Beyond The (General Overview)

Shaaban Khalil Center for Fundamental Physics

Zewail City of Science and Technology 1 The Standard Model

• Standard Model is defined by

– 4-dimension QFT (Invariant under Poincare group)

– : Local SU(3)C SU(2)L x U(1)Y – Particle content (Point particles):

» 3 (quark & ) Generations » No Right-handed → Massless Neutrinos

– Symmetry breaking: one Higgs doublet

• No candidate for

• SM does not include gravity.

2 Evidence for Physics beyond SM

• Three firm observational evidences of new physics BSM: 1. Masses. The discovery of the neutrino oscillations in the nineties of the last century in Super-Kamiokande experiment implies that neutrinos are massive.

 ne, nm, nt are not mass eigenstates

 Mass states are n1, n2, and n3  not conserved 2. Dark Matter

Most astronomers, cosmologists and particle physicists are convinced that 90% of the mass of the Universe is due to some non-luminous matter, called `Dark Matter/Energy'.

The explanation for these flat rotation curves is to assume that disk galaxies are immersed in extended dark matter halos • The Big-Bang nucleosynthesis, which explains the origin of the elements, sets a limit to the number of baryons that exists in the Universe: Ωbaryon <0.04

• Dark Matter must be non-baryonic.

• The properties of a good Dark Matter candidate:

– stable (protected by a conserved ), – relic abundance compatible to observation, – electrically neutral, no color, – weakly interacting (i.e., WIMP)

• No such candidate in the Standard Model

• SM describes the interactions between quarks, & the force carriers very successfully.

• NP beyond SM (SUSY) provides this type of candidate for dark matter.

5 3. Baryon Asymmetry (Matter- Antimatter Asymmetry)

• Why is our universe made of matter and not antimatter?

• Neither the standard model of , nor the theory of general relativity provides an obvious explanation

• In 1967, A. Sakharov showed that the generation of the net in the universe requires:

• Baryon number violation • Thermal non-equilibrium • C and CP violation

All of these ingredients were present in the early Universe! • Do we understand the cause of CP violation in particle interactions? • Can we calculate the BAU from first principles? (n - n )/ n = 6.1 x 10-10 B 푩 γ There are a number of questions we hope will be answered:

 Electroweak symmetry breaking, which is not explained within the SM.

 Why is the symmetry group is SU(3) x SU(2) x U(1)?

 Can forces be unified?

 Why are there three families of quarks and leptons?

 Why do the quarks and leptons have the masses they do?

 Can we have a quantum theory of gravity?

 Why is the much smaller than simple estimates would suggest? DIRECTIONS BEYOND THE STANDARD MODEL 1. Extension of gauge symmetry

2. Extension of Higgs Sector

3. Extension of Matter Content

4. Extension with Flavor Symmetry

5. Extension of Space-time dimenstions (Extra-dimensions)

6. Extension of Lorentz Symmetry ()

7. Incorporate Gravity ()

8. One dimension object (Superstring) 1. Extension of gauge symmetry

• The idea of the Grand Unified Theories (GUTs) is to embed the SM gauge groups into a large group G and try to interpret the additional resultant symmetries.

• Currently the most interesting candidates for G are SU(5), SO(10), E6 .

• The SU(5) model of Georgi and Glashow is the simplest and one of the first attempts in which the SM gauge are combined into a single gauge group.

• In SU(5) leptons and quarks are combined into single irreducible representations. elds Aμ comes in SU(5) in the 24-dimensional adjoint representation. Since the 24ﰀ The gauge representation decomposes under the SM subgroup as following

We can identify 8 gauge , G8; transform as (8,1)0, which are the 8 gluons of SU(3)C. + − 3 Similarly, we have 3 gauge bosons (W , W ,W ) transforming as (1,3)0, which correspond to the weak gauge bosons.

The adjoint representation of Higgs scalars Φ breaks SU(5) to SUc(3) × SUL(2) × UY (1). The most general Lagrangian is U(1)B-L Extension of the SM

• The minimal extension is based on the gauge group

GB−L ≡ SU(3)C × SU(2)L × U(1)Y × U(1)B−L This model accounts for the exp. results of the light neutrino masses

New particles are predicted:

− Three SM singlet (right handed neutrinos) (cancellation of gauge anomalies) − Extra gauge corresponding to B−L gauge symmetry − Extra SM singlet scalar (heavy Higgs)

These new particles have Interesting signatures at the LHC U(1)B-L Model

. Under U(1)B−L we demand:

iYBL (x) iYBL (x)  L  e  L ,  R  e  R ,

. Derivatives are covariant if a new gauge field Cμ is introduced: ig ig ig D   (  W r  YB  Y C )  L  2  r 2  2 BL  L ig ig D   (  YB  Y C )  R  2  2 BL  R

. Lagrangian: fermionic and kinetic sectors

LBL  Lleptons  Lgauge 1 1 1  ilD  l  ie D e  i D    W r W r  B B  C C   R  R R  R 4  4  4  U(1)B-L Symmetry Breaking

. The U(1)B−L gauge symmetry can be spontaneously broken by a SM singlet complex scalar field χ:   v 2

. The SU(2)L×U(1)Y gauge symmetry is broken by a complex SU(2) doublet of scalar field φ:   v 2 . Lagrangian: Higgs and Yukawa sectors

  LHiggsYukawa  (D)(D )  (D )(D ) V (, ) ~ 1  ( le   l    c   h.c.) e R  R 2  R R R . Most general Higgs potential: 2  2  V (, )  m1    m2    2  2  1( )  2 ( )    3 ( )( ) U(1)B-L Symmetry Breaking (Cont.)

. For V(φ,χ) bounded from below, we require:

3  2 12 , 2 ,1  0

. For non-zero local minimum, we require 2 3  412 . Non-zero minimum: 4 m2  2 m2  2(m2   v2 ) 2 2 1 3 2 2 1 1 v  2 , v  3  412 3

. Two symmetry breaking scenarios depending on λ3:

λ3  0  v  v : Two stages symmetrybreaking at different scales

λ3  0  v  v : low scale v of order the electroweak . Interesting scale: 0  3  2 12

. After the B−L gauge symmetry breaking, the gauge field Cμ acquires mass: 2 2 2 M z  4g v

. Strongest Limit on Mz’/g’’ comes from LEP II:

M z  O(TeV ), g  O(1)  v  O(TeV ) g ZB-L Discovery at LHC

 The interactions of the Z′ boson with the SM fermions are described by   YBL g Z' f f f  Branching ratios Y 2 g2 (Z  l l  )  l M 24 Z Y 2 g2  (Z  bb,cc, ss)  q M (1 s ) 8 Z 

Y 2 g2 m2 4m2   m2  q t t 1/ 2 s s t (Z  tt )  M Z (1 2 )(1 2 ) [1  O( 2 ))] 8 M Z M Z  M Z

 Branching ratios of Z’ → l+l- are relatively high compared to Z’ → qq:

BR(Z l l  )  30%, BR(Z  qq)  10%

 Search for Z’ at LHC via dilepton channels are accessible at LHC. 2. Extension of Higgs Sector • Why one Higgs doublet only in SM …. (just economically )

• Most of theories BSM include more than one Higgs doublet.

• In SM

• SM + Singlet scalar

The Higgs sector of this model is given by

Two physics Higgs bosons are obtained:

With • Two Higgs doublets

• In the SU(2)×U(1) , if there are n scalar multiplets φi, with weak Ii, weak Yi, and vev vi, then the parameter ρ is defined as

• Experimentally ρ is very close to one. • Both SU(2) singlets with Y =0 and SU(2) doublets with Y =±1 give ρ=1.

• The most general scalar potential for two doublets Φ1 and Φ2 with hypercharge +1 is

• The minimization of this potential gives • With two complex scalar SU(2) doublets there are eight fields:

• Three of those get ‘eaten’ to give mass to the W± and Z0 gauge bosons; the remaining five are physical scalar (‘Higgs’) fields: H± , H, h and A

• Fermions can couple to both Φ1 or Φ2 in principle • Depending on that several types of 2HDM are possible

• We take Type-II, where down-type quarks and leptons couple to Φ1 and up-type quarks couple to Φ2 3. Extension of Matter Content

1. SM + νR • SM predicts massless neutrinos. Gauge symmetry of e.m. interaction  massless . For massless ν no such symmetry. • Neutrino oscillations confirmed massive neutrinos.

• We can introduce a Dirac mass term if νR exists in addition to νL

• The neutrino mass matrix

• Then 2. 4th Generation • SM describes the presence of three fermion families. • Experimental Measurements are in good consistence with the three family but don’t not exclude a neutrino of a fourth family with mν4 > mZ . • The existence of a fourth generation neutrino would also mean the presence of two additional quarks and a charged lepton in the same family

The current mass limits on fourth generation fermions at a 95% confidence limit. 4. Extension with Flavor Symmetry The problem of flavour: the problem of the undetermined fermion masses and mixing angles (including neutrino masses and mixing angles) together with the CP violating phases

SM with S3 flavor symmetry

The smallest non-Abelian discrete symmetry is the group S3 of the permutation of three objects.

It has six elements, and is isomorphic to the symmetry group of the equilateral triangle (identity, rotations by ±2π/3, and three reflections)

It has three irreducible representations 1, 1′, 2, with the multiplication rules: Let us assign the quarks as follows:

0 − Also assume three Higgs doublets Φi = (φ i , φ i ) with assignments:

In this case, the c-t and s-b quark Yukawa interactions are given by:

The 3 × 3 quark mass matrices are given by 5. Extension of Space-time dimenstions (Extra-dimensions) • Once upon a time (1920s) Kaluza and Klein tried to unify gravity and electromagnetism in 5 dimensions

4D graviton 4D vector 4d scalar (GR) (QED)

• The idea did not work .... – Gravity couples universally to energy .. and was forgotten for many years • New motivation for Extra Dimensions came from (1980s) • 6 extra dimensions are predicted in consistent string models • They were considered to be tiny small

 Higher dimensional fields decompose in massless modes plus modes with masses

 ED effects irrelevant at low energies Braneworld Gravity

• Braneworld gravity allows many new possibilities

 SM ADD (1998): 2 or more ED with R~0.1 ED Bulk mm~1/(10-4 eV) are allowed  RS (1999): Infinite (strongly curved) ED are allowed Gravity  ...

in ADD models M* ~ 1 TeV, in order to eliminate the of the Standard Model. This energy scale is perhaps in reach of the Fermilab • In 1998, L. Randall and R. Sundrum proposed the model of warped extra dimension as an alternative solution to the hierarchy problem.

1 • The extra-dimension is compactified on the orbifold S /Z2

• The Planck scale

• Physical mass scale is set by: Collider signals can also be dramatically different

H. Davoudiasl, J. Hewett, T. Rizzo 6. Extension of Lorentz Symmetry (Supersymmetry)

• Supersymmetry (SUSY): a symmetry between bosons and fermions.

• Introduced in 1973 as a part of an extension of the special relativity. • Super Poincare algebra  {Q ,Q }  ( ) P

• SUSY = a translation in Superspace SUSY Particle Spectrum

Extends the Standard Model (SM) by predicting a new symmetry: spin-1/2 matter particles (fermions) ↔ spin-1 force carriers (bosons)

+ퟏ 푺푴 풑풂풓풕풊풄풆풔 ⇒ 푹 = (−ퟏ)푩+푳+ퟐ풔 New Quantum Number R-Parity 푷 −ퟏ 푺푼푺풀 풑풂풓풕풊풄풍풆풔

If Rp conserved Lightest Sparticle (LSP) stable! Supersymmetric Miraculous

 With supersymmetry, the SM gauge couplings are unified at 16 GUT scale MG ≈ 2 x10 GeV.

 SUSY ensures the stability of hierarchy between the week and the Planck scales.

 SUSY predicts SM-like Higgs mass is less than 130 GeV.

 Local supersymmetry leads to a partial unificationof gravity of the SM with gravity 'supergravity'.

39 7. Incorporate Gravity (Supergravity)

• Let us start with abelian local U(1) gauge theory - QED • The Lagrangian is invariant under the global transformation

• Under a local gauge transformation

• If we make the following replacement

• by introducing some vector field Aμ, we get instead

• With the transformation • The Wess-Zemino Lagrangian is invariant under the global SUSY:

With constant ξ. If ξ depends on xμ , ξ=ξ(xμ), then the Lagrangian is no longer invariant:

where Jμ is the Noether current. To cancel this term, a gauge field α with spin-3/2 : ψμ has to be introduced: where k is coupling of dimension -1. Also Ψμ should

Under the local SUSY • where Tμν is the energy-momentum tensor. This term can be cancelled by

introducing a new gauge field gμν that transforms as

• The corresponding spin 2-field, the graviton, is the SUSY partner of the gravitino, a spin 3/2-field.

• In order to complete the invariance, one finds normal derivative in δψα should be changed to covariant derivative where

ab • with w μ is a spin connection needed to define the covariant derivative acting on the spoinors. Thus, we find the following Lagrangian for the pure gravitational part:

• This confirms that the local version of supersymmetry is indeed a su- persymmetric theory of gravity 8. One dimension object (Superstring) • According to string theory the fundamental particles are not point- like but a tiny one-dimensional ”string”, which can be closed or open

• The action for string moving in flat space-time is given by

• The string equation of motion takes the simple form of wave equation

• The most general solution to equation is a superposition of left- moving and right-moving waves:

• The general solution of closed string is • Unlike bosonic string theory, superstring theories can contain space-time fermions.

• The consistent Poincare invariant string theories exist in 26(bosonic) and 10(superstring) dimensions.

• The absence of tachyons (infrared instability) leads us to 5 superstrings in 10 dimensions: IIA, IIB, Type I: SO(32),

Hetero: E8 x E8, Hetero: SO(32) x SO(32) Thank you

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