Physics Beyond the SM Wim de Boer, KIT Prof. Dr. Max Mustermann | Name of Faculty

Outline Details in Many lsummerschool lectures on Supersymmetry in: 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 Prof. Dr. Max Mustermann | Name of Faculty

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

What is SUSY? Supersymmetry is a Boson-Fermion symmetry, which allows to unify all forces of 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 NOT observed! SUSY Shadow World One half is observed! One half is NOT observed!

Particle spectrum in SUPERSYMMETRY

Gauge coupling unification

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 from Heisenberg Field around a coloured quark reduced by screening of quark pairs, BUT enhanced by gluon pairs (gluons have self-interaction in contrast to photons) Antiscreening dominates-> field at large distance larger than at short distance-> Coupling at low energy larger than at high energy. Field around an electric charge reduced by screening from electron-positron and other fermion-antifermion pairs (Vacuumpolarisation)

   Why are gauge couplings running? Electric charge in electron Answer: couplings  charges, but bare charges shielded by quantum fluctuations Electric charge in electron Spatiol charge distribution of electromagnetic charges (reduced at large distance because of screening by vacuum polarization)   Colour charge in proton In strong interactions: vacuum fluctuations from gluons->qq AND gluons->gg Latter dominates, thus enhancing colour charge 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 TeV SM SUSY Update from Amaldi, dB, Fürstenau, PLB 260 1991

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

We like elegant solutions Oh! Before doing that I should remark, again with the help of Sidney Harris, that the elegance of the model shown on the previous slide really is important.

On the 1000+ citation list..

Prediction of Higgs mechanism in SUSY

The Higgs Mechanism Particles slowed down by interactions 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

Higgs Mechanism

SUSY Higgs Bosons SM MSSM 4=2+2=3+1 8=4+4=3+5 = 5 Higgs bosons one degree of freedom left = 1 Higgs boson MSSM 8=4+4=3+5 = 5 Higgs bosons

The Higgs Potential Minimization Solution At the GUT scale No SSB in SUSY theory !

Lightest Supersymmetric Particle (LSP) =Neutralino Mass terms changed by radiative correction Common masses at GUT scale: m0 for Scalars m1/2 for S=1/2 Gauginos m1,m2 for Higgs bosons 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 Lightest Supersymmetric Particle (LSP) =Neutralino

Higgs-Boson-Masses in SUSY CP-odd neutral Higgs A CP-even charged Higgses H CP-even neutral Higgses h,H Excluded, but rad. corr. increase mass Mh  125 GeV für mstop  few TeV (below 1 TeV in NMSSM)

Higgs mass in MSSM and NMSSM WDB et al., arXiv:1308.1333 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

The gigantic dark energy problem Vacuum energy of Higgs field estimated to be 55-120 orders of magnitude larger than observed density. WHY IS THE UNIVERSE SO EMPTY??? Did EWSB provide another burst of inflation, thus diluting energy density of Higgs field?? Or is this way of estimating energy density wrong? (Brodsky et al.) V(=0) = -mH2mW2/2g2 = 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 Prof. Dr. Max Mustermann | Name of Faculty

Summary on Higgs 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!

Yukawa Unification

Yukawa Coupling Unification

Approximate triple Yukawa coupling unification for large tan wdb 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 tanratio of vev‘s of Higgs d

Relic Density

Expansion rate of universe determines WIMP annihilation cross section T>>M: f+f->M+M; M+M->f+f T<M: M+M->f+f T=M/22: M decoupled, stable density (wenn Annihilationrate  Expansionrate, i.e. =<v>n(xfr)  H(xfr) !) Thermal equilibrium abundance Actual abundance Comoving number density WMAP -> h2=0.1130.009 -> <v>=2.10-26 cm3/s DM increases in Galaxies: 1 WIMP/coffee cup 105 <ρ>. DMA (ρ2) restarts again.. Annihilation into lighter particles, like quarks and leptons -> 0’s -> Gammas! T=M/22 Only assumption in this analysis: WIMP = THERMAL RELIC! x=m/T Jungmann,Kamionkowski, Griest, PR 1995

Annihilation cross sections in m0-m1/2 plane (μ > 0, A0=0) Annihilation cross sections can be calculated,if masses are known (couplings as in SM). Assume not only gauge coupling unification at GUT scale, but also mass unification, i.e. all Spin 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 10-24 bb t t  WW 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.

(assuming thermal relic) (Z-tag less bg, more sens.) What else is known about DM cross sections? DM p,b ≈ 10 pb from relic density W (assuming thermal relic) II x DM p < 10-8 pb from direct DM searches I DM p < 10-8 pb DM from tag by Z or monojet (Z-tag less bg, more sens.) III In blob: only Z or Higgs particles to explain neutral and weak interactions But 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 large Higgs 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) (CMS 1408.3583 mono Atlas 1402.3244 inv Prof. Dr. Max Mustermann | Name of Faculty

Higgs invisible Width in Higgs Portal Models Search for: pp-> ZH->2l+Emiss pp-> ZH->2b+Emiss pp-> qqH->2q+Emiss 1402.3244 1404.1344 Upper limit on invisible width: 2-3 MeV for DM mass < MH/2

Status of NMSSM 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,

Higgs mass in MSSM and NMSSM WDB et al., arXiv:1308.1333 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

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 H3H2+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. Prof. Dr. Max Mustermann | Name of Faculty

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 H3H2+H1 , see e.g. Kang, Li, Li, Shu, arxiv:1301.0453 114.3 2 Phys. Lett. B565 (2003) 61 Aleph, Delphi, L3, Opal Prof. Dr. Max Mustermann | Name of Faculty

Expected coupling precision (SM) Prof. Dr. Max Mustermann | Name of Faculty

Time evolution of Universe Cosmology badly needs evidence for symmetry breaking via scalar field. Idea: High vacuum density of such a scalar field in early universe during breaking of GUT would provide a burst of inflation by „repulsive“ gravity. Otherwise no explanation why the universe has matter, is flat and is isotropic. Discovery of Higgs field 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: 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.

Higgs mass IS below 130 GeV, as PREDICTED by SUSY! 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 Prof. Dr. Max Mustermann | Name of Faculty

Where is SUSY? 1308.1333 Gluino Exp. for 3000/fb Now: sensitivity 1200 GeV Exp. for 3000/fb at 14 TeV 3000 GeV 1308.1333

Radiative corrections to gauginos Gluino Chargino Neutralino Weakly interacting particles have only weak radiative corrections so charginos and neutralinos naturally lighter than gluinos

However: Weak cross section are weak: 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)

Who can see DM first? LHC or direct DM Searches Answer: depends on model, see e.g arXiv:1402.4650 XENON1T not sens. LHC 14 3000 /fb non-sens. region Higgs+W allowed Higgs 125 CMSSM NMSSM 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 Prof. Dr. Max Mustermann | Name of Faculty

Future of Superparticles? Discovery of the new world of SUSY Back to 60’s New discoveries every year

Complementarity with colliders and cosmology THEORY X-sect. clustering Direct searches: σ(p-WIMP) x ρ(WIMPlocal) x f(local DM clustering, corotation) WIMP mass Cosmology: Relic density WIMP Annihilation x-section, IF THERMAL RELIC Indirect searches: σ(WIMP-WIMP) x ρWIMP(r) x f(DM clustering(r)) Colliders: No direct prod. of WIMPs WIMPS only in decays Measure theory parameters and WIMP mass by missing ET Can infer cross sections for direct and indirect searches

Verknüpfung Supersymmetrie und Gravitation Der Kommutator der SUSY-Operatoren gibt Impuls. Dies bedeutet eine Transformation von Fermion zu Boson und wieder zurück ergibt einen Impuls, also Verschiebung in Ort-Zeit. Letztere unterliegt die Rotations- und Translationssymmetrie der Poincare-Gruppe. Die SUSY – Symmetrie ist die einzig bekannte Erweiterung der Poincare-Gruppe mit einer „internen“ Symmetrie, d.h. eine Symmetrie die von den Quantenzahlen der Teilchen abhängt. Wenn man verlangt, dass die Lagrange Dichte invariant ist unter lokale SUSY Transformationen, muss man S=2 und S=3/2 Teilchen einführen, die dem Graviton und Gravitino entsprechen. Daher beinhaltet eine lokale supersymmetrische Theorie automatisch 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 Krümmung der 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 Verschiebung des Interferenzmusters eines Michelson-Morley Interferometers über ca. 10 km Abstand. Der tiefere Grund der Verknüpfung zwischen SUSY und Gravitation ist die Tatsache, dass die 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.

Neutralino ist perfekter Kandidat für DM 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. Streuung an 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!!!!!!!!!!!!!!!!!!!!!!!!!!!!

R-Parität

Neutralino ist meistens LSP 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). Leichtestes Neutralino hat großen Bino-Anteil, d.h. Eigenschaften eines S=1/2 Photons

Die R-Parität (Normale) Elementarteilchen: R = +1 Superpartner: R = -1 Die R-Parität ist eine zusätzliche multiplikative Quantenzahl, die Elementarteilchen und ihre Superpartner unterscheidet. (Normale) Elementarteilchen: R = +1 Superpartner: 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 Die Zerfallsteilchen von Superpartnern beinhalten auch immer Superpartner. 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.

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) -> Präzisionsmessungen ermöglichen ein Fenster zur neuen Physik!!!

g – 2 Messergebnisse (g-2)/2 = 11659203  7 (PDG 2004) Messung der MUG2 Kollaboration (Brookhaven) (g-2)/2 = 11659203  7 (PDG 2004) 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  f Z W  0 ~ A Dominanter Prozess:  +   A  MONOENERGETISCHE b bquer Quarks Gamma-Spektrum monoenergetischer Quarks wurde bei LEP gut studiert!

Zusammenfassung Was sollte man sich merken? 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, bs LHC wird über SUSY-Modelle entscheiden Nicht besprochen: große Extra-Dimensionen, Top-Color, …

Arbeitsprogramm für den LHC Entdecke das leichteste Higgs-Boson Suche nach SUSY-Teilchen Suche nach Evidenz für zusätzliche Raumdimensionen

SU(5) als einfachstes Beispiel einer GUT SU(5)  SU(3)FarbeSU(2)LU(1)Y SU(5) ist die einfachste Symmetriegruppe (Rang 4), in die sich die SM Symmetriegruppen einbetten lassen. Fermionen einer Generation werden zwei verschiedenen Representationen der SU(5) zugeordnet (Quintett = 5*, Dekuplett = 10). U(1) hat Rang 1, SU(2) hat Rang 1, SU(3) hat Rang 2 => minimale Gruppe zur Vereinheitlichung muss Rang 4 haben. Alle Fermionen sind linkshändig. Rechtshändige Felder werden durch die konjugierten linkshändigen ersetzt. 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 Elektrische Ladung Q ist ein Operator der SU(5). Spur (Q) = 0 in 5* und 10, d.h. Summe der Ladungen gleich null.  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)

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. Rotationssymmetrie, SU(n), Kleeblatt,e SU3, global farbladung erhalten, lokal, muss austauschteilchen einfuehren, kovariante ableitung

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 Vorhersage: Lebensdauer ist modellabhängig: p = 2  10291.7 a Partieller Lebensdauer:  (p  e+ + 0) = 4.5  10291.7 a Experimente:  (p  e+ + 0) > 1.6  1033 a (PDG 2004) Die SU(5) scheidet als GUT aus !

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

Zum Mitnehmen Notwendigkeit für Physik außerhalb des SMs Zauberwort Supersymmetrie 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 Lösung dieser 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 Baryonasymmetrie und einen Kandidaten für die DM bietet LHC bietet gute Chancen die Supersymmetrie zu entdecken! Sie könnten dabei sein!

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. 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 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) Prof. Dr. Max Mustermann | Name of Faculty

Higgs Couplings proportional to Mass