Transcript Classically conformal BL extended Standard Model

The minimal B-L model naturally
realized at TeV scale
Yuta Orikasa(SOKENDAI)
Satoshi Iso(KEK,SOKENDAI)
Nobuchika Okada(University of Alabama)
Phys.Lett.B676(2009)81
Phys.Rev.D80(2009)115007
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• The Standard Model is the best theory of
describing the nature of particle physics, which is
in excellent agreement with almost of all current
experiments.
• However SM has hierarchy problem. It is the
problem that the quadratic divergence in quantum
corrections to the Higgs self energy, which should
be canceled by the Higgs mass parameter with
extremely high precision when the cutoff scale is
much higher than the electroweak scale.
Λ:cutoff scale
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Conformal symmetry
and hierarchy problem
SM is classically conformal invariant except
for the Higgs mass term.
W.A. Bardeen,
Possibility
FERMILAB-CONF-95-391-T
The classical conformal symmetry protects mass scale.
Even in quantum level this symmetry may protect the
quadratic divergences. Therefore once this symmetry
is imposed on SM, it can be free from hierarchy
problem.
We know one similar example.
The chiral symmetry protects fermion masses,
even in quantum level no fermion mass.
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Classically conformal SM
If theory has the classical conformal invariance,
the Higgs mass term is forbidden.
Therefore there is no electroweak symmetry
breaking at the classical level.
We need to consider origin of the symmetry
breaking.
Coleman-Weinberg Mechanism
(radiative symmetry breaking)
Calculate quantum
correction
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CW potential in SM
The extremum condition
The CW mechanism occurs under the balance between the treelevel quartic coupling and the terms generated by quantum
correction.
The stability condition
?
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However, top quark is heavy, so the stability
condition does not satisfy.
The effective potential
is not stabilized.
In the classically conformal SM, due to the large top
mass the effective potential is rendered unstable, and
CW mechanism does not work.
We need to extend SM.
We propose classically conformal minimal B-L
extended model.
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Classically conformal
B-L extended Model
 Gauge symmetry
 New particles
right-handed neutrino
Three generations of right-handed
neutrinos are necessarily introduced
to make the model free from all the
gauge and gravitational anomalies.
SM singlet scalar
The SM singlet scalar works to break
the U(1)B-L gauge symmetry by its VEV.
gauge field
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 Lagrangian
We assume classical conformal invariance
 Yukawa sector
Dirac Yukawa
Majorana Yukawa
See-Saw mechanism associates with B-L
symmetry breaking.
• Potential
The mass terms are forbidden by classical
conformal invariance.
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B-L symmetry breaking
If the mixing term of SM doublet Higgs and singlet
Higgs is very small, we consider SM sector and singlet
Higgs sector separately.
small
First, we consider singlet Higgs sector.
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1-loop CW potential
The extremum condition
The potential minimal is realized by the balance between
the tree-level quartic coupling and the 1-loop correction.
The stability condition
This coupling relation generates the mass hierarchy
between singlet scalar and Z’ boson.
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In our model, if majorana Yukawa coupling is small,
the stability condition satisfies.
The potential has non-trivial minimum.
B-L symmetry is broken by CW mechanism.
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Electroweak symmetry breaking
Once the B-L symmetry is broken, the SM Higgs
doublet mass is generated through the mixing term
between H and Φ in the scalar potential.
Φ has VEV M.
Effective tree-level mass squared is induced, and
if λ’ is negative, EW symmetry breaking occurs as
usual in the SM.
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LEP bound
LEP experiments provided a severe constraint.
LEP bound
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Theoretical bound
Planck
scale
The bound of B-L gauge coupling
αB-L
We impose the condition that B-L gauge
coupling does not blow up to Planck scale.
For TeV scale B-L symmetry breaking,
we find
scale
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Naturalness constraint
We have imposed the classical conformal invariance
to solve the gauge hierarchy problem.
Once B-L symmetry is broken, heavy states associated
with this breaking contribute to effective Higgs boson
mass.
We should take care of the loop effects of the heavy
states, since there is a small hierarchy between the
electroweak scale and the B-L breaking scale.
Here we estimate the loop corrections of heavy states
on the Higgs boson mass.
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Naturalness constraint
The dominant contribution comes from 2-loop effect
involving the top-quarks and the Z’ boson, because of
the large top Yukawa coupling.
This contribution should be smaller than the EW
scale.
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Summary of phenomenological bound
Coupling blow up
LEP
excluded
Disfavored by
naturalness
U(1)Y
The figure indicates that if the B-L gauge coupling
in not much smaller than the SM gauge couplings, Z’
boson mass is around a few TeV.
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Z’ boson at LHC
We calculate the dilepton production
cross section through the Z’ boson
exchange together with the SM
processes mediated by Z boson and
photon.
Z’ exchange
A clear peak of
Z’ resonance
SM background
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Z’ boson at ILC
(International Linear Collider)
We calculate the cross section of the process
→
at the ILC with a collider energy
=1 TeV.
The deviation of the cross section in our model from the
SM one is shown as a function of Z’ boson mass.
Assuming the ILC is
accessible to 1%
deviation, the TeV scale
Z’ boson can be
discovered at ILC.
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Allowed parameter region together
with search reach at future colliders
The figure indicates that if the B-L gauge coupling
in not much smaller than the SM gauge couplings, Z’
gauge boson can be discovered by near future
collider experiments.
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Conclusions
• The classical conformal theory may be free from
the hierarchy problem.
• CW mechanism does not work in classically
conformal SM since the large top Yukawa
coupling destabilizes the effective Higgs
potential. SM needs to be extended.
• We propose the classically conformal minimal BL model.
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conclusion
• B-L symmetry and EW symmetry are
broken by CW mechanism.
• Our model naturally predicts B-L breaking scale
at TeV. Z’ boson can be discovered in the near
future.
• Because of CW type symmetry breaking, the
singlet Higgs boson mass is smaller than the Z’
gauge boson mass.