Document

Report
Int. Summer School on HEP:
SM and BEYOND
25-30 Sept. 2007, Akyaka, Turkey
LECTURE I
WHY TO GO BEYOND THE SM:
THE SUSY ROAD
Antonio Masiero
Univ. of Padova and INFN, Padova
FIGURE OF MERIT OF THE SM
•
•
•
•
POSITIVE ASPECTS:
Renormalizable Spont. Broken Gauge Th.
Excellent agreement with ALL exps.
Automatic conservation of Baryon (B) and Lepton (L) quantum numbers
•
•
NEGATIVE ASPECTS:
Complete lack of prediction of Fermion masses and mixings, even of the number of
fermion generations (FLAVOR PROBLEM)
•
The SM does not “truly” unify fundamental interactions: still three gauge coupling
constants to describe the 3 strong, weak and elm. Interactions, not to speak of
gravity which is just ignored by the SM ( UNIFICATION PROBLEM)
•
•
GAUGE HIERARCHY PROBLEM;
i) how come that the elw, energy scale is 17 orders of magnitude smaller than the
Planck scale? No dynamical reason for that within the SM ( “fundamental” aspect of
the gauge hierarchy problem);
Ii) even if we fix the tree level values of the higgs sector to ensure that the Higgs
mass corresponds to the correct elw. scale ( i.e., it is of O(100-1000 GeV), radiative
corrections are going to push the mass of the Higgs to the highest available scale
present in the theory ( indeed, there exists no symmetry protection for scalar
masses differently to what happens for fermion and gauge boson masses) (
“technical aspect of the gauge hierarchy problem)
•
WHY TO GO BEYOND THE SM
“OBSERVATIONAL” REASONS
•HIGH ENERGY PHYSICS
Z
bb
NO (but AFB……)
•FCNC, CP
NO
NO (but b sqq penguin …)
•HIGH PRECISION LOW-EN.
NO
NO (but (g-2) …)
•NEUTRINO PHYSICS
YES
YE m 0,  0


•COSMO - PARTICLE PHYSICS
YES
YE (DM, ∆B cosm, INFLAT., DE)
THEORETICAL REASONS
•INTRINSIC INCONSISTENCY OF
SM AS QFT
NO (spont. broken gauge theory
without anomalies)
•NO ANSWER TO QUESTIONS
THAT “WE” CONSIDER
“FUNDAMENTAL” QUESTIONS TO
BE ANSWERED BY
“FUNDAMENTAL” THEORY
YES (hierarchy, unification, flavor)
THE FERMION MASS PUZZLE
UNIFICATION of
FUNDAMENTAL INTERACTIONS
Courtesy of H. Murayama
Fundamental COUPLING CONSTANTS
are NOT CONSTANT
Fundamental interactions
unify
SSUSY (MZ)
Sexp (MZ)=0.1170.002
SSM (MZ) < 0.080
Hall, Nomura
“MASS PROTECTION”
For FERMIONS, VECTOR (GAUGE) and SCALAR BOSONS
-FERMIONS
SIMMETRY
PROTECTION
chiral symmetry
fL fR not invariant
under SU(2)x U(1)
-VECTOR BOSONS
gauge symmetry
FERMIONS and W,Z VECTOR BOSONS can get a mass
only when the elw. symmetry is broken mf, mw ≤ <H>
NO SYMMETRY PROTECTION FOR SCALAR MASSES
“INDUCED MASS PROTECTION”
Create a symmetry (SUPERSIMMETRY)
Such that FERMIONS
BOSONS
So that the fermion mass “protection” acts also on bosons as long
as SUSY is exact
SUSY BREAKING ~ SCALE OF 0 (102-103 Gev)
LOW ENERGY SUSY
ON THE RADIATIVE CORRECTIONS
TO THE SCALAR MASSES
Prove that for fermion masses the rad.
corrections are only logarith. divergent .
DESTABILIZATION OF THE ELW.
SYMMETRY BREAKING SCALE
SCALAR MASSES ARE “UNPROTECTED” AGAINST LARGE CORRECTIONS
WHICH TEND TO PUSH THEM UP TO THE LARGEST ENERGY SCALE
PRESENT IN THE FULL THEORY
EX:
SYMMETRY
MASS = 0 LIMIT
NO NEW SYMMETRY IN THE LIMIT
On the contrary, in the limit of massless electron one
recovers the chiral symmetry, i.e. the invariance under
a separate rotation of the LH and RH components of
the electron
FERMION AND
GAUGE BOSON MASSES
WHEN SENT TO ZERO THE THEORY ACQUIRES A NEW
SYMMETRY OR, EQUIVALENTLY, THEY ARISE ONLY
WHEN A CERTAIN SYMMETRY IS BROKEN, i.e. THEIR
VALUE CAN NEVER EXCEED THE SCALE AT WHICH
SUCH SYMMETRY IS BROKEN
THE FINE-TUNING PROBLEM
OR
NATURALNESS PROBLEM
When SM is embedded in a larger theory
where a new scale M>> the electroweak
scale
the SM higgs mass
receives corrections of O(M), i.e.
M higgs= M higgs tree-level+ aM +bM +…
Need a and b to cancel each other with a
precision of O(elw. scale / M)
IS THE FINE-TUNING A REAL PROBLEM?
• WARNING: THERE EXISTS AN EVEN “LARGER”
HIERARCHY OR FINE -TUNING OR NATURALNESS
PROBLEM: THE COSMOLOGICAL CONSTANT PROBLEM
(“ THE NOTHER” OF ALL NATURALNESS PROBLEMS
• QUANTUM CORRECTIONS PUSH THE VALUE OF THE
COSMOLOGICAL CONSTANT UP TO THE LARGEST
SYMMETRY SCALE PRESENT IN THE THEORY, I.E. THE
“NATURAL” VALUE OF THE COSM. CONST. SHOULD BE
OF O(MPLANCK) OR O(MGUT)
• WE DON’T HAVE ANY SOLUTION FOR THE
COSMOLOGICAL CONSTANT PROBLEM SO FAR, I.E.
WE “ACCEPT” THE FINE TUNING IN THIS CASE
• YET I THINK THAT WE NEED TO “SOLVE” THESE FINE
TUNINGS PROBLEMS AND NOT SIMPLY ACCEPTING
THEM AS GIVEN VALUES FOR DIFFERENT MASS
PARAMETRS OF THE FINAL THEORY
THREE PATHS TO “SOLVE” THE
GAUGE HIERARCHY PROBLEM
• 1. FIND A “ULTRAVIOLET COMPLETION” OF
THE SM STABILIZING THE ELW. SCALE AT ITS
PHENOMENOGICALLY NEEDED VALUE: NEW
PHYSICS AT THE ELW. SCALE PROVIDING A
NATURAL CUTOFF FOR THE HIGGS SCALAR
MASS AT THAT SCALE
THE NEW
PARTICLES AND INTERACTIONS SHOULD
CANCEL THE QUADRATIC DIVERGENCES
WHICH WERE THE SOURCE OF THE ELW.
SCALE DE-STABILIZATION
DYNAMICAL ELECTROWEAK
SYMMETRY BREAKING
• 2. THE SM HIGGS BOSON IS NOT AN
ELEMENTARY PARTICLE BUT RATHER A
COMPOSITE PARTICLE ( FOR INSTANCE ARISING
FROM A FERMION CONDENSATE)
ANALOGOUSLY TO THE PION
NO
NEED FOR A HIGGS MASS STABILIZATION,
THERE IS A NATURAL CUTOFF TO SUCH MASS
WHICH IS THE SCALE AT WHICH THE HIGGS
CONDENSATE FORMS
EXTRA - DIMENSIONS
• 3. THERE IS NO HIERARCHY PROBLEM
BECAUSE THE LARGEST SCALE IS ACTUALLY
THE ELECTROWEAK SCALE: THE WEAKNESS OF
GRAVITATIONAL INTERACTIONS IS NOT LINKED
TO A SUPERLARGE VALUE OF THE PLANCK
SCALE, BUT RATHER TO THE FACT THAT
GRAVITY “FEELS” NEW DIMENSIONS BEYOND
THE 3 + 1 SPACE-TIME ORDINARY DIMENSIONS
AND HENCE GOOD PART OF IUTS FLUX LINES
GEY “LOST” IN THE BULK OF SUCH EXTRA
DIMENSIONS
HOW TO COPE WITH THE
HIERARCHY PROBLEM
• LOW-ENERGY SUSY
• LARGE EXTRA DIMENSIONS
• DYNAMICAL SYMMETRY
BREAKING OF THE ELW.
SYMMETRY
• LANDSCAPE APPROACH
(ANTHROPIC PRINCIPLE)
THE LARGE EXTRA-DIMENSIONS
WAYOUT
• The idea: Gravity is a very weak force not because of
the extremely large scale appearing in the Newton
coupling ( i.e., the Planck Mass), but because a (
major) part of the gravity flux lines are “lost” in the
bulk, while “we” live on a slice (brane) which
receives only a small portion of such lines
• Virtues: i) we don’t have to explain why Mplanck is
much larger than the elw. Scale simply because the
Tev scale is the ONLY scale present ; ii) there exist
experimental signatures of such idea which could
possibly be tested at LHC
• Problem: i) How to stabilize the very large extra
dimensions; ii) no “predictive” unification of
interactions
THE DYNAMICAL ELW. SYMMETRY BREAKING WAYOUT
• The idea: a new strong interaction ( “technicolor”)
becomes strong at a scale roughly 2000 times larger
than the scale where QCD gets strong. The
“techniquarks” condensates break the ELW.
Symmetry and give rise to the elw. Gauge boson and
fermion masses.
• Virtues: i) there is a dynamics accounting for the
large hierarchy between the Planck and elw. Scale; ii)
the only examples in Nature of spontaneous
symmetry breaking are through fermion condensates;
iii) the problem to stabilize the Higgs mass does not
exist since the Higgs mass cannot exceed the scale
at which the composite higgs exists (cfr. The pion
situation
• Problems: no phenomenologically viable model has
been so far constructed; in particular the very precise
elw. tests from LEP place very severe contraints on
any attempt to put new paticles such the
“techniquarks” at the elw. Scale.
WHY TO GO BEYOND THE SM
“OBSERVATIONAL” REASONS
•HIGH ENERGY PHYSICS
Z
bb
NO (but AFB……)
•FCNC, CP
NO
NO (but b sqq penguin …)
•HIGH PRECISION LOW-EN.
NO
NO (but (g-2) …)
•NEUTRINO PHYSICS
YES
YE m 0,  0


•COSMO - PARTICLE PHYSICS
YES
YE (DM, ∆B cosm, INFLAT., DE)
THEORETICAL REASONS
•INTRINSIC INCONSISTENCY OF
SM AS QFT
NO (spont. broken gauge theory
without anomalies)
•NO ANSWER TO QUESTIONS
THAT “WE” CONSIDER
“FUNDAMENTAL” QUESTIONS TO
BE ANSWERED BY
“FUNDAMENTAL” THEORY
YES (hierarchy, unification, flavor)
Neutrinos are MASSIVE:
New Physics IS there!
THE FATE OF LEPTON NUMBER
L VIOLATED
L CONSERVED
 Dirac ferm.
(dull option)
 Majorana ferm.
h LH R
SMALLNESS of m
m=h H
M5 eV
h10-11
EXTRA-DIM. R in the bulk: small overlap?
PRESENCE OF A NEW PHYSICAL MASS SCALE
SEE - SAW MECHAN.
MAJORON MODELS
Minkowski; Gell-Mann,
Ramond, SlansKy,
Vanagida
OF THE
R ENLARGEMENT
FERMIONIC SPECTRUM
MR R + h L  R
L
L
R
~O

h 
R

h 
M
Gelmini, Roncadelli

LR
Models?
ENLARGEMENT OF THE
HIGGS SCALAR SECTOR
h L L 
m= h   
N.B.: EXCLUDED BY LEP!
MICRO
MACRO
PARTICLE PHYSICS
GWS STANDARD MODEL
COSMOLOGY
HOT BIG BANG
STANDARD MODEL
HAPPY MARRIAGE
Ex: NUCLEOSYNTHESIS
BUT ALSO
POINTS OF
FRICTION
-COSMIC MATTER-ANTIMATTER ASYMMETRY
-INFLATION
- DARK MATTER + DARK ENERGY
“OBSERVATIONAL” EVIDENCE FOR NEW PHYSICS BEYOND
THE (PARTICLE PHYSICS) STANDARD MODEL
THE COSMIC MATTER-ANTIMATTER ASYMMETRY PUZZLE:
-why only baryons
-why Nbaryons/Nphoton ~ 10-10
•
•
•
•
•
NO EVIDENCE OF ANTIMATTER WITHIN THE SOLAR SYSTEM
ANTIPROTONS IN COSMIC RAYS: IN AGREEMENT WITH PRODUCTION AS
SECONDARIES IN COLLISIONS
IF IN CLUSTER OF GALAXIES WE HAD AN ADMIXTURE OF GALAXIES MADE
OF MATTER AND ANTIMATTER
THE PHOTON FLUX PRODUCED
BY MATTER-ANTIMATTER ANNIHILATION IN THE CLUSTER WOULD EXCEED
THE OBSERVED GAMMA FLUX
IF Nba . = Nantibar AND NO SEPARATION WELL BEFORE THEY DECOUPLE .
WE WOULD BE LEFT WITH Nbar./Nphoton << 10-10
IF BARYONS-ANTIBARYONS ARE SEPARATED EARLIER
DOMAINS OF BARYONS AND ANTIBARYONS ARE TOO SMALL SMALL TODAY
TO EXPLAIN SEPARATIONS LARGER THAN THE SUPERCLUSTER SIZE
ONLY MATTER IS PRESENT
HOW TO DYNAMICALLY PRODUCE A BARYON-ANTIBARYON
ASYMMETRY STARTING FROM A SYMMETRIC SITUATION
COSMIC MATTER-ANTIMATTER
ASYMMETRY
Murayama
SM FAILS TO GIVE RISE TO A SUITABLE COSMIC
MATTER-ANTIMATTER ASYMMETRY
• SM DOES NOT SATISFY AT LEAST TWO OF THE THREE
SACHAROV’S NECESSARY CONDITIONS FOR A
DYNAMICAL BARYOGENESIS:
• NOT ENOUGH CP VIOLATION IN THE SM
NEED FOR
NEW SOURCES OF CPV IN ADDITION TO THE PHASE
PRESENT IN THE CKM MIXING MATRIX
• FOR MHIGGS > 80 GeV THE ELW. PHASE TRANSITION OF
THE SM IS A SMOOTH CROSSOVER
NEED NEW PHYSICS BEYOND SM. IN PARTICULAR,
FASCINATING POSSIBILITY: THE ENTIRE MATTER IN
THE UNIVERSE ORIGINATES FROM THE SAME
MECHANISM RESPONSIBLE FOR THE EXTREME
SMALLNESS OF NEUTRINO MASSES
MATTER-ANTIMATTER ASYMMETRY
NEUTRINO
MASSES CONNECTION: BARYOGENESIS THROUGH
LEPTOGENESIS
• Key-ingredient of the SEE-SAW mechanism for neutrino
masses: large Majorana mass for RIGHT-HANDED neutrino
• In the early Universe the heavy RH neutrino decays with Lepton
Number violatiion; if these decays are accompanied by a new
source of CP violation in the leptonic sector, then
it is possible to create a lepton-antilepton asymmetry
at the moment RH neutrinos decay. Since SM interactions
preserve Baryon and Lepton numbers at all orders in
perturbation theory, but violate them at the quantum level, such
LEPTON ASYMMETRY can be converted by these purely
quantum effects into a BARYON-ANTIBARYON ASYMMETRY
( Fukugita-Yanagida mechanism for leptogenesis )
INFLATION

SEVERE
COSMOGICAL
PROBLEMS



CAUSALITY
(isotropy of CMBR)
FLATNESS
( close to 1 today)
AGE OF THE UNIV.
PRIMORDIAL MONOPOLES
COMMON SOLUTION FOR THESE PROBLEMS
VERY FAST (EXPONENTIAL) EXPANSION IN THE UNIV.

V()
VACUUM
ENERGY
 dominated by
vacuum en.
TRUE
VACUUM
NO WAY TO GET AN “INFLATIONARY SCALAR
POTENTIAL” IN THE STANDARD MODEL
NO ROOM IN THE PARTICLE
PHYSICS STANDARD MODEL FOR
INFLATION
V=2 2 + 4
no inflation
Need to extend the SM scalar potential
Ex: GUT’s, SUSY GUT’s,…
ENERGY SCALE OF “INFLATIONARY PHYSICS”:
LIKELY TO BE Mw
»
DIFFICULT BUT NOT IMPOSSIBLE TO OBTAIN
ELECTROWEAK INFLATION IN SM EXTENSIONS
THE UNIVERSE ENERGY BUDGET
DM: the most impressive evidence at the
“quantitative” and “qualitative” levels of
New Physics beyond SM
• QUANTITATIVE: Taking into account the latest WMAP
data which in combination with LSS data provide stringent
bounds on DM and B
EVIDENCE
FOR NON-BARYONIC DM AT MORE THAN 10
STANDARD DEVIATIONS!! THE SM DOES NOT
PROVIDE ANY CANDIDATE FOR SUCH NONBARYONIC DM
• QUALITATIVE: it is NOT enough to provide a mass to
neutrinos to obtain a valid DM candidate; LSS formation
requires DM to be COLD
NEW PARTICLES NOT
INCLUDED IN THE SPECTRUM OF THE FUNDAMENTAL
BUILDING BLOCKS OF THE SM !
THE RISE AND FALL OF NEUTRINOS AS
DARK MATTER
• Massive neutrinos: only candidates in the SM to
account for DM. From here the “prejudice” of
neutrinos of a few eV to correctly account for DM
• Neutrinos decouple at ~1 MeV ; being their
mass<<decoupling temperature, neutrinos remain
relativistic for a long time. Being very fast, they
smooth out any possible growth of density fluctuation
forbidding the formation of proto-structures.
• The “weight” of neutrinos in the DM budget is
severely limited by the observations disfavoring
scenarios where first superlarge structures arise and
then galaxies originate from their fragmentation
LSS PATTERN AND
NEUTRINO MASSES
m = 0 eV
m = 1 eV
m = 7 eV
m = 4 eV
(E..g., Ma 1996)
Cosmological Bounds
on the sum of the
masses of the 3
neutrinos from
increasingly rich
samples of data sets
WIMPS (Weakly Interacting Massive Particles)
# exp(-m/T)
# does not change any more
#~#
m

Tdecoupl.
typically ~ m /20
 ) and “cosmological” quantities (H, T , …
  depends on particle physics (annih.
0
 h2_~
10-3
<(annih.) V  > TeV2
~
2 /
M 2
From T0 Mplaeli
h2 in the range 10-2 -10-1 to be cosmologically interesting (for DM)
m ~ 102 - 103 GeV (weak interaction)
h2 ~ 10-2 -10-1 !!!
STABLE ELW. SCALE WIMPs from
PHYSICS
1) ENLARGEMENT
OF THE SM
SUSY
(x, )
EXTRA DIM.
(x, ji)
Anticomm.
Coord.
2) SELECTION
RULE
DISCRETE SYMM.
PARTICLE
New bosonic
Coord.
LITTLE HIGGS.
SM part + new part
to cancel 2
at 1-Loop
R-PARITY LSP
KK-PARITY LKP
T-PARITY LTP
Neutralino spin 1/2
spin1
spin0
STABLE NEW
PART.
3) FIND REGION (S)
PARAM. SPACE
WHERE THE “L” NEW
PART. IS NEUTRAL +
ΩL h2 OK
mLSP
mLKP
mLTP
~100 - 200
~600 - 800
~400 - 800
GeV *
GeV
GeV
* But abandoning gaugino-masss unif.
Possible to have mLSP down to 7 GeV
Bottino, Donato, Fornengo, Scopel
The Energy Scale from the
“Observational” New Physics
neutrino masses
dark matter
baryogenesis
inflation
NO NEED FOR THE
NP SCALE TO BE
CLOSE TO THE
ELW. SCALE
The Energy Scale from the
“Theoretical” New Physics
Stabilization of the electroweak symmetry breaking at
MW calls for an ULTRAVIOLET COMPLETION of the SM already
at the TeV scale
+
CORRECT GRAND UNIFICATION “CALLS” FOR NEW PARTICLES
AT THE ELW. SCALE
Int. Summer School on HEP:
SM and BEYOND
25-30 Sept. 2007, Akyaka, Turkey
Lectures II and III
BEYOND THE SM:
THE SUSY ROAD
Antonio Masiero
Univ. of Padova and INFN, Padova
THE SUSY PATH
HIERARCHY PROBLEM: THE SUSY WAY
SUSY HAS TO BE BROKEN AT A SCALE CLOSE
TO 1TeV
LOW ENERGY SUSY
m2  2
Scale of susy breaking
F
f
F
B
f

B

Sm2  ~( B - 2f ) 2
16 2
[m2 B - m2F ]1/2 ~ 1/√GF
B
F In SUSY multiplet
SPLITTING IN MASS BETWEEN B and F of O ( ELW. SCALE)
NO – GO AND NO NO-GO ON
THE ROAD TO GET A SUSY SM
ON THE WAY TO
SUPERSYMMETRIZE THE SM
D. KAZAKOV
IN SUSY WE NEED TO INTRODUCE AT LEAST TWO
HIGGS DOUBLETS IN ORDER TO PROVIDE A MASS
FOR BOTH THE UP- AND DOWN- QUARKS
BREAKING SUSY
• The world is clearly not supersymmetric:
for instance, we have not seen a scalar of
Q=1 and a mass of ½ MeV, i.e. the
selectron has to be heavier than the electron
and, hence, SUSU has to be broken
SUSY HAS TO BE BROKEN AT A SCALE > 100 GeV
SINCE NO SUSY PARTNERS HAVE BEEN SEEN
UP TO THOSE ENERGIES, roughly
COLORED S-PARTICLE MASSES > 200 GeV
UNCOLORED S- PARTICLE MASSES > 100 GeV
Little digression: how to break a symmetry
• EXPLICIT BREAKING: add to a Lagrangian
invariant under a certain symmetry S some
terms which do not respect such symmetry S.
Advantage: freedom in choosingsuch terms
and possibility to dapt them to the
phenomenological requests one has
Disadvantage: losing the virtues related to the
presence of a symmetry in the theory ( ex: if
S is the elw. symmetry, adding an explicit
mass tem to the W boson would spoil the
renormalizability of the theory)
SPONTANEOUS BREAKING:: THE THEORY IS
INVARIANT UNDER A CERTAIN SYMMETRY S ( i.e.,
the FULL Lagrangian respects S), however THE
VACUUM OF THE THEORY IS NOT INVARIANT
UNDER S TRANSFORMATIONS.
ADVANTAGE: POSSIBILITY OF PRESERVING THE
NICE PROPERTIES RELATED TO THE PRESENCE
OF A SYMMETRY ( EX: SPONTANEOUSLY BROKEN
GAUGE THEORIES ARE RENORMALIZABLE )
DISADVANTAGE: SCHEME IS MORE
CONSTRAINED; ONE CANNOT CHOOSE THE
BREAKING TERMS “ARBITRARILY”
SPONTANEOUS BREAKING OF
SUSY
• FIRST ATTEMPT: SPONTANEOUS
BREAKING OF SUSY ( letting history teach:
since spontaneous breaking of the
electroweak symmetry was so successful, try
to repeat it in the SUSY case)
PROBLEM: NO phenomenologically
viable model results from spontaneously
broken SUSY ( ex: one of the two selectrons
remains lighter than the electron…)
2nd ATTEMPT TO BREAK SUSY:
THE EXPLICIT BREAKING
• WISH: add to the SUSY version of the SM
Lagrangian some terms which are NOT SUSY
invariant, i.e. add an explicit breaking of SUSY, but
try to PRESERVE the nice properties of having
SUSY in the game ( for instance, still quadratic
divergences should be absent even when SUSY is
explicitly broken)
special class of
SOFT
BREAKING TERMS OF SUSY
explicitly breaking terms called
THE BASKET WHERE TO PICK UP
THE WANTED ( OR NEEDED) SUSY SOFT BREAKING TERMS
THE SOFT BREAKING TERMS
OF THE MINIMAL SUSY SM
(MSSM)
WHICH SUSY
HIDDEN
SECTOR SUSY
BREAKING AT
SCALE F
F = (105 - 106) GeV
F = MW MPl
GRAVITY
Mgravitino ~ F/MPl ~
(102 -103) GeV
GAUGE
INTERACTIONS
Mgravitino ~ F/MPl ~
OBSERVABLE
SECTOR
SM + superpartners
MSSM : minimal content
of superfields
(102 - 103)eV
D. kAZAKOV
THE FATE OF B AND L IN THE
SM AND MSSM
• IN THE SM B AND L ARE “AUTOMATIC” SYMMETRIES: NO B or L
VIOLATING OPERATOR OF DIM.≤4 INVARIANT UNDER THE GAUGE
SIMMETRY SU(3) X SU(2) X U(1) IS ALLOWED ( B AND L ARE
CONSERVED AT ANY ORDER IN PERTURBATION THEORY, BUT
ARE VIOLATED AT THE QUANTUM LEVEL (ONLY B – L IS EXACTLY
PRESERVED )
• IN THE MSSM, THANKS TO THE EXTENDED PARTICLE SPECTRUM
WITH NEW SUSY PARTNERS CARRYING B AND L, IT IS POSSIBLE
TO WRITE ( RENORMALIZABLE) OPERATORS WHICH VIOLATE
EITHER B OR L
•
IF BOTH B AND L VIOLATING OPERATORS ARE
PRESENT, GIVEN THAT SUSY PARTNER MASSES ARE OF O(TEV),
THERE IS NO WAY TO PREVENT A TOO FAST PROTON DECAY
UNLESS THE YUKAWA COUPLINGS ARE INCREDIBLY SMALL!
ADDITIONAL DISCRETE SYMMETRY IN THE
MSSM TO SLOW DOWN P - DECAY
•
SIMPLEST (and nicest) SOLUTION: ADD A SYMMETRY WHICH FORBIDS ALL B
AND L VIOLATING OPERATORS
R PARITY
•
SINCE B AND L 4-DIM. OPERATORS INVOLVE 2 ORDINARY FERMIONS AND A
SUSY SCALAR PARTICLE, THE SIMPLEST WAY TO ELIMINATE ALL OF THEM:
R = +1 FOR ORDINARY PARTICLES
R = - 1 FOR SUSY PARTNERS
IMPLICATIONS OF IMPOSING R PARITY:
i) The superpartners are created or destroyed in pairs;
ii) THE
LIGHTEST SUPERPARTNER IS ABSOLUTELY
STABLE
BROKEN R PARITY
• PROTON DECAY REQUIRES THE VIOLATION
OF BOTH B AND L
NOT NECESSARY TO HAVE R
PARITY TO KILL B AND L VIOLATING
OPERATORS
ENOUGH TO IMPOSE AN
ADDITIONAL DISCRETE SYMMETRY TO
FORBID EITHER B OR L VIOLATING
OPERATORS; RESTRICTIONS ON THE
YUKAWA COUPLINGS OF THE SURVIVING B
OR L VIOLATING OPERATORS
D. KAZAKOV
FROM THE MSSM TO THE CMSSM ( constrained MSSM)
•
PROLIFERATION OF PARAMETRS IN THE SOFT BREAKING SECTOR OF
THE MSSM: OVERALL NUMBER OF PARAM. IN THE MSSM IS 124 (large
number, but are we sure that a fundamental theory should have a “small” number
of parameters?)
•
MOST OF THIS ENORMOUS PARAM. SPACE IS IN ANY CASE ALREADY
RULED OUT BY THE VARIOUS PHENOMENOLOGICAL CONSTRAINTS ON
SUSY)
•
POSSIBLE TO DRASTICALLY REDUCE THE NUMBER OF PARAM. IMPOSING
( REASONABLE?) THEORETICAL ASSUMPTIONS ON THE SOFT BREAKING
SECTOR:
FLAVOR UNIVERSALITY IN THE SCALAR SOFT TERMS
AND
GAUGINO MASS UNIVERSALITY
AT THE GRAND UNIFICATION SCALE
D. KAZAKOV
RADIATIVE ELECTROWEAK
SYMMETRY BREAKING IN MSSM
• CMSSM
both higgses have positive
masses squared at the GUT scale (like having
µ2 positive in the SM scalar potential), hence
the tree level potential of the CMSSM does
not lead to the spontaneous breaking of the
elw. symmetry
• The masses squared of the higgses
decrease during the running from the GUT
scale down to lower energies; in particular,
the decrease is enhanced for the mass of the
higgs coupled to the top quark given the large
value of the top Yukawa coupling
CMSSM + RADIATIVE ELW. BREAKING:
A 4 – PARAMETER WORLD
• FREE PARAM. IN THE CMSSM :
IMPOSING THE RAD. BREAKING OF THE ELW.
SYMMETRY ONE ESTABLISHES A RELATION BETWEEN
THE ELW. BREAKING SCALE AND THE SOFT SUSY
PARAMETERS FURTHER REDUCING THE NUMBER OF
THE FREE PARAM. IN THE CMSSM TO FOUR , FOR
INSTANCE THE FIRST FOUR PARAM. ABOVE + THE SIGN
OF µ ( THE ELW. SYMM. BREAKING FIXES ONLY THE
SQUARE OF µ
D. KAZAKOV
LOW-ENERGY SUSY AND
UNIFICATION
Int. Summer School on HEP:
SM and BEYOND
25-30 Sept. 2007, Akyaka, Turkey
LECTURE IV
(DESPERATELY) SEEKING SUSY:
ACCELERATOR PHYSICS, FLAVOR
AND DARK MATTER SYNERGY
Antonio Masiero
Univ. of Padova and INFN, Padova
VIRTUAL EFFECTS for
REAL NEW PHYSICS
THE HEISENBERG’S UNCERTAINTY PRINCIPLE
ENSURES THAT MEASUREMENTS OF PROCESSES
INVOLVING LOOPS ( I.E., WITH THE PRESENCE OF
VIRTUAL PARTICLES) CAN GIVE ACCESS TO HIGH
MASS SCALE PHYSICS BEFORE ACCELERATORS
ARE ABLE TO DIRECTLY PROBE THOSE SCALES
EX. : the suppression of KL
+ - hint for the
existence of the CHARM quark. Calculation of its
mass from the observed rate of K - K oscillations.
Heaviness of the TOP quark from observed
largeness of B - B oscillations.
Flavor Physics: the Triumph of the CKM
flavor structure of the SM
By now we have
achieved a “redundant”
determination of the
CKM mixing elements
entering the quark
mixing in the SM, i.e. we
are probing the validity
of the CKM ansatz
predicted by the SM
The CKM flavor structure of the SM is the DOMINANT SOURCE of the
hadronic flavor mixing ( with new physics sources of flavor confined to be not
larger than 20% of the CKM source)
ELW. SYMM. BREAKING STABILIZATION VS.
FLAVOR PROTECTION: THE SCALE TENSION
Isidori
UV SM COMPLETION TO STABILIZE THE ELW.
SYMM. BREAKING: UV ~ O(1 TeV)
FLAVOR BLINDNESS OF THE NP AT THE ELW. SCALE?
• THREE DECADES OF FLAVOR TESTS ( Redundant
determination of the UT triangle
verification of the
SM, theoretically and experimentally “high precision”
FCNC tests, ex. b
s + γ, CP violating flavor
conserving and flavor changing tests, lepton flavor
violating (LFV) processes, …) clearly state that:
• A) in the HADRONIC SECTOR the CKM flavor pattern of
the SM represents the main bulk of the flavor structure
and of CP violation;
• B) in the LEPTONIC SECTOR: although neutrino flavors
exhibit large admixtures, LFV, i.e. non – conservation of
individual lepton flavor numbers in FCNC transitions
among charged leptons, is extremely small: once again
the SM is right ( to first approximation) predicting
negligibly small LFV
FROM DETERMINATION TO VERIFICATION
OF THE CKM PATTERN FOR HADRONIC
FLAVOR DESCRIPTION
TREE LEVEL
ONE - LOOP
A. BURAS et al.
Single channels
understood?
Allowed to take the
avg.?
Is CP violation entirely due to the KM
mechanism? Y.Nir
For CPV in FLAVOR CHANGING* PROCESSES it is VERY LIKELY** that
the KM mechanism represents the MAIN SOURCE***
•
*FC CPV : as for flavor conserving CPV there could be new phases different from the CKM
phase ( importance of testing EDMs!)
•
**VERY LIKELY: the alternative is to invoke some rather puzzling coincidence (e.g., it could
be that sin2 is not that predicted by the SM , but HSM + HNP in the Bd-Bd mixing has the
same phase as that predicted by the SM alone or it could be that the phase of the NP
contribution is just the same as the SM phase)
•
*** MAIN SOURCE : Since SK is measured with an accuracy ~ 0.04, while the SM
accuracy in predicting sin2 is ~0.2
still possible to have
HNP ≤ 20% HSM in Bd-Bd mixing
What to make of this triumph of
the CKM pattern in flavor tests?
New Physics at the Elw.
Scale is Flavor Blind
CKM exhausts the flavor
changing pattern at the elw.
Scale
MINIMAL FLAVOR
VIOLATION
MFV : Flavor originates only
from the SM Yukawa coupl.
New Physics introduces
NEW FLAVOR SOURCES in
addition to the CKM pattern.
They give rise to
contributions which are
<20% in the “flavor
observables” which have
already been observed!
What a SuperB can do in testing CMFV
L. Silvestrini at SuperB IV
SCKM basis
SUPER CKM: basis in the LOW - ENERGY phenomenology
where through a rotation of the whole superfield (fermion +
sfermion) one obtains DIAGONAL Yukawa COUPL. for the
corresponding fermion field
fio
fi
~
~
fi
~
~ x
fi ~
fj
ijf
ijf  ijf / mf~ave
Unless mf and mf~are aligned, f
is not a mass eigenstate
Hall, Kostelecki, Raby
BOUNDS ON THE HADRONIC
FCNC: 1 - 3 DOWN GENERATION
SuperB vs. LHC Sensitivity
Reach in testing SUSY
SuperB can probe MFV ( with small-moderate tan) for TeV
squarks; for a generic non-MFV MSSM
sensitivity
to squark masses > 100 TeV ! L. Silvestrini
LFV and NEW PHYSICS
• Flavor in the HADRONIC SECTOR:
CKM paradigm
• Flavor in the LEPTONIC SECTOR:
- Neutrino masses and (large) mixings
- Extreme smallness of LFV in the charged
lepton sector of the SM with massive
neutrinos:
li
lk suppressed by (m 2 - m 2 ) / MW2
i
k
SUSY SEESAW: Flavor universal SUSY breaking and
yet large lepton flavor violation
Borzumati, A. M. 1986 (after discussions with
W. Marciano and A. Sanda)
L  fl eR Lh1  f  R Lh2  M  R R
m 
2
L
ij
~
1
8
2

(3m  A ) f f
2
0
2
0
†

M
ij log
MG
Non-diagonality of the slepton mass
matrix in the basis of diagonal lepton
mass matrix depends on the unitary
matrix U which diagonalizes (f+ f)
LFV in SUSYGUTs with SEESAW
MPl
MGUT
MR
MW
Scale of appearance of the SUSY soft breaking terms
resulting from the spontaneous breaking of supergravity
Low-energy SUSY has “memory” of all the multi-step RG
occurring from such superlarge scale down to MW
potentially large LFV
Barbieri, Hall; Barbieri, Hall, Strumia; Hisano, Nomura,
Yanagida; Hisano, Moroi, Tobe Yamaguchi; Moroi;A.M.,, Vempati, Vives;
Carvalho, Ellis, Gomez, Lola; Calibbi, Faccia, A.M, Vempati
LFV in MSSMseesaw: 
e Borzumati, A.M.

 Blazek, King;
General analysis: Casas Ibarra; Lavignac, Masina,Savoy; Hisano, Moroi, Tobe, Yamaguchi; Ellis,
Hisano, Raidal, Shimizu; Fukuyama, Kikuchi, Okada; Petcov, Rodejohann, Shindou, Takanishi;
Arganda, Herrero; Deppish, Pas, Redelbach, Rueckl; Petcov, Shindou
Bright prospects for the experimental
sensitivity to LFV
Experiments:
Running: BaBar, Belle
Upcoming: MEG (2007)
Future: SuperKEKB (2011)
PRISM/PRIME (next decade)
Super Flavour factory (?)
µ
CALIBBI,
FACCIA,
A.M.,
VEMPATI
e+ in SUSYGUT: past and future
and PRISM/PRIME conversion experiment
LFV from SUSY GUTs
Lorenzo Calibbi
LFV
LHC SENSITIVITIES IN
PROBING THE SUSY PARAM.
SPACE
CALIBBI, FACCIA, A.M., VEMPATI
Large  mixing
large b-s
transitions in SUSY GUTs
In SU(5) dR
lL connection in the 5-plet
Large (l23)LL induced by large f of O(ftop)
is accompanied by large (d23)RR
In SU(5) assume large f (Moroi)
In SO(10) f large because of an underlying Pati-Salam
symmetry
(Darwin Chang, A.M., Murayama)
See also: Akama, Kiyo, Komine, Moroi; Hisano, Moroi, Tobe,
Yamaguchi, Yanagida; Hisano, Nomura; Kitano,Koike, Komine,
Okada
FCNC HADRON-LEPTON
CONNECTION IN SUSYGUT
If
MPl
MGUT
MW
soft SUSY breaking terms arise
at a scale > MGUT, they have to respect
the underlying quark-lepton GU symmetry
constraints on quark from LFV and
constraints on lepton from hadronic FCNC
Ciuchini, A.M., Silvestrini, Vempati, Vives PRL
general analysis Ciuchini, A.M., Paradisi, Silvestrini, Vempati, Vives
hep-ph/0702144
DEVIATION from  - e UNIVERSALITY
A.M., Paradisi, Petronzio
H mediated LFV SUSY contributions
to RK
Extension to B
Isidori, Paradisi
l deviation from universality
SUSY & DM : a successful marriage
• Supersymmetrizing the SM does not lead necessarily to
a stable SUSY particle to be a DM candidate.
• However, the mere SUSY version of the SM is known to
lead to a too fast p-decay. Hence, necessarily, the SUSY
version of the SM has to be supplemented with some
additional ( ad hoc?) symmetry to prevent the pdecay catastrophe.
• Certainly the simplest and maybe also the most
attractive solution is to impose the discrete R-parity
symmetry
• MSSM + R PARITY
LIGHTEST SUSY
PARTICLE (LSP) IS STABLE .
• The LSP can constitute an interesting DM candidate in
several interesting realizations of the MSSM ( i.e., with
different SUSY breaking mechanisms including gravity,
gaugino, gauge, anomaly mediations, and in various
regions of the parameter space).
WHO IS THE LSP?
• SUPERGRAVITY ( transmission of the
SUSY breaking from the hidden to the
obsevable sector occurring via
gravitational interactions): best candidate
to play the role of LSP:
NEUTRALINO ( i.e., the lightest of
the four eigenstates of the 4x4
neutralino mass matrix)
In CMSSM: the LSP neutralino is
almost entirely a BINO
GRAVITINO LSP?
• GAUGE MEDIATED SUSY BREAKING
(GMSB) : LSP likely to be the GRAVITINO ( it
can be so light that it is more a warm DM than a cold
DM candidate )
Although we cannot directly detect the
gravitino, there could be interesting signatures
from the next to the LSP ( NLSP) : for instance
the s-tau could decay into tau and gravitino,
Possibly with a very long life time, even of the order of
days or months
HUNTING FOR DARK MATTER
INDIRECT DM SEARCHES
DIRECT DM SEARCHES
INDIRECT SEARCHES OF DM
• WIMPs collected inside celestial bodies ( Earth, Sun):
their annihilations produce energetic neutrinos
• WIMPs in the DM halo: WIMP annihilations can take place
( in particular, their rate can be enhanced with there exists
a CLUMPY distribution of DM as computer simulations of
the DM distribution in the galaxies seem to suggest. From
the WIMP annihilation:
-- energetic neutrinos ( under-ice, under-water exps
Amanda, Antares, Nemo, Antares, …)
--photons in tens of GeV range ( gamma astronomy on
ground Magic, Hess, … or in space Glast…)
--antimatter: look for an excess of antimatter w.r.t. what is
expected in cosmic rays ( space exps. Pamela, AMS, …)
SEARCHING FOR
WIMPS HYPOTHESIS
DM made of particles with
mass 10Gev - 1Tev
ELW scale
WIMPs
LHC, ILC may
PRODUCE WIMPS
WIMPS escape the detector
MISSING ENERGY
SIGNATURE
With WEAK INTERACT.
FROM “KNOWN” COSM. ABUNDANCE OF WIMPs
PREDICTION
FOR WIMP PRODUCTION AT COLLIDERS WITHOUT SPECYFING
THE PART. PHYSICS MODEL OF WIMPs
BIRKEDAL, MATCHEV, PERELSTEIN ,
FENG,SU, TAKAYAMA
Tightness of the DM constraints in
Minimal Supergravity
Ellis et al.
Tightness of the DM constraint on
minimal supergravity
Ellis, Olive, Santoso, Spanos
Tightness …3
LFV - DM CONSTRAINTS IN MINIMAL
SUPERGRAVITY
A.M., Profumo, Vempati, Yaguna
A.M., PROFUMO, ULLIO
A.M., PROFUMO,ULLIO
DM SUSY:HOW FAR ARE WE IN
DIRECT SEARCHES?
Ellis et al.
SPIN - INDEPENDENT NEUTRALINO - PROTON CROSS
SECTION FOR ONE OF THE SUSY PARAM. FIXED AT 10 TEV
REACH OF FUTURE FACILITIES FOR NEUTRALINO DETECTION
THROUGH ANTIMATTER SEARCHES WITH FIXED M1 = 500 GEV
N03 adiabatically contracted profile
Burkert profile
SEARCHING FOR
WIMPS HYPOTHESIS
DM made of partcles with
mass 10Gev - 1Tev
ELW scale
WIMPs
LHC, ILC may
PRODUCE WIMPS
WIMPS escape the detector
MISSING ENERGY
SIGNATURE
With WEAK INTERACT
FROM “KNOW” COSM. ABUNDANCE OF WIMPs
PREDICTION
FOR WIMP PRODUCTION AT COLLIDERS WITHOUT SPECYFING
THE PART. PHYSICS MODEL OF WIMPs
BIRKEDAL, MATCHEV, PERELSTEIN ,
FENG,SU, TAKAYAMA
DM
DE
DO THEY “KNOW” EACH OTHER?
DIRECT INTERACTION  (quintessence) EITH DARK
DANGER:
MATTER
 Very LIGHT
m ~ H0-1 ~ 10-33 eV
Threat of violation of the equivalence principle
constancy of the fundamental “constants”,…
INFLUENCE OF  ON THE NATURE AND THE
ABUNDANCE OF CDM
Modifications of the standard picture of
WIMPs FREEZE - OUT
CDM CANDIDATES
NEUTRALINO RELIC ABUNDANCE IN
GR AND S-T THEORIES OF GRAVITY
ON THE COMPLEMENTARITY OF
DM and LFV SEARCHES to DIRECT
LHC SEARCHES FOR NP
•
Twofold meaning of such complementarity:
i) synergy in “reconstructing” the
“fundamental theory” staying behind the
signatures of NP;
ii) coverage of complementary areas of the NP
parameter space ( ex.: multi-TeV SUSY
physics)
ILC
TEVATRON
DM - FLAVOR
A MAJOR
LEAP AHEAD
IS NEEDED
for DISCOVERY
and/or FUND. TH.
RECONSTRUCTION
NEW
PHYSICS AT
THE ELW
SCALE
m n …
FCNC, CP ≠, (g-2), ()0
LINKED TO COSMOLOGICAL EVOLUTION
LFV
NEUTRINO PHYSICS
Possible interplay with dynamical DE
LEPTOGENESIS
LES JEUX SONT FAITS;
RIEN NE VA PLUS
FINALLY AFTER SO MUCH
SPECULATION THE WORD
COMES TO THE EXPERIMENT:
LHC WILL TELL US WHETHER
THERE IS AND POSSIBLY WHAT
IT IS THE NP RELATED TO THE
ELW. SYMMETRY BREAKING
ON THE SUSY BET
• Dialogue between a professor and a student at a
summer school :
- Q: professor, what is the most likely NP?
- A: no doubt, SUSY (MSSM)
- Q: professor, what is the probability that SUSY is the
right NP at the TeV scale?
- A: let’s say, 5% or so
- Q: But, professor, you said that SUSY is the most
likely NP, and now you say that it has 5% chance to be
it?
- A: yes, but you should consider that all the rest has
been proposed as NP has 5 per mille probabibility
to be right!

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