Physics Beyond the SM - KIT · Grand Unified Theories How can one unify the different forces? Answer: forces are in principle equally strong. Difference at low energies by quantum

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

2 Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014

Outline Ø  Lecture I (SM+Cosmology) Ø  What are the essentials of a Grand Unified Theory (GUT)? Ø  Which predictions follow from a GUT? Ø  Dark energy and dark matter Ø  Inflation and accelerated expansion of the universe Ø  Lecture II (Supersymmetry) Ø  Gauge and Yukawa coupling unification in SUSY Ø  Prediction of electroweak symmetry breaking in SUSY Ø  Prediction of the top mass in SUSY Ø  Prediction of the Higgs mass in SUSY Ø  Prediction of Relic density Ø  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


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 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 observed! One half is NOT observed!

SUSY Shadow World


Particle spectrum in SUPERSYMMETRY



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 an electric charge reduced by screening from electron-positron and other fermion-antifermion pairs (Vacuumpolarisation)

- + - 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.


Why are gauge couplings running? Answer: couplings ∝ charges, but bare

charges shielded by quantum fluctuations

Spatiol charge distribution of electromagnetic charges

(reduced at large distance because of screening by

vacuum polarization)

Electric charge in electron

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 U

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SM SUSY


Unification yields hint for SUSY masses

Energy [GeV]

Unification for gluino and squark masses around 1-4 TeV


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

13


We like elegant solutions


On the 1000+ citation list..

15



The Mass Problem

"   SM = successful relativistic quantum qauge field theory "   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 " For Refs. see arxiv.1309.0721 "   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 β≡ v/c =p/E, so if m=0 then β≡1 and if m>0 then β<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

20 Wim de Boer KSETA Lecturese „Beyond the SM“ Kalsrsuhe, Oct. 2014 20

The Higgs Mechanism Particles slowed down by interactions with Higgs bosons


The Higgs Mechanism

Particles slowed down by interactions with Higgs bosons means particles get mass. Proof: E2=p2+m2

β=v/c=p/E if β<1 then p<E, hence m2=E2-p2>0

or

or Particle slowed down by flipping the spin via interactions with Higgs field


What is spontaneous symmetry breaking?

Higgsfeld: Φ = Φ0 e iϕ

When phases arbitrary, then averaged vacuum-expectation-value < Φ|Φ> =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

22


Higgs Mechanism


SUSY Higgs Bosons 0 v v

exp( )2 22 0

S iP SH

H iH H

ξσ−

−

+⎛ ⎞ ⎛ ⎞+ +⎛ ⎞ ⎜ ⎟ ⎜ ⎟= = =⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠⎝ ⎠ ⎝ ⎠

rr

( ) vexp( ) 2

2 0

SH H i H Hα ξασ =−

⎛ ⎞+⎜ ⎟ʹ′ ʹ′→ = ⎯⎯⎯→ = ⎜ ⎟⎜ ⎟⎝ ⎠

rrr r

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 HH H S iPH HH

β

++

−−

+ ⎛ ⎞⎛ ⎞+⎛ ⎞ ⎛ ⎞ ⎜ ⎟⎜ ⎟= = = = +⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟ +⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎜ ⎟⎝ ⎠ ⎝ ⎠

≡

4=2+2=3+1 one degree of freedom left = 1 Higgs boson

8=4+4=3+5 = 5 Higgs bosons


The Higgs Potential 2 2 2 2 2

1 2 1 1 2 2 3 1 22 2 2

2 2 2 21 2 1 2

( , ) | | | | ( . .)

(| | | | ) | |8 2

treeV H H m H m H m H H h c

g g gH H H H+

= + − +

ʹ′++ − +

2 22 2 2 211 1 3 2 1 2 12

12 2

2 2 2 212 2 3 1 1 2 22

2

( ) 0,4

( ) 0.4

V g gm v m v v v vHV g gm v m v v v vH

δδ

δδ

ʹ′+= − + − =

ʹ′+= − − − =

Minimization Solution 2 2 2

2 1 22 2 2

23

2 21 2

4( tan ) , ( )(tan 1)

2sin 2

m mvg g

mm m

ββ

β

−=

ʹ′+ −

=+

At the GUT scale

2 22 '2

4 0v mg g

= − <+

No SSB in SUSY theory !

2 2 2 2 21 2 0 0 3 0At the GUT scale: , m m m m Bµ µ= = + = −

1 1 2 2cos , sin ,H v v H v vβ β< >≡ = < >≡ =


Common masses at GUT scale: m0 for Scalars

m1/2 for S=1/2 Gauginos m1,m2 for Higgs bosons

Lightest Supersymmetric Particle (LSP) =Neutralino

Mass terms changed by radiative correction

26

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


SUSY Particles


Lightest 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 tanβ and large λ NO MULTI-TEV stops needed

WDB et al., arXiv:1308.1333


The gigantic dark energy problem

V(φ=φ0) = -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: ρcrit = 2 x 10-29 g/cm3

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  The Higgs boson is a new class, at a pivot point of energy, intensity, cosmic frontiers. “Naturally speaking”: v  It should not be a lonely particle; has an

“interactive friend circle”: and partners … v  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.

v  An exciting journey ahead of us!

t, W±, Z

t̃, W̃±, Z̃, H̃±,0

Summary on Higgs



Corrections to Higgs mass

SUSY: every fermion loop has bosonic loop in addition with opposite sign. Automatic cancellation of quadratic divergencies, if SUSY masses not too heavy (below a few TeV)



Yukawa Coupling Unification

Amazing: requiring Yukawa couplings of tau lepton and bottom quark to be equal at the GUT scale predictcs by rad. corr. correcct b/tau mass ratio!


Running of Yukawa couplings



Expansion rate of universe determines WIMP annihilation cross section

Thermal equilibrium abundance

Actual abundance

T=M/22 Com

ovin

g nu

mbe

r den

sity

x=m/T Jungmann,Kamionkowski, Griest, PR 1995

WMAP -> Ωh2=0.113±0.009 -> <σv>=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+f T<M: M+M->f+f T=M/22: M decoupled, stable density (wenn Annihilationrate ≅ Expansionrate, i.e. Γ=<σv>nχ(xfr) ≅ H(xfr) !)

Annihilation into lighter particles, like quarks and leptons -> π0’s -> Gammas!

Only assumption in this analysis: WIMP = THERMAL RELIC!


Annihilation cross sections in m0-m1/2 plane (µ > 0, A0=0)

bb t t

ττ WW

10-24 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 <σv>≅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 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 largeè 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)

DM DM

p p

σ  < 10-8 pb from direct DM searches

I DM

DM

p

p

σ  < 10-8 pb DM from tag by Z or monojet

(Z-tag less bg, more sens.)

III DM

DM

p,b

p,b

σ  ≈ 10 pb from relic density Ω

(assuming thermal relic)

II

x

x


NMSSM 1) solves µ-problem (µ 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 tanβ and large λ 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 Γtot may be reduced somewhat by mixing with singlet (singlet component does not couple to SM particles) and new decay modes, like H3èH2+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 2σ 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

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Expected coupling precision (SM)


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: 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

Documents

Physics Beyond the SM - KIT · Grand Unified Theories How can one unify the different forces? Answer: forces are in principle equally strong. Difference at low energies by quantum