Standard Model
Motivation
U0 (1) Model Building
Resemblance with SM
Effects of New Z0 Boson
FYP Defense
New Physics via Z0 gauge boson
Muhammad Daud
Supervisor: Dr. M. Ali Paracha
National University of Science and Technology
July 25, 2020
Standard Model
Motivation
U0 (1) Model Building
Resemblance with SM
Effects of New Z0 Boson
table of contents
Standard Model(SM)
Motivation
Need For Beyond SM Physics
Limitations of SM
U 0 (1) Model building
Changes and relations with SM
Effects of New Z0 boson.
Standard Model
Motivation
U0 (1) Model Building
Resemblance with SM
Effects of New Z0 Boson
Standard Model
A theory of fundamental
particles and interactions.
Gauge symmetry group for
standard model
SUC (3) ⊗ SUL (2) ⊗ UY (1).
Theory was re-normalized by
massive Higgs boson. Only
photon and glouns are
massless.
L =iψ̄γ µ Dµ ψ + Dµ φ† Dµ φ
1
Figure: Standard Model of
− F µν Fµν + ιYij ψ¯L φψR
4
Elementary Particles
− ιYij ψ̄L φ̃ψR − V φφ† + Lint
Standard Model
Motivation
U0 (1) Model Building
Resemblance with SM
Effects of New Z0 Boson
Standard Model
Spontaneous symmetry breaking of SM gauge group
SUC (3) ⊗ SUL (2) ⊗ UY (1) −→ Uem (1) leaving electric charge
unbroken Q = τ3 + YGWS
2
Higgs mechanism generates masses for vector bosons. Yukawa
interactions gives mass to fermions.
To diagonalize mass matrix of fermions
a unitary transformation
†
which gives rise to CKM matrix V CKM = VLu VLu .
This rotation governs the interaction of fermions with the help of
GIM mechanism.
Structure of currents
µ
Photonic Current: Jem
=
P3
ψ̄i γ µ eQi ψi
Qi = τ3 +
P3
µ
5
= + i=1 ψ̄i γ (1 − γ )τ ± ψi
i=1
±µ
Weak Charged Current: Jcc
P3
µ
Neutral Current: JN C = i=1 ψ̄i γ µ (τ 3 − 2Qi sin2 θ − γ 5 τ 3 )ψi
Yi
2
Standard Model
Motivation
U0 (1) Model Building
Resemblance with SM
Effects of New Z0 Boson
Need For Beyond SM Physics
Motivation For U0 (1) models
Need for Beyond SM Physics
SM although experimentally tested has its limitations.
Gravity is not incorporated. GUT deals with it but its energy
scale of O(1019 ).
Dark matter constitutes 85% of the total mass in universe but
SM have no particle for that.
SM fails in high energy regime because of its perturbative build
up.
SM have 3 families of matter particles. SUSY extention of SM
and Extra dimension models deals with it.
Standard Model
Motivation
U0 (1) Model Building
Resemblance with SM
Effects of New Z0 Boson
Need For Beyond SM Physics
Motivation For U0 (1) models
U0 (1) extension of SM
1
2
Extracting SM gauge group from GUTs or Extra dimension
model gives an extra U(1) coupled with it.
U0 (1) extension of MSSM is favored for extended sector of
N-MSSM.
Decomposition
SO(10) −→ SU (3) ⊗ SU (2) ⊗ U (1) ⊗ U 0 (1)
SU (5) −→ SU (3) ⊗ SU (2) ⊗ U (1) ⊗ U 0 (1)
Standard Model
Motivation
U0 (1) Model Building
Resemblance with SM
Effects of New Z0 Boson
Need For Beyond SM Physics
Motivation For U0 (1) models
U0 (1) Models
Unbroken U0 (1) gives rise to an invisible new boson such models
deals with fifth force hypothesis.
Broken models have two different types of models:
I
II
Light Z 0 model.
Heavy Z 0 model.
New heavy gauge boson model deals with two issues (1) FCNC at
tree level. (2) Extended Higgs sector.
SM forbids FCNC at tree level. we build U0 (1) extended version
of SM to bring FCNC at tree level.
Standard Model
Motivation
U0 (1) Model Building
Resemblance with SM
Effects of New Z0 Boson
Ingredients
Cooking
Ingredients
we will stick to Electro-Weak part with a U0 (1) extension that
will be SUL (2) ⊗ UY (1) ⊗ U0 (1)
Unbroken generator that corresponds to massless photon is given
as: Q = τ3 + YGWS
where YGWS = aY + bK.
2
Two Higgs model with a doublet φ and a SU(2) singlet χ is used
for masses.
We will need three mixing angles θ, ψ, ξ for Weinberg mixing,
Z − Z0 mass mixing, U(1) − U0 (1) mixing respectively.
 
Wµ3
Sθ
 Bµ  =  CθSξ
CθCξ
Cµ

−CθSψ
CξCψ + SθSξSψ
−SξCψ + SθCξSψ
 
Aµ
−CθCψ
CψSθSξ − CξSψ   Zµ 
Zµ0
CψSθCξ + SξSψ
Standard Model
Motivation
U0 (1) Model Building
Resemblance with SM
Effects of New Z0 Boson
Ingredients
Cooking
Construction
For scalar particles we find the invariant form of Klien-Gordan
Eq to be:
LSCALAR = Dµ φ† Dµ φ + Dµ χ† Dµ χ
where Dµ = ∂µ + ιgτ · Wµ + ι g12Y Bµ + ι g22K Cµ
We apply SSB which gives SU(2) ⊗ U(1) ⊗ U0 (1) −→ Uem (1)
which renders photon massless
Covariant derivative normalized in mass eigenstate after applying
higgs mechanism gives:
Dµ = ∂µ − ι g2 Wµ+ τ − + H.c. − ιeQAµ −
h
i
ψ
sin θ cot ψ
2
ιgZµ sin
Q
sin
θ
−
τ
+
−
[aY
(cot
ξ
+
tan
ξ)
−
Y
tan
ξ]
3
GWS
cos θ
2
h
i
ψ
sin θ tan ψ
2
ιgZµ0 cos
[aY (cot ξ + tan ξ) − YGWS tan ξ]
cos θ Q sin θ − τ3 −
2
Standard Model
Motivation
U0 (1) Model Building
Resemblance with SM
Effects of New Z0 Boson
Ingredients
Cooking
Fermionic Contruction
We used the fermion content of standard model with Y as free
parameter but YGWS as a fixed parameter.
Fermion masses are to be generated by Yukawa like terms by
demanding
invariance off gauge group. −Yij ψ̄Li φψRj − Yij ψ̄Li φ̃ψRj
Family non-universal approach
1st family
2nd family
3rd family
YFree
= YFree
6= YFree
When aligned with mass eigenstates we get off diagonal couplings
for Z0 thus bringing FCNC at tree level in Feynman diagrams.
couplings
†
d†
Z0 couplings: BijL = VLu LZ 0 VLd
BijR = VRu R
V
0
Z
R
ij
ij L
u L
d†
R
u R d†
Z couplings: Z = VL Z VL Z = VR Z VR
Standard Model
Motivation
U0 (1) Model Building
Resemblance with SM
Effects of New Z0 Boson
Resemblance with SM
We get an extra massive but neutral gauge boson as consequence
extended gauge.
We can see that when ψ −→ 0 or π2 covariant derivative of
extended model becomes same as for SM.
Z and Z0 bosons are interchangeable as ψ −→ ψ +
π
2
Co-variant Derivative of Extended Model
Dµ = ∂µ − ι g2 Wµ+ τ − + H.c. − ιeQAµ −
h
i
ψ
sin θ cot ψ
2
Q
sin
θ
−
τ
+
[aY
(cot
ξ
+
tan
ξ)
−
Y
tan
ξ]
−
ιgZµ sin
3
GWS
cos θ
2
h
i
sin θ tan ψ
ψ
2
ιgZµ0 cos
[aY (cot ξ + tan ξ) − YGWS tan ξ]
cos θ Q sin θ − τ3 −
2
Co-variant Derivative of SM
Dµ = ∂µ − g2 Wµ† τ + + H.c − ιeQAµ − ι cosgθW Zµ Q sin2 θw − τ 3
Standard Model
Motivation
U0 (1) Model Building
Resemblance with SM
Effects of New Z0 Boson
Physics of Non-Universal Heavy Z0 Boson
Existence of Z0 probes to Extended Higgs sector or Exotic
fermion sector for cancellation of triangular anomalies and
renormalizability.
We have worked with family non-universal model to see that
mediation of FCNC is allowed at tree level for Z0 .
Off-diagonal couplings of both Z and Z0 gives FCNC at tree level
is if their mixing is allowed.