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.
Nobuchika Okada(University of Alabama)
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.
SM is classically conformal invariant except for the Higgs mass term.
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.
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.Classically conformal SM
(radiative symmetry breaking)
Calculate quantum correction
The extremum condition
The CW mechanism occurs under the balance between the tree-level quartic coupling and the terms generated by quantum correction.
The stability condition
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.
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.
We assume classical conformal invariance
See-Saw mechanism associates with B-L symmetry breaking.
The mass terms are forbidden by classical conformal invariance.
If the mixing term of SM doublet Higgs and singlet Higgs is very small, we consider SM sector and singlet Higgs sector separately.
First, we consider singlet Higgs sector.
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.
In our model, if majoranaYukawa coupling is small, the stability condition satisfies.
The potential has non-trivial minimum.
B-L symmetry is broken by CW mechanism.
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.
Φhas VEV M.
Effective tree-level mass squared is induced, and if λ’ is negative, EW symmetry breaking occurs as usual in the SM.
LEP experiments provided a severe 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.
The dominant contribution comes from 2-loop effect involving the top-quarks and the Z’ boson, because of the large top Yukawacoupling.
This contribution should be smaller than the EW scale.
Coupling blow up
Disfavored by naturalness
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.
We calculate the dilepton production cross section through the Z’ boson exchange together with the SM processes mediated by Z boson and photon.
A clear peak of Z’ resonance
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.
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.