physics beyond the sm
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Physics Beyond the SM. Wim de Boer, KIT. Outline. Lecture I ( SM+Cosmology ) What are the essentials of a Grand Unified Theory (GUT)? Which predictions follow from a GUT? Dark energy and dark matter Inflation and accelerated expansion of the universe - PowerPoint PPT PresentationTRANSCRIPT
KIT – University of the State of Baden-Wuerttemberg and National Research Center of the Helmholtz Association
Institut für Experimentelle Kernphysik
www.kit.edu
Physics Beyond the SM
Wim de Boer, KIT
2Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Outline Lecture I (SM+Cosmology)
What are the essentials of a Grand Unified Theory (GUT)?
Which predictions follow from a GUT?
Dark energy and dark matter
Inflation and accelerated expansion of the universe
Lecture II (Supersymmetry)
Gauge and Yukawa coupling unification in SUSY
Prediction of electroweak symmetry breaking in SUSY
Prediction of the top mass in SUSY
Prediction of the Higgs mass in SUSY
Prediction of Relic density
Prospects for discovering SUSY
Details in Many lsummerschool lectures on Supersymmetry in: http://www-ekp.physik.uni-karlsruhe.de/~deboer/html/Lehre/Susy/W. de Boer, hep-ph/9402266, arXiv:1309.0721
3Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Fundamental Questions
Particle Physics Cosmology
• What is the origin of mass?• Why hydrogen atom neutral?• Why forces so different strength?
• Why more matter than antimatter ?• What is dark matter?• How did galaxies form?
Magic solution: SUPERSYMMETRIC GRAND UNIFIED THEORIES
4Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
| | | |Q boson fermion Q fermion boson
2 3/2 1 1/2 0spin spin spin spin spin
What is SUSY?
Supersymmetry is a Boson-Fermion symmetry, which allows to unify all forcesof nature (including gravity).
SUSY can exist in nature ONLY, if there are as many bosons as fermions Doubling the particle spectrum (Waw, Eldorado for experimental particle physicists)
In modern theories particles are excitations of strings in 10-dimensional space (String theory)
5Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
One half is observed! One half is NOT observed!
SUSY Shadow World
6Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Particle spectrum in SUPERSYMMETRY
7Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Gauge couplingunification
8Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Grand Unified Theories
How can one unify the different forces?
Answer: forces are in principle equally strong.Difference at low energies by quantum fluctuations!
Greetings fromHeisenberg
Field around an electric charge reduced by screening from electron-positron and other fermion-antifermion pairs(Vacuumpolarisation)
-+- -+
-+
- +
- +
-+
-+
-+
Field around a coloured quark reduced by screening of quarkpairs, BUT enhanced by gluon pairs (gluons have self-interaction in contrast to photons) Antiscreeningdominates-> field at large distancelarger than at short distance->Coupling at low energy largerthan at high energy.
9Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Why are gauge couplings running?
Answer: couplings charges, but bare charges shielded by quantum fluctuations
Spatiol charge distribution of electromagnetic charges
(reduced at large distancebecause of screening by
vacuum polarization)
Electric chargein electron
Colour chargein protonIn strong interactions: vacuum fluctuations
from gluons->qq AND gluons->ggLatter dominates, thus enhancing colourcharge at large distances (antiscreening)
Because of opposite screening effects, opposite running of electromagnetic and strong interactions!
At higher energies also SUSY particles in vacuum -> change of running!
10Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Evidence for Running coupling constants
Elektromagn. interaction increases at high energies.Finestructur constant 1/137 becomes 1/128 at LEP!
Strong interaction decreases at high energies(= small distances)-> Asymptotic freedom of quarks in p,n.
11Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Gauge unification perfect for SUSY scales 1-4 TeVU
pd
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ürs
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SM SUSY
12Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
mSUGRA: need to solve 28 coupled differential RGEs(From W. de Boer, Review, hep-ph/9402266)
12
13Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
We like elegant solutions
14Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
On the 1000+ citation list..
14
15Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Prediction of Higgs mechanism
in SUSY
16Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 201416
The Higgs Mechanism
Particles slowed down byinteractions with Higgs bosons
17Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
What is spontaneous symmetry breaking?
Higgsfeld: = 0 e i
When phases arbitrary, then averaged vacuum-expectation-value < |> =0
When phases all equal, then v.e.v ≠ 0!
Spontaneous means if order parameter falls below a certain value, like temperature in superconductivity or freezing of water
17
18Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Higgs Mechanism
19Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
SUSY Higgs Bosons0 v v
exp( )2 22
0
S iP SH
H iH
H
( ) vexp( ) 2
20
S
H H i H H
1 10 211 2
1 2 0 2 221 2
1
2 2 21 2 2 1
v, ,2
v2
v +v =v , v /v tan
S iP HH H
H H S iPH H
H
4=2+2=3+1one degree offreedom left =1 Higgs boson
8=4+4=3+5= 5 Higgs bosons
20Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
The Higgs Potential2 2 2 2 2
1 2 1 1 2 2 3 1 2
2 2 22 2 2 2
1 2 1 2
( , ) | | | | ( . .)
(| | | | ) | |8 2
treeV H H m H m H m H H h c
g g gH H H H
2 22 2 2 211 1 3 2 1 2 12
1
2 22 2 2 212 2 3 1 1 2 22
2
( ) 0,4
( ) 0.4
V g gm v m v v v v
H
V g gm v m v v v v
H
Minimization Solution2 2 2
2 1 22 2 2
23
2 21 2
4( tan ),
( )(tan 1)
2sin 2
m mv
g g
m
m m
At the GUT scale
2 22 '2
40v m
g g
No SSB in SUSY theory !
2 2 2 2 21 2 0 0 3 0At the GUT scale: , m m m m B
1 1 2 2cos , sin ,H v v H v v
21Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Common masses at GUT scale:m0 for Scalars
m1/2 for S=1/2 Gauginosm1,m2 for Higgs bosons
Lightest Supersymmetric Particle (LSP) =Neutralino
Mass terms changed by radiative correction
21
m2 gets radiative corrections from top mass. Top mass has to be heavy enough to get m2 < 0 when running from GUT to EW
scale: 140<mtop<190 GeV
22Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 201422
Higgs-Boson-Masses in SUSY
CP-odd neutral Higgs ACP-even charged Higgses H
CP-even neutral Higgses h,H
2 2 21 2
2 2 2
A
A WH
m m m
m m M
2 2 2 2 2 2 2 2 2,
1[ ( ) 4 cos 2 ]
2h H A Z A Z A Zm m M m M m M
2
2 ' 2
2 22
2 22
gW
g gZ
M v
M v
Excluded, but rad. corr. increase mass
Mh 125 GeV für mstop few TeV (below 1 TeV in NMSSM)
23Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Higgs mass in MSSM and NMSSM
MSSM
Higgs mass in MSSM 125 GeV for mstop 3 TeV
NMSSM: mixing with singlet
increases Higgs mass at TREE level for small tan and large NO MULTI-TEV stops needed
WDB et al., arXiv:1308.1333
24Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
The gigantic dark energy problem
V(=0) = -mH2mW
2/2g2
= O(108 GeV4) = 1026 g/cm3
1 GeV4=(GeV/c2 )(GeV3/(ħc)3)= 10-24 g 1042 cm-3 = 1018 g/cm3
Average density in universe:
crit = 2 x 10-29 g/cm3
Problem:
Vacuum energy of Higgs field estimated to be 55-120 orders of magnitude larger thanobserved density.
WHY IS THE UNIVERSESO EMPTY???
Did EWSB provide anotherburst of inflation, thus dilutingenergy density of Higgs field??
Or is this way of estimating energy density wrong?(Brodsky et al.)
25Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
The Higgs boson is a new class, at a pivot point of energy, intensity, cosmic frontiers. “Naturally speaking”: It should not be a lonely particle; has an
“interactive friend circle”: and partners … If we do not see them at the LHC, they may
reveal their existence from Higgs coupling deviations from the SM values at a few percentage level.
An exciting journey ahead of us!
Summary on Higgs
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Yukawa Unification
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Yukawa Coupling Unification
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29Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Approximate triple Yukawa coupling unification for large tan
Yukawa coupling Unificationwdb et al, PLB 2001,arXiv:hep-ph/0106311
SUSY not only provides UNIFICATION of gauge couplings, but also unification of Yukawa couplings.
Since quarks and leptons in same multiplet in GUTs
Quark and lepton masses related. Indeed,correct b/ mass ratio (in same multiplet in SU(5) and in SO(10) also top mass (which gets mass from different Higgs doublet) can get correct mass with same Yukawa coupling! for large tanratio ofvev‘s of Higgs d
30Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
RelicDensity
31Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Expansion rate of universe determines WIMP annihilation cross section
Thermal equilibrium abundance
Actual abundance
T=M/22Co
mo
vin
g n
um
ber
den
sity
x=m/TJungmann,Kamionkowski, Griest, PR 1995
WMAP -> h2=0.1130.009 -> <v>=2.10-26 cm3/s
DM increases in Galaxies:1 WIMP/coffee cup 105 <ρ>. DMA (ρ2) restarts again..
T>>M: f+f->M+M; M+M->f+fT<M: M+M->f+fT=M/22: M decoupled, stable density(wenn Annihilationrate Expansionrate, i.e. =<v>n(xfr) H(xfr) !)
Annihilation into lighter particles, likequarks and leptons -> 0’s -> Gammas!
Only assumption in this analysis:WIMP = THERMAL RELIC!
32Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Annihilation cross sectionsin m0-m1/2 plane (μ > 0, A0=0)
bb t t
WW
10-24Annihilation cross sections can be calculated,if masses are known (couplings as in SM).Assume not only gauge couplingunification at GUT scale, butalso mass unification, i.e. allSpin 0 (spin 1/2) particles have masses m0 (m1/2).
For WMAP x-section of <v>2.10-26 cm3/s one needs relatively small LSP masses
mSUGRA: common masses m0 and m1/2 for spin 0 and spin ½ particles
33Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
R-Parity
34Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
R-Parity prevents proton decay
R-Parity requires TWO SUSÝ particles at each vertex.Therefore proton decay forbidden, but DM annihilation allowed leading to indirect detection by observing stable annihilation products and also elastic scattering allowed leading to possible direct detection. No decay of lightest SUSY particle (LSP)in normal particles allowed->LSP is stable and perfect candidate for DM.
35Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
What else is known about DM cross sections?
In blob: only Z or Higgs particles to explain neutral and weak interactionsBut 9 orders of magnitude between I and II most easily explained by Higgs exchange, since Higgs couples only weakly to light quarks
Need DM as SM singlet, so little coupling to Z, since else I would be largeHiggs Portal models: in III Higgs is portal between visible and invis. sector!(see Kanemura, Matsumoto,Nabeshima, Okada arXiv:1005.5651)SUSY with singlet Higgs: NMSSM (DM = „singlino-like“)Or DM bino-like neutralino, which does not couple to Z either (MSSM)
DM DM
p p
s < 10-8 pb fromdirect DM searches
I DM
DM
p
p
s < 10-8 pb DM fromtag by Z or monojet
(Z-tag less bg, more sens.)
IIIDM
DM
p,b
p,b
s ≈ 10 pb fromrelic density W
(assuming thermal relic)
II
x
x
36Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Higgs invisible Width in Higgs Portal Models
1402.3244
Search for:pp-> ZH->2l+Emisspp-> ZH->2b+Emisspp-> qqH->2q+Emiss
1404.1344
Upper limit on invisible width: 2-3 MeV for DM mass < MH/2
37Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
NMSSM 1) solves m-problem (m parameter =vev of singlet, so naturally small)
2) predicts naturally Mh>MZ, so no need for radiative corrections from multi-TeV stop masses.
Many papers since discovery of 125 GeV Higgs, see e.g. arXiv:1408.1120, arXiv:1407:4134, arXiv:1407.0955, arXiv:1406.7221, arXiv:1406.6372, arXiv:1405.6647, arXiv:1405.5330, arXiv:1405.3321, arXiv:1405.1152,
arXiv:1404.1053, arXiv:1403.1561, arXiv:1402.3522, arXiv:1401.1878, arXiv:1312.4788, arXiv:1311.7260, arXiv:1310.8129, arXiv:1310.4518, arXiv:1309.4939, arXiv:1309.1665, arXiv:1405.5330, arXiv:1308.4447, arXiv:1308.4447, arXiv:1308.1333, arXiv:1307.7601, arXiv:1307.0851, arXiv:1306.5541, arXiv:1306.3926, arXiv:1306.3646, arXiv:1306.0279, arXiv:1305.3214, arXiv:1305.0591, arXiv:1305.0166, arXiv:1304.5437, arXiv:1304.3670, arXiv:1304.3182, arXiv:1303.6465, arXiv:1303.2113, arXiv:1303.1900, arXiv:1301.7584, arXiv:1301.6437, arXiv:1301.1325, arXiv:1301.0453, arXiv:1212.5243, arXiv:1211.5074, arXiv:1211.1693, arXiv:1211.0875, arXiv:1209.5984, arXiv:1209.2115, arXiv:1208.2555, arXiv:1207.1545, arXiv:1206.6806, arXiv:1206.1470, arXiv:1205.2486, arXiv:1205.1683, arXiv:1203.5048, arXiv:1203.3446, arXiv:1202.5821, arXiv:1201.2671, arXiv:1201.0982, arXiv:1112.3548, arXiv:1111.4952, arXiv:1109.1735, arXiv:1108.0595, arXiv:1106.1599, arXiv:1105.4191, arXiv:1104.1754, arXiv:1101.1137,
Status of NMSSM
38Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Higgs mass in MSSM and NMSSM
MSSM
Higgs mass in MSSM 125 GeV for mstop 3 TeV
NMSSM: mixing with singlet
increases Higgs mass at TREE level for small tan and large NO MULTI-TEV stops needed
WDB et al., arXiv:1308.1333
39Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Branching ratios in NMSSM may differ from SM
Total width of 125 GeV Higgs tot may be reduced somewhat by mixing with singlet (singlet component does not
couple to SM particles) and new decay modes, like H3H2+H1
Mixing depends on unknown masses, so deviations not precisely known. Expect O(<10%) deviations.
Higgs with largest singlet component usually lightest one. Since it has small couplings to SM particles, it is NOT excluded by LEP limit. Dark Matter candidate is Singlino instead of BINO in MSSM. Singlino mass typically 30-100 GeV.
40Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Lightest singlet Higgs at LEP?
NMSSM consistent with H1=98 GeV, H2=126 GeV, motivated by 2 excess observed at LEP at 98 GeV with signal strength well below SM.(Belanger, Ellwanger, Gunion, Yian, Kraml, Schwarz,arXiv:1210.1976)
H1 hard to discover at LHC, may be in decay mode H3H2+H1 , see e.g. Kang, Li, Li, Shu, arxiv:1301.0453
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41Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Expected coupling precision (SM)
42Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Time evolution of Universe
Cosmology badly needsevidence for symmetry breakingvia scalar field.
Idea:High vacuum density of such ascalar field in early universeduring breaking of GUTwould provide a burst of inflation by „repulsive“ gravity.
Otherwise no explanation why the universe has matter, is flat and is isotropic.
Discovery of Higgsfield as origin of ewsb important
43Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Is the Higgs Field the „Origin of Mass“?
Answer: Yes and No. Energy or mass in Universe has little to do with the Higgs field. Higgs field gives only mass to elementary particles.
Mass in universe:
1) Atoms: most of mass from binding energy of quarks in nuclei, provided by energy in colour field, not Higgs field. (binding energy potential energy of quarks kinetic
energie of quarks, ca. 1 GeV, but mass of u,d quarks below 1 MeV!
2) Mass of dark matter: unknown, but in Supersymmetry by breaking of this symmetry, not by breaking of electroweak symmetry.
44Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Summary on SUSY
Higgs mass IS below 130 GeV,
as PREDICTED by SUSY!
SUSY provides UNIFICATION of gauge couplings
SUSY provides UNIFICATION of Yukawa couplings
SUSY predicted EWSB for 140 < Mtop < 190 GeV
SUSY provides WIMP Miracle: annihilation x-section -> correct relic density
SUSY solves hierarchy problem
SUSY provides connection with gravity
45Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Where is SUSY?
Gluino sensitivity
Now: 1200 GeV
Exp. for 3000/fb at 14 TeV 3000 GeV
1308.1333
46Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Gluino
Chargino
Neutralino
Radiative corrections to gauginos
Weakly interacting particles have only weak radiative correctionsso charginos and neutralinos naturally lighter than gluinos
47Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Where is SUSY?
Remind: Chargino/gluino ≈ 1/3 from radiative corrections
So charginos more likely to be in reach of LHC.
However: Weak cross section are weak:
Observed at LHC: 250 WZ pairs (into leptons)
Expect: WinoZino pairs with masses 5x as large: 250/5^4= 1/3 of an event.
NEED MUCH MORE LUMI before deciding SUSY is dead.Expect to reach 1 TeV chargino limit only after HL-LHC (≈ 2030 (3000/fb)
48Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
XENON1T
not sens.
LHC 143000 /fb non-sens.region
Higgs+Wallowed
Higgs 125allowed
CMSSM NMSSM
Answer: depends on model, see e.g arXiv:1402.4650
Who can see DM first? LHC or direct DM Searches
LHC better for CMSSM (WIMP mass related to gluino mass by rad. corr.)
Direct DM searches better for NMSSM (WIMP mass indep. of SUSY masses, since singlino)
49Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Example of SUSY production and decay chain
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Main SUSY signature: missing energy
51Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Summary
Higgs boson with mass of 125 GeV well established
All properties (Br and Spin) consistent with SM Higgs boson
Higgs hunt not over, since mass in range expected from Supersymmetry, which predicts more Higgs bosons. NMSSM does not need multi-TeV stops.
Like to see branching ratios at level of a few % to check possible deviations from SM, as expected in NMSSM
Looking forward to LHC at higher energies, ILC, dark matter searches
52Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Discovery of the new world of SUSY
Back to 60’s
New discoveries every year
Future of Superparticles?
53Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
THEORYX-sect.clustering
Direct searches: σ(p-WIMP) x ρ(WIMPlocal) x f(local DM clustering,corotation)
WIMP mass
Cosmology:Relic densityWIMP Annihilation x-section,IF THERMAL RELIC
Indirect searches: σ(WIMP-WIMP) x ρWIMP(r) x f(DM clustering(r)) WIMP mass
Colliders:No direct prod. of WIMPsWIMPS only in decays
Measure theory parametersand WIMP mass by missing ET
Can infer cross sections fordirect and indirect searches
Complementarity with colliders and cosmology
54Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 201454
Verknüpfung Supersymmetrie und Gravitation
Der Kommutator der SUSY-Operatoren gibt Impuls. Dies bedeutet eine Transformationvon Fermion zu Boson und wieder zurück ergibt einen Impuls, also Verschiebungin Ort-Zeit. Letztere unterliegt die Rotations- und Translationssymmetrie der Poincare-Gruppe.
Die SUSY – Symmetrie ist die einzig bekannte Erweiterung der Poincare-Gruppe miteiner „internen“ Symmetrie, d.h. eine Symmetrie die von den Quantenzahlen der Teilchenabhängt. Wenn man verlangt, dass die Lagrange Dichte invariant ist unter lokale SUSYTransformationen, muss man S=2 und S=3/2 Teilchen einführen, die dem Gravitonund Gravitino entsprechen. Daher beinhaltet eine lokale supersymmetrische Theorieautomatisch die Gravitation und wird Supergravitation genannt, auch MSUGRA genannt,wenn man die minimale Erweiterung des SMs im Auge hat.Die Gravitonen wurden bisher nicht entdeckt, aber die Hoffnung ist, dass man mit dem Laser Interferometer Space Antenna (LISA) die lokale Krümmungder Raum-Zeit durch Gravitationswellen, die z.B. bei Supernovae-Explosionen entstehen,messen kann. Man misst dann (ab 2020) die Dehnung der Raum-Zeit durch eine Verschiebungdes Interferenzmusters eines Michelson-Morley Interferometers über ca. 10 km Abstand. Der tiefere Grund der Verknüpfung zwischen SUSY und Gravitation ist die Tatsache, dassdie Raum-Zeit inkompressibel ist, d.h. wenn man eine Krümmung der Raum-Zeit durch eine Energie-Änderung erzwingt, dies ein tensorieller Charakter – beschrieben durch den Energie-Impuls Tensor - hat: eine Stauchung in eine Richtung erzwingt eine Ausdehnung in eine andere Richtung. Nur Spin 2 Teilchen haben genügend Freiheitsgrade um diese Transformationen zu beschreiben.
55Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 201455
Dies ist perfekter DM Kandidat, denn i) neutral ii) schwach wechselwirkend(kein Photon- Gluon- oder W-Austausch wegen fehlender elektr. -, Farb- und schwache Ladung, daher nur Z- und Higgsaustausch in elast. Streuungan Materie) iii) nur elast. Streuung an Materie wegen R-Parität iv) Selbst-Annihilation möglich. Annihilationswirkungsquerschnitt bekannt aus Kosmologie, elast. WQ extrem klein (mindestens 10 Größenordnungen kleiner als Annihilations-WQ aus direkter Suche nach DM)
Diese Tatsachen stimmen perfekt für Neutralino!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Neutralino ist perfekter Kandidat für DM
56Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 201456
R-Parität
57Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014
Neutralino ist meistens LSP
Leichtestes Neutralino hat großen Bino-Anteil, d.h. Eigenschaften eines S=1/2 Photons
57
Leichteste SUSY Teilchen ist meistens das Neutralino.Die 4 Neutralinos sind Mischunen aus den zwei neutralenEichbosonen der SU(2)xU1 Gruppe und zwei neutralen Higgsinos (alle S=1/2).
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Die R-ParitätDie R-Parität ist eine zusätzliche multiplikative Quantenzahl, die Elementarteilchen und ihre Superpartner unterscheidet.
(Normale) Elementarteilchen: R = +1Superpartner: R = -1
59Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 201459
R-Paritätserhaltung verhindert Protonzerfall
R-Parität verlangt dass am jeden Vertex ZWEI SUSÝ Teilchen vorkommen! Daher ist obenstehendes Diagramm verboten.Spin ½ Quark Austausch verboten durch Drehimpulserhaltung.
60Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 201460
Konsequenzen der R-Paritäts-Erhaltung
Das leichteste Super-Teilchen (LSP) ist stabil. Es kann den Urknall überleben und ist ein Kandidat für dunkle Materie. Der beste LSP-Kandidat ist das Neutralino. Als dunkle Materie wäre es das Analogon der Photonen der kosmischen Hintergrundstrahlung.
Die Zerfallsteilchen von Superpartnern beinhalten auch immer Superpartner.
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Endzustände: Chargino-Neutralino-Produktion
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Endzustände: Gluinoproduktion
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Wino-Bino-Produktion
SUSY-Analog der WZ Produktion im Standardmodell.
Endzustand:
3 Leptonen + fehlender Transversalimpuls
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5. Physik jenseits des Standardmodells
5.5 Experimentelle Tests von Supersymmetrie
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Was wissen wir über die SUSY-Parameter?
Einschränkungen an den SUSY Parameterraum
5.5.1 Das leichteste Higgs < 130 GeV (Strahlungskorrekturen)
5.5.2 LEP Massengrenzen und Higgs-Hinweise
5.5.3 g-2 Messungen
5.5.4 Radiative B-Zerfälle (b s)
5.5.5 WMAP Messung der Energie der DM EGRET DM-Signal
5.5.6 Vereinigung der Eichkopplungen
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Was ist g-2 ?
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Wodurch entsteht g-2?
Mögliche Abweichungen vom SM, wenn neue schwere Teilchen im Vakuum kurzfristig erzeugt werden.(Erlaubt nach Heisenberg)
-> Präzisionsmessungenermöglichen ein Fensterzur neuen Physik!!!
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g – 2 Messergebnisse
(g-2)/2 = 11659203 7 (PDG 2004) Messung der MUG2 Kollaboration (Brookhaven)
Daten weichen (etwas) ab vom SM -> OBERE Massengrenze für SUSY
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5.5.4 b s +
b s + und g-2 beide chargino +Spin 0 Teilchen in der Schleife->daher stark korreliert.
Daten fast wie im SM vorhergesagt ->UNTERE Massengrenze für SUSY
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Annihilation of dark matter
Dominanter Prozess: + A MONOENERGETISCHE b bquer Quarks
Gamma-Spektrum monoenergetischerQuarks wurde bei LEP gut studiert!
f
f
f
f
f
f
Z
Z
W
W 0
f~
A Z
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Zusammenfassung
Es gibt weiterhin spannende, offene Fragen in der Elementarteilchenphysik
Große vereinheitlichte Theorien und supersymmetrische Theorien sind Vorschläge zur Beantwortung wichtiger Fragen
Basis der Ansätze sind:
größere zugrunde liegende Symmetriegruppe
Symmetrie zwischen Quarks und Leptonen
Vereinigung der Kräfte bei einer hohen Energieskala
Untergrenzen auf Protonlebensdauer schließen einfache GUTheorien aus
Experimentelle Einschränkungen an SUSY-Modelle
Direkte Suchen, g-2, bs
LHC wird über SUSY-Modelle entscheiden
Nicht besprochen: große Extra-Dimensionen, Top-Color, …
Was sollte man sich merken?
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Arbeitsprogramm für den LHC
1. Entdecke das leichteste Higgs-Boson
2. Suche nach SUSY-Teilchen
3. Suche nach Evidenz für zusätzliche Raumdimensionen
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SU(5) als einfachstes Beispiel einer GUT
Fermionen einer Generation werden zwei verschiedenen Representationen der SU(5) zugeordnet (Quintett = 5*, Dekuplett = 10).
SU(5) SU(3)FarbeSU(2)LU(1)Y
SU(5) ist die einfachste Symmetriegruppe (Rang 4), in die sich die SM Symmetriegruppen einbetten lassen.
vector antisymmetrischer Tensor
Quarks und Leptonen im gleichen Multiplet
Übergänge zwischen den Teilchen eines Multiplets
es gibt Baryon- und Leptonzahl verletzende Übergänge
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Erklärung der Ladungsquantisierung
Beziehung zwischen der Quantelung der elektrischen Ladung
von Quarks (1/3 e, 2/3 e) und Leptonen (1 e)
erklärt, warum Proton- und Elektronladung gleich sind (Atome sind neutral)
Elektrische Ladung Q ist ein Operator der SU(5).
® Spur (Q) = 0 in 5* und 10, d.h. Summe der Ladungen gleich null.
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Eichbosonen in der SU(5)• Fundamentale Darstellung: 5 und 5* Anzahl der Generatoren 5 5 - 1 = 24 24 Vektorteilchen
• Die SU(5) beinhaltet die bekannten Eichbosonen: Gluonen, W, Z0, .• Es treten 12 neue intermediäre Teilchen auf: X, Y
vermitteln die Umwandlung von Leptonen in Quarks und umgekehrt.
• X- und Y-Teilchen tragen schwache Ladung (IW = 1), elektrische Ladung (q=1/3 und q=4/3) und zwei Farbladungen.
• Es gibt nur eine, universale Kopplungskonstante G, die an der Vereinigungs- skala MG definiert ist. Alle Kopplungen bei niedrigeren Energien leiten sich von der universalen Kopplung ab.
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Protonzerfall in der SU(5)In der SU(5) ist der Zerfall des Protons über den Austausch eines virtuellen X-Bosons möglich.
p e+ + 0
p = 2 10291.7 a
Partieller Lebensdauer:
(p e+ + 0) = 4.5 10291.7 a
Experimente:
(p e+ + 0) > 1.6 1033 a (PDG 2004)
Die SU(5) scheidet als GUT aus !
Vorhersage:Lebensdauer ist modellabhängig:
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Be aware: more phase transitions than GUT one, e.g. Electrow. one.Hence many models to explain Baryon Asym.
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Notwendigkeit für Physik außerhalb des SMs
Zum Mitnehmen
• SM erklärt nur 5% der Energie des Universums
• SM erklärt nicht, warum es keine Antimaterie gibt
• SM erklärt nicht, warum es vier sehr unterschiedliche Kräfte gibt
• SM hat viele ad hoc Parameter (Massen, Mischungsmatrizen, Kopplungen,..)
• SM erklärt die Massen der Teilchen mit dem HIGGS MECHANISMUS. Jedoch noch keine Higgs Teilchen gefunden und ad hoc SSB
• SM hat quadratische Divergenzen bei hohen Energien
GUTs geben gute Ansätze zur Lösungdieser Probleme
SUPERSYMMETRIE ist die einfachste(einzige?)Erweiterung des SMs, die gleichzeitig eine GUT bildet, den Higgs Mechanismus vorhersagt,die quad. Divergenzen im SM beseitigt,Möglichkeiten zur Baryonasymmetrieund einen Kandidaten für die DM bietet
LHC bietet gute Chancen die Supersymmetrie zu entdecken!Sie könnten dabei sein!
Zauberwort Supersymmetrie
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The Mass Problem (solution given in 3 papers in same PRL 16.11.1964)
SM = relativistic quantum field theory based on local gauge symmetries
BUT: local gauge symmetries incompatible with mass
(mass = 0 for chiral fermions and gauge bosons)
1962: Schwinger proposed that masses can be generated dynamically by interactions with a vacuum field
Problem: Goldstone theorem predicted massless bosons after spontaneous symmetry breaking, but these were not observed
1963 Anderson applied idea to superconductivity and postulated that Goldstone bosons become longitudinal degrees of freedom of the „plasmons“
1964 Higgs applied the idea of Anderson to relativistic gauge bosons
1964 Brout and Englert showed that spontaneous symmetry breaking gives mass to gauge bosons (but did not discuss the Goldstone boson problem)
1964 Guralnik, Hagen, and Kibble showed in a model that the Goldstone theorem is not applicable after breaking a symmetry locally
2012: Brout-Englert-Higgs-Guralnik-Hagen-Kibble Boson discovered
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Predicted Properties of the Higgs Boson
Idea: Higgs field gives mass to electroweak gauge bosons W,Z, and not to photon and gluon, by INTERACTIONS.
Giving mass means slowing down: E2= p2 +m2 and v/c =p/E, so if m=0 then 1 and if m>0 then <1.
(Like photon getting mass, if it enters superconductor by interactions with the Cooper pairs or classically, a diver is slowed down by the interaction with the water and the quanta of the water „field“ are H2O molecules, just like quanta of the Higgs field are the Higgs bosons)
Strong predictions:
Higgs field must have weak isospin (to couple to W,Z) Must be electrically neutral (not to interact with the photon) Must have spin 0 with positive parity (no preferred direction in
vacuum) Particle masses proportional to couplings to the Higgs boson
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Higgs Couplings proportional to Mass