Physics Beyond the SM

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

http://arxiv.org/abs/hep-ph/9402266

http://arxiv.org/abs/hep-ph/9402266


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


| | | |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)


One half is observed! One half is NOT observed!

SUSY Shadow World


Particle spectrum in SUPERSYMMETRY


Gauge couplingunification


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.


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!


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.


Gauge unification perfect for SUSY scales 1-4 TeVU

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SM SUSY


mSUGRA: need to solve 28 coupled differential RGEs(From W. de Boer, Review, hep-ph/9402266)

12


We like elegant solutions


On the 1000+ citation list..

14


Prediction of Higgs mechanism

in SUSY


The Higgs Mechanism

Particles slowed down byinteractions with Higgs bosons


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


Higgs Mechanism


SUSY Higgs Bosons0 v v

exp( )2 22

0

S iP SH

H iH

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( ) vexp( ) 2

20

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H H i H H

1 10 211 2

1 2 0 2 221 2

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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


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


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


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)


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

http://arxiv.org/abs/arXiv:1308.1333



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.)


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


Yukawa Unification


Yukawa Coupling Unification



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

http://arxiv.org/abs/hep-ph/0106311v2









RelicDensity


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!


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


R-Parity


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.


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


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


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


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




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.


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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Expected coupling precision (SM)


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


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.


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


Where is SUSY?

Gluino sensitivity

Now: 1200 GeV

Exp. for 3000/fb at 14 TeV 3000 GeV

1308.1333


Gluino

Chargino

Neutralino

Radiative corrections to gauginos

Weakly interacting particles have only weak radiative correctionsso charginos and neutralinos naturally lighter than gluinos


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)


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)


Example of SUSY production and decay chain


Main SUSY signature: missing energy


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


Discovery of the new world of SUSY

Back to 60’s

New discoveries every year

Future of Superparticles?


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


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.


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


R-Parität


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).


Die R-ParitätDie R-Parität ist eine zusätzliche multiplikative Quantenzahl, die Elementarteilchen und ihre Superpartner unterscheidet.

(Normale) Elementarteilchen: R = +1Superpartner: R = -1


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.


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.


Endzustände: Chargino-Neutralino-Produktion


Endzustände: Gluinoproduktion


Wino-Bino-Produktion

SUSY-Analog der WZ Produktion im Standardmodell.

Endzustand:

3 Leptonen + fehlender Transversalimpuls


5. Physik jenseits des Standardmodells

5.5 Experimentelle Tests von Supersymmetrie


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


Was ist g-2 ?


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!!!


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


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


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


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?


Arbeitsprogramm für den LHC

1. Entdecke das leichteste Higgs-Boson

2. Suche nach SUSY-Teilchen

3. Suche nach Evidenz für zusätzliche Raumdimensionen


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


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.


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.


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:



Be aware: more phase transitions than GUT one, e.g. Electrow. one.Hence many models to explain Baryon Asym.

78


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


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


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


Higgs Couplings proportional to Mass

Documents

Physics Beyond the SM