Unification of fundamental interactionsThe Standard Model (SM) Three basic questions Reasons to go...
Transcript of Unification of fundamental interactionsThe Standard Model (SM) Three basic questions Reasons to go...
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Unification of fundamentalinteractions
Hans Peter Nilles
Physikalisches Institut
Universitat Bonn
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Standard Model
We have a standard model of elementary particle physics.It is based on
gauge symmetries SU(3)× SU(2)× U(1)
three families of quarks and leptons
a scalar Higgs boson
It is extremely successful,
but there are many free parameters
and some open questions.
Is there physics beyond the standard model?
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Outline
The Standard Model (SM)
Three basic questions
Reasons to go beyond the SM
Grand unification and supersymmetry
Extra dimensions and "Local Grand Unification"
Some group theory: The beauty of SO(10)
Strong motivation for E8
Extra dimensions from String Theory
How to test?
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History
Gravity 1915
Quantum Electrodynamics (QED) ca. 1950
Yang-Mills theory for weak interactions 1954
"Higgs" mechanism 1964
Electroweak standard model 1967
Renormalizability of nonabelian gauge theoriesca. 1972
Quantum chromodynamics (QCD) ca. 1973
Discovery of gauge bosons W± and Z0 1983
Discovery of Higgs boson 2012
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Standard Model
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A family of quarks and leptons
The gauge group is SU(3)× SU(2)× U(1)Y
(uα, dα)Y=1/6 (νe, e)Y=−1/2
(uα)Y=−2/3 (e)Y=1
(dα)Y=1/3
with α = 1, 2, 3 the SU(3)-index.Observe that
∑
i
Yi = 0 and∑
i
Y 3
i = 0
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A family of quarks and leptons
The gauge group is SU(3)× SU(2)× U(1)Y
(uα, dα)Y=1/6 (νe, e)Y=−1/2
(uα)Y=−2/3 (e)Y=1
(dα)Y=1/3 (ν)Y=0
with α = 1, 2, 3 the SU(3)-index.Observe that
∑
i
Yi = 0 and∑
i
Y 3
i = 0
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Three basic questions
Some fundamental questions remain unanswered
The origin of the structure of a family?
Why three copies ?Question of I. Rabi: who ordered the muon?
Why gauge group SU(3)× SU(2)× U(1)?
and require physics beyond the Standard Model.
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Three basic questions
Some fundamental questions remain unanswered
The origin of the structure of a family?
Why three copies ?Question of I. Rabi: who ordered the muon?
Why gauge group SU(3)× SU(2)× U(1)?
and require physics beyond the Standard Model.
Some other reasons to go beyond the SM
dark matter of the universe
baryon asymmetry, neutrino oscillations
“Landau Pole” of electromagnetic U(1)
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The Quest for Unification
magnetism
electricityel.mag
weak interactions
SU(2)×U(1)
100 GeV
strong interactions (QCD)1016 GeVMGUT
celestrialmovementterrestrialmovement
GUT
Gravitation
?
1019 GeVMPlanck
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Grand Unification
Embed the SM gauge group
into a single grand unified group!
examples are SU(5) and SO(10).
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Grand Unification
Embed the SM gauge group
into a single grand unified group!
examples are SU(5) and SO(10).
But there are a few obstacles:
“equality” of gauge coupling constants
the “doublet-triplet” splitting problem
the breakdown of the grand unified gauge group.
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Standard Model
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Supersymmetric SM
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Susy thresholds
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New particles
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Supersymmetry
Unification of matter and radiation
consistent with grand unification
stabilizes the weak scale
provides candidates for dark matter
allows for a mechanism of baryogenesis
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Supersymmetry
Unification of matter and radiation
consistent with grand unification
stabilizes the weak scale
provides candidates for dark matter
allows for a mechanism of baryogenesis
Preferred grand unified gauge groups
SO(10) and SU(5) include SU(3)× SU(2)× U(1)
explain the structure of families of quarks and leptons
5 + 10 representations of SU(5)
16-dimensional spinor representation of SO(10)
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Binary code for quarks and leptons
(n1, n2, n3, n4, n5) with ni = 0, 1 and∑
i
ni = even
(1, 1, 1, 1, 0) 5 combinations
(1, 1, 0; 1, 1) d
(1, 1, 1; 0, 1) (νe, e)
(1, 1, 0, 0, 0) 10 combinations
(1, 1, 0; 0, 0) u
(1, 0, 0; 1, 0) (u, d)
(0, 0, 0; 1, 1) e
(0, 0, 0, 0, 0) 1 combination νe
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Basic questions: where are we?
We have made some pogress.
The origin of the structure of a family:answer is 16-dim. spinor representation of SO(10)
Why three copies: not known yet,but group theory is proven to be unsuccessful.
Why SU(3)×SU(2)×U(1): is replaced by: why SO(10)?
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Basic questions: where are we?
We have made some pogress.
The origin of the structure of a family:answer is 16-dim. spinor representation of SO(10)
Why three copies: not known yet,but group theory is proven to be unsuccessful.
Why SU(3)×SU(2)×U(1): is replaced by: why SO(10)?
Reminder: still some problems with grand unification:
evolution of couplings requires supersymmetry
“doublet-triplet” splitting
breakdown of grand unified group
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Why SO(10): Dynkin diagrams
Lie groups come in 4 infinite series SU(N), SP (2N),SO(2N + 1), SO(2N) and 5 exceptional groups.
Not all of them are useful for grand unification as they donot provide chiral representations to explain parity violationof weak interactions.
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Simply Laced Lie Groups
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Maximal Group E8
E8 is the maximal group.
There are, however, no chiral representations in d = 4.
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E7
Next smaller is E7.
No chiral representations in d = 4 either.
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E6
E6 allows for chiral representations even in d = 4.
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E5 = D5
E5 is usually not called exceptional.
It coincides with D5 = SO(10).
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E4 = A4
E4 coincides with A4 = SU(5).
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E3
E3 coincides with A2 × A1 which is SU(3)× SU(2).
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Strong motivation for E8
E8 would require higher dimensions
E8 is strongly motivated from string theory(E8 × E8 heterotic string and M/F theory)
E8 has chiral representations in d = 8n+ 2
String theory requires d = 10
E8 broken in process of compactification (e.g. to E5)
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Strong motivation for E8
E8 would require higher dimensions
E8 is strongly motivated from string theory(E8 × E8 heterotic string and M/F theory)
E8 has chiral representations in d = 8n+ 2
String theory requires d = 10
E8 broken in process of compactification (e.g. to E5)
Extra dimensions allow for the concept of“Local Grand Unification”:
this solves the doublet-triplet splitting problem
and provides the breakdown of the GUT group.
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Local Grand Unification
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The Quest for Unification
magnetism
electricityel.mag
weak interactions
SU(2)×U(1)
100 GeV
strong interactions (QCD)1016 GeVMGUT
celestrialmovementterrestrialmovement
GUT
Gravitation
?
1019 GeVMPlanck
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Three basic questions, again
Some basic questions are answered.
The origin of the structure of a family:answer is 16-dim representation of SO(10)
Why three copies:topological properties of compactified extra dimensions
Why SO(10)?It is the grand-grand daughter E5 of E8.
Local Grand unification:allows for “incomplete multiplets”
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Three basic questions, again
Some basic questions are answered.
The origin of the structure of a family:answer is 16-dim representation of SO(10)
Why three copies:topological properties of compactified extra dimensions
Why SO(10)?It is the grand-grand daughter E5 of E8.
Local Grand unification:allows for “incomplete multiplets”
Answers require physics beyond the SM!
We need new experimental input.
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Physics beyond the SM
Standard model is incomplete
problems with unification
dark matter
baryogenesis
inclusion of gravity
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Physics beyond the SM
Standard model is incomplete
problems with unification
dark matter
baryogenesis
inclusion of gravity
There must be new physics somewhere.
Where is it?
Is it at the TeV scale?
Why is there no signal yet at the LHC?
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LHC and physics beyond SM
0 2 4 6 8 10 12 140.10
0.15
0.20
0.25
0.30
Ρ
Ξf
500 1000 15002000
m 3� 2=15 TeV
Ξ3=0.33
BP2
Strong constraints on MSSM from 126 GeV Higgs mass.The coloured regions are excluded while the hatchedregion indicates the current reach of the LHC.
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Pre-LHC expectations
0 2 4 6 8 10 12 140.10
0.15
0.20
0.25
0.30
Ρ
Ξf
500 1000 15002000
m 3� 2=15 TeV
Ξ3=0.33
BP2
Constraints on MSSM from the Higgs mass.The coloured regions are excluded while the hatchedregion indicates the current reach of the LHC.
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LHC and physics beyond SM
0 2 4 6 8 10 12 140.10
0.15
0.20
0.25
0.30
Ρ
Ξf
500 1000 15002000
m 3� 2=15 TeV
Ξ3=0.33
BP2
Strong constraints on MSSM from 126 GeV Higgs mass.The coloured regions are excluded while the hatchedregion indicates the current reach of the LHC.
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Benchmark model
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The quest for “Precision Susy”
Two important arguments for supersymmetry
solution to the hierarchy problem
gauge coupling unification
We want to take these two arguments as serious aspossible and reanalyze the MSSM within this scheme.We make two assumptions:
demand precision gauge unification
require smallest supersymmetric masses possible
What are the consequences for the search at LHC?
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Susy thresholds
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Precision gauge unification
1
g2i (MGUT)=
1
g2i (MZ)−
bMSSMi
8π2ln
(
MGUT
MZ
)
+1
g2i,Thr
Low scale thresholds:
1
g2i,Thr
=bMSSMi − bSM
i
8π2ln
(
MSUSY
MZ
)
The measure for gauge unification:
ǫ3 =g23(MGUT)− g2
1,2(MGUT)
g21,2(MGUT)
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Unification versus MSUSY
200 500 1000 2000 5000 10 000-0.03
-0.02
-0.01
0.00
0.01
0.02
MSUSY @GeVD
Ε 3
precision unification
tan Β = 10
MSUSY should thus be in the few-TeV range.
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The Susy-Scale
If all supersymmetric partners have the same mass M,then MSUSY = M .For non-universal masses we have an effective scale:
MSUSY ∼
m32/19
Wm
12/19
hm
3/19H
m28/19g
Xsfermion
with
Xsfermion =∏
i=1...3
m3/19
L(i)
m3/19
D(i)
m7/19
Q(i)L
m2/19
E(i)m
5/19
U (i)
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LHC limits are weak
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Dark Matter Relic Density
-3 -2 -1 0 1 2 3
log10 WΧh 2
WD
Mh
2
Distribution of thermal neutralino relic density for thebenchmark sample with (solid) or without (dashed) theassumption of precision gauge coupling unification.
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LHC limits are weak
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Limits from direct detection
10 20 50 100 200 500 1000 200010-48
10-47
10-46
10-45
10-44
10-43
m Χ�
1@GeVD
Σp@c
m2 D XENON 100
Direct detection experiments might check the scheme.
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Conclusions
The quest for unification of fundamental interactions
requires new physics beyond the Standard Model:like e.g. supersymmetry and extra dimensions
Basic questions could be answered
family as a 16-dim spinor of SO(10)
SO(10) as the grand-grand daughter of E8
extra dimensions explain repetition of families
Consequences:
we need new experimental input to test the ideas!
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The LHC shows us where to go
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