Three examples for possible new
physics at LHC: Supersymmetry, Tev
Scale B
B-L,
L, Extra dimensions
Shaaban Khalil
Center for theoretical Physics
British University in Egypt
1
Outline
„
Why New Physics at TeV scale?
„
Supersymmetry
„
SUSY signatures in LHC
„
TeV Scale B-L extended SM (MSSM)
„
Signatures
g
of TeV scale B-L in LHC
„
Extra dimensions and Radion scalar field
„
Radion signatures in LHC
„
Conclusions
2
Introduction
The SM, based on the gauge symmetry SU(3)C x SU(2)L x U(1)Y , is in
excellent agreement with experimental results.
Strong indications that it is just an effective of fundamental one:
1) Gauge hierarchy problem & Unification of forces
forces.
2) Neutrinos are massless
3) Flavor problem
3)) Dark Matter & Dark Energy
gy p
problem.
4) Why matter dominates antimatter.
Motivation For Supersymmetry
SUSY ensures the stability of hierarchy between the week and the Planck scales.
Supersymmetric theories are promising candidate for unified theory beyond the
SM.
In supersymmetric theories, the mechanism of the electroweak symmetry breaking
is natural.
Local supersymmetry leads to a partial unification of the SM with gravity
'supergravity'.
Supersymmetry is a necessary ingredient in string theory.
MSUSY = 1 TeV
60
1/α 1
50
40
1//αi
With supersymmetry, the SM gauge
couplings are unified at GUT scale
MG ≈ 2 x1016 GeV.
GeV
1/α 2
30
20
1/α 3
10
0
10 2
10 4
10 6
10 8
1010
μ(GeV)
1012
1014
1016
Hierarchy problem and SUSY
ƒ String and GUT unification -> A cutoff scale ~ Planck scale (1019 GeV).
ƒ SUSY is
i a symmetry to avoid
id the
h fine
fi tuning
i in
i the
h renormalization
li i off the
h Higgs
Hi
b
boson
mass at the level of O(1034).
ƒ
In SUSY, the loop diagrams that are quadratically divergent cancel, term by term
against the equivalent diagrams involving superpartners.
ƒ
If mH ~ O(100) GeV, the masses of superpartners should be ≤ O(1) TeV.
ƒ
Thus, some of the superpartners will be detected at the LHC.
What is Supersymmetry
„
Supersymmetry (SUSY): a symmetry between bosons and fermions.
„
Introduced in 1973 as a p
part of an extension of the special
p
relativity.
y
„
Super Poincare algebra.
{Qα , Qβ } = (γ μ )αβ Pμ
• SUSY = a translation in Superspace.
Superfields &Supersymmetric Lagrangian
‰
We define superfied Φ( x,θ ,θ ) as function of the superspace coordinates.
1- Chiral Superfields D Φ = 0 :
Φ ( x ,θ ) = φ ( x ) +
2 θψ ( x ) + θθ F ( x )
2- Vector Superfields V=V+:
V ( x , θ , θ ) = − θσ
„
m
2
θ v m + i θ 2 θ α& λ α& ( x ) − i θ θ α& λ α ( x ) +
1 2
θ θ
2
2
D (x)
The most general supersymmetric lagrangian takes the form:
L
=
Σ
− Σ a
+ i
i
(|D
1
φ |2
i
2 Σ
ia
a
mn
((v
4 g 2
a
g
a
+ iψ
ψ
i
T
ψ * + |F | 2 )
m
i
i
1
) 2 − i λ a D σσ a −
(D
2
i
σ m D
a λ a A *
+ h.c.
ƒ SUSY is broken if <0|F|0>≠0 or <0|D|0> ≠0
+
Σ
ij
a
)2
1
∂ 2 W
2 ∂ A ∂ A
i
)
ψ
j
i
ψ
j
.
Supersymmetry Breaking
¾
¾
SUSY must be broken symmetry or else SUSY particles should have been observed
(with same mass as SM
SM-partners)
partners)
What happens to the cancellation of quadratic divergences?
‰
SUSY partners must be not heavier than ~TeV.
The general structure for the SUSY breaking includes three sectors:
1) Observable sector: which comprises all the ordinary particle and their SUSY
particles,
particles
2) Hidden sector: where the breaking ofSUSY occurs,
3) The messengers of the SUSY breaking from hidden to observable sector.
¾
SUSY breaking is parameterized in observable sector by soft SUSY breaking terms.
Minimal Supersymmetric Standard Model
Higgs
gg in MSSM
„
„
„
In SUSY, two Higgs doublets are
needed
needed.
This means: 8 degrees of freedom, 3
eaten up by the W± and Z î 5 Higgs
fields: h0,A0,H0,H±
Connection between Higgs masses
and gauge boson masses:
M2H± = M2A + M2W î MH± > MW
MA2 =m12 + m22
2
2
M2H,h
H h = 1/2 [M A + M Z ±
((M2A+M2Z)2 - 4 M2AM2Z cos2β)0.5]
Æ Mh < M Z
This is only true at tree level. When including
higher order contributions:
Mh < ~ 130 GeV ((or so…))
R-parity and the LSP
„
Unconstrained SUSY would lead to the proton decaying with lifetime of ~hours!!!
„
Introduce R-parity
„
All SM particles have R=+1, all sparticles R=-1
„
R = ((-1)
1)3(B-L)+2s
R-parity conservation implies that:
1)
SUSY particles are produced or destroyed only in pairs
2)
The LSP is absolutely stable and it is a candidate for Dark Matter.
Events with missing energy is the major signature for R-parity conserving models
‰
The neutralinos ci (i=1,2,3,4) are the physical (mass) superpositions of fermionic partners
of bino,
bino wino and Higgsinos.
Higgsinos
The lightest neutralino can LSP, Stable Weakly Interacting Massive Particle (WIMP).
Interesting Candidate for DM.
DM
Charginios & Sfermions
‰ The mixing of the charged gauginos and charged Higgsinos is described by:
‰
The up squark mass matrices
Experimental Constraints
„
Today's negative SUSY search provide
the following lower maas limits.
ƒ The LHC at CERN is the machine that will take
particle physics into a new phase of discovery.
m
χ
±
> 100
m
χ
0
>
36
GeV
GeV
m
q~
>
300
GeV
m
g~
> 195
G V
GeV
SUSY signatures at LHC
Creation of the pair of gluino with
further cascade decay
Creation of superpartners
main decay modes
and the
‰ Squarks/gluinos decay to leptons+jets+missing energy (LSPs). By studying decay
ki
kinematics,
ti
li ht t neutralino
lightest
t li mass to
t be
b measured
d to
t ~10%
10% precision
i i
Indirect SUSY Search: LHCb
14
15
TeV Scale B-L
ƒ
The minimal extension of SM to account for Neutrino oscillations and
observed baryon asymmetry is based on the gauge group
GB−L ≡ SU(3)C × SU(2)L × U(1)Y × U(1)B−L
ƒ
TeV scale B−L symmetry breaking and see-saw mechanism have been
considered recently:
–
account for the experimental results of the light neutrino masses and their
large mixing
ƒ
New particles are predicted:
−
Three SM singlet fermions (nR) (cancellation of gauge anomalies)
−
Extra gauge boson corresponding to B−L gauge symmetry
−
Extra SM singlet scalar (heavy Higgs)
ƒ
These new particles have significant impact on the SM phenomenology
−
Interesting signatures at the LHC
U(1)
( )BB-LL Model
B − Lθ ( x )
ψ L → eiY
ψ L,
B − Lθ ( x )
ψ R → eiY
ƒ
Under U(1)B−L we demand:
ƒ
D i ti
Derivatives
are covariant
i t if a new gauge field
fi ld Cμ is
i introduced:
i t d
d
ψ R,
ig r
ig ′
ig ′′
Dμψ L ≡ (∂ μ − Wμ τ r − YBμ −
YB − LCμ )ψ L
2
2
2
ig ′
ig ′′
Dμψ R ≡ (∂ μ − YBμ −
YB − L Cμ )ψ R
2
2
ƒ
Lagrangian:
g
g
fermionic and kinetic sectors
LB − L
1 r rμν 1
1
μν
= il Dμγ l + ieR Dμ eR + iν R Dμ γ ν R − W μν W − Bμν B − Cμν C μν
4
4
4
μ
μ
Lagrangian: Higgs and Yukawa sectors
1
LHiggs+Yukawa = (Dμφ)(D φ) + (Dμ χ )(D χ ) −V (φ, χ ) − (λel φeR + λν l φν R + λν Rν Rc χνR + h.c.)
2
μ
μ
~
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:
χ = v′
ƒ
The SU(2)
( )L×U(1)
( )Y g
gauge
g symmetry
y
y is broken by
y a complex
p
SU(2)
( ) doublet of
scalar field φ:
φ =v
ƒ
2
2
Most g
general Higgs
gg potential:
p
V (φ , χ ) = m12φ +φ + m22 χ + χ + λ1 (φ +φ ) 2
+ λ2 ( χ + χ ) 2 + λ3 (φ +φ )( χ + χ )
ƒ
After the B−L gauge symmetry breaking, the gauge field Cμ acquires
mass:
M z2′ = 4 g ′′2 v′2
ƒ
Strongest Limit comes from LEP II:
M z′
≈ O(TeV ), g ′′ ≈ O(1) ⇒ v′ > O(TeV )
g ′′
SUSY and B-L radiative symmetry
S.K., A. Masiero, 2007
b ki
breaking.
TeV scale B-L from GUT
„
GB-L can be obtained from SO(10) in the following branching rule:
SO(10)
fl
SU(4)C x SU(2)L x SU(2)R
fl
AT scale ~ GUT though
(1,1,1) in 54H or 210H.
Below GUT scale
(15,1,3) Higgs
SU(3)C x SU(2)L x U(1)Yx U(1)B-L
fl
SU(3)C x SU(2)L x U(1)Y
At TeV scale via
(1,1,0,2) Higgs
Neutrino masses and mixing
ƒ
Left and right-handed neutrino form 2x2 mass matrix:
‰
MR Majorana mass (U(1)B−L symmetry breaking)
M R = λν R v′
‰
⎛ 0
⎜⎜
⎝mD
m
D
M
R
v′ ~ O(TeV ), λν R ~ O(1) ⇒ M R ≈ O(TeV )
mD Dirac mass ((Electroweak symmetry
y
y breaking)
g)
mD = hν v
hν ~ O (1) ⇒ mD ≈ O (100 )GeV , hν ~ he ⇒ mD ≈ O (10 −4 )GeV
‰ In order to fix the angles of R,
R one needs a favor symmetry.
symmetry
⎞
⎟⎟
⎠
Z’ Decay
ƒ
The interactions of the Z′ boson with
the SM fermions are described by
∑Y
B−L
g ′′Cμ fγ μ f
f
¾ Branching ratios
Yl 2 g ′′ 2
Γ(Z ′ → l l ) ≈
M Z′
24 π
+ −
Γ ( Z ′ → b b , cc , s s ) ≈
Γ ( Z ′ → tt ) ≈
ƒ
ƒ
Yq2 g ′′ 2
8π
Yq2 g ′′ 2
8π
M Z ′ (1 +
αs
)
π
4 m t2 1 / 2
αs
α s m t2
m t2
)(1 −
) [1 +
+ O(
))]
M Z ′ (1 −
π
M Z2 ′
M Z2 ′
M Z2 ′
Branching ratios of Z’ → l+l- are relatively high
compared to Z’ → qq:
Search for Z’ at LHC via dilepton channels are
accessible
ibl att LHC.
LHC
Z ′ → l +l − BR = 30%
Z ′ → qq BR = 10%
Higgs Sector
ƒ
One complex SU(2)L doublet and one complex scalar singlet
‰
‰
‰
ƒ
ƒ
Six scalar degrees of freedom
Four are eaten by C,Z0,W± after symmetry breaking
Two physical degrees of freedom: φ,
φ χ
Mass matrix:
⎛ λ1v 2 λ2 vv′ / 2 ⎞
1 2
⎟
M (φ , χ ) = ⎜⎜
2 ⎟
2
⎝ λ2 vv′ / 2 λ2 v′ ⎠
Mass eigenstates:
⎛ φ1 ⎞ ⎛ cos θ − sin θ ⎞⎛ φ ⎞
⎜⎜ ⎟⎟ = ⎜⎜
⎟⎟⎜⎜ ⎟⎟,
⎝ φ2 ⎠ ⎝ sin θ cos θ ⎠⎝ χ ⎠
λ3 vv′
tan 2θ =
λ1v 2 − λ2 v′2
m12, 2 = λ1v 2 + λ2 v′2 m (λ1v 2 − λ2 v′2 ) 2 + λ32 v 2 v′2
ƒ
Masses:
ƒ
Mixing is controlled by λ3:
λ3 = 0 → mφ = λ1 v, mψ = λ2 v′
Higgs Production
ƒ
Heavy and light Higgses are
produced through same
processes:
‰
‰
‰
‰
g
gluon-gluon
g
fusion
vector boson fusion
associated production with W/Z/Z’
associated production with heavy
q
quarks
Higgs Decay
ƒ
Branching Ratios of Light Higgs
are very close to those of SM
‰
‰
‰
Couplings
p g are cancelled in the ratio
Decay width of H→Z’Z’ is very tiny
Low mass range MH < 130 GeV:
BR
WW
ZZ
bb
ττ
tt
gg
cc
Z ′Z ′
γγ
H → bb
BR = 60 - 90%
H → τ +τ − ,cc ,gg BR = a few %
‰
H → γγ , γZ BR = a few %
High mass range MH > 130 GeV:
2 1
H →WW,ZZ (BR = , )
3 3
H → tt BR ≤ 20%
Interesting mass range of Heavy
Higgs (200<mH’):
‰
H’→WW/ZZ channel is dominant
ss
μμ
γZ
WW
gg
γZ
cc
ss
μμ
bb
ττ
γγ
ZZ
tt
Z ′Z ′
Signatures for nR at the LHC
The decay modes, which go through the Higgs
g
H or H’ and Z boson,, can be neglected
compared to the main mode nR→ W l .
These decays are very clean with four hard leptons in the final states and
l
large
missing
i i
energy due
d to
t the
th associated
i t d neutrinos.
ti
The transverse momentum distribution for the charged leptons and the missing
transverse momentum, for the
signal at the LHC for MN = 200 GeV and
MN = 400 GeV.
GeV
Integrated luminosity ~ 300 fb-1 gives 71 events for the right handed neutrino
mass of 200 GeV while it gives 46 events for the right handed neutrino mass of
400 GeV.
G V
Warped Extra Dimension
Why Extra dimensions
„
„
„
String theory: at least six unseen dims.
G
General
l Relativity:
R l ti it why
h 4?
New ways of approaching old problems: Hierarchy problem:
„
„
What do extra dimensions look like?
How many? What shape? How big are they?
Are they all the same?
„
We don
don’’tt know how many.
many Up to six (seven?) in string theory .
„
Extra dimension can be curled up : Can be simple (circle, torus ) or
complicated (Calabi – Yau)
„
They can be bounded between branes
They can be flat or they can be warped.
„
„
„
Kaluza-Klein theory
„
5-Dimensional spacetime
‰
‰
In 1919, Kaluza united Einstein’s and Maxwell’s equation using a fourth
spatial dimension
extra dimension ‘wrapped up’ in a tight circle
Warped Extra Dimensions: RS I model
Search for Extra Dimensions
Stabilization RS and Radion Field
„
GW proposed a mechanism for stabilizing the size of the extra dimension
in RS model.
„
The corresponding
p
g action is given
g
by:
y
„
The potential for the modulus field that sets the size of the fifth dimension
is generated by a bulk scalar with quartic interactions localized on the two
3-branes.
32
„
The mass of the radion is
„
Radion can be lighter than the lightest graviton KK mode.
„
The radion couple to standard model fields via the trace of the energymomentum tensor with a coupling given by 1/Lf
The cross-section of the radion production
via the gluon fusion process at the evatron
and at the LHC
compared
d to
t the
th cross- sections
ti
off the
th SM
Higgs boson production.
33
„
the radion predominantly decays into a gluon pair at low mass or W
pair above the WW mass threshold.
„
The phenomenology of the radion resembles the phenomenology of
th SM Higgs
the
Hi
b
boson
exceptt for
f
th coupling
the
li
t gluons
to
l
which
hi h is
i
enhanced in the case of the radion because of the trace anomaly.
branching ratios of a radion of 300 GeV mass
Possible radion and SM Higgs mixing allows
new physical mass eigenstates.
The decay branching ratios of these
eigenstates are different from those of the
SM Higgs boson.
34
Summary
‰
‰
The importance of the LHC for the future of high energy physics cannot be
overemphasized. Some of the most interesting/ well motivated topics
include:
„
Electroweak Symmetry Breaking (Higgs, Technicolor, ...)
„
Supersymmetry
„
D kM
Dark
Matter
tt (LSP)
„
Extra Dimension (Kaluza Klein excitation)
„
Neutral gauge boson (Z’)
(Z )
„
Exotic States ( Magnetic Monopoles, Fractionally charged color
singlets, Z flux tubes, Leptoquarks, ...).
Discovery of any New Physics beyond the SM would be a revolution of physics
in 21st century.
Summary
y
„
Three Possible Scenarios for the future of Particle Physics,
based on LHC results:
„
1- Higgs
gg and other p
particles,, confirm p
physics
y
beyond
y
the SM,, are found.
Very optimistic scenario
„
2- Higgs only is found.
„
3- Higgs is not found but other (expected) particles are detected.
Interesting scenario
Very bad for particle physics future.
36