rate 

- 2) Rare decay rate

- Considering world average measurement,
- and large theoretical uncertainty
- 2    allowed range for new physics  ==>

- Latest result from Belle ==>

-     **SUSY charged Higgs  can contribute to flavor changing effects **
**      ****and affect in a relevant way the results for these  B-meson observables **

## In SUSY Neutral Higgs can mediate Flavor changing transitions 

- A Bs-meson can virtually produce a SUSY
-      neutral Higgs boson and sometimes allow
-      it to decay into two muons
-                    This rare decay occurs at much larger rates than in the SM
-      ==> can be directly probed at colliders (Tevatron and LHC)
- Other B-observables which received contributions from charged Higgs and A/H
- Virtual production:               and
- Strong correlation between direct
- SUSY Higgs searches and virtual
- Higgs effects in B-meson observables
- Important information about the type
- of Supersymmetry that may be
- realized in nature

- B-observables allowed

- Example for set of squark/higgs SUSY mass parameters

## Indirect searches for MSSM Higgs bosons via direct Dark Matter experiments

-  ==> Weakly interacting particles (WIMPS) with masses and
-    interaction cross sections of order of the electroweak scale

- SUSY with R-parity discrete symmetry conserved
- ==> naturally provides a neutral stable DM candidate: LSP ==>

-  **Collider experiments will find evidence of DM through        signature**
- knowledge of new physics particle masses and couplings will allow to compute
- DM-annihilation cross sections and elastic scattering WIMP -proton cross sections

-     **But only Direct Detection Experiments will confirm **
**the existence of Dark Matter particles**

- Dark Matter: one of the fundamental open questions                 ==> demands new physics

- _Indirect searches for MSSM Higgs bosons via direct Dark Matter experiments_

## Direct Detection of WIMPs

-  The local halo density, inferred by fitting to models of galactic halo: assumed ==>

- WIMPs elastically scatter off nuclei in
-    targets,

- producing nuclear recoils with _x001f_

- Main Ingredients to calculate signal:
- Local density & velocity distribution of WIMPs and
-  ==> rate per unit time, per unit detector material mass

- Number of target nuclei in
- the detector prop.to
- Detector mass/Atomic mass

- local WIMP density

- Scattering Cross section off nuclei

- averaged over relative wimp velocity

-  The galactic rotation velocity ≈ (230 +- 20) km/sec

## Direct DM experiments: CDMS, ZEPLIN, EDELWEISS, CRESST,WARP,...sensitive mainly to spin-independent elastic scattering cross section

- Direct DM experiments: CDMS, ZEPLIN, EDELWEISS, CRESST,WARP,...sensitive mainly to spin-independent elastic scattering cross section

- Direct DM searches Vs the Tevatron and LHC  H/A searches

- ==> dominated by virtual exchange of H and h,
-          coupling to strange quarks and to gluons
-          via bottom loops

- Both MSSM Higgs searches and neutralino direct DM searches depend on

- CDMS 2007

- SCDMS 150 Kg

** ****Direct detection of DM**
** ****<==>  detection of A/H**
**at the Tevatron  and LHC**

## CDMS  DM searches Vs the Tevatron  and LHC H/A searches 

-       typically within the reach of present (future) direct DM detection experiments.
-             (strong    dependence)

- CDMS  DM searches Vs the Tevatron  and LHC H/A searches

- If the lightest neutralino makes up the DM of the universe

- Tevatron reach

- LHC reach

## The International Linear Collider (ILC)      ( 2010 ? )

- a telescopic view to the highest energies of nature

- A proposed international
- accelerator, colliding
- electrons against positrons at

-    Super high-tech machine
-  Accelerate the beam over > 15 km
-  Focus the beams to a few nanometers and made them collide

## Exploring the Higgs Sector

-       **Unique powerful feature of the ILC**
-   **it can observe the Higgs no matter how it decays !**

- Initial beam Energy and Z decay well known

- Determine if the Higgs is Standard
- and responsible for mass,
-                              or
- if it comes from a more complex theory
- and has modified properties.
- A complex Higgs interacts with other Higgs particles and can be a source of extra Charge-Parity violation
- Explain the Matter-Antimatter imbalance
- in the universe

- The SM Higgs interactions with particles
- are proportional to particle masses

## The Power of ILC: Cosmological Implications

-  Detect light stop in the whole regime
- compatible with DM and Baryogenesis

**m****stop**** (GeV)**

**m****LSP****(GeV)**

**LEP excluded**

_**The Power of ILC: Cosmological Implications**_

- Precise measurement of SUSY parameters
-          -- stop mass and mixing angles
- from production cross sections at different beam
-  polarizations.
-          -- LSP mass and nature
- from threshold scan, energy distribution endpoints
- and polarized cross sections

- ILC measurements provide crucial information on the SUSY origin of Matter

- ==> DM relic density computation with precision
-     comparable to cosmological measurements

## Conclusions

**Experiments at particle accelerators around the world give us the capability to observe the Higgs particle and thereby test the EWSB mechanism**
*  *-- The Tevatron has the first opportunity for testing the Higgs sector beyond LEP bounds
-   -- The LHC will test it in many different ways and provide some useful precision measurements
-   -- Precision tests that can truly reveal the nature of EWSB will only become available at the ILC
**There are many reasons to believe that the SM must be superceded by a more fundamental theory at the TeV scale**
-                                  **Supersymmetry is the leading candidate**
**     **
**     **This opens the possibility of a more complex Higgs structure and
-    connects Higgs physics with Flavor physics and Cosmology
*              **We are about to reveal the Mystery of mass and, most probably,*
*  **arrive at findings which will revolutionize our understanding of nature  *

-                              EXTRAS

## The MSSM can explain both Dark Matter and Baryogenesis

- Sufficiently strong first order phase transition
- to preserve generated baryon asymmetry:

- LEP bounds on the SM- like Higgs mass

*** *****Higgs masses up to 120 GeV**
**  ****Lightest stop mass below top quark mass**

- Baryon Asymmetry
- for maximal CP violation

-  Preferred:  Gaugino and Higgsino masses of
- the order of the weak scale  and smaller
- Resonant enhancement:

##  What is Dark Matter (DM)?  

- The challenge is to create Dark Matter in the laboratory to study it!

- Visible matter would not keep the stars in their orbits

- Dark matter holds the universe together. What is it?

-  First, the universe was hot and dense: particles and antiparticles annihilated to
-    form dark matter particles and vice-versa.
-   As the universe expanded and cooled down,
-    encounters between particles became rarer and
-    finally the # of DM particles became a constant.
-  The present DM density depends on mass &
-    properties of DM particles: calculations are
-    consistent with

- Many possible hypothetical candidates:
- Most likely WIMPs
-           with weak interactions & TeV-scale masses
-              -- in SUSY, Extra Dimensions, many types of particles --

- Belyaev,
- Matchev,
- Perelstein

## Direct Detection and Collider Searches

**Constrained H/A  discovery potential at the Tevatron (4 fb****-1****)**

- Current CDMS

- 2007 CDMS
-  projection

- LEP excluded

- M.C, Hooper, Skands, hep-ph/0603180

##  What Happened to the Antimatter?

-  Anti-matter is governed by the same interactions as Matter.
-  Was produced with same abundance as  regular matter at the birth of the universe.

-  But....observable Universe is mostly
-   made of Matter

- To remove preferentially antimatter,
- the CP symmetry which transforms
-  Matter into Antimatter must be violated.

-  CP-violation is present in the SM but
- is insufficient by many orders of magnitude

- We search for new sources of CP-violation:
-  in quarks or neutrinos,
- in the Higgs properties, in SUSY.

*A tiny imbalance should have occurred at some point *
*or it all would have annihilated, leaving only radiation*
* **What generated                                         ?*

## SUSY provides a solution to the Matter-Antimatter Asymmetry 

- _SUSY provides a solution to the Matter-Antimatter Asymmetry _

-  If the Higgs is heavier but
-           below 200 GeV
- then some sort of split SUSY can do the job as well !
- -Heavier stops and charginos  and neutralinos more strongly coupled
- -One Light stop and weakly coupled charginos/neutralinos
- with heavier squarks.

- M.C., Quiros , Wagner, Megevand.

- M.C., Quiros , Wagner, Nardini.

## Slide 43

## Measuring Higgs Couplings at LHC

-                                                     of decay widths             assumptions
-                                                   ratios of couplings

_**Measuring Higgs Couplings at LHC**_

**Measuring  HWW and HZZ couplings of order one (SM-like) will be evidence of  a Higgs responsible for the EWSB**
**      ****==> WW fusion most relevant channel**

- LHC rates for partonic processes are given by

- Precision of 10-40% for
- ==> 5-20% in the couplings

- Duehrssen, Heinemeyer, Logan
- Rainwater, Weiglein, Zeppenfeld

## SM Higgs at the ILC 

- Extraction of most couplings with 2-4% accuracy
- HZZ coupling meas. via
-             independent of
- Higgs decay modes!!

- _SM Higgs at the ILC _

-  SM Higgs Branching Ratios

- Higgs Decay Width:

- Production mainly through:

- for mass of 120 GeV

## Other Important Higgs Properties to measure

_**Spin and Parity:**_
- from threshold dependence of the excitation curve and angular distributions

- *  **Higgs Self Couplings                      * Invisible Higgs Decays**
*** CP nature of the Higgs Boson**

## ILC discoveries will allow us to:

-   Solve the Mysteries of Matter
-    at the TeV scale.
-   Probe the essence of Dark Matter.
-  Zoom in to bring into focus Einstein’s vision
-   of a Unified Theory.

- Determine how and why the Higgs works
- with a minimum of theoretical input
- Find Extra source of CP violation

- Identify its nature and measure its properties
- Compute DM candidate’s density in the universe
- to match astrophysical measurements.

- Remarkable high precision Opens the window to explore energies
-                                                     that no accelerator will ever reach directly.

- Supersymmetry particles at the TeV scale allow for unification of the three forces at scales 20 trillions times larger.

## The Hierarchy/naturalness problem of the SM: 

- _The Hierarchy/naturalness problem of the SM: _

- New Physics at the TeV scale is needed to stabilize the Higgs mass quantum corrections and to answer the fundamental questions of particle physics

**The Higgs is expected to have  a mass of about 10****19**** GeV but a**
**200 GeV Higgs is necessary to solve the mass puzzle of the SM.**

## The scale of SUSY breakdown must be of order 1 TeV, if SUSY is 

- SUSY must be broken             in nature: no SUSY partner, degenerate in mass with its SM particle has been seen

**The scale of SUSY breakdown must be of order 1 TeV, if SUSY is **
**    ****associated  with scale of electroweak symmetry breakdown**

- For every fermion there is a boson of equal mass and couplings

- Cancellation of quadratic divergences in Higgs mass quantum corrections has to do with SUSY relation between couplings and bosonic and fermionic degrees of freedom

- In low energy SUSY:  quadratic sensitivity to              replaced by quadratic
- sensitivity to SUSY breaking scale

## A daring alternative: Warped Extra Dimensions

-  Warped extra Dimensions, offer a solution to the hierarchy problem,
-                                                    why
-        without relying on unnatural cancellations, strong interactions or  SUSY.
-        All fundamental parameters are of the order of the Planck  scale, and yet,
-        due to the curvature of the extra-dimensional metric and the localization
-        of the Higgs field, the Higgs v.e.v. is naturally of order of the TeV scale
-        _**4-D effective theory**_:
-   SM particles + Gravitons + tower of new particles: Kaluza Klein (KK) excited states with same quantum number as a graviton  and/or the SM particles
-        _**Signatures: **_

-  KK Gravitons, with masses of the order of the weak scale and couplings of order 1/TeV to SM particles  simplest mechanism
-  Fermions and gauge boson KK modes of the order of the TeV scale may also exist, (strongly constrained by precision electroweak data.)

- KK states produced as resonances or contribute to fermion pair production at colliders

## Space is compact, of size 2 L, with orbifold  conditions  x, y                   x,-y
Brane at y = 0  ( Ultraviolet or Planck Brane)
      Brane at y = L  (Infrared or TeV Brane)
Non-factorizable metric:
                                                               solution to 5d Einstein equations

Newton’s law modified:  5d Planck mass relates to MPl:

  Natural energy scale at the UV brane: Fundamental Planck scale   
      At the TeV brane, all masses are  affected by an exponential warp factor                  .  
                                                           Assuming fundamental scales all of same order:              

                                                                                Solution to Hierarchy problem : 
                                                                    Higgs field lives on the TeV brane 

                                                                                          with 

- Brane at y = 0  ( Ultraviolet or Planck Brane)
-       Brane at y = L  (Infrared or TeV Brane)
- Non-factorizable metric:
-                                                                solution to 5d Einstein equations
- Newton’s law modified:  5d Planck mass relates to MPl:
-   Natural energy scale at the UV brane: Fundamental Planck scale
-       At the TeV brane, all masses are  affected by an exponential warp factor                  .
-                                                            Assuming fundamental scales all of same order:
-                                                                                 Solution to Hierarchy problem :
-                                                                     Higgs field lives on the TeV brane
-                                                                                           with

- Solution to the Hierarchy Problem

- UV

- TeV

## MSSM Higgs 

- Charged Higgs

- SM-like Higgs

_**Present Status of MSSM Higgs searches**_95%C.L. limits

- main decay mode