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Problem
Local nonabelian gauge symmetry + gauge bosons massless
Solution Higgs mechanism . State of lowest energy breaks qymmetry (spontaneously):
UarO, ntO
M2<0, A>o
E-)t2h2+.1 ho
< O ist necessary +-+
parameter Higgs mechanism + additional field: Higgs boson interacts with all particles with the strength proportional to mass
not observed (yet) --- LHC (CERN)
Weaknesses
r Higgs mechanism not really understood lvr2 < O . Higgs boson not observed (pt) Mass
Higgs boson unkno^rn + experimental search difflcult (110
r Gravlty not involved in unlflcation (Planck scale) r Uniflcation
weak and strong fcce. Indlcations: . quarlG, leptons compatible with higher gauge q/mmetry
constants at higher scale
Ir
50
Q
30
n
l0
tr f-J.--.--la/+-i---------r-5 l0 15
ttogQ
Haerarchy Quantum
problem
corrections to Higgs boson mass:
+ Quadratic sensitivity to highest scale in the theory
Planck
levl
After inclusion in larger theory: No stabilisation
boson mass at the SM scale C:mp:r-,s:n Photon and quark masses protected by gauge symmetry and chiral symmetry, respectively
Standardmodel
(,.Higgs
Higgs
Indirect Search for Supersymmetry
. H iera rc hy prob le m :
Higgs /-\. Higgs
Planck
Supersymmetry (Boson Fermion Symmetry) stabilizes the low-energy theory
=0
SM + Supersymmetric SM (MSSM)
E'",eryccCr .reeds a SuOerpartner, -\1r,.r < 1000Gel'
Global fit to electroweak data: SM .-' MSSM (Susy contributions decouple) Mechanism
SUSY breaking unknown
rrrânv free parameters Many
solutions to the hierarchy problem
market: little higgs models, extra dimensions, ...
However: Coleman-Mandula Theorem
Higgs /-\ Higgs
IeVI
Coleman-Mandula Theorem There is no nontrivial relation between internal and space-time symmetries in relativistic quantum field theory. Poincaré-Symmetry is the maximal symmetry
C I1.. n. a n- Ma ndulJ
However: Supersymmetry does connect these two kinds of symmetry tra nsform ations:
BoG(
nf
SUSY SUSY Fermion Boson Fermion Supersymmetry generalizes the former symmetry concept (as- sumed within the Coleman-Mandula theorem) by connecting fermions and bosons I
Further Arguments for Supersymmetry
compatibel with all present data (SUSY contributions de- cou ple!) . model-independent prediction
boson mass:
' 130 (;, \
. allows for deeper understanding
mechanism
E
Planck-
J
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to flavour violation
contributions from ÀI+, 1* exchanges
matrix + Su persym metric flavour problem Dynamics
breaking Tvro approaches: Model-independent anallrsis may provide important hints
theory of soft SUSY breaking FCNC processes also allo\^/ for stringent constraints on specific supersymmetric models (mSUGRA, GMSB, AMSB). B - .Y. r- is sensitive to the mechanism
breaking, because in the limit of exact supersymmetry:
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