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Beyond The Standard Model
(General Overview)
Shaaban Khalil
Center for Fundamental Physics
Zewail City of Science and Technology
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The Standard Model
• Standard Model is defined by
– 4-dimension QFT (Invariant under Poincare group)
– Symmetry: Local SU(3)C x SU(2)L x U(1)Y
– Particle content (Point particles):
» 3 fermion (quark & Lepton) Generations
» No Right-handed neutrinos → Massless Neutrinos
– Symmetry breaking: one Higgs doublet
• No candidate for Dark Matter
• SM does not include gravity.
2
Evidence for Physics beyond SM
• Three firm observational evidences of new physics BSM:
1.
Neutrino 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

Lepton number 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 quantum number),
– 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, leptons & the force carriers
very successfully.
•
NP beyond SM (SUSY) provides this type of candidate for dark matter.
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3. Baryon Asymmetry (Matter- Antimatter Asymmetry)
•
Why is our universe made of matter and not antimatter?
• Neither the standard model of particle physics, nor the theory of general
relativity provides an obvious explanation
• In 1967, A. Sakharov showed that the generation of the net baryon number 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?
(nB - n )/ nγ= 6.1 x 10-10
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 cosmological constant 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
(Supersymmetry)
7. Incorporate Gravity (Supergravity)
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.
The gauge 􏰀elds Aμ comes in SU(5) in the 24-dimensional adjoint representation. Since the 24
representation decomposes under the SM subgroup as following
We can identify 8 gauge bosons, G8; transform as (8,1)0, which are the 8 gluons of SU(3)C.
Similarly, we have 3 gauge bosons (W+, W−,W3) 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 fermions (right handed neutrinos)
(cancellation of gauge anomalies)
− Extra gauge boson 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:
B L ( x )
 L  eiY

 L,
B L ( x )
 R  eiY
 R,
Derivatives are covariant if a new gauge field Cμ is introduced:
ig r
ig 
ig 
D L  (   W  r  YB 
YB  L C ) L
2
2
2
ig 
ig 
D R  (   YB 
YB  L C ) R
2
2

Lagrangian: fermionic and kinetic sectors
LB  L  Lleptons  Lgauge
1
1
1
 il D   l  ieR D eR  i R D   R  WrW r  B B   C C 
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4
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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
~
 (el eR   l   R   R Rc  R  h.c.)
2

Most general Higgs potential:
V ( ,  )  m12   m22   
 1 (  ) 2  2 (    ) 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
32  412

Non-zero minimum:
2
2
4

m

2

m
3 2
v2  2 2 1
,
3  412

v2 
 2(m12  1v 2 )
3
Two symmetry breaking scenarios depending on λ3:
λ3  0  v   v : Two stages symmetry breaking at different scales
λ3  0  v   v : low scale v  of order the electrowea k
 Interesting scale:
0  3  2 12
 After the B−L gauge symmetry breaking, the gauge field Cμ
acquires mass:
M z2  4 g 2v2
 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



Y
g
Z
'
f

 BL  f
f
 Branching ratios
( Z   l  l  ) 
( Z   bb , cc , ss ) 
 ( Z   tt ) 

Yq2 g 2
8
Yl 2 g 2
M Z
24
Yq2 g 2
8
M Z  (1 
s
)

mt2
4mt2 1/ 2
s
 s mt2
M Z  (1  2 )(1  2 ) [1 
 O( 2 ))]
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) gauge theory, if there are n scalar multiplets φi,
with weak isospin Ii, weak hypercharge 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 photons. 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:
Also assume three Higgs doublets Φi = (φ0i , 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
(GR)
(QED)
• The idea did not work ....
– Gravity couples universally to energy
.. and was forgotten for many years
4d scalar
• New motivation for Extra Dimensions came from string theory (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



ADD (1998): 2 or more ED with R~0.1
mm~1/(10-4 eV) are allowed
RS (1999): Infinite (strongly curved) ED
are allowed
...
in ADD models M* ~ 1 TeV, in order to
eliminate the hierarchy problem of the
Standard Model. This energy scale is
perhaps in reach of the Fermilab Tevatron
ED Bulk
Gravity
SM
• In 1998, L. Randall and R. Sundrum proposed the model of warped
extra dimension as an alternative solution to the hierarchy problem.
• The extra-dimension is compactified on the orbifold S1/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)
New Quantum Number R-Parity ⇒ 𝑹𝑷 = (−𝟏)𝑩+𝑳+𝟐𝒔
If Rp conserved Lightest Sparticle (LSP) stable!
+𝟏
−𝟏
𝑺𝑴 𝒑𝒂𝒓𝒕𝒊𝒄𝒆𝒔
𝑺𝑼𝑺𝒀 𝒑𝒂𝒓𝒕𝒊𝒄𝒍𝒆𝒔
Supersymmetric Miraculous

With supersymmetry, the SM
gauge couplings are unified at
GUT scale MG ≈ 2 x1016 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'.
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7. Incorporate Gravity (Supergravity)
•
Let us start with abelian local U(1) gauge theory - QED
• The Lagrangian
the global transformation
is invariant under
• 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
with spin-3/2 : ψμα 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
•
with wabμ 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 supersymmetric theory of gravity
8. One dimension object (Superstring)
•
According to string theory the fundamental particles are not pointlike 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 leftmoving 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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